This paper presents fundamental findings on equivalence of rolling contact fatigue (RCF) driven surface damage and torsional fatigue modes of failure. Fatigue experiments were conducted for both modes of failure using AISI 4130 case carburized steel specimens. A Thrust Bearing Surface Pitting Rig (TBSPR) was designed and developed to perform RCF tests on flat test specimens using thrust ball bearings. The experiments were conducted in boundary lubrication regime, simulating the contact conditions in tribological machine components. The current investigation presents a novel approach where the effect of contact pressure and number of fatigue cycles on the initiation of surface damage was characterized by surface profilometry of the wear track after each test to generate a stress-life (S-N) map. The S-N map provides unique insights to early detection of RCF driven fatigue damage. The S-N map was utilized to generate the surface damage S-N curve. Torsional fatigue experiments were conducted on the same material, and the S-N curves of both modes of failure were compared. The comparison shows key similarities between the two S-N curves, as they differ by a simple scaling factor. This investigation demonstrates that RCF driven surface damage characteristics can be predicted by conducting much simpler, and faster, torsion fatigue tests. This paper also presents a novel methodology to determine contact pressures to avoid incipient micropitting/microdenting damage.
This article presents an experimental and analytical investigation into the rolling contact fatigue (RCF) performance of AISI M50 bearing steel across a range of Hertzian contact pressures (Ph = 2.6 GPa to 3.4 GPa). RCF experiments were conducted using a ball-on-rod test rig at three contact pressures to experimentally establish the relationship between contact pressure (contact stress) and the RCF life of M50. Simultaneously, a previously developed continuum damage mechanics finite element (CDM-FE) model, employing the Fatemi-Socie critical plane approach as the failure criteria, was utilized to provide analytical predictions of RCF life. The CDM-FE model’s damage rate equation was calibrated using open literature AISI M50 bearing steel torsion stress life (SN) data. The CDM-FE model incorporated Voronoi tessellations to represent the material microstructure and capture the material topological effect on fatigue scatter. RCF simulations were conducted at seven contact pressures ranging from 1.0 GPa to 3.4 GPa in 0.4 GPa increments. Similar to the experimental results, the analytical RCF life data set yielded a relationship between contact pressure and simulation life for M50. Good corroboration is observed between the contact pressure – life relationships from the experimental and analytical RCF life data sets. This is significant as it supports the use of a hybrid approach combining experimental tools (e.g. torsion fatigue and ball-on-rod) and a CDM-FE computational model to efficiently assess the RCF performance of bearing materials.
This work presents an improved probabilistic continuum damage mechanics (CDM) finite element (FE) model to simulate the degradation of material as a function of cycle in order to estimate rolling contact fatigue (RCF) life of critical tribological components. Traditionally, CDM-FE models consider the shear reversal to be the damage causing stress in RCF; however, in this investigation, the CDM-FE model also considers the octahedral shear stress, the maximum shear stress, the Fatemi-Socie criteria, and the Dang Van multi-axial fatigue parameter as failure criteria. The critical damage material parameters (σr and m) were obtained from open literature torsion fatigue results. Further, to enable a probabilistic CDM-FE model, the critical damage material parameters (σr and m) were described via a distribution as opposed to fixed values. This allows for the variation of a material’s resistance to fatigue that is present in both torsion and rolling contact fatigue to be captured. Forty unique material microstructure models were created using Voronoi tessellations to capture the random pathways for crack growth. RCF simulations were conducted at five contact pressures between 1.0GPa and 3.4GPa. Regression analysis between contact pressure and cycles to failure for each of the failure criteria yielded five unique predictive fatigue life equations, one for each failure criteria investigated. These fatigue life equations were then compared to Lundberg-Palmgren theory considering appropriate material and lubrication factors. The results demonstrated that the Fatemi-Socie and shear stress reversal failure criteria compared favorably to Lundberg-Palmgren theory. Notably, the Fatemi-Socie criteria exhibited closer agreement with Lundberg and Palmgren theory at higher contact pressures, in contrast to the shear reversal criteria.
A 3D finite element (FE) model was developed to investigate the effects of refurbishing on rolling contact fatigue (RCF) behavior of through-hardened bearing steel in a circular contact. In this investigation, the material degradation due to fatigue in original and refurbished domains was modeled using continuum damage mechanics (CDM). Material damage, crack initiation, and propagation in a circular contact were modeled to estimate the fatigue life of original and refurbished domains using CDM. RCF lives of pristine domains were predicted to define the baseline for the through-hardened steel. Then, a layer of material was removed to simulate the refurbishment while the accumulated damage for a set number of contact cycles was preserved in the domain. The refurbished domains were subjected to RCF cycles using the 3D FE model until a crack reached the surface indicating final life. A parametric study was conducted to evaluate the influence of material removal depth, loading cycles before refurbishing, applied load, and spall formation in the circular contact. The model results demonstrated that refurbishing increased fatigue life. Higher fatigue cycles before refurbishing and greater regrinding depth enhanced the total fatigue life. Furthermore, as expected, increasing the applied load reduced the fatigue life extension of restored domains.
Bearing refurbishing has become a popular method of extending the life of rolling element bearings. In the refurbishing process the raceways of the bearing may be ground to remove any surface damage prior to repolishing and reassembly with larger sized rolling elements. In the current study a continuum damage mechanics finite element model was developed to quantify the damage in original and refurbished bearings. After calculating the damage accumulation for a set number of contact cycles with the original bearing geometry, refurbishing is simulated by removing a layer of the original surface. The refurbished microstructural model is then subjected to additional computational contact cycles until a fatigue crack reaches the surface, signifying failure. This model preserves the fatigue damage accumulated prior to refurbishing and evaluates its influence on the refurbished bearing fatigue life. All refurbished bearing surfaces showed a significant amount of life after refurbishing with L10 lives from the point of refurbishment, varying from 20% to 94% of the original L10 life. The results indicate that the remaining life of the refurbished bearing population is inversely related to the time before refurbishing and is proportional to the depth of the regrinding. Results obtained from this investigation are in good agreement when compared to the Lundberg-Palmgren bearing life equation modified for analyzing the life of a refurbished bearing.
Rolling contact fatigue (RCF) is the dominant failure mode in properly installed and maintained ball and roller element bearings. Lundberg and Palmgren in their seminal publication indicated that this failure is due to the alternating component of shear stress. Thus, torsional fatigue experiments have been used to predict the RCF behavior of bearing materials. In non-conformal contacts, due to Hertzian pressure the contact experiences large compressive stresses. Hence, it is critical to take into account the effect of these large compressive stresses in torsional fatigue to better simulate RCF conditions. This paper presents an investigation of torsional fatigue of bearing steels, while the effects of combined compressive stress and its relevance to material behavior in rolling contact fatigue is examined. An MTS test rig was used to investigate the fatigue life of several bearing steels and their failure mechanisms were evaluated through fractography. Then the effects of compressive stresses on torsional fatigue were investigated. A set of custom designed clamp fixtures were designed, developed and used to apply Hertzian pressures of up to 2.5 GPa on the torsion specimens. The experimental results indicate that at high cycle fatigue, a combination of shear and biaxial compression, by application of Hertzian contact, is more detrimental to fatigue life than shear alone; however, as expected it has little to negligible effects in the low cycle fatigue regime. Also the failure mode changes such that fracture planes form a cup and cone pair with multiple internal cracks as opposed to helical planes observed in pure torsion which are formed by a single crack. A 3D finite element model (using ABAQUS) was developed to investigate the fatigue damage accumulation, crack initiation, and propagation in the material. The topology of steel microstructure is modeled employing a randomly generated Voronoi tessellation wherein each Voronoi cell represents a material grain and the boundaries between the cells are assumed to represent the weak plane in the steel matrix. Continuum damage mechanics (CDM) was used to model material degradation during the fatigue process. A comprehensive damage evolution equation is developed to account for the effect of mean stress on fatigue. The model predicts the fatigue lives and crack patterns successfully both in presence and absence of compressive stresses.
A 3D finite element model was developed to investigate the influence of microstructure topology on the stochastic nature of rolling contact fatigue. Grains of the material microstructure are modeled with random Voronoi tessellations. Continuum damage mechanics and mesh partitioning are implemented to capture the initiation and propagation phases of fatigue damage that lead to spalling. Simulated fatigue spalling is shown to progress similarly to experimental observations of rolling contact fatigue. The fatigue lives obtained with the model exhibit scatter on par with empirical measures and are fit well by 2 and 3-parameter Weibull distributions.
Rolling contact fatigue of rolling element bearings is a statistical phenomenon that is strongly affected by the heterogeneous nature of the material microstructure. Heterogeneity in the microstructure is accompanied by randomly distributed weak points in the material that lead to scatter in the fatigue lives of an otherwise identical lot of rolling element bearings. Many life models for rolling contact fatigue are empirical and rely upon correlation with fatigue test data to characterize the dispersion of fatigue lives. Recently developed computational models of rolling contact fatigue bypass this requirement by explicitly considering the microstructure as a source of the variability. This work utilizes a similar approach but extends the analysis into a 3D framework. The bearing steel microstructure is modeled as randomly generated Voronoi tessellations wherein each cell represents a material grain and the boundaries between them constitute the weak planes in the material. Fatigue cracks initiate on the weak planes where oscillating shear stresses are the strongest. Finite element analysis is performed to determine the magnitude of the critical shear stress range and the depth where it occurs. These quantities exhibit random variation due to the microstructure topology which in turn results in scatter in the predicted fatigue lives. The model is used to assess the influence of (1) topological randomness in the microstructure, (2) heterogeneity in the distribution of material properties, and (3) the presence of inherent material flaws on relative fatigue lives. Neither topological randomness nor heterogeneous material properties alone account for the dispersion seen in actual bearing fatigue tests. However, a combination of both or the consideration of material flaws brings the model’s predictions within empirically observed bounds. Examination of the critical shear stress ranges with respect to the grain boundaries where they occur reveals the orientation of weak planes most prone to failure in a threedimensional sense that was not possible with previous models.
Surface-initiated fatigue caused by surface defects is one of the most dominant failure modes for bearing contacts. In this study, a damage mechanics-based Voronoi finite-element model (VFEM) is developed and used to investigate the effects of surface defects (such as dents and fretting wear) in elastohydrodynamic lubricated line contacts. A line contact elastohydrodynamic lubricated model is used to calculate the pressure distributions acting over the surface defects, which are then employed by Voronoi finite-element model to determine subsurface stresses. Continuum damage mechanics-based approach is used to incorporate cyclic damage accumulation and progressive degradation of material properties with rolling contact cycling. The model also takes into account the effects of residual stresses generated during the debris denting process. Using this methodology, the model is used to simulate microcrack initiation, coalescence, and propagation stages, finally a fatigue spall. The locations and patterns of dent-initiated spalls are found to be consistent with experimental observations. The fatigue model is used to study the effects of the topology of the material microstructure, dent sharpness, and material properties on rolling contact fatigue (RCF) life and Weibull slopes.
It has been widely accepted that the microstructure of bearing materials can significantly affect their rolling contact fatigue (RCF) lives. Hence, microlevel topological features of materials will be of significant importance to RCF investigation. In order to estimate the fatigue lives of bearing elements and account for the effects of topological randomness of the bearing materials, in this work, damage mechanics modeling approach is incorporated into a Voronoi finite element method recently developed by the authors. Contrary to most of the life models existing in the literature for estimating the RCF lives, the current model considers microcrack initiation, coalescence, and propagation stages. The proposed model relates the fatigue life to a damage parameter D, which is a measure of the gradual material degradation under cyclic loading. In this investigation, 40 semi-infinite domains with different microstructural distributions are subjected to a moving Hertzian pressure. Using the fatigue damage model developed, the initiation and total lives of the 40 domains are obtained. Also, the effects of initial material flaws and inhomogeneous material properties (in the form of normal distribution of the elastic modulus) on the fatigue lives are investigated. It is observed that the fatigue lives calculated and their Weibull slopes are in good agreement with previous experimental and analytical results. It is noted that introducing inhomogeneous material properties and initial flaws within the domains decreases the fatigue lives and increases their scatters.
Sub-surface-initiated spalling, which is the classical mode of failure in rolling element bearings is significantly influenced by the inhomogeneous and stochastic nature of the material microstructure. This microstructural disorder is one of the primary reasons for scatter in fatigue lives for a seemingly identical batch of bearings. In this study, a stochastic fatigue model that takes the material microstructure explicitly into account is used to investigate dispersion in spalling lives for rolling element bearings. Material microstructures are generated stochastically using the process of Voronoi tessellation. Input parameters to the fatigue model are obtained from torsional fatigue tests. Spalling lives are found to follow a three-parameter Weibull distribution more closely compared with the conventionally used two-parameter Weibull distribution. The stress-life results generated using the model are found to correlate well with the Lundberg-Palmgren theory. Based on parametric studies, a new statistical life equation for bearing life is proposed which is similar in structure to the Lundberg-Palmgren equation with a modification term. Parameters in the life equation are functions of torsional fatigue parameters for the material.
Microlevel material failure has been recognized as one of the main modes of failure for rolling contact fatigue (RCF) of bearing. Therefore, microlevel features of materials will be of significant importance to RCF investigation. At the microlevel, materials consist of randomly shaped and sized grains, which cannot be properly analyzed using the classical and commercially available finite element method. Hence, in this investigation, a Voronoi finite element method (VFEM) was developed to simulate the microstructure of bearing materials. The VFEM was then used to investigate the effects of microstructure randomness on rolling contact fatigue. Here two different types of randomness are considered: (i) randomness in the microstructure due to random shapes and sizes of the material grains, and (ii) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus. In this investigation, in order to determine the fatigue life, the model proposed by Raje (“A Numerical Model for Life Scatter in Rolling Element Bearings,” ASME J. Tribol., 130, pp. 011011-1–011011-10), which is based on the Lundberg–Palmgren theory (“Dynamic Capacity of Rolling Bearings,” Acta Polytech. Scand., Mech. Eng. Ser., 1(3), pp. 7–53), is used. This model relates fatigue life to a critical stress quantity and its corresponding depth, but instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. We consider the maximum range of orthogonal shear stress and the maximum shear stress as the critical stress quantities. Forty domains are considered to study the effects of microstructure on the fatigue life of bearings. It is observed that the Weibull slope calculated for the obtained fatigue lives is in good agreement with previous experimental studies and analytical results. Introduction of inhomogeneous elastic modulus and initial flaws within the material domain increases the average critical stresses and decreases the Weibull slope.
Sub-surface-initiated spalling, which is the classical mode of failure in rolling element bearings is significantly influenced by the inhomogeneous and stochastic nature of the material microstructure. This microstructural disorder is one of the primary reasons for scatter in fatigue lives for a seemingly identical batch of bearings. In this study, a stochastic fatigue model that takes the material microstructure explicitly into account is used to investigate dispersion in spalling lives for rolling element bearings. Material microstructures are generated stochastically using the process of Voronoi tessellation. Input parameters to the fatigue model are obtained from torsional fatigue tests. Spalling lives are found to follow a three-parameter Weibull distribution more closely compared with the conventionally used two-parameter Weibull distribution. The stress-life results generated using the model are found to correlate well with the Lundberg-Palmgren theory. Based on parametric studies, a new statistical life equation for bearing life is proposed which is similar in structure to the Lundberg-Palmgren equation with a modification term. Parameters in the life equation are functions of torsional fatigue parameters for the material.
Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the mechanisms responsible for the bearing failure process. Life models that account for this dispersion are empirical in nature and do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the inhomogeneous nature of the bearing material. Here, a new approach based on a discrete material representation is presented that simulates this inherent material randomness. In this investigation, two levels of randomness are considered: (1) the topological randomness due to geometric variability in the material microstructure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress field in Hertzian line contacts is studied. Fatigue life is formulated as a function of a critical stress quantity and its corresponding depth, following a similar approach to the Lundberg–Palmgren theory. However, instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. A new critical stress quantity is introduced that considers shear stress acting along internal material planes of weakness. It is found that there is a scatter in the magnitude as well as depth of occurrence of this critical stress quantity, which leads to a scatter in computed fatigue lives. Further, the range of depths within which the critical stress quantity occurs is found to be consistent with experimental observations of fatigue cracks. The life distributions obtained from the numerical simulations are found to follow a two-parameter Weibull distribution closely. The L10 life and the Weibull slope decrease when a nonuniform distribution of elastic modulus is assumed throughout the material. The introduction of internal flaws in the material significantly reduces the L10 life and the Weibull slope. However, it is found that the Weibull slope reaches a limiting value beyond a certain concentration of flaws. This limiting value is close to that predicted by the Lundberg–Palmgren theory. Weibull slopes obtained through the numerical simulations range from 1.29 to 3.36 and are within experimentally observed values for bearing steels.
This paper presents a novel approach to predict the effect of surface roughness on surface damage in rolling contacts. Rolling contact fatigue (RCF) tests were conducted on AISI 4130 case carburized steel specimens at two different roughness levels, and , under Ra=0.3 𝜇𝑚 0.1 𝜇𝑚 boundary lubrication regime. The RCF experiments were performed using a Thrust Bearing Surface Pitting Rig employing a ball-on-flat configuration. Surface damage was assessed at different combinations of contact pressure and fatigue cycles using optical surface profilometry. Subsequently, the surface damage stress-life (S-N) results were generated at both roughness levels. Torsional fatigue experiments were also performed on the same material. The torsional fatigue SN results were combined with stress concentrations at the RCF test surfaces due to roughness to predict the surface damage S-N results. A dry circular contact model incorporating the surface roughness was developed and utilized to compute the stress concentration at the contact. The SN results based on the von-Mises stresses were compared for RCF and torsional fatigue. The predicted results corroborated well with the experimental findings. The approach developed in this investigation illustrates the fundamental relationship between RCF and torsional fatigue.
A finite element model was developed to investigate the influence of near surface orthogonal shear stress (OSS) on the competitive failure mechanism between surface originated pitting (SOP) and subsurface originated spalling (SOS), which is intrinsic to rolling contact fatigue (RCF). Surface roughness in heavily loaded non-conformal contacts causes competition between SOS and SOP. In this investigation, tribo-surface roughness has been represented as sinusoidal waveform based on surface measurements of rolling element bearings. These measurements outlined the range of roughness frequency and amplitude. The effects of these surfaces on the contact were investigated and the resulting pressure distributions were used in a finite element model in order to quantify the effects of pressure distribution on near surface orthogonal shear stress concentration. The resulting pressure distributions obtained from rough surfaces were also used in a continuum damage mechanics finite element model (CDM-FEM). The results indicate that a contact with a low frequency surface roughness (pressure distribution) is more susceptible to surface failure, whereas the contact with high frequency surface roughness frequency will resist surface failure. To quantify surface originated failure for a given surface roughness, the probability of surface failure parameter, which is defined as the ratio of contacts exhibiting SOP characteristics to the total tested is proposed. The near surface stress analysis and failure mechanism results were used to establish a relation between the near surface OSS concentration and surface failure parameter. This relation is described by a 2-parameter Weibull cumulative distribution function (CDF). The results indicate that roughness frequency and half contact width are the main parameters controlling the probability of surface failure.
In this study, a continuum damage mechanics (CDM) finite element (FE) model was developed to investigate the effects of surface roughness on rolling contact fatigue (RCF) life of non-conformal contacts. In order to assess the surface roughness of tribo-components, twelve deep groove rolling element bearings from various companies in different sizes were procured and measured using an optical surface profilometer. The roughness average (Ra) and the root mean square of surface roughness (RMS, σ) ranged from a low of 0.03, 0.05 µm to a high of 0.14, 0.20 µm, respectively. The number of peaks and valleys per 400 µm were measured and calculated. The number of peaks ranged from 11 to 31 (greater than 99.5% Confidence Interval). The measured surfaces also revealed that a sinusoidal pattern can be used to accurately represent the surface patterns. The sinusoidal surface pattern was used to determine the elastohydrodynamic lubrication (EHL) pressure distribution between an equivalent rough surface in contact with a smooth surface. Four roughness amplitude were used to generate specific film thicknesses (λ-ratios) resulting in full to mixed EHL lubrication regimes. The EHL pressure distributions were replaced with representative symmetric Hertzian pressure distributions in order to remove the effect of asymmetry of an EHL pressure distribution. The resulting symmetric pressure distributions were used in a finite element continuum damage mechanics model to determine RCF life of machine elements operating in specific film thickness range of 1 < λ < 10. The RCF results from the FE model indicate that as roughness amplitude increases or lambda ratio decreases, the fatigue lives decrease for the various frequencies. Additionally, subsurface failure fatigue lives are reduced as roughness frequency increases regardless of amplitude or Hertzian pressure. The RCF results also indicate that for the low frequency pressure distribution the contact is most susceptible to surface failure, whereas for high frequency pressure distribution the contact resists surface failure. The results from this investigation were used to develop surface roughness effects for various RCF life equations commonly used in rolling element bearing application.
A coupled multibody elastic–plastic finite element (FE) model was developed to investigate the effects of surface defects, such as dents on rolling contact fatigue (RCF). The coupled Voronoi FE model was used to determine the contact pressure acting over the surface defect, internal stresses, damage, etc. In order to determine the shape of a dent and material pile up during the over rolling process, a rigid indenter was pressed against an elastic plastic semi-infinite domain. Continuum damage mechanics (CDM) was used to account for material degradation during RCF. Using CDM, spall initiation and propagation in a line contact was modeled and investigated. A parametric study using the model was performed to examine the effects of dent sharpness, pile up ratio, and applied load on the spall formation and fatigue life. The spall patterns were found to be consistent with experimental observations from the open literature. Moreover, the results demonstrated that the dent shape and sharpness had a significant effect on pressure and thus fatigue life. Higher dent sharpness ratios significantly reduced the fatigue life.
This paper presents a continuum damage mechanics-based elastic-plastic FE model developed to quantify the rolling contact fatigue (RCF) life of refurbished bearings made from case carburized steel. Using the model developed for this investigation, case carburized steel fatigue performance was compared to that of through hardened steels. To simulate the characteristics of case carburized steel, a series of micro-indentation tests was performed to determine the hardness gradient and the case depth for the case carburized 8620 steel.
The hardness gradient in the material was modeled by changing the yield strength as a function of depth. Therefore, the finite element modeling approach employed the von Mises plasticity-based model with kinematic hardening to incorporate the effect of material plasticity. Furthermore, the residual stress distribution resulting from the carburization process was modeled by modifying the damage evolution law. In order to simulate the refurbishing process, damage accumulation was calculated for a set number of fatigue cycles with the original bearing geometry. A layer of the original surface was then removed, but the fatigue damage accumulated prior to refurbishing was preserved. The refurbished geometry was then subjected to additional fatigue cycles until the damage was detected. The model as developed also accounts for the effects of topological randomness in the material microstructure through the use of Voronoi tessellations.
The model was used to compare the RCF lives of refurbished bearings made from through hardened and case carburized bearing steel at contact pressures ranging from 2 to 3.5 GPa. The number of fatigue cycles prior to the refurbishing and the depth of material removal were varied to analyze their influence on refurbished life. It was found that greater regrinding depth (more than 0.5 times the half-width) and more fatigue cycles prior to refurbishing enhanced the total fatigue life of refurbished bearings.
The model predicted that the ratio of the total RCF life of refurbished bearing to that of unrefurbished bearing is more for through hardened bearings than case carburized bearings with case depth of 500 μm. This is as expected, because in through hardened steel there is no case, so material properties are not affected by refurbishing. In the case hardened bearing steel, however, the refurbishing process removes part of the hardened case region and exposes the softer core to stress which reduces the fatigue performance of the refurbished bearing. Since this effect diminishes as the case depth increases; the increase in the fatigue life after refurbishing was larger for case carburized bearings with case depth of 1000 μm than through hardened bearings.
Case carburized steels are widely used in high performance ball and rolling element bearings. They are characterized by the hardened exterior and gradient in the material properties as a function of depth. In this investigation, an elastic-plastic finite element model based on micro-indentation tests was developed to investigate the rolling contact fatigue of case carburized steels. A series of micro-indentation tests were conducted to obtain the hardness gradient in the case carburized 8620 steel. The results demonstrated that the hardness varies linearly from the surface to the core of the material. The finite element modeling approach employs Mises based plasticity model with kinematic hardening to incorporate the effect of material plasticity. The hardness gradient in the material was modeled by changing the yield strength as a function of depth. Linear relationship between hardness and yield strength was assumed. The FE model was coupled with continuum damage mechanics approach to capture material degradation due to fatigue damage. It considers both; stress and accumulated plastic strain based damage evolution laws for fatigue failure initiation and propagation. The residual stress distribution due to carburization process was modeled by modifying the damage evolution law. Material dependent parameters used in the damage evolution laws were determined using the SN results for torsional fatigue of the bearing steel. The effects of topological randomness in the material microstructure are accounted in the model through the use of Voronoi tessellations.
The model was used to compare the rolling contact fatigue (RCF) lives of through hardened and case carburized bearing steel with different case depths at contact pressures ranging from 2 to 3.5 GPa. The effect of residual stress distribution on RCF lives was also investigated. The results show that there is an optimum case depth for which maximum RCF lives can be attained. The spall shapes and the depth below the surface where damage initiates were found to be dependent on the case depth. The model was also used to study the effect of initial material imperfections. The fatigue lives and their dispersion quantified by Weibull slopes obtained from the model correlate well with the experiments.
An analytical model has been developed to investigate the effects of dent on spall initiation and propagation in lubricated contacts. The model is based on the damage mechanics concept that the fatigue spall initiation and propagation is due to the accumulated plastic strain process rather than the stress intensity at the tip of the crack. The contact surface layer was divided into small metal matrix (cell) and for each cell a damage law was applied to determine whether the cell is undergoing damage or not. In this model, spall will be formed when a cell is damaged. A dent profile from finite element analysis for a spherical debris denting the contact surface was used in a point EHL model. The pressure and traction profiles were then used to obtain the internal stresses and accumulated plastic strain for each cell. A damage variable was calculated for each cell based on the accumulated plastic strain. When the damage in a cell reaches a certain level, the cell is damaged and is assumed to fall off the contact surface layer, hence, spall is generated. The spall will further modify the contact surface resulting in new pressure and traction profiles. The accumulated plastic strain and damage are calculated again based on which new spalls may be generated. The entire procedure is repeated which allows the spall to propagate. Spall size and growth rate versus cycle number are presented. The results indicate that spall will always initiate at the dent edge.
In this investigation the effect of various spatial hardness gradients (e.g. linear and nonlinear) on rolling contact fatigue (RCF) life are examined through a Mises-based plasticity framework. The plasticity framework, which utilizes kinematic hardening was embedded into a finite element (FE) model, which utilized continuum damage mechanics (CDM) to facilitate life calculations by simulating material deterioration as a function of cycle. CDM critical parameters – elastic damage law resistance stress, elastic damage rate exponent, plastic damage law resistance stress, plastic damage rate exponent – were established from open literature experimental torsion stress-life data. A parametric study was then performed to quantify the relation between RCF life and (1) type of spatial gradient (e.g. linear, polynomial degree 4, polynomial degree 0.25), (2) depth of spatial gradient normalized with respect to half-contact width (e.g. 1b, 2.5b, 5b, 10b), (3) magnitude of residual stress, and (4) contact pressure. Additionally, FE simulations were conducted on non-graded, or uniform hardness microstructures and used to compare to the results from the parametric study. The RCF results indicated that polynomial gradients with degree greater than 1 outperform linear and polynomial gradients with degree less than 1, with differences between gradient types more apparent at shallower gradient depths. RCF resistance is improved with increasing gradient depth and increasing compressive residual stress. Regression analysis of the results from this investigation yielded a fatigue life expression that was formed as a function of the 4 input variables, with life improvement factors comparing well with experimental data from the open literature.
Fatigue failure in rolling element bearings (REBs) is a highly stochastic process influenced by the anisotropy of bearing material and the coupled elastohydrodynamic lubrication (EHL). In this investigation, the finite element method (FEM) was used to couple the effects of anisotropic bearing steel microstructure and EHL. This FEM framework was used to investigate RCF failure in line EHL contacts. The granular bearing steel microstructure was modeled using Voronoi tessellations, where each grain is modeled as cubic elastic material to simulate anisotropy. Continuum damage mechanics and cohesive element method were used to model RCF crack evolution along the grain boundaries. The damage accumulation in the cohesive grain boundaries was used to model the crack initiation and propagation and estimate fatigue life. The life predictions from the model show the effect of anisotropy and EHL in RCF and exhibit a strong stochasticity that is characteristic of bearing failures observed in the open literature.
Rolling element bearing failures are typically initiated by a two-stage process where a subsurface microcrack formed in the material microstructure subsequently grows to a spall spanning the bearing surface. While the crack propagation phase can be modeled using macroscopic models, the localized initiation phase must account for microstructural inhomogeneity. This paper describes such a two-stage approach that uses two distinct models for the initiation and propagation phases in RCF. Both the initiation and propagation models use Voronoi tessellations to account for the granular topology of bearing steel grains. The RCF initiation phase is simulated using a localized submodel approach, where a crystal plasticity (CP) framework is implemented to characterize plastic strain accumulation at the microscale. CP-based metrics are used to correlate the microplasticity developed under RCF loading with the formation of fatigue micro-cracks and the corresponding initiation life estimations. The subsequent macrocrack growth phase is modeled with an intergranular crack propagation model using cohesive elements. The total fatigue life estimates derived from the two-stage model demonstrate a good correlation with RCF bench test data.
This paper presents a finite element model (FEM) to investigate the effect of prior austenite grain refinement on rolling contact fatigue (RCF). RCF life was determined using continuum damage mechanics (CDM), which simulated material deterioration as a function of cycle. Continuum damage mechanics calculations in this investigation considered the subsurface shear (orthogonal) reversal to be responsible for RCF failure. To establish the CDM critical parameters—resistance stress (σr) and damage rate exponent (m)—torsion stress-life data from open literature of three different grain sizes for the same material was used. It was observed from the torsion S-N (stress-life) data that the resistance stress exhibits a linear relationship with grain diameter. As grain diameter was refined, the resistance stress was found to increase. The damage rate exponent (m) displayed no relation to grain diameter; hence, the average value from the three torsion S-N curves was used in this investigation. In order to assess the effect of grain refinement on RCF life, a series of unique material microstructures were constructed using the Voronoi tessellation process at eight mean grain diameters. Finite element (FE) simulations were devised at three contact pressures, typical of heavily loaded lubricated contacts, and the RCF life was determined for each set of microstructures of a given mean grain diameter. The RCF results at the eight grain diameters indicate that fatigue performance is improved exponentially with finer grain diameter. The observed life improvements from the RCF simulations resulting from grain refinement exhibit good corroboration with existing experimental results found in open literature. A single predictive fatigue life equation was constructed from this investigation’s RCF simulations to evaluate the stochastic RCF performance, given grain diameter and contact pressure, of non-conformal contacts.
Varying levels of retained austenite (RA) were achieved through varying undercooling severity in uniformly treated case carburized 8620 steel. Specimens were characterized via XRD and EBSD techniques to determine RA volume fraction and material characteristics prior to rolling contact fatigue (RCF). Higher RA volume fractions did not lead to improvement in RCF lives. XRD measurements after RCF testing indicated that little RA decomposition had occurred during RCF. A continuum damage mechanics (CDM) finite element model (FEM) was then developed to investigate the effects of RA stability on RCF. The results obtained from the CDM FEM captured similar behavior observed in the experimental results. Utilizing the CDM FEM, a parametric study was undertaken to examine the effects of RA quantity, RA stability, and applied pressure on RCF performance. The study demonstrates that the energy requirements to transform the RA phase are critical to RCF performance.
In this paper, the contact problem between a cylinder and a half-space with a crystalline anisotropic behavior is solved. The model is based on semi-analytical methods to solve a three dimensional contact problem. A numerical technique based on a Voronoi tessellation is implemented using the Eshelby's equivalent inclusion method to account for the effect of the material microstructure on the contact pressure distribution and subsurface stresses. Fast Fourier Transforms (3D and 2D) are used to reduce the computation cost of the simulations. An application of this method to compute the scatter in fatigue life of rolling element bearings is also presented. Three different critical stresses are used in the Lundberg-Palmgren equation and results are compared in term of Weibull plot slope.
Rolling contact fatigue (RCF) is the primary mode of fatigue failure in well-lubricated rolling element bearings. Typical fatigue failures in bearings are characterized by microcrack formation (initiation phase), which then coalesce to a large crack that grows to the surface (propagation phase). Hence, RCF is a micromechanical phenomenon driven by microstructural inhomogeneity. This paper presents a coupled damage mechanics - cohesive element method (DM-CEM) to model crack initiation and propagation in polycrystalline material aggregates subject to RCF loading. The material microstructural topology is represented using Voronoi tessellations. The grain boundaries are modeled using cohesive elements. Each grain is composed of cubic anisotropic material and is randomly oriented in material space. A quasi-static Hertzian pressure profile is passed over the surface to simulate a bearing race under dynamic loading. Damage is initiated at the grain boundaries by degradation of the cohesive elements and the rate of damage/degradation is used to characterize the fatigue life evolution. The resulting final spall patterns and fatigue life scatter corroborate well with existing results from open literature. The model was extended and used to demonstrate the feasibility of the Fatemi - Socie criterion as a possible approach for estimating RCF life.
This paper presents a damage modeling approach to simulate the formation of butterfly wings in rolling contact fatigue coupled with a fast method for solving 3D contact problems with the presence of a spherical heterogeneity. The damage model is implemented in a semi-analytical model using the Eshelby’ s equivalent inclusion method in the contact solver. The proposed technique can easily include the effects of heterogeneous inclusions to the homogeneous solution in the contact algorithm. Contact pressure and subsurface stress field computation time is kept small due to the use of 3D and 2D Fast Fourier Transforms. Cuboidal inclusions with the same size as the discretization of the half-space are superimposed to represent the microstructural alterations during butterfly wings formation.
Retained austenite (RA) transformation in martensitic steels subjected to rolling contact fatigue (RCF) is a well‐established phenomenon. In this investigation, a novel approach is developed to predict martensitic transformations of RA in steels subjected to RCF. In order to achieve the objectives, a 2‐dimensional finite element model was developed to determine subsurface stresses due to rolling contact. These stresses are utilized within a continuum damage mechanics framework to determine RA transformations as a function of depth and cycles. Phase transformations were determined by comparing the required thermodynamic driving force for transformations to the energy dissipation of the microstructure. The results obtained from the combined FEA and continuum damage mechanics model were corroborated to the experimental results for RA decomposition as a function of depth and cycle for SAE 52100 steel. The results obtained are in good agreement with observed RA decomposition and DER formation as compared with the experimental results.
Rolling contact fatigue (RCF) is one of the primary modes of failure in bearings and in this study it is hypothesized and demonstrated that RCF is strongly influenced by inhomogeneity in polycrystalline material microstructure. This paper presents a three-dimensional modeling approach to include the effects of microstructure topology and material anisotropy in a polycrystalline microstructural bearing steel subject to RCF loading. A randomly generated 3D Voronoi tessellation is used to represent the microstructural topology of the material. A cubic material definition with random spatial orientation is specified for the material grains to simulate the polycrystalline anisotropy. The size of the RVE was chosen such that it represented the macroscopic linear elastic material properties of a polycrystalline aggregate. The semi-infinite domain is then subjected to a moving Hertzian pressure to simulate a load cycle. Due to inhomogeneity in the polycrystalline material local stress risers occur at the grain boundaries, however, in general, the locations of the maximum shear stresses compare well to the experimental RCF results readily available in literature. Elemental shear stresses averaging scheme was employed to illustrate that the finite element model is mesh independent. The estimated fatigue life scatter obtained from the inhomogeneous polycrystalline material model corroborates well with the fatigue life scatter obtained from the RCF experiments.
In this study, the effects of refurbishing on rolling contact fatigue (RCF) in case carburized AISI 8620 steel were experimentally and analytically investigated. A thrust bearing test apparatus (TBTA) was designed and developed to simulate RCF. Initial RCF tests were conducted on AISI 8620 steel specimens to determine the baseline for pristine. Then new specimens were exposed to fatigue cycles equal to 90% of the L10 life of the pristine material. These specimens were then refurbished to the depths of 0.13b and 1.27b (b is the half width of Hertzian contact). The refurbished specimens were then subjected to RCF cycles in the TBTA until a spall appeared on the surface. The experimental results of refurbished specimens indicated a significant amount of fatigue life after refurbishing for both grinding depths. Moreover, it was observed that the remaining useful life of the refurbished test specimens was extended by increasing the depth of the regrinding.
For the analytical investigation, a two-dimensional elastic-plastic finite element model was developed to estimate RCF life for pristine and refurbished specimens of case carburized steel. The characteristics of case carburized materials (e.g., variations in hardness and residual stresses) were incorporated in the 2D finite element model. In the present study, a continuum damage mechanics approach was employed to determine fatigue damage accumulation in original and refurbished domains. The results obtained from the experimental and FEA models for pristine and refurbished case carburized steel are in good agreement for both grinding depths.
Microstructural alterations in bearing steels during rolling contact cycling have been reported in the literature for more than 60 years. These changes appear in different shapes and locations. One class of such alterations is “butterfly wings”: regions of microstructurally transitioned material that appear diagonally around nonmetallic inclusions and may serve as fatigue crack initiation sites. Over the course of the past half a century numerous experimental and multiple analytical efforts have been made to understand and model this phenomenon, yet a lot is to be discovered and understood about root causes and mechanisms leading to butterfly formation. This article presents a comprehensive overview of the crack nucleation phenomena due to butterfly formation, its characteristics, and its negative impact on bearing service life. Significant attempts that have been made to solve the problem over the past half a century are mentioned, with a focus on recent work. Unanswered dilemmas are particularly discussed to highlight avenues of future research.
Non-metallic inclusions such as sulfides and oxides are byproducts of the bearing steel manufacturing process. Stress concentrations due to such inclusions can originate cracks that lead to final failure. This paper proposes a model to simulate subsurface crack formation in bearing steel from butterfly-wing origination around non-metallic inclusions until final failure. A 2D finite element model was developed to obtain the stress distribution in a domain subjected to Hertzian loading with an embedded non-metallic inclusion. Continuum Damage Mechanics (CDM) was used to introduce a new variable called Butterfly Formation Index (BFI) that manifests the dependence of wing formation on depth. The value of critical damage inside the butterfly wings was obtained experimentally and was used to simulate damage evolution. Voronoi tessellation was used to develop the FEM domains to capture the effect of microstructural randomness on butterfly wing formation, crack initiation and crack propagation. Then, the effects of different inclusion characteristics such as size, depth, and stiffness on RCF life are studied. The results show that stiffness of an inclusion and its location have a significant effect on the RCF life: stiffer inclusions and inclusions located at the depth of maximum shear stress reversal are more detrimental to the RCF life. Stress concentrations are not significantly affected by inclusion size for the cases investigated; however, a stereology study showed that larger inclusions have a higher chance to be located at the critical depth and cause failure. Crack maps were recorded and compared to spall geometries observed experimentally. The results show that crack initiation locations and final spall shapes are similar to what has been observed in failed bearings.
Nonmetallic inclusions such as sulfides and oxides are byproducts of the steel manufacturing process. For more than half a century, researchers have observed microstructural alterations around the inclusions commonly referred to as “butterfly wings.” This paper proposes a model to describe butterfly wing formation around nonmetallic inclusions. A 2D finite element model is developed to obtain the stress distribution in a domain subject to Hertzian loading with an embedded nonmetallic inclusion. It was found that mean stress due to surface traction has a significant effect on butterfly formation. Continuum damage mechanics (CDM) was used to investigate fatigue damage and replicate the observed butterfly wing formations. It is postulated that cyclic damage accumulation can be the reason for the microstructural changes in butterflies. A new damage evolution equation, which accounts for the effect of mean stresses, was introduced to capture the microstructural changes in the material. The proposed damage evolution law matches experimentally observed butterfly orientation, shape, and size successfully. The model is used to obtain S-N results for butterfly formation at different Hertzian load levels. The results corroborate well with the experimental data available in the open literature. The model is used to predict debonding at the inclusion/matrix interface and the most vulnerable regions for crack initiation on butterfly sides. The proposed model is capable of predicting the regions of interest in corroboration with experimental observations.
Rolling contact fatigue (RCF) is one of the primary damage modes for properly installed and lubricated rolling element bearings. Historically, because RCF is a stochastic process, extensive testing with subsequent statistical analysis is required to calibrate models that enable confident prediction of expected bearing service life. Recent research has focused on using computational models of microstructure topology to simulate the scatter in bearing life results. In this study, the anisotropy of the grain crystals and the grain texture of the microstructure are taken into account in addition to the explicit representation of the microstructure topology. Starting with a topological microstructure of Voronoi elements representing the material grains, each grain is assigned a cubic material definition and a set of random Euler angles to define the orientation. This microstructure is then converted into a 2D finite element model and a Hertzian contact is passed over the surface of the polycrystalline microstructure to simulate a roller bearing loading cycle. The maximum shear stress reversal and its location are calculated. Due to mismatch in the orientations of grains, stress concentrations develop on the grain boundaries leading to higher shear stress ranges than those calculated for an isotropic material. Depths of the maximum shear stress range show good agreement with experimental observations of crack initiation locations. The shear stress range and location are used to calculate the relative life of the bearing; evaluating many microstructural domains demonstrates that the life scatter produced by various microstructures relates well to the experimentally observed scatter in bearing life.
Microstructural alterations in bearing steels during rolling contact cycling have been reported in the literature for more than half a century. These structural changes are primarily caused by the decay of parent martensite and have been designated as white and dark etching regions due to their preferential etching characteristics. One of the most striking features of the white etching bands is their repeatable directionality, which has puzzled investigators for decades. Despite numerous attempts, a satisfactory explanation for the orientation of these bands is still not available. In this article (Part 1), an overview of the phenomenon is presented with detailed discussion of various experimental observations from the literature. The article also examines the previous approaches adopted to explain white etching bands and address their limitations. In Part II of the article, a J2-based elastic–plastic finite element model coupled with a carbon diffusion model is developed that directionally predicts the occurrence and orientation of the white etching bands.
Several 2D and 3D numerical models have been developed to investigate rolling contact fatigue (RCF) by employing a continuum damage mechanics approach coupled with an explicit representation of microstructure topology. However, the previous 3D models require significant computational effort compared to 2D models. This work presents a new approach wherein efficient computational strategies are implemented to accelerate the 3D RCF simulation. In order to reduce computational time, only the volume that is critically stressed during a rolling pass is modeled with an explicit representation of microstructure topology. Furthermore, discontinuities in the subsurface stress calculation in the previously developed models for line and circular contact loading are removed. Additionally, by incorporating a new integration algorithm for damage growth, the fatigue damage simulations under line contact are accelerated by a factor of nearly 13. The variation in fatigue lives and progression of simulated fatigue spalling under line contact obtained using the new model were similar to the previous model predictions and consistent with empirical observations. The model was then extended to incorporate elastic–plastic material behavior and used to investigate the effect of material plasticity on subsurface stress distribution and shear stress–strain behavior during repeated rolling Hertzian line contact. It is demonstrated that the computational improvements for reduced solution time and enhanced accuracy are indispensable in order to conduct investigations on the effects of advanced material behavior on RCF, such as plasticity.
Fatigue lives of rolling element bearings exhibit much scatter due to the statistical nature of the failure process. The localized character of contact stresses enhances the effects of microstructural features on fatigue life. In this paper, the growth of intergranular fatigue damage in rolling contacts is investigated. An explicit finite element model is developed which models the grain boundaries using an irreversible cohesive zone approach. The effects that the grain boundary properties play in fatigue life scatter and final spall patterns are presented and discussed. The predicted fatigue lives and spall patterns were found to be similar to experimental results.
Material inclusions in the form of hydrogen embrittlement, carbides, etc., are by-products of manufacturing processes and commonly present in bearing steel. The objective of this study was to develop a life equation for rolling contact fatigue phenomenon that accounts for the effects of inclusions. The life equation was developed using the fatigue results previously obtained using the damage model (Jalalahmadi and Sadeghi, Journal of Tribology vol. 132, 2010). Four modifying factors counting for effects of the stiffness, size, depth, and number of the inclusions are used to modify the life equation. These modifying coefficients are extracted from the simulations obtained from the Voronoi Finite element (FE) model and the Lundberg-Palmgren-based fatigue criterion (Jalalahmadi and Sadeghi, Journal of Tribology vol. 131, 2009). These simulations predict Weibull slopes and L 10 lives that are in good agreement with the previous theoretical and experimental results. It is seen that as inclusions become larger or shallower, they cause a larger decrease in the fatigue lives and their scatter. Also, introduction of more inclusions to the material significantly reduces the fatigue lives and their Weibull slopes.
The continuum theory of elasticity and/or homogeneously discretized finite element models have been commonly used to investigate and analyze subsurface stresses in Hertzian contacts. These approaches, however, do not effectively capture the influence of the random microstructure topology on subsurface stress distributions in Hertzian contacts. In this paper, a finite element model for analyzing subsurface stresses in an elastic half-space subjected to a general Hertzian contact load with explicit consideration of the material microstructure topology is presented. The random internal geometry of polycrystalline microstructures is modeled using a 3D Voronoi tessellation, where each Voronoi cell represents a distinct material grain. The grains are then meshed using finite elements, and an algorithm was developed to eliminate poorly shaped elements resulting from “near degeneracy” in the Voronoi tessellations. Hertzian point and line contacts loads are applied as distributed surface loads, and the model’s response is evaluated with commercial finite element software ABAQUS . Internal stress results obtained from the current model compare well with analytical solutions from theory of elasticity. The influence of the internal microstructure topology on the subsurface stresses is demonstrated by analyzing the model’s response to an over rolling element using a critical plane approach.
Fatigue behavior of polycrystalline materials is significantly influenced by their microstructural topology. The microstructural heterogeneity is one of the primary reasons for dispersion in high cycle fatigue lives of such materials. In this work, a damage mechanics based fatigue model that incorporates gradual material degradation under cyclic loading is presented in conjunction with a discrete material representation that takes the material microstructural topology into account. Microstructures are generated stochastically through the process of Voronoi tessellation. Micro-crack initiation, coalescence and propagation stages are modeled using damaged zones in a unified framework. The model is applied to study high cycle fatigue in rolling contacts. The effect of material topological disorder and inhomogeneity on fatigue life dispersion is studied. Fatigue damage is found to originate sub-surface and propagate towards the surface. Sub-surface damage patterns from the model are consistent with experimental observations. Propagation life is found to constitute a significant fraction of total life. Lives are found to follow a 3-parameter Weibull distribution. The relative proportion of lives spent in the initiation and propagation stages are in good quantitative agreement with experiments.
In this work, for development and sustainability of compressive residual stresses (RS) in bearing steel materials is examined. Of particular interest is the role of retained austenite (RA) transformation in fatigue performance. Cyclic torsional loading was performed for a prescribed number of cycles at specific stress levels. Specimens were then examined using X-ray diffraction techniques to observe RS values and RA volume fraction. Based on the experimental results, an empirical model incorporating RA transformation and material relaxation was developed to predict RS formation. The results obtained from the model corroborate well with experimental measurements. Experimental results indicate that much of the RA present is not useful for generating compressive RS. However, by controlling applied loading, compressive RS can be generated and maintained throughout fatigue life. These findings were then translated into rolling contact fatigue (RCF) scenarios to identify loading conditions to maximize the benefits associated with RA transformation. The experimental and modeling results highlight the utility of RA transformation in increasing compressive residual stresses within the material, but emphasize the limitations of RA in the system.
Rolling contact fatigue (RCF) induces a complex subsurface stress state, which produces significant microstructural alterations within bearing steels. A novel modeling approach is presented in this paper, which investigates the effects of microstructural deterioration, phase transformations, and residual stress (RS) formation occurring within bearing steels subject to RCF. The continuum damage mechanics approach was implemented to capture microstructural decay. State and dissipation functions corresponding to the damage mechanics process were used via an energy criterion to predict the phase transformations of retained austenite (RA). Experimental measurements for RA decomposition and corresponding RS were combined to produce a function providing RS formation as a function of RA decomposition and stress history within the material. Microstructural decay, phase transformations, and internal stresses were implemented within a two-dimensional (2D) finite element analysis (FEA) line contact model to investigate variation in microstructural alterations due to RSs present within the material. In order to verify the model developed for this investigation, initial simulations were performed implementing conditions of previously published experimental work and directly comparing to observed RA decomposition and RS formation in 52100 steel deep groove ball bearings. The finite element model developed was then used to implement various RS profiles commonly observed due to manufacturing processes such as laser-shot peening and carburizing. It was found that some RS profiles are beneficial in altering RA decomposition patterns and increasing life while others proved less advantageous.
In this study the rolling contact fatigue (RCF) of case carburized AISI 8620 steel was numerically and experimentally investigated. For the numerical study, a two dimensional finite element (FE) RCF model based on the continuum damage mechanics (CDM) was developed to investigate the fatigue damage accumulation, crack propagation and final fatigue life of carburized AISI 8620 steel under various operating conditions. A randomly generated Voronoi tessellation was used to model the effects of material microstructure topology. The boundaries of the Voronoi elements were assumed to be the weak planes where damage accumulates, cracks initiate and propagate to simulate inter-granular cracks. A series of torsional fatigue tests were conducted on carburized AISI 8620 steel specimens containing 0% and 35% retained austenite (RA) to determine fatigue load (S) vs. life (N) of the material. The S–N results were then used to determine the material parameters necessary for the rolling contact fatigue model. The torsional fatigue test results indicate that the carburized AISI 8620 specimens with higher RA demonstrate higher life than the specimens with lower RA. The RCF model also indicates that the material with higher level of compressive residual stresses (RS) and retained austenite demonstrates higher RCF life. In order to corroborate the results of RCF model, a three-ball-on-rod rolling contact fatigue test rig was used to determine the RCF lives of carburized AISI 8620 steels with different amounts of RA. The fatigue life and cracks evolution pattern from the numerical and experimental results were corroborated. The results indicate that they are in good agreement.
10.1080/10402004.2012.665987
In this study, a three-dimensional (3D) continuum damage mechanics (CDM) finite element (FE) model was developed to investigate the effects of fretting wear on rolling contact fatigue (RCF) of bearing steels. In order to determine the fretting scar geometry, a 3D arbitrary Lagrangian-Eulerian (ALE) adaptive mesh (AM) FE model was developed to simulate fretting wear between two elastic bodies for different initially pristine fretting pressures (0.5, 0.75 and 1 GPa) and friction coefficients (0.15, 0.175 and 0.25) resulting in stick zone to contact width ratios, c/a = 0.35, 0.55 and 0.75. The resulting wear profiles were subjected to various initially pristine RCF pressures (1, 2.2 and 3.4 GPa). The pressure profiles for RCF were determined by moving the contact over the fretted wear profiles in 21 steps. These pressure profiles were then used in the CDM-FE model to predict the RCF life of fretted surfaces. The CDM-FE model uses Fatemi-Socie (FS) criteria for damage evolution and accounts for scatter in RCF life by implementing material topological variation through Voronoi tessellation. The results from CDM-FE RCF model indicate that fretting scar generated at 1 GPa with c/a = 0.35 has the most detrimental effect on RCF life at 1 GPa, reducing life by as much as 99.8% from pristine condition. However, it is to be noted that the remaining life expectancy at this RCF pressure (1 GPa) is significant and more than 17 billion cycles. As the RCF pressure increases (PRCF ≥ 2.2 GPa), the effect of fretting on RCF life decreases for all fretting pressures and c/a values, indicating that life is primarily governed by the RCF pressure. The results from CDM-FE model were also used to develop a life equation for evaluating the L10 life of fretted M-50 bearing steel for the range of tested conditions.
The objectives of this investigation were to develop a 3D efficient elastic-plastic finite element model to characterize the rolling contact fatigue behavior of through hardened steel at high loads (∼5 GPa) and to corroborate analytical and experimental results. The efficient FE model developed for this investigation was coupled with the continuum damage mechanics to simulate rolling contact fatigue (RCF). The new computationally efficient approach developed uses Delaunay mesh to reduce the number of elements without compromising the accuracy of stress distribution induced during a rolling contact pass. In order to validate the newly developed approach, the results obtained from the current 3D model for line contact were corroborated to previously published results. The fatigue lives obtained from the new model are consistent with the previously published model predictions and empirical observations. In order to simulate the RCF for high load conditions, the increase in the contact width observed in the experiments and consequently the decrease in the contact pressure with loading cycles were implemented in the model. Furthermore, the damage evolution law was modified to incorporate the compressive residual stresses induced by the plastic deformation. The L10 life and the scatter in the fatigue lives obtained from the model correlated well with the experimental results. As a part of this investigation, a Thrust Bearing Test Apparatus (TBTA) was designed and developed to simulate RCF. RCF experiments were conducted on through hardened AISI 52100 steel flat specimens at high contact stress levels (5 GPa) to induce plastic deformation. The results demonstrated that the contact width increased as the cycles increased due to plastic strain accumulation. The results from FE model corroborate well with experimental results obtained from TBTA.
In this study, a new approach has been developed to simulate three-dimensional (3D) experimental rolling contact fatigue (RCF) spalls using a two-dimensional (2D) finite element (FE) model. The model introduces a novel concept of dividing the 3D Hertzian pressure profile into 2D sections and utilizing them in a 2D continuum damage mechanics (CDM) RCF model. The distance between the two sections was determined by the size of the grains in the material microstructure. The 2D RCF model simulates characteristics of case carburized steels by incorporating hardness gradient and residual stress (RS) distribution with depth. The model also accounts for the topological randomness in the material microstructure using Voronoi tessellation. In order to define the failure criterion for the current model, sub-surface stress analysis was conducted for the Hertzian elliptical contact. It was predicted that the high shear stress region near the end of the major axis of the contact is the cause of catastrophic damage and spall formation. This prediction was validated by analyzing the spalls observed during RCF experiments using a surface profilometer. The model was implemented to predict RCF lives for 33 random material domains for different contact geometry and maximum Hertzian pressures. The model results were then compared to the RCF experiments conducted on two different test rigs, a three-ball-on-rod and a thrust bearing test apparatus (TBTA). It was found that the RCF lives obtained from the model are in good agreement with the experimental results. The results also demonstrated that the spalls generated using the analytical results resemble the spalls observed in experiments.
The objectives of this study were to investigate the effects of elastohydrodynamic lubrication pressure on the rolling contact fatigue life of non-conformal contacts. In order to achieve the objectives a finite element elastohydrodynamic lubrication (EHL) model was coupled with a continuum damage mechanics model. The coupled finite element damage mechanics and EHL (DMEHL) model was then used to investigate the effects of speed and damage variable on the fatigue life of non-conformal contacts. The results demonstrate that the damage variable has a significant effect on pressure distribution within the contact and depending on the level of damage; the pressure distribution can significantly deviate from the undamaged EHL pressure. The results also demonstrated that speed has a significant effect on fatigue and failure. A parametric study was conducted to examine the effects of the damage variable on the progression of fatigue and evolution of the EHL pressure profile. The results demonstrate that the critical damage value is important to fatigue and can drastically affect the EHL pressure profiles.
NO ABSTRACT
Large bearings employed in wind turbine applications have half-contact widths that are usually greater than 10mm. Previous numerical models developed to investigate rolling contact fatigue (RCF) require significant computational effort to study large rolling contacts. This work presents a new computationally efficient approach to investigate RCF life scatter and spall formation in large bearings. The modeling approach incorporates damage mechanics constitutive relations in the finite element (FE) model to capture fatigue damage. It utilizes Voronoi tessellation to account for variability occurring due to the randomness in the material microstructure. However, to make the model computationally efficient, a Delaunay triangle mesh was used in the FE model to compute stresses during a rolling contact pass. The stresses were then mapped onto the Voronoi domain to evaluate the fatigue damage that leads to the formation of surface spall. The Delaunay triangle mesh was dynamically refined around the damaged elements to capture the stress concentration accurately. The new approach was validated against previous numerical model for small rolling contacts. The scatter in the RCF lives and the progression of fatigue spalling for large bearings obtained from the model show good agreement with experimental results available in the open literature. The ratio of L10 lives for different sized bearings computed from the model correlates well with the formula derived from the basic life rating for radial roller bearing as per ISO 281. The model was then extended to study the effect of initial internal voids on RCF life. It was found that for the same initial void density, the L10 life decreases with the increase in the bearing size.
An explicit finite element model was developed to investigate crack initiation and spall formation in machine elements subject to rolling contact fatigue. The modeling approach utilizes continuum damage mechanics to capture the initiation and propagation of fatigue damage that leads to the formation of a surface spall. The material microstructure is modeled via a randomly generated Voronoi tessellation. The material parameters for the model were obtained independently from torsional fatigue life data for 52100 bearing steel. The life scatter (Weibull slope) and the spall geometry obtained from the model correlate well with experimental results available in the open literature.
Ball and rolling element bearings are perhaps the most widely used components in industrial machinery. They are used to support load and allow relative motion inherent in the mechanism to take place. Subsurface originated spalling has been recognized as one of the main modes of failure for rolling contact fatigue (RCF) of bearings. In the past few decades a significant number of investigators have attempted to determine the physical mechanisms involved in rolling contact fatigue of bearings and proposed models to predict their fatigue lives. In this paper, some of the most widely used RCF models are reviewed and discussed, and their limitations are addressed. The paper also presents the modeling approaches recently proposed by the authors to develop life models and better understanding of the RCF.
Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the rolling contact fatigue failure process. Empirical life models that account for this dispersion do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the stochastic nature of the bearing material. Here, a damage mechanics based fatigue model is introduced in conjunction with the idea of discrete material representation that takes the effect of material microstructure explicitly into account. Two sources of material randomness are considered: (1) the topological randomness due to geometric variability in the material microstructure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress fields in rolling element line contacts is studied. The damage model, which incorporates cyclic damage accumulation and progressive degradation of material properties with rolling contact cycling, is used to study the mechanisms of subsurface initiated spalling in bearing contacts. Crack initiation as well as propagation stages are modeled using damaged material zones in a unified framework. The spalling phenomenon is found to occur through microcrack initiation below the surface where multiple microcracks coalesce and subsequent cracks propagate to the surface. The computed crack trajectories and spall profiles are found to be consistent with experimental observations. The microcrack initiation phase is found to be only a small fraction of the total spalling life and the scatter in total life is primarily governed by the scatter in the propagation phase of the cracks through the microstructure. Spalling lives are found to follow a three-parameter Weibull distribution more closely compared to the conventionally used two-parameter Weibull distribution. The Weibull slopes obtained are within experimentally observed values for bearing steels. Spalling lives are found to follow an inverse power law relationship with respect to the contact pressure with a stress-life exponent of 9.35.
Inclusions are the primary sites for subsurface fatigue crack initiation in bearing contacts. To understand the mechanisms of subsurface crack nucleation under contact loading, a detailed description of the stress field around these inclusions is necessary. This paper presents a new approach to computing stresses in an inhomogeneous medium where inclusions are treated as inhomogeneities in a homogeneous material matrix. The approach is based on the Discrete Element (DE) Method in which the material continuum is replaced by a set of rigid discrete interacting elements. The elements are connected to each other along their sides through springs and dampers to form the macro-continuum and undergo relative displacements in accordance with Newton’s laws of motion under the action of external loading. The spring properties are derived in terms of the overall elastic properties of the continuum. The relative motion between elements gives rise to contact forces due to stretching or compression of the inter-element springs. These forces are evaluated at each time-step and the corresponding equations of motion are solved for each element. Stresses are calculated from the inter-element joint forces. A Hertzian line contact case, with and without the presence of subsurface inclusions, is analyzed using the DE model. The DE model was used to determine stresses for an inclusion-free medium that compares well with that obtained from the continuum elasticity models. Parametric studies are then carried out to investigate the effects of size, location, orientation, and elastic properties of inclusions on the subsurface stress field. Both inclusions that are stiffer and/or softer than the base material are seen to give rise to stress concentrations. For inclusions that are stiffer than the base material (semi-infinite domain), the stress concentration effect increases with their elastic modulus. The stress concentration effect of a softer inclusion is higher than that of a stiffer inclusion. Inclusions that are oriented perpendicular to the surface give rise to much higher von Mises stresses than the ones that are oriented parallel to the surface. There is little change in the maximum von Mises stress for inclusions that are located deep within the surface.
A new approach to computing sub-surface stresses in an elastic half-space subjected to a line loading is presented. The approach is based on the discrete element method (DEM) in which the material continuum is replaced by a set of convex, rigid, interacting elements connected through visco-elastic fibers. A Hertzian pressure profile with, and without surface traction is applied to a semi-infinite domain created by gluing together discrete elements. Stresses are calculated from the inter-element joint forces that develop due to relative motion of the elements. Newton’s laws are employed to simulate the motion of each element. The stress distribution obtained from the discrete element model compares very well with that obtained from continuum elasticity models. The paper illustrates the applicability of the DEM to analysis of contacts at the microlevel and serves as a foundation to further studies in fracture and fatigue of bearing materials.
Elastohydrodynamically lubricated point contact was investigated using a two-way partitioned fluid–solid interaction (FSI) model. Ansys Mechanical finite element modeling software was used to compute elastic (and plastic) deformation of the solid bodies, while ansys fluent computational fluid dynamics software was used to model the fluid with the Navier–Stokes equations. The current model is not limited by Reynolds equation assumptions, allowing for the investigation of pressure, viscosity, and temperature variation across point contact elastohydrodynamic lubrication (EHL) films. Solid body material stress distribution and fluid behavior such as cavitation were also investigated. The details of model development are described. Validation of the model is presented across a range of loads and speeds for cases when the Reynolds equation is applicable. The results are in excellent agreement. Various slide-to-roll ratios were investigated considering a non-Newtonian fluid with thermal effects to characterize lubricant properties within the EHL film. Results demonstrate notable lubricant viscosity and temperature variations within the EHL film thickness both along and perpendicular to the rolling direction for cases with high slide-to-roll ratio. Cavitation was also considered, and cavitation bubble lengths were found to agree well with results found in open literature. Finally, the effects of material plasticity on solid body response were investigated. The FSI model developed in this research provides new insights on a classical EHL problem.
This paper presents a partitioned, two-dimensional fluid structure interaction (FSI) model developed to investigate the effects of surface cracks in rolling/sliding line contacts operating under elastohydrodynamic lubrication (EHL). The lubricant behavior as it flows over and through the crack is determined by solving the Navier-Stokes equations using the Ansys Fluent computational fluid dynamics (CFD) solver. The structural response of the solid body is governed via an elastic-plastic constitutive relationship and solved using the Ansys Mechanical finite element solver. The exchange of (i) forces due to fluid pressure, and (ii) displacements due to solid deformation across the fluid-solid interface (including the crack faces) is facilitated by an iterative implicit coupling scheme. A smoothing based dynamic meshing technique is utilized to capture the deformation of the fluid region. The FSI model developed for this investigation is capable of modeling surface cracks with inclined geometries, overcoming the limitations of the classical Reynolds based approach. The fluid pressure results are presented for different loads, speeds and slide-to-roll ratios. The effects of crack geometry (i.e. location, dimension, inclination, crack tip radius, etc.) on fluid pressure and structural response are investigated. The FSI model presents the details of pressure distribution, fluid streamlines and stress concentration in the solid simultaneously. The model results can be used to provide accurate boundary conditions on the crack faces for crack propagation modeling in rolling contact fatigue. The results of this investigation identify the crack geometries that affect fatigue life of rolling elements in EHL contact by predicting the location and severity of stress concentrations in the material.
This paper presents a partitioned fluid-structure interaction (FSI) solver to model elastohydrodynamic lubrication (EHL) of line contacts. The FSI model was constructed using the multiphysics simulation software ANSYS wherein an iterative implicit coupling scheme is implemented to facilitate the interaction between fluid and solid components. The model employs a finite volume method (FVM) based computational fluid dynamics (CFD) solver to determine the lubricant flow behavior using the Navier-Stokes equations. Additionally, the finite element method (FEM) is utilized to model the structural response of the solid. Fluid cavitation, compressibility, non-Newtonian lubricant rheology, load balance algorithm and dynamic meshing were incorporated in the FSI model. The pressure and film thickness results obtained from the model are presented for a wide range of loads, speeds, slide to roll ratios (SRR), surface dent, material properties (elastic plastic), etc. The model presents a detailed understanding of EHL contacts by removing any assumptions relative to the Reynolds equation. It provides the (i) two-dimensional variation of pressure, velocity, viscosity etc. in the fluid, and (ii) stress, elastic/plastic strain in the solid, simultaneously. The FSI model is robust, easy to implement and computationally efficient. It provides an effective approach to solve sophisticated EHL problems. The FSI model was used to investigate the effects of surface dents, plasticity and material inclusions under heavily loaded lubricated line contacts as can be found in gears and rolling element bearings. The results from the model exhibit excellent corroboration with published results based on the Reynolds equation solvers.
This paper presents a partitioned strongly coupled fluid–solid interaction (FSI) model to solve the 2D elastohydrodynamic (EHD) lubrication problem. The FSI model passes information between a control volume finite-difference discretized Reynolds equation and abaqus finite element (fe) software to solve for the fluid pressure and elastic deformation within heavily loaded lubricated contacts. Pressure and film thickness results obtained from the FSI model under a variety of load and speed conditions were corroborated with open published results. The results are in excellent agreement. Details of the model developed for this investigation are presented with a focus on the simultaneous solution of the Reynolds equation, load balance, and the coupling of the solid abaqus fe with the finite-difference fluid (Reynolds) model. The coupled FSI model developed for this investigation provides the critical venue needed to investigate many important tribological phenomena such as plasticity, subsurface stress, and damage. The current FSI model was used to explore and demonstrate the efficacy of the model to investigate the effects of microstructure inhomogeneity, material fatigue damage, and surface features on heavily loaded lubricated contacts as can be found in a wide range of industrial, automotive, and aeronautical drive systems.
Highly loaded ball and rolling element bearings are often required to operate in the mixed elastohydrodynamic lubrication regime in which surface asperity contact occurs simultaneously during the lubrication process. Predicting performance (i.e., pressure, temperature) of components operating in this regime is important as the high asperity contact pressures can significantly reduce the fatigue life of the interacting components. In this study, a deterministic mixed lubrication model was developed to determine the pressure and temperature of mixed lubricated circular and elliptic contacts for measured and simulated surfaces operating under pure rolling and rolling/sliding condition. In this model, we simultaneously solve for lubricant and asperity contact pressures. The model allows investigation of the condition and transition from boundary to full-film lubrication. The variation of contact area and load ratios is examined for various velocities and slide-to-roll ratios. The mixed lubricated model is also used to predict the transient flash temperatures occurring in contacts due to asperity contact interactions and friction. In order to significantly reduce the computational efforts associated with surface deformation and temperature calculation, the fast Fourier transform algorithm is implemented.
Inclusions are common in bearing materials and are a primary site for subsurface fatigue crack initiation in rolling element bearings. This paper presents a new approach for computing the pressure, film thickness, and subsurface stresses in an elastohydrodynamic lubrication (EHL) contact when inclusions are present in the elastic half-space. The approach is based on using the discrete element method to determine the surface elastic deformation in the EHL film thickness equation. The model is validated through comparison with the smooth EHL line contact results generated using linear elasticity. Studies are then carried out to investigate the effects of size, location, orientation, and elastic properties of inclusions on the EHL pressure and film thickness profiles. Both inclusions that are stiffer than and/or softer than the base material are seen to have effects on the pressure distribution within the lubricant film and to give rise to stress concentrations. For inclusions that are stiffer than the base material (hard inclusions), the pressure distribution within the lubricant film behaves as though there is a bump on the surface, whereas for inclusions that are less stiff than the base material (soft inclusions), the pressure distribution behaves in a manner similar to that of a dented surface. Inclusions close to the surface cause significant changes in the contact stresses that are very significant considering the stress life relationship. For inclusions that are located deep within the surface, there is little change in the EHL pressure and film thickness.
In this paper, the start-up process of line contact elastohydrodynamic lubrication with astationary central surface pocket is studied. The solution of the pressure profile and filmthickness distribution in the contact area is achieved by using a mixed lubricated-solidcontact model. The mass balance of pocket lubricant flow is enforced by using a simplealgorithm which adjusts the pocket cavitation boundary. With the surface pocket in thecenter of contact, the Hertzian contact area is divided into two micro-EHL contacts: theinlet micro-EHL contact and the outlet micro-EHL contact. The amount of lubricanttrapped inside the pocket determines the overall start-up behavior. If the lubricanttrapped is less than a critical amount, the two micro-EHL contact would be in start-upcondition in serial: the lubricant film builds up in the inlet micro-EHL contact area firstand then the lubricant film builds up in the outlet micro-EHL contact after the inletlubricant flow fills the pocket. The start-up time in this case is longer than the start-uptime for smooth surface start-up. If the lubricant trapped is more than the critical amount,the two micro-EHL contact would be in start-up condition in parallel: a lubricant filmbuilds up in the inlet micro-EHL contact and at the same time a lubricant film builds upin the outlet micro-EHL contact. The start-up time in this case is much smaller than thatof the smooth surface start-up. Compared with the smooth surface start-up condition,because the solid contact vanishes faster, there would be less frictional heat generated inthe contact area and thus the surface temperature rise during the start-up process wouldbe much smaller. These effects could prove beneficial in applications with frequent startand stop or oscillating running conditions, in which direct solid to solid contact occurs atthe start (restart) of motion.
In this paper, an isothermal study of the shut down process of elastohydrodynamic lubrication under a constant load is performed. The surface mean velocity is decreased linearly from the initial steady state value to zero. The details of the pressure and film thickness distributions in the contact area are discussed for the two stages of shut down process, namely the deceleration stage and the subsequent pure squeeze motion stage with zero entraining velocity. The nature of the balance between the pressure, the wedge and the squeeze terms in Reynolds equation enables an analytical prediction of the film thickness change on the symmetry line of the contact in the deceleration period, provided that the steady state central film thickness relationship with velocity is known. The results indicate that for a fixed deceleration rate, if the initial steady state surface mean velocity is large enough, the transient pressure and film thickness distributions in the deceleration period solely depend on the transient velocity. The pressure and film thickness at the end of the deceleration period are then the same and do not depend on the initial steady state velocity. From the same initial steady state velocity, larger deceleration rates provide higher central pressure increase, but also preserve a higher film thickness in the contact area at the end of the deceleration period. Later in the second stage when the axisymmetric pressure and film thickness patterns typical of pure squeeze motion form, the pressure distribution in the contact area resembles a Hertzian contact pressure profile with a higher maximum Hertzian pressure and a smaller Hertzian half contact width. As a result, the film thickness is close to a parabolic distribution in the contact area. The volume of the lubricant trapped in the contact area is then estimated using this parabolic film thickness profile.
A model was developed to study the effects of a rigid debris on elastohydrodynamic lubrication of rolling/sliding contacts. In order to achieve the objectives the time dependent Reynolds equation was modified to include the effects of an ellipsoidal shaped debris. The modified time dependent Reynolds and elasticity equations were simultaneously solved to determine the pressure and film thickness in EHL contacts. The debris force balance equation was solved to determine the debris velocity. The model was then used to obtain results for a variety of loads, speeds, and debris sizes. The results indicate that the
A numerical model of surface temperature rise in elastohydrodynamic lubrication start up process is presented. The frictional heat flux is modeled as the product of lubricated contact pressure or solid contact pressure with its respective coefficient of friction. The temperature rise is calculated by numerically integrating the solution of point heat source moving over a half space. The constant speed restriction is removed to allow calculation of temperature rise on a surface with a variable speed. The FFT method is incorporated to speed up the temperature rise calculation. Surface temperature rise in elastohydrodynamic lubrication start up condition is calculated, for the case when speed increase from zero to desired speed occurs in one step and the case when speed is linearly increased to desired speed.
In this paper a model is presented to investigate the start up condition in elastohydrodynamic lubrication. During start up the lubrication condition falls into the mixed lubrication regime. The transition from solid contact to lubricated contact is of importance when investigating the start up process and its effects on bearing performance. The model presented uses the multigrid multilevel method to solve the lubricated region of the contact and a minimization of complementary energy approach to solve the solid contact region. The FFT method is incorporated to speed up the film thickness calculation. An iteration scheme between the lubrication and the solid contact problems is used to achieve the solution of the mixed lubrication contact problem. The results of start up with smooth surfaces are provided for the case when speed increases from zero to desired speed in one step and the case when speed is linearly increased to desired speed. The details of the transition from full solid contact to full lubricated contact in EHL start up are presented. The change of pressure and film thickness as well as contact forces and contact areas are discussed.
Dents in elasto-hydrodynamic lubricated (EHL) contacts will initiate spalls and shorten the fatigue life significantly. Experimental results are provided from a ball-on-rod rolling contact fatigue tester with the rod predented with a single large dent. The results indicate that the spall usually initiated at the trailing edge of the dent on the driving surface. These cracks and spalls can also be created in the absence of lubricant. Based on the accumulated plastic strain and damage mechanics concept, a line contact spall initiation model was developed to investigate the dent effects on spall initiation and propagation. The near surface volume of the contact solid was divided into many small metal cells and for each cell the damage law was applied to determine whether the cell is undergoing damage or not. If the cell on the surface is damaged, then it is removed from the surface and a spall will be formed. If the damaged cell occurs below the surface, then a subsurface void is generated, this void could grow to the surface depending on the running conditions. The spall will further modify the surface geometry and initiate a new spall, hence, the spall will propagate. The results indicate that the location of spall initiation depends on the EHL and dent condition. Spalls can initiate at either the leading or trailing edge of the dent depending on the surface traction.
Debris in lubricated contacts significantly reduces the contact fatigue life. The life reduction is due to the surface damage caused by debris denting and the subsequent overrolling of the dent in the EHL contact. High pressure spikes are generated due to the dent which will modify the contact stress profiles, leading to stress concentration at or near the surface. In this paper, the residual stresses caused by debris effects are investigated. The residual stresses originate from the debris denting process and from the overrolling process of the dent in EHL contacts. The finite element method was used to investigate the residual stresses due to each process and their combined effects on the internal stress distribution of an EHL contact. It was found that the residual stress from debris denting will increase the internal stresses in an EHL contact. However, the residual stresses from overrolling of dent will reduce the internal stresses. The residual stresses are largely dependent on the plastic modulus of the contacting materials and need to be considered when investigating the internal stresses in heavily loaded lubricated contacts.
A finite element model was developed to investigate the effects of a spherical debris on elastohydrodynamically lubricated rolling/sliding contacts. Three dimensional dent profiles were obtained using finite element method showing horseshoe shape material pile-up along the rolling direction. The dent profiles obtained from the finite element analysis (FEA) were compared with the experimental results. There is good qualitative agreement between FEA and experimental dent profiles. The FEA dent profiles were then used in a time dependent thermal elastohydrodynamic lubrication (EHL) point contact model to analyze the dent effects on the pressure, film thickness and temperature profiles. The presence of a dent in lubricated contacts generates high pressure spikes and increases the peak temperature. The internal stresses were calculated based on the pressure and traction data obtained from the EHL analysis. The results indicate that a dent created by a debris will cause the internal maximum Von Mises stress to occur near the surface, which contributes to surface initiated failures.
A line contact elastoplastohydrodynamic lubrication (EPHL) model has been developed to investigate the effect of a dent on heavily loaded rolling/sliding contacts. The Jinite element analysis (FEA) was used to obtain the plastic deformation of the surfaces caused by the high-pressure spikes that occur in the contact due to the presence of a dent. The effects of various dent sizes on the pressure and film thickness were studied. The results indicate that by including the plastic deformation of the surfaces in the analysis, the pressure spikes that occur due to a dent in the contact are smaller than those of the purely elastic case, and local material yielding occurs, resulting in bumps at the edges of the dent. Effects of diflerent bump shapes at the dent edges were then studied in elastohydrodynamic lubrication (EHL) contacts and the results indicated that these bumps can reduce the magnitude of pressure spikes.
Time dependent thermal EHL circular contact results with measured surface roughness were obtained to analyze the effects of roughness on pressure, film thickness, temperature, and coefficient of friction. Both contact surfaces are considered to be rough. Multilevel multigrid techniques (with multigrid integration) were used to solve the system of two dimensional Reynolds, elasticity and three dimensional energy equations simultaneously. The effects of surface roughness under various loads, speeds, and slip conditions have been studied. Surface roughness causes pressure and temperature spikes and increases the coefficient of friction, and surface roughness flattens due to the high pressure in EHL contact. The higher the load, speed and slide to roll ratio, the more significant the effect of the surface roughness. A comparison between rough EHL and smooth EHL results indicates that surface roughness cannot be ignored in EHL analysis.
A time-dependent thermal compressible elastohydrodynamic lubrication of line contact model has been developed to investigate the effects of a single bump or dent in heavily loaded rolling/sliding contacts. The results illustrate the transient behavior of the film thickness, pressure and temperature distributions as a bump or a dent travels through the contact. The multigrid multilevel technique was used to simultaneously solve the discretized time dependent Reynolds, elasticity and energy equations. The effects of various loads and speeds have been investigated. Results are presented for the nondimensional loads of W = 1.3 × 10−4 , 2.3 × 10−4 and nondimensional speeds ranging from U = 1 × 10−11 to U = 10−10 under pure rolling and rolling/sliding conditions.
A numerical solution of time dependent compressible elastohydrodynamic lubrication of line contacts has been obtained. The results show the effects of various operating parameters on the transient response behavior of a lubricated contact. The analysis models a startup situation where the surfaces are initially at rest and in contact. Then, with the contacts operating at a given load and speed, the analysis is run until the pressure and film thickness reach a steady-state condition. A multigrid/multilevel technique is used to simultaneously solve the time dependent Reynolds and elasticity equations. The effects of various loads and speeds have been investigated. Results are presented for nondimensional loads ranging from W = 2.0 × 10−5 to W = 2.3 × 10−4 and nondimensional speeds ranging from U = 1.0 × 10−12 to U = 1.0 × 10−10 .
A numerical study of Newtonian thermal elastohydrodynamic lubrication (EHD) of rolling/sliding point contacts has been conducted. The two-dimensional Reynolds, elasticity and the three-dimensional energy equations were solved simultaneously to obtain the pressure, film thickness and temperature distribution within the lubricant film. The control volume approach was employed to discretize the differential equations and the multi-level multi-grid technique was used to simultaneously solve them. The discretized equations, as well as the nonorthogonal coordinate transformation used for the solution of the energy equation, are described. The pressure, film thickness and the temperature distributions, within the lubricant film at different loads, slip conditions and ellipticity parameters are presented.
A complete numerical solution of Newtonian thermal compressible elastohydrodynamic lubrication of rolling/sliding point (circular) contact has been obtained. The multilevel multigrid technique was used to solve the simultaneous system of thermal Reynolds, elasticity and the energy equations with their boundary conditions. The effects of various loads, speeds, and slip conditions on the lubricant temperature, film thickness, and friction force have been investigated. The results indicate that the temperature rise in the contact is significant and thermal effects cannot be neglected.
A numerical solution to the problem of isothermal non-Newtonian elastohydrodynamic lubrication of rolling/sliding point contacts has been obtained. The multigrid technique is used to solve the simultaneous system of two-dimensional modified Reynolds and elasticity equations. The effects of various loads, speeds, and slide to roll ratios on the pressure distribution, film thickness, and friction force have been investigated. Results for the dimensionless load W = 4.6 × 10−6 and 1.1 × 10−6 , and the dimensionless velocity U = 3 × 10−10 and 3 × 10−11 are presented. The results indicate that slide to roll ratio has negligible effect on the minimum film thickness, however, it significantly reduces the pressure spike.
A comparison between the effects of Newtonian, hyperbolic, and Eyring fluid models on the internal stresses in EHD lubrication of a smooth and rough stationary surface in contact with a moving smooth surface was obtained. The Newton-Raphson technique was used to solve the simultaneous system of Reynolds and modified elasticity equations. The elasticity equation was modified with the experimental surface measurements obtained from a typical bearing. The pressure and film thickness results obtained from the EHD solution were used to calculate the surface shear stress and the internal stresses. Results have been presented for the dimensionless loads of W = 1.3 × 10−4 , 2.3 × 10−4 and speeds of U = 5.46 × 10−11 , 1.092 × 10−10 for smooth and rough surface conditions. The results indicate that surface roughness of typical bearings do not significantly affect the depth at which the maximum shear stress occurs.
A numerical solution to the problem of thermal and non-Newtonian fluid model in elastohydrodynamic lubrication is presented. The generalized Reynolds equation was modified by the Eyring rheology model to incorporate the non-Newtonian effects of the fluid. The simultaneous system of modified Reynolds, elasticity and energy equations were numerically solved for the pressure, temperature and film thickness. Results have been presented for loads ranging from W = 7 × 10−5 to W = 2.3 × 10−4 and the speeds ranging from U* = 2 × 10−11 to U* = 6 × 10−11 at various slip conditions. Comparison between the isothermal and thermal non-Newtonian traction force has also been presented.
A numerical model was developed to investigate the subsurface mechanical and thermal stresses in rolling/sliding machine elements operating under elasto-hydrodynamic (EHD) lubrication of line contacts. A thermal non-Newtonian EHD lubrication model was modified to include the thermoelastic displacement of the solids. The pressure, film thickness, and temperature distribution obtained from the model were used to calculate the subsurface mechanical and thermal stresses within the rolling/sliding machine elements. The thermoelastic effects on the magnitude and location of the maximum shear stresses are presented.
A numerical solution to the problem of thermal and compressible elastohydrodynamic (EHD) lubrication of rolling/sliding rough surfaces was obtained by neglecting the transient effects. The technique involves the simultaneous solution of thermal Reynolds and modified elasticity equations using the Newton-Raphson technique, and the energy equation using the control volume finite element method. The effects of various loads, amplitude of asperity, and radius of curvature of asperity have been investigated. Results have been presented for moderate dimensionless load of W = 9.03 × 10−5 to heavy load of W = 2.3 × 10−4 at the speed of U* = 9.2 × 10−11 . The results indicate that surface roughness significantly affect the pressure, temperature, and traction in EHD lubrication.
A complete numerical solution of thermal compressible elastohydrodynamic lubrication of rolling/sliding contacts has been obtained. The Newton-Raphson technique is used to solve the simultaneous system of Reynolds and elasticity equations. The control volume finite element modeling was employed to solve the energy equation and its boundary conditions. The effects of various loads, speeds, and slip conditions on the lubricant temperature, film thickness, and friction force have been investigated. The results indicate that the temperature effects are significant and cannot be neglected.
The internal stress distribution in elastohydrodynamic lubrication of rolling/sliding line contact was obtained. The technique involves the full EHD solution and the use of Lagrangian quadrature to obtain the internal stress distributions in the x, y, z-directions and the shear stress distribution as a function of the normal pressure and the friction force. The principal stresses and the maximum shear stress were calculated for dimensionless loads ranging from (2.0452 × 10−5) to (1.3 × 10−4) and dimensionless velocity of 10−10 to 10−11 for slip ratios ranging from 0 to pure sliding condition.
A complete numerical solution of compressible elastohydrodynamic lubrication of rough surfaces has been obtained. The Newton-Raphson technique is used to solve the simultaneous system of modified compressible Reynolds and elasticity equations. The effects of various loads, surface pattern, and roughness parameter have been investigated. Results have been presented for loads ranging from W = 2.0452 × 10−5 to W = 2.3 × 10−4 at the speed of U = 1.0 × 10−11 . The results indicate that the compression effects are significant and cannot be neglected.
An approximate method for mid-film temperature and traction force in elastohydrodynamic (EHD) lubrication of sliding contacts is obtained. The results are obtained at the point of maximum pressure where the pressure gradient is zero. The results indicate excellent correlation exists between this approximate method and results of a previous paper by the authors [1].
A two dimensional numerical solution to the problem of thermal elastohydrodynamic lubrication of rolling/sliding contacts was obtained using a finite difference formulation. The technique involves the simultaneous solution of the thermal Reynolds’ equation, the elasticity equation, and the two dimensional energy equation. A pressure and temperature dependent viscosity for a synthetic paraffinic hydrocarbon lubricant (XRM-109F) was considered in the solution of the Reynolds’ and energy equations. The experimental pressure and surface temperature measurements obtained by Dow and Kannel [1] were used in evaluating the results of the numerical analysis for the cases of pure rolling and slip conditions.
This paper presents an investigation into oil starvation in different cage pocket shapes of a horizontally mounted ball bearing. The Counter Rotating Angular Contact ball bearing Test Rig (CRACTR) was used to visualize the oil distribution inside specially manufactured transparent bearing cages using detailed images from a high-speed camera. Three different cage types were investigated using various oils dyed with ultraviolet dye. The identification of oil and air regions elucidated the oil distribution in the cage pocket and the formation of oil-air striations on the ball surface under various operating conditions. The experimental results demonstrated that raceway motion, ball submersion level, oil properties, and cage pocket shape influenced oil starvation inside the bearing cage. Ansys Fluent software was used to develop an equivalent two-phase computational fluid dynamics (CFD) model for the test bearing. Results from the CFD model corroborate well with the experimentally observed oil distribution for all test cages and establish the strong influence of cage geometry on oil starvation and bearing lubrication.
The objectives of this investigation are to determine the effects of cage pocket conformality on lubrication in a cylindrical roller bearing (CRB) cage. A custom Bearing Cage Friction Test Rig (BCFTR) was configured with a sealed enclosure to emulate a lubricant bath environment. The enclosure was designed to accommodate CRB raceway segments and swappable cage pockets with adjustable roller-pocket clearance. Three transparent cage segments were fabricated with differing pocket conformality with respect to the roller surface. A high-speed camera was used to visualize the in-situ lubricant flow within the roller-pocket contact for all cage types. An equivalent two-phase computational fluid dynamics (CFD) model was developed using Ansys Fluent software. The CFD results corroborated well with the experimentally observed trends of lubricant distribution and cage pocket friction. The findings demonstrated that the impact of pocket conformality was two-fold. The least conformal pocket design experienced minimum pocket friction. However, the same design introduced challenges with retaining lubricant at the roller-pocket contact and increasing air entrapment in the oil.
A test rig was designed and developed to assess the lubrication and friction of a single cylindrical roller and a conformal cage pocket. The roller was lubricated via oil bath in a sealed housing. Inner and outer bearing raceway pieces were fixed above and below the roller to mimic the internal geometry of an actual bearing. The cage pocket was made from transparent acrylic to look inside the cage and observe oil flow during operation. A six-axis load cell was used to measure the torque generated by the entire test rig with and without the cage pocket, and used to isolate the friction of the cage pocket. Experiments were conducted to investigate the effects of roller-pocket clearance, roller-race clearance, and roller oil submersion level at rest. Results suggest that roller bearing cage pocket friction increases with decreasing pocket clearance, increasing oil availability, and increasing operating speed. The oil was observed to coalesce into stable striations inside the cage pocket for many operating conditions. Striation width was observed to decrease with increasing speed, increasing pocket clearance, and decreasing oil availability. The striations were summarized by oil volume fraction inside the cage pocket, which decreased with increasing speed, decreasing pocket clearance and decreasing oil availability. The current results provide new information about oil behavior inside roller bearing cage pockets during operation, and an approach is presented to estimate roller bearing cage pocket friction.
The objectives of this investigation were to experimentally and analytically study the oil flow inside an angular contact ball bearing using Bubble Image Velocimetry (BIV). A counter-rotating angular contact ball bearing test rig (CRACTR) was designed and developed such that both bearing races can be rotated simultaneously in opposite directions, allowing for detailed observation of a single cage pocket in a stationary reference frame. Transparent acrylic cages were developed based on the original geometry of the cage and installed in the bearing. The oil flow inside the cage and bearing were analyzed using a high-speed camera. BIV was used to track bubbles in the oil and to understand the flow pattern inside the bearing. Ansys Fluent software was used to develop a computational fluid dynamics (CFD) model for the bearing. Results from the analytical model corroborate well with the experimentally observed oil flow streamlines and demonstrate the influence of operating conditions and cage designs on fluid flow. The CFD model provided details such as oil velocity at different locations in the bearing and fluid drag torque. The quantitative and qualitative validation of CFD results provides a basis for cage design for efficient lubricant flow inside a bearing.
The objective of this study was to experimentally and analytically investigate the lubrication condition and visualize the fluid flow in a ball bearing cage under various operating conditions. To achieve the experimental aspects of this investigation, a test apparatus incorporating a transparent cage was designed and developed. The transparent cage was manufactured based on the original geometry of the bearing cage. The transparent cage was positioned in the test rig relative to the ball using a precision XYZ table. This allowed for critical observation and examination of air and oil entrapment conditions within the cage. A high-speed camera was utilized to capture the fluid flow and air distribution inside the cage. To address the analytical aspects of this study, Ansys Fluent computational fluid dynamics (CFD) software was used to develop a multiphase lubrication model simulating the same conditions as the test apparatus. Lubricant and air distribution within the cage were investigated for various operating speeds and cage positions relative to the ball. Results from the experimental and analytical studies were corroborated and found to be in good agreement. The results demonstrate that as the cage was moved closer to the ball, lubrication conditions changed and fluid striated over the ball surface, resulting in greater air entrapment within the cage. The CFD model predicted similar trends and results. Increasing ball speed promoted starvation of lubricant supply to the cage. The CFD model confirmed that lubricant surface tension plays a key role in the striation patterns over the ball surface.
This paper presents an experimental and analytical investigation into the lubrication of deep groove ball bearing (DGBB) cage pockets. A custom acrylic replica of a cage segment was designed, developed, and installed on a cage friction test rig for the simultaneous measurement of frictional torque and visualization of oil flow inside of the cage pocket. A broad set of experiments was conducted with different lubrication methods, oil viscosities, cage positions, and ball speeds to characterize the state of lubrication inside of the cage pocket. The quantity of oil inside of the pocket was found to correlate closely with the measured frictional torque. Videos of oil flow were subsequently analyzed to estimate the volume of oil present within the cage pocket at each operating condition. This oil volume information was then used to define an equivalent fluid to be used in a numerical cage pocket lubrication model. The model solves the Reynolds equation over a spherically defined cage pocket domain and produces estimates of frictional torque. Predictions from the model agree well with experimental friction measurements. The cage pocket friction results exhibit a dichotomous relationship – first increasing with speed then decreasing due to the dominating evacuation of lubricant from the cage pocket. Curve fit equations are presented to describe both behaviors, allowing for the prediction of cage pocket friction spanning a range of Reynolds numbers from 2 to 5000.
This article presents a novel experimental test rig for the investigation of friction between a ball and cage of a deep groove ball bearing (DGBB). The experimental apparatus was designed and developed to replicate the orientation and dynamics of a full bearing in steady-state operation while collecting measurements of cage friction. A six-axis load cell was used to record force and torque values generated due to a rotating ball inside of a rigidly fastened cage segment. The test rig can be set up in two different configurations to collect cage friction measurements: (a) A position control configuration where measurements of friction torque on the ball are collected for specific positions of the ball and the cage and (b) a load control configuration where a constant force is applied between the ball and the cage and a friction coefficient is calculated from the results. The test rig was used to investigate four different DGBB cage varieties: (a) a snap-on polymeric cage, (b) a low-profile polymeric cage, (c) a stamped steel cage, and (d) a machined brass cage. The friction performance of each cage type is shown to be related to the shape of the lubricating film between the ball and the cage wall. In addition, measurements of friction torque at specific positions provide insight into the mixture of oil and air inside the cage pockets. Friction coefficients from experiments in the load control configuration are shown to increase with speed and reduce with applied load for all four cage varieties.
This article presents an efficient cavitation model for fluid film bearings, considering both gaseous and vaporous cavitation. This work presents a modification of Elrod’s cavitation algorithm, where the bulk fluid is similarly considered to be a mixture of liquid and bubbles, without the need for a switch function. By solving for properties of the bulk fluid in the film, the distribution of the gaseous, vapor, and liquid states is captured without detailed tracking of bubble dynamics, as well as the variable compressibility of the bulk fluid in both ruptured and full film regions. The model developed is implemented in a numerical algorithm to solve the compressible Reynolds equation. Finally, the approach developed is applied to test cases to demonstrate its potential, as well as for comparison with Elrod’s algorithm.
A Four Bearing Test Rig was designed and developed to measure frictional torque of oil lubricated rolling element bearings under various operating conditions. Deep groove ball bearings and radial needle roller bearings were tested for a range of speeds and lubricants. In this investigation, the portion of frictional torque caused by fluid drag losses was determined by analyzing the difference between a fully flooded (submerged) and a minimally lubricated bearing. Ansys Fluent computational fluid dynamics software was used to corroborate and model the different bearing geometries and operating conditions evaluated in the test rig. Drag force of bearing components was calculated from the CFD simulations and compared to the experimental results. The results demonstrate that they are in good agreement. Frictional torque due to fluid drag was further compared to an empirical friction model available in open literature. The CFD model provides a physics-based estimate of fluid drag which corroborates well with the experimental results, while the open literature empirical model tends to over-predict frictional torque from fluid drag. Experimental and analytical results from this investigation suggest that bearing cage design has a small impact on overall fluid drag losses, while substantial improvements can be made by optimizing lubrication conditions and bearing type. The presented CFD model provides an efficient approach to asses fluid drag losses for various bearing geometries and operating conditions.
ANSYS FLUENT computational fluid dynamics (CFD) software was used to develop a full-scale model of a single-phase oil flow in a deep groove ball bearing (DGBB). The CFD model was used to investigate fluid flow characteristics as a function of bearing geometry and operating conditions. The underlying theory, boundary conditions and development of the model are described in detail. Major features of the model, including meshing techniques, mesh density and geometric clearances, were determined by performing parametric studies. Streamlines, velocity vectors and pressure contours are used to investigate various DGBB aspects such as cage design and lubricant properties. The CFD model developed provides a novel approach to study DGBB fluid flow and the effect of cage geometry on bearing performance.
The objectives of this study were to experimentally measure motion of a floating valve plate and analytically investigate the effects of floating valve plate surface modifications on the lubricant film thickness and temperature distribution. In order to achieve the experimental objectives, a previously developed axial piston pump test rig was instrumented with proximity probes to measure the motion of the valve plate. To achieve the objectives of the analytical investigation, the thermal Reynolds equation augmented with the Jakobsson-Floberg-Olsson (JFO) boundary condition and the energy equation were simultaneously solved to determine the pressure, cavitation regions, and temperature of the lubricant at the valve plate/cylinder block interface. The lubricating pressures were then coupled with the equations of motion of the floating valve plate to develop a dynamic lubrication model. The stiffness and damping coefficients of the floating valve plate system used in the dynamic lubrication model were determined using a parametric study. The elastic deformation of the valve plate was also considered using the influence matrix approach. The experimental and analytical motions of the valve plate were then corroborated and found to be in good agreement. Four- and eight-pocket designs were then added as surface modifications to the floating valve plate in the dynamic lubrication model. The addition of surface modifications on the valve plate resulted in increased minimum film thicknesses and lowered lubricant temperatures at the same operating conditions.
This article presents the results of an experimental and analytical investigation of the fluid flow in a pocketed thrust bearing. An experimental test rig was designed, developed, and used to visualize fluid flow in pocketed thrust bearings. Microparticle image velocimetry (μPIV) was used to measure fluid flow inside the pocket of a thrust bearing. The thrust bearings were constructed by gluing precision shim stocks to a flat BK7 glass disk in contact with a polished steel disk. The precision shim stock provides the desired pocket depth for the bearing. A polished steel disk in contact with the thrust bearing was driven by a motor in order to induce fluid flow within the pockets. μPIV was then employed to measure the shear-driven cavity flow and generate the quiver plots of the flow field. Three different lubricants were used at various speeds and a constant load to measure the effects of speed and viscosity on the flow out of the pocketed thrust bearing. In order to achieve the analytical aspect of this research, a model was developed to predict the film thickness, cavitation area, and pressure distribution generated within the bearing. The cavitation areas obtained from the model were compared with the experimental results. The results corroborate well. The calculated pressure and film thickness were then used to determine the 3D velocity profiles within the pocketed thrust bearing. The measured velocities obtained from the experimental images were compared to the analytical velocity fields. Comparing the measured velocities with the analytical model, the depth of the microparticles in the bearing pocket was determined. Using this approach, the μPIV-measured 2D velocity field was converted into a 3D velocity field, which illustrates the fluid motion inside a pocketed thrust bearing at various speeds and viscosities.
This article presents an experimental and numerical investigation of temperature distribution in a pocketed thrust washer. An experimental test rig was designed and developed to measure the temperature in the thrust washer contact under various operating conditions. To measure the temperature in the contact, a thin layer of thermochromic material was placed beneath the pocketed surface. The thermochromic material allowed temperature measurements across the contact through color contours displayed on the sheet. Video recording during operation showed the thermochromic sheet dynamically adapting to the rising temperature in the bearing. For the numerical investigation, the thermal Reynolds and energy equations were simultaneously solved subject to boundary condition to determine the pressure and temperature within the thrust washer. The thermal Reynolds equation was augmented with the Jacobsson-Floberg-Olsson (JFO) boundary condition to model cavitation and the energy equation was used to determine temperature and viscosity variations across the film. Experimental and numerical results showed significantly lower temperatures within the cavitation region due primarily to lower heat transfer from the gas to the solid. The temperature profile and corresponding operating conditions of the bearing obtained from the model correlated well with the experimental results.
The objective of this study was to experimentally investigate hydrodynamic pressure generation in surface-pocketed thrust washers. A novel method of pressure mapping was developed to allow for in situ measurement of the pressure generated by surface modifications. Thin-film pressure transducers, located just below the thrust washer surface, were used to measure pressure variations as a function of the operating conditions. Contour maps showing the cavitation region and the location of peak pressure were clearly displayed. The experimental work presented maps the pressure profiles with real-time, high-resolution sensors. The thin-film pressure transducers were used to investigate the pressure interactions between surface features. In addition to the experimental setup, a model of the contact was developed using ANSYS FLUENT. Cavitation, friction, film thickness, and load support were all compared with experimental results and the two were shown to be in good agreement. The model demonstrated an accurate prediction of the pressure profile but varied slightly with the predicted load support of the thrust washer. The simulation was then used to optimize the pocket density for the experimental operating conditions. The optimal bearing design had the highest load-carrying capacity with a low friction coefficient.
The objectives of this study were to experimentally and numerically investigate oil flow in surface-pocketed thrust washers. In order to achieve the experimental aspects of this investigation, a thrust washer test rig was designed and developed to visualize the lubricant flow at the contact interface. A novel approach for creating the pockets was developed to allow optical inspection of the lubricant during thrust washer operation. The thrust washers were fabricated using a glass disk with a thin layer of steel shim stock adhered to the surface. The micrometer-thick shim stock was machined using an Nd:YAG laser to create the circular pocket geometries and then glued to the glass disk. A mirror and camera were placed below the semitransparent washer to observe the lubricant flow in the pocket. The results obtained from this configuration illustrate a cavitation bubble forming on the leading edge of the pocket followed by a sharp transition back to liquid. The size of the cavitation area was found to be a function of rotational speed, nominal bearing pressure (NBP), viscosity, and pocket geometry. The cavitation area ratio (gaseous region divided by the pocket area) increased for greater speeds and higher viscosities and decreased for larger pocket diameters, deeper pockets, and higher NBPs. The friction force for various thrust washer designs was also measured as a function of load, speed, and lubricant. The results showed that shallower, wider pockets provided the lowest friction. It was found that, generally, the conditions that minimize friction also result in a stable cavitation region. ANSYS Fluent computational fluid dynamics software was used to develop a three-dimensional model of the pocketed thrust washer utilizing the full Navier-Stokes equations to investigate the cavitation and pressure distribution occurring at the contact and corroborate the experimental results.
This paper presents a new high temperature dynamic viscosity sensor for in situ condition monitoring of engine lubricants. The sensor is used to measure the variation in the quality factor of a vibrating piezoelectric cantilever beam due to viscous damping. The sensor was used to measure the dynamic viscosity of various single and multi-grade engines oils up to 180 cP from 25 °C to 60 °C. The sensor is capable of detecting degradation and dilution of engine oil for both new and used samples of 5W-30 and 10W-40 and diluted SAE 30 engine oils. All of the viscosity measurements presented are within 0.13–9.8% of the results obtained using the standard Walther equation at various temperatures. An equation relating dynamic viscosity of an oil sample to the quality factor of the beam is presented. The quality factor measurement circuit presented in this research can be implemented in automotive applications for in situ condition monitoring of lubricant viscosity.
This article presents the results of experimental investigations of lubricant flow out of a micropocket in a conformal contact due to surface shear. A test rig was designed and developed to perform a micropocket flow under boundary and starved lubrication conditions. The test rig consists of a laser-machined circular micropocket on a flat specimen operating against a rotating glass disk under an applied load. Silicone oil was used as the test fluid. Optical microvideography was used to investigate lubricant extraction from micropockets. A high-speed camera was used to observe the lubricant extraction phenomena from micropockets under various operating conditions. Microparticle image velocimetry was also implemented to quantify and analyze lubricant flow from a micropocket. The following results were obtained: (1) the role of a micropocket by comparing the lubrication mechanism of a contact with and without a micropocket; (2) the effects of load, speed, and micropocket geometry on lubricant extraction; and (3) the detail of the micropocket flow during the extraction using microparticle image velocimetry (µ-PIV).
This article presents the results of an experimental and corresponding analytical investigation of fluid flow out of a shallow microcavity (dimple) due to surface shear. An experimental test rig was designed, developed, and used to demonstrate shear-driven fluid flow out of a microcavity. The experimental test rig consists of a flat steel belt driven against a microcavity filled with a fluid. Microparticle image velocimetry (μ PIV) was employed to visualize the shear-driven cavity flow and generate the streamline contours of the flow field. Two different sets of experiments were conducted. The first set examines the important factors that affect the flow field, and these include the cavity depth-to-width ratio (aspect ratio) and the speed of the flat belt. The second set of experiments was designed to observe the important fluid flow phenomena including the extraction and stagnation of the fluid above and below a critical cavity depth. A model was also developed using the computational fluid dynamic software COMSOL Multiphysics (1) to corroborate the experimental and analytical results. The results are in good agreement.
Friction coefficient, bearing performance (i.e., torque generation and temperature rise), and rolling contact fatigue of steel and ceramic (silicon nitride) materials operating in the presence of JP-8+100 jet fuel and Mil-L-23699 turbo jet oil were investigated. A ball-on-disk test machine was used to measure the coefficient of friction of a steel ball on a steel disk operating under various loads and slide-to-roll ratios when lubricated with JP-8+100 jet fuel. The results indicate that the fuel provides an extremely low friction coefficient under the conditions considered in this investigation. A three-ball-on-rod rolling contact fatigue testing machine was used to determine the fatigue life for different combinations of materials (i.e., silicon nitride and steels) and lubricants. As expected, the Weibull analysis indicates that the rolling fatigue life operating in the presence of jet fuel was less than that of an oil-lubricated contact. A bearing test machine was also designed, developed, and used to obtain the friction (torque) and the temperature characteristics of bearings operating in jet fuel and oil. The result from the bearing rig indicates that the fuel has a lower generated torque and temperature rise than oil.
In this study the effect of water as a contaminant in lubricated contacts was analytically and experimentally investigated. A steel ball on glass disc apparatus was used to measure lubricant film thickness of pure oil and water in oil emulsions under various operating conditions. A steel ball on steel disc rig was used to measure friction as a function of various loads, slide to roll ratios and water in oil emulsions. A finite difference numerical model was developed using the continuum theory of mixtures and results were corroborated with the experimental measurements. Numerical results are in excellent agreement with the experimental results and indicate that water will flow around the contact. The experimental and analytical results suggest that for heavily loaded contacts water-in-oil emulsions perform essentially the same as pure oils.
An experimental apparatus and an analytical model have been developed to investigate and determine the lubrication condition and frictional losses at the interface between a piston ring and cylinder liner. In order to obtain a solution for the lubrication condition between the piston ring and cylinder liner, the system of Reynolds and film thickness equations subject to boundary conditions were simultaneously solved. The effects of boundary and mixed lubrication conditions were implemented using the Greenwood –Tripp stochastic approach. The Elrod cavitation algorithm was used to investigate the effects of fluid rupture and reformation at the top and bottom dead centres. The experimental results indicate that the piston ring and liner experience all the different lubrication regimes (i.e. boundary, mixed, and hydrodynamic lubrication) during a stroke. A comparison between experimental and analytical results indicated that they are in good agreement and the analytical model developed for this study can capture the different lubrication regimes that the piston ring and liner experience.
A numerical model was developed to investigate the effects of groove geometry on the hydrodynamic lubrication mechanism of thrust washers. In order to achieve the objectives the isothermal, time-dependent, polar-coordinate Reynolds equation, including the cavitation and centrifugal effects, was solved numerically to determine the pressure distribution for various groove geometries and operating conditions. The polar coordinate Reynolds equation was discretized using the control volume finite difference approach. The results indicate that thrust washers are capable of supporting a significant amount of load with proper groove geometries. Design curves were generated for load support and other operating parameters as a function of each of the groove geometrical parameters (i.e., depth, width, number of grooves, and shape) as well as the operating conditions so that thrust washers performance can be predicted and optimized.
In this study a dynamic bearing apparatus is designed, developed and used to evaluate noise and vibration of bearings lubricated with various greases under different operating conditions. Eight different greases are evaluated for their vibration and noise characteristics. The threshold, kurtosis and mean square methods are used to quantify grease vibration and rank the greases based on their bearing vibration. The results indicate that ultra-filtered greases exhibit the lowest bearing vibration in the mid-frequency range amongst all greases tested.
During start up and shut down of heavily loaded rolling/sliding contacts, the lubricant film separating the surfaces is extremely thin and not fully developed. The load is supported by both the solid and the lubricant. Under extreme conditions, there is no lubricant film and the load is solely supported by the solid contact. However, when surface pockets are engineered on the surface of rolling/sliding elements, lubricant can be trapped in the pockets and deform with the pockets. Finite element analysis [FEA] of the deformation of a single empty pocket indicates that the volume of the pocket significantly decreases under an applied load. Therefore, when the pocket is filled with a lubricant, the lubricant will undergo significant compression. This compression enables lubricant to support part of the load and provide beneficial effects, such as reducing friction and expelling the lubricant during start up and shut down. This research presents an FEA model of a rigid cylinder in contact with an elastic and/or elastic-linear-kinematic-hardening-plastic half space with lubricant filled surface pocket(s). Results of lubricant filled pockets are compared with those of empty pockets. The results demonstrate the beneficial effects of load sharing mechanism by the lubricant.
An extensive test program was conducted to determine the performance characteristics (friction, wear, temperature) of a linear high temperature perfluoroalkylpolyether (PFPE) and two branched PFPE lubricants under normal and severe operating conditions. These include temperatures up to 200° C and Hertzian pressures as high as 2.8 GPa. A four-ball wear tester was used to measure wear scar and a two-disk machine was used to measure friction. The linear perfluoroalkylpolyether lubricant demonstrated low friction and wear at elevated temperatures under the test conditions considered. A bearing testing apparatus was used to measure friction and temperature of tapered roller bearings under various operating conditions for a branched PFPE and the results are reported.
The objectives of this study were to analytically and experimentally investigate the motion of the floating valve plate in an axial piston pump under various operating conditions. To achieve the objectives of the analytical investigation, the equations of motion for the valve plate were coupled with a time-dependent lubrication model. The balance pistons that support the floating valve plate were represented by equivalent spring and dashpot systems. The system of equations was then solved using the Runge-Kutta and the control volume finite difference methods to determine the pressure, film thickness, and motion of the valve plate for various operating conditions. To achieve the experimental objectives, a previously developed axial piston pump test rig was instrumented with proximity probes to measure the motion of the valve plate. The stiffness and damping of the balance pistons supporting the floating valve plate were determined using the impact and frequency response methods. Using the experimentally determined stiffness and damping coefficients in the coupled dynamic lubrication model, the analytical and experimental results of the valve plate motions were compared. The model was then used to conduct a parametric study to determine the overall system stiffness and damping coefficients during pump operation. Using the stiffness and damping coefficients from the parametric study in the dynamic lubrication model, the pressure, film thickness, and motion of the valve plate were calculated for various operating conditions. The experimental and analytical displacements of the valve plate were then corroborated and found to be in good agreement.
The purpose of this investigation was to experimentally measure the motion of the floating valve plate in an axial piston pump under various operating conditions and to develop a model to determine how the floating valve plate motion affected the lubricating pressures between the valve plate and cylinder block. In order to achieve the objectives, a hydraulic circuit was designed and developed to incorporate and operate a floating valve plate axial piston pump. The hydraulic circuit integrating the axial piston pump (axial piston pump apparatus, APPA) consists of a series of valves, pressure sensors, a charge pump, flow meters, temperature sensors, a heat exchanger, and proximity probes. The floating valve plate axial piston pump housing was modified to incorporate three proximity probes to measure the valve plate position and motion relative to the cylinder block, thus allowing for determination of the film thickness within this contact. The results illustrate that as the pump starts up the valve plate experiences vibrations and begins to lift relative to the cylinder block. Then as the pump reaches steady-state operation the valve plate achieves a fixed position and tilt. The results also demonstrate that under steady-state operation, the valve plate vibrates and this vibration correlates well with the speed and the number of pistons in the pump. The measured film thickness results were then used in a lubrication model to determine the pressures generated between the floating valve plate and the cylinder block. The analytical results highlight how the motion of the valve plate directly correlates to the pressure pulsations seen in the lubricating gap.
A numerical model was developed to investigate the effects of groove geometry on the hydrodynamic lubrication mechanism of thrust washers. In order to achieve the objectives the isothermal, time-dependent, polar-coordinate Reynolds equation, including the cavitation and centrifugal effects, was solved numerically to determine the pressure distribution for various groove geometries and operating conditions. The polar coordinate Reynolds equation was discretized using the control volume finite difference approach. The results indicate that thrust washers are capable of supporting a significant amount of load
Rolling/sliding contact of two layered rotating cylinders is analyzed. The substrate of each cylinder is modeled as an elastic body. Under loading, the surface layer is allowed to deform as an elastic or viscoelastic body and lubricant can release from this layer and enter the contact providing the lubrication with limited flow rate. The influence of the surface layer properties on contact pressure, film thickness and friction coefficient is analyzed for various operating conditions. The results indicate that due to the bleeding properties of the surface layer the EHD regime of lubrication has some distinctive properties. The film thickness tends to a constant value and the coefficient of rolling friction decreases as the Sommerfeld number increases for both the elastic and viscoelastic models of the surface layer.
A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.
An optical micro-apparatus was designed and developed to visualize and measure adhesion and friction forces for a steel ball in contact with a sapphire window. The apparatus allows for in situ optical investigation of the contact interface during the initiation, separation and simultaneous measurement of the normal force generated within the contact. A high precision z-stage was utilized to move the steel ball at low velocities (0.1 μm/s) to bring it into contact with the fixed sapphire window. In this study, the adhesion force between a 1–mm-diameter steel ball and sapphire window was measured and visualized when the surfaces approach and retract from each other. The experimental results demonstrated the presence of the adhesion force and stick area during the retraction of the contacting surfaces. The optical micro-apparatus is also equipped with a piezoelectric actuator to reciprocate the ball against the sapphire window to conduct sliding friction experiments at various normal loads. In this investigation, a new optical technique was also developed to measure the tangential displacement of the contacting interfaces during sliding friction tests. In this technique, the video of the contacting bodies during sliding friction cycle was processed to trace the center of the contact area and, consequently, measure the relative tangential displacement of the contact. The friction loops obtained using the measured tangential displacement exhibited a rectangular shape thus eliminating the system stiffness commonly observed in friction loop studies. The vertical and horizontal segments of the rectangular friction loops characterize the stick and slip regions of the contact, respectively.
Highly loaded ball and rolling element bearings are often required to operate in the mixed elastohydrodynamic lubrication regime in which surface asperity contact occurs simultaneously during the lubrication process. Predicting performance of components operating in this regime is important as the high asperity contact pressures can significantly reduce the fatigue life of the interacting components. Rolling contact fatigue is one of the most dominant causes of failure of components operating in mixed lubrication regime. Contact fatigue begins with the initiation of microscopic fatigue cracks in the rolling contact surfaces or within the sub-surface regions due to cyclic shear stresses. Investigation of mixed lubrication effects on performance of machine components is of significant importance in order to understand and enhance their load carrying capacity. This article investigates the effects of mixed lubrication and surface roughness on machine components performance. Results from a mixed lubrication model are utilized to investigate the effects of different operating conditions on fatigue life of the components. Simple rough surfaces consisting of single hemispherical bump as well as complex rough surfaces consisting of a numerically generated 3D rough surface operating under mixed lubrication conditions are studied and results presented. The stress-based Ioannides and Harris model incorporating the fatigue limit is used to evaluate the fatigue life variation. Fast Fourier Transform (FFT) technique is used to significantly reduce the time required for the computation of internal stresses.
An experimental apparatus and an analytical model have been developed to investigate and determine the lubrication condition and frictional losses at the interface between a piston ring and a honed cylinder liner (PRCL). The experimental apparatus was used to measure the friction at the PRCL interface under various conditions. The analytical model developed to corroborate with experimental results includes the effects of boundary and mixed lubrication conditions using a fully deterministic approach. The procedure for analyzing the honed profile and generating a numerical equivalent for use in the mixed lubrication model is discussed. A comparison of measured and generated surfaces indicates that the model is capable of reproducing a honed cylinder liner surface profile with good accuracy. A comparison of experimental and analytical friction results shows good agreement. The model is used to analyze the effects of a cross-hatch angle on frictional behavior at the piston ring/cylinder liner contact.
The human femoral artery can bleed dangerously following the removal of a catheter during cardiac catheterization. In this study, a modified technique of needle insertion, simply inserting the needle bevel-down instead of the standard bevel-up approach, was tested as a means to reduce bleeding after catheter removal. Large bore needle punctures were made in surgically exposed arteries of anesthetized pigs using either a standard technique (45 degree approach, bevel up) or a modified technique (25 degree approach, bevel down). For half the punctures, topical phenylephrine solution (1 mg/ml) was applied to the adventitia of the artery to cause constriction. Median bleeding rates were reduced from 81 to less than 1 ml/min/100 mmHg intraluminal pressure by the modified technique with application of phenylephrine. In most cases zero bleeding, that is selfsealing, of the arteries occurred. It is postulated that a flap-valve of tissue created by the modified technique produced this self-sealing behavior. Sophisticated modeling studies are needed to fully understand this new phenomenon.
A model of a thin annular plate sliding against an elastic foundation was developed and used to study thermoelastic instability (TEI) in clutches. The analysis examines the stability of the quasi-steady state solution of the governing equations by considering nonaxisymmetric perturbations. The results indicate that above critical values of temperature and sliding speed the response of the plate becomes unstable and exhibits large deformations. Two mechanisms account for this behavior: thermal buckling and bending. It is shown that a conservative approximation of the stability boundaries can be constructed by computing only two points on the stability curve. The boundary between stable and unstable behavior depends on the material properties, geometry, and boundary conditions. The model was used to conduct a parametric study which indicates that stability of the sliding system can be improved by reducing the sliding speed, decreasing the modulus of elasticity of the plate, increasing the thermal conductivity, or increasing the thickness. In addition, for a range of sliding speeds, increasing the stiffness of the friction material improves the stability of the system. For speeds outside this range, increasing the stiffness makes the system less stable.
A six degrees-of-freedom Dynamic Bearing Model (DBM) was modified to include a novel cage pocket lubrication model. The motion of the cage was determined using the finite difference method to solve for the pressure generation and resultant forces inside of each cage pocket at each time step of the dynamic model. The computational domain of the finite difference model was designed to reflect the specific cage pocket geometry of four common cage designs. Additionally, a bearing cage friction test rig was utilized to characterize the lubrication state inside of each cage. Experiments were performed that reveal the relationship between cage shape, ball speed, and relative ball – cage position. Specifically, information on the occurrence of kinematic starvation, the speed dependent evacuation of oil from a cage pocket, was collected for use as an input condition to the dynamic bearing model. An inverse distance weighting scheme was utilized to predict starvation parameters for a general ball position inside of the cage pocket. Results from the dynamic simulation reveal new knowledge on the effect of cage geometry and lubrication on dynamic behavior. The inclusion of lubrication effects inside of the cage pocket reduces the median contact force between the balls and cage pocket and improves the stability of the predicted cage motion.
In this paper, a model was developed to study the effects of rotor and support flexibilities on the performance of rotor–bearing–housing system. The system is composed of a flexible rotor and two supporting deep-groove ball bearings mounted in flexible bearing housings. The dynamics of the ball bearings were simulated using an existing dynamic bearing model, which was developed using the discrete element method (DEM). The explicit finite element method (EFEM) was used to model the flexibilities of the rotor and bearing support. In order to combine the dynamic bearing model with finite element rotor and support system, new contact algorithms were developed for the interactions between the various components in the system. The total Lagrangian formulation approach was applied to decrease the computational effort needed for modeling the rotor–bearing–housing system. The combined model was then used to investigate the effects of bearing clearances and housing clearances. And it was found that, as the rotor is deformed due to external loading, the clearances have a significant impact on the bearing varying compliance motion and reaction moments. Results also show that deformation of the flexible housing depends on the total force and moment generated within the bearing due to rotor deformation. The first critical speed of rotor was simulated to investigate the unbalance response of the rotor–bearing system. It was demonstrated that rotor critical speed has a significant effect on inner race displacement and reaction moment generated at bearing location.
This article presents both experimental and analytical investigations on the dynamic behavior of the cage in a ball bearing. For the experimental investigation, a wireless sensor telemeter system was designed and developed to monitor the cage motions. The sensor, which was integrated on the bearing cage, is composed of a commercially available capacitor–inductor (LC) circuit. The LC circuit on the rotating cage was coupled to a transceiver that was stationary and positioned in close proximity to the cage. In order to achieve the objective of the analytical investigation, the explicit finite element method (EFEM) was used to simulate the bearing cage. The EFEM cage model was then combined with the dynamic bearing model to simulate the cage motion during operation. The results from the experimental measurement using the telemeter were then compared with the analytical modeling. The developed telemeter demonstrated the capability of the cage telemeter in detecting various bearing frequencies. These include the cage frequency, shaft frequency, and ball pass frequency on the outer race (BPFO), which was introduced by creating a spall on the bearing outer race. Compared to standard accelerometers that are commonly used to measure vibrations on the bearing housing, the cage telemeter has shown advantages in sensing cage motions and detecting bearing defects regardless of the location of the damage. Analytical simulation using the EFEM cage model correlated well with the experimental results and provided more insight into the bearing cage dynamics.
This work presents a numerical simulation which studies the effect of elastomeric bushing on the dynamics of a deep-groove ball bearing. To achieve the objective, a three-dimensional (3D) explicit finite element method (EFEM) was developed to model a cylindrical elastomeric bushing, which was then coupled with an existing dynamic bearing model (DBM). Constitutive relationship for the elastomer is based on the Arruda–Boyce model combined with a generalized Maxwell-element model to capture both hyperelastic and viscoelastic behaviors of the material. Comparisons between the bushing model developed for this investigation and the existing experimental elastomeric bushing study showed that the results are in good agreement. Parametric studies were conducted to show the effects of various elastomeric material properties on bushing behavior. It was also shown that a desired bushing support performance can be achieved by varying bushing geometry. Simulations using the combined EFEM bushing and DBM model demonstrated that the elastomeric bushing provides better compliance to bearing misalignment as compared to a commonly used rigid support model. As a result, less ball slip and spin are generated. Modeling with a bearing surface dent showed that vibrations due to surface abnormalities can be significantly reduced using elastomeric bushing support. It has also been shown that choosing a proper bushing is an efficient way to tuning bushing vibration frequencies.
The objective of this investigation was to determine the effect of housing support on bearing performance and dynamics. In order to achieve the objective, an existing dynamic bearing model (DBM) was coupled with flexible housing model to include the effect of support structure on bearing dynamics and performance. The DBM is based on the discrete element method, in which the bearing components are assumed to be rigid. To achieve the coupling, a novel algorithm was developed to detect contact conditions between the housing support and bearing outer race and then calculate contact forces based on the penalty method. It should be noted that although commercial finite element (FE) software such as abaqus is available to model flexible housings, combining these codes with a bearing model is quite difficult since the data transfer between the two model packages is time-consuming. So, a three-dimensional (3D) explicit finite element method (EFEM) was developed to model the bearing support structure for both linear elastic and nonlinear inelastic elastomeric materials. The constitutive relationship for elastomeric material is based on an eight chain model, which captures hyperelastic behavior of rubber for large strains. The viscoelastic property is modeled by using the generalized Maxwell-element rheological model to exhibit rate-dependent behaviors, such as creep and hysteresis on cyclic loading. The results of this investigation illustrate that elastomeric material as expected has large damping to reduce vibration and absorb energy, which leads to a reduction in ball–race contact forces and friction. A parametric study confirmed that the viscoelastic stress (VS) contributes significantly to the performance of the material, and without proper amount of viscoelasticity it loses its advantage in vibration reduction and exhibits linear elastic material characteristics. As expected, it is also demonstrated that housing supports made of linear elastic material provide minimal damping and rely on the bearing friction to dissipate energy. A study of housing support geometry demonstrates that bearing support plays a large role on the dynamic performance of the bearing. Motion of bearing outer race is closely related to the geometry and symmetry of the housing.
In this investigation, a new approach was developed to study the influence of cage flexibility on the dynamics of inner and outer races and balls in a bearing. A 3D explicit finite element model (EFEM) of the cage was developed and combined with an existing discrete element dynamic bearing model (DBM) with six degrees of freedom. The EFEM was used to determine the cage dynamics, deformation, and resulting stresses in a ball bearing under various operating conditions. A novel algorithm was developed to determine the contact forces between the rigid balls and the flexible (deformable) cage. In this new flexible cage dynamic bearing model, the discrete and finite element models interact at each time step to determine the position, velocity, acceleration, and forces of all bearing components. The combined model was applied to investigate the influence of cage flexibility on ball-cage interactions and the resulting ball motion, cage whirl, and the effects of shaft misalignment. The model demonstrates that cage flexibility (deflection) has a significant influence on the ball-cage interaction. The results from this investigation demonstrate that the magnitude of ball-cage impacts and the ball sliding reduced in the presence of a flexible cage; however, as expected, the cage overall motion and angular velocity were largely unaffected by the cage flexibility. During high-speed operation, centrifugal forces contribute substantially to the total cage deformation and resulting stresses. When shaft misalignment is considered, stress cycles are experienced in the bridge and rail sections of the cage where fatigue failures have been observed in practice and in experimental studies.
A model for deep-groove and angular-contact ball bearings was developed to investigate the influence of a flexible cage on bearing dynamics. The cage model introduces flexibility by representing the cage as an ensemble of discrete elements that allow deformation of the fibers connecting the elements. A finite element model of the cage was developed to establish the relationships between the nominal cage properties and those used in the flexible discrete element model. In this investigation, the raceways and balls have six degrees of freedom. The discrete elements comprising the cage each have three degrees of freedom in a cage reference frame. The cage reference frame has five degrees of freedom, enabling three-dimensional motion of the cage ensemble. Newton’s laws are used to determine the accelerations of the bearing components, and a fourth-order Runge–Kutta algorithm with constant step size is used to integrate their equations of motion. Comparing results from the dynamic bearing model with flexible and rigid cages reveals the effects of cage flexibility on bearing performance. The cage experiences nearly the same motion and angular velocity in the loading conditions investigated regardless of the cage type. However, a significant reduction in ball-cage pocket forces occurs as a result of modeling the cage as a flexible body. Inclusion of cage flexibility in the model also reduces the time required for the bearing to reach steady-state operation.
A six-degree-of-freedom model was developed and used to simulate the motion of all elements in a cylindrical roller bearing. Cage instability has been studied as a function of the roller-race and roller-cage pocket clearances for light-load and high-speed conditions. The effects of variation in inner race speed, misalignment, cage asymmetry, and varying size of one of the rollers have been investigated. In addition, three different roller profiles have been used to study their impact on cage dynamics. The results indicate that the cage exhibits stable motion for small values of roller-race and roller-cage pocket clearances. A rise in instability leads to discrete cage-race collisions with high force magnitudes. Race misalignment leads to a rise in instability for small roller-cage pocket clearances since skew control is provided by the sides of the cage pocket. One roller of larger size than the others causes inner race whirl and leads to stable cage motion for small roller-race clearances without any variation in roller-cage pocket clearance. Cage asymmetry and different roller profiles have a negligible impact on cage motion.
In this study, a novel test rig was designed and developed to investigate roller slip, tilt, and skew in a spherical roller bearing (SRB). The test rig utilized a double-row 22313 SRB and was designed to allow for direct visual access to each row. A high-speed camera was used to capture the motion and angular position of the various rollers as they traversed the bearing. Successive frames captured from the videos were analyzed to determine roller slip and the SRB load zone. Roller tilt and skew angles were also measured by inserting a nearly weightless pin into the center of a roller. In a similar manner, high-speed videography was used to assess the tilt and skew of the roller for a complete revolution of the roller around the inner race of the SRB. The dynamic behavior of the rollers was then corroborated with a previously developed SRB dynamic bearing model (DBM). The experimental and analytical results indicate that the roller tilt angle increases with axial load, remains constant with speed, and decreases with increasing radial load when the roller is located in the load zone. Further, roller skew in the load zone increases with axial load and shaft speed; however, it decreases with the radial load. The results indicate that when the radial-to-axial load ratio is greater than 4, roller tilt and skew are minimized. Due to roller intermittent slip and roller-cage pocket collision in the unload zone, tilt and skew become chaotic. The magnitude of the tilt and skew in the unload zone is directly related to the roller-race and roller-cage pocket clearances, respectively.
Ball bearing turbochargers (TCs) incorporate an angular contact ball bearing cartridge to reduce friction and oil consumption, improving the efficiency of internal combustion engines. In this investigation, axial and radial TC rotor motion was experimentally measured and used to develop a model of the TC rotor-bearing system, allowing for a detailed analysis of the TC bearing under varying operating conditions. In order to achieve the experimental objectives of this investigation, eddy-current proximity probes were used to measure the radial motion at the turbine and compressor sides of the TC. The measured radial motion shows whirl with subharmonics at low speed. The measured axial motion of the rotor was found to increase with TC speed. In order to analytically investigate the bearing dynamics, a complete TC model was developed which includes the mass distribution and flexibility of the TC compressor, shaft and turbine, and squeeze film dampers (SFDs) which support the bearing cartridge. The model was used to replicate the whirl and axial motion of the test rig and then to determine which model parameters could be adjusted to minimize whirl without negatively affecting the bearing dynamics. Simulation results revealed that centrifugal effects cause a change in the bearing internal geometry, with a small clearance becoming a preload at higher speeds. When this effect is coupled with less compliant SFDs, the subharmonics are reduced and the overall sliding and number of large load cycles at the ball-race contacts are minimized, contributing to lower bearing friction and improved overall life.
The objective of this investigation was to analytically investigate the performance of a spherical roller bearing (SRB) operating under various loading and speed combinations. In order to achieve the objective, a full six degrees-of-freedom SRB dynamic model was developed. The model was corroborated with results in the open literature. An adaptive slicing method was developed to optimize the accuracy and computational effort of the roller force, skew, and tilt calculations. A comprehensive roller–race contact analysis in terms of slip velocity and contact area was then carried out to identify how bearing load and inner race (IR) speed variations change slip velocity and skew at the roller–race contact. The results from this investigation demonstrate that roller skew increases with IR speed, while the roller tilt remains relatively constant. The IR speed and roller slip velocity correlate well, which causes the traction force to increase and therefore produce greater skew. Skew and tilt angles also increase with applied axial load. However, at a certain load, the skew angle begins to decrease.
The objectives of this investigation were to experimentally examine the cage motion and ball-cage contact forces for an angular contact ball bearing (ACBB) operating under various load and speed combinations. In order to achieve the objectives, a Counter Rotating Angular Contact Ball Bearing Test Rig (CRACTR) was designed and developed such that both the races of an ACBB can be rotated simultaneously in opposite directions, providing valuable insights into the ball-cage interaction. Five proximity probes were used concurrently to measure the in-plane (radial) and out-of-plane (axial) motion for three commercially available cage designs. Two load cells were used to measure the contact forces between the balls and cage pocket. The experimental results demonstrate that high inner race speeds and high axial loads develop the smallest and most circular cage whirl motions. Additionally, cage radius, cage pocket clearance, cage pocket area and cage inertia were the prominent factors affecting the magnitude of cage whirl. Experimental results also indicate that contact forces between the ball and cage pocket increase linearly with the increased race speeds. Ball-cage contact force was shown to be different for the three cages and was primarily governed by the cage pocket area and the cage radius. Results from this investigation can be utilized to predict the correlation between the ball-cage contact forces and the race speeds, and identify the key parameters governing the stable cage motion during bearing operation.
The objective of this investigation was to utilize thin film pressure sensors to evaluate the pressure distribution between rolling element bearings and a housing. A test rig was constructed to place thin film sensors around the perimeter of a test bearing inside of a housing. High precision drive shafts were manufactured that produce a light and heavy interference fit with each of the test bearings. Pressure map results are used to evaluate the effect of internal clearance on the load distribution of different bearing types. The thin film sensor system was also used to investigate the circumferential load distribution on the housing. The presented apparatus and test method could be used to validate bearing fit selection and housing design.
The objectives of this investigation were to experimentally and analytically investigate the dynamics of a medium-sized, relatively high-speed ball bearing–supported turbocharger (TC). In order to achieve the objectives, a TC test rig was designed, developed, and instrumented with a combination of strain gauge–based load sensors and proximity probes. The sensors were used to measure the axial and frictional loads on the TC bearing, as well as the whirl of the compressor and turbine rotors, under various operating conditions. In this TC, the compressor and turbine shaft are supported by a pair of unloaded back-to-back angular contact ball bearings. The bearing cartridge is supported by squeeze film dampers (SFDs) and is prevented from rotation by an anti-rotation pin. To achieve the analytical aspects of this investigation, an equivalent bearing model was developed to investigate the bearing dynamics and whirl of the TC rotating assembly. The TC bearing cartridge was modeled with a single deep groove ball bearing (DGBB) using the discrete element method. The rotating shaft, compressor, and turbine were considered to be rigid and integrated with the inner race of the bearing. The SFD that supports the bearing was modeled with a bilinear spring and damper. A DGBB was used because it can support axial load in both directions. The results from the analytical model correlate well with the experimentally observed loads and whirl and show that whirl can have a significant effect on the dynamics of the individual bearing components.
The objectives of this investigation were to design and develop an experimental turbocharger test rig (TTR) to measure the shaft whirl of the rotating assembly and the axial and frictional loads experienced by the bearings. The TTR contains a ball bearing turbocharger (TC) that was instrumented and operated under various test conditions up to 55,000 rpm. In order to measure the thrust loads on the compressor and turbine sides, customized sensors were integrated into the TC housing. The anti-rotation (AR) pin that normally prevents the bearing cartridge from rotating was replaced with a custom-made load cell adapter system. This sensor was used to measure the frictional losses in the bearing cartridge without altering the operation of the TC. Proximity sensors (probes) were also installed in the compressor housing to monitor shaft whirl. Axial load results indicated that the compressor side bears most of the thrust load. As the backpressure or the speed of the TC was increased, the thrust load also increased. Frictional measurements from the AR pin sensor demonstrated low power losses in the ball bearing cartridge. For certain shaft speed ranges, the data from the sensors illustrated periodic trends in response to the subsynchronous whirl of the shaft.
This paper studies the stick–slip oscillations of discrete systems interacting with translating energy source through a non-linear smooth friction curve. The stick–slip limit cycle oscillations of a single degree-of-freedom model are examined by means of numerical time-integration and analytical methods. Similar approaches are also applied to the model of the coupled friction oscillator. Particularly, it is found that the steady-state response of the coupled oscillator can be divided into two different forms of oscillation (mode-merged and mode-separated oscillations) according to the frequency separation of two modes. The oscillation pattern of the steady-state response is shown to depend on system parameters such as detuning factor, energy source speed, and normal contact load.
A multi-degree-of-freedom (m.d.o.f.) system excited by a rough moving surface has been developed to study friction-induced oscillations. The normal degrees of freedom allow for oscillatory normal forces, while the normal–tangential coupling of friction produces parametric excitation in the slipping equations of motion. After a modal change of variables, first order averaging has been used to produce a set of autonomous equations of motion. Eigenvalue analysis of the averaged equations has produced stability predictions for the steady sliding position. Numerical integration of the original system of equations has verified the existence of locally unstable oscillations for a system excited by a rough surface input. The combination of velocity-dependent friction and a harmonically varying normal force have been shown to produce large-amplitude oscillations, in some cases leading to stick–slip responses.
A finite element model has been developed to investigate the engagement of rough, grooved, paper-based permeable wet clutches. The finite element (Galerkin) approach was used to discretize the modified Reynolds and force balance equations, and the solution domain geometry was described using an isoparametric formulation. Surface roughness effects were modeled via the Patir and Cheng (1978) average flow model, while asperity load sharing was calculated using the Greenwood and Williamson (1966) approach. The finite element model developed, was used to investigate the effects of applied load, friction material permeability, and groove size on the engagement characteristics of wet clutches (i.e., torque, pressure, engagement time, and film thickness). The results indicate that the applied load, friction material permeability, and groove width significantly influence the engagement characteristics. Higher facing pressures increase peak torque and decrease engagement time. Higher permeability of the friction material significantly decreases engagement time but dramatically increases peak torque. Wider grooves decrease the peak torque and increase the engagement time. Groove depth does not significantly affect engagement characteristics for this model.
A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.
A simple mathematical model for the engagement of rough, permeable, grooved wet clutches has been developed and used to determine the effect of various input parameters (applied load, grooved area, and friction material permeability) on engagement. The model includes the effects of surface roughness according to Patir and Cheng (1978), friction material permeability according to Natsumeda and Miyoshi (1994) and Beavars and Joseph (1967), and grooving in the friction material according to a new approximation. The approach reduces the system of Reynolds and force balance equations to a single, first-order differential equation in film thickness and time. A line searching algorithm, exploiting the low computational cost of function evaluations for the new model, is used to find the set of input parameter combinations yielding the same engagement characteristics. This set of design points is presented as an engagement isosurface in the parameter space (Fapp, Φˆ, Ared). The isosurface implicitly gives information about engagement time, and it shows regions in which the desired engagement characteristics cannot be achieved. The input parameters are classified as those affecting the transient portion of engagement and those affecting the steady-state portion.
A test rig has been designed to quantify the torque transmission characteristics of wet clutches. This apparatus is presented and its features discussed. A comparison is made between the torque measurements from the test rig and simulations using a previously developed mathematical model. Results are given for a variety of operating conditions. The data presented here validate the computational model as an accurate tool for wet clutch design and analysis. Important results include accurate torque transfer prediction capabilities, with the limiting factor being precise knowledge of the sliding friction coefficient μc. Another important conclusion of the work is that torque transfer during a single engagement event can be adequately predicted using the isothermal model presented here. The simplicity of the isothermal model, along with its computational efficiency, makes it attractive for wet clutch torque transfer prediction and wet clutch design.
The simplified isothermal model for wet clutch engagement previously developed by Berger, Sadeghi, and Krousgrill (Berger, E. J., Sadeghi, F., and Krousgrill, C. M., 1996, “Analytical and Numerical Modeling of Engagement of Rough, Permeable, Grooved Wet Clutches,” ASME J. Tribol., 119, p. 143) was extended to include fluid thermal effects. The modified Reynolds and thermal diffusion equations were simultaneously solved to obtain torque and temperature characteristics during wet clutch engagement. The modified Reynolds equation was integrated using the Adams-Gear scheme and the alternating direction implicit method (ADI) finite difference technique was used to solve the thermal diffusion equation. The model was used to study the effects of speed, temperature, and load on the torque transfer and lubricant temperature variation during wet clutch engagement. A comparison of thermal and isothermal results indicates that the thermal model generally predicts a longer engagement time and smaller peak torque than the isothermal model. Comparison of analytical and experimental results indicates that including fluid thermal effects in the model is critical for achieving good correlation between analytical and experimental results. [S0742-4787(00)01501-0]
A model of a thin annular plate sliding against an elastic foundation was developed and used to study thermoelastic instability (TEI) in clutches. The analysis examines the stability of the quasi-steady state solution of the governing equations by considering non-axisymmetric perturbations. The results indicate that above critical values of temperature and sliding speed the response of the plate becomes unstable and exhibits large deformations. Two mechanisms account for this behavior: thermal buckling and bending. It is shown that a conservative approximation of the stability boundaries can be constructed by computing only two points on the stability curve. The boundary between stable and unstable behavior depends on the material properties, geometry, and boundary conditions. The model was used to conduct a parametric study which indicates that stability of the sliding system can be improved by reducing the sliding speed, decreasing the modulus of elasticity of the plate, increasing the thermal conductivity, or increasing the thickness. In addition, for a range of sliding speeds, increasing the stiffness of the friction material improves the stability of the system. For speeds outside this range, increasing the stiffness makes the system less stable.
The objectives of this investigation were to develop a coupled dynamic model for turbocharger ball bearing rotor systems, correlate the simulated shaft motion with experimental results, and analyze the corresponding bearing dynamics. A high-speed turbocharger test rig was designed and developed in order to measure the dynamic response of a rotor under various operating conditions. Displacement sensors were used to record shaft motion over a range of operating speeds. To achieve the objectives of the analytical investigation, a discrete element angular contact ball bearing cartridge model was coupled with an explicit finite element shaft to simulate the dynamics of the turbocharger test rig. The bearing cartridge consists of a common outer ring, a pair of split inner races, and a row of balls on each end of the cartridge. The dynamic cartridge model utilizes the discrete element method in which each of the bearing components (i.e., races, balls, and cages) has six degrees-of-freedom. The rotor is modeled using the explicit finite element method. The cartridge and rotor models are coupled such that the motion of the flexible rotor is transmitted to the inner races of the cartridge with the corresponding reaction forces and moments from the bearings being applied to the rotor. The coupled rotor–cartridge model was used to investigate the shaft motion and bearing dynamics as the system traverses critical speeds. A comparison of the analytical and experimental shaft motion results resulted in minimal correlation but showed similarity through the critical speeds. The cartridge model allowed for thorough investigation of bearing component dynamics. Effects of ball material properties were found to have a significant impact on turbocharger rotor and bearing dynamics.
The objective of this experimental investigation was to design and develop a high speed turbocharger test rig (TTR) in order to critically examine the whirl and frictional characteristics of floating ring and ball bearing turbochargers. In order to achieve the objective, a high speed TTR was designed and developed with the capability of reaching speeds in excess of 100,000 rpm and was equipped with speed and displacement sensors to obtain the necessary results for comparison between the two turbocharger models. The TTR was used to compare and contrast the whirl and friction characteristics of two identical turbochargers differing only by the support structure of the rotor system: one containing a floating ring bearing turbocharger (FRBT) and the other a ball bearing turbocharger (BBT). The TTR is driven by an industrial compressor powered by a six cylinder 14 liter diesel engine. This configuration closely resembles turbocharger operation with an actual engine and was able to operate in both nominal and extreme operating conditions. A pair of displacement sensors was installed to measure the whirl of the rotor near the end of the compressor. Whirl results indicated that the BBT was significantly more rigid and stable than the FRBT. Waterfall plots were used to compare the frequency response of the two turbochargers over the full range of operating speeds. The majority of motion for the BBT was the whirl of the synchronous excitation due to a negligible inherent imbalance with some larger motions caused by vibrational modes. The whirl of the FRBT consists of not only the synchronous motion but also subsynchronous motions as a result of oil film instabilities throughout the entire operating range of speeds. The TTR was also used to compare frictional losses within the bearings. A study of the run-down times after the pressurized air supply was removed indicated that the BBT has significantly lower frictional losses under all operating conditions tested.
The objectives of this investigation were to design and construct a high speed turbocharger test rig (TTR) to measure dynamics of angular contact ball bearing rotor system, and to develop a coupled dynamic model for the ball bearing rotor system to corroborate the experimental and analytical results. In order to achieve the objectives of the experimental aspect of this study, a test rig was designed and developed to operate at speeds up to 70,000 rpm. The rotating components (i.e., turbine wheels) of the TTR were made to be dynamically similar to the actual turbocharger. Proximity sensors were used to record the turbine wheel displacements while accelerometers were used to monitor the rotor vibrations. The TTR was used to examine the dynamic response of the turbocharger under normal and extreme operating conditions. To achieve the objectives of analytical investigation, a discrete element ball bearing model was coupled through a set of interface points with a component mode synthesis rotor model to simulate the dynamics of the turbocharger test rig. Displacements of the rotor from the analytical model were corroborated with experimental results. The analytical and experimental results are in good agreement. The bearing rotor system model was used to examine the bearing component dynamics. Effects of preloading and imbalance were also found to have significant effects on turbocharger rotor and bearing dynamics.
The objectives of this investigation were to design and construct a high speed turbocharger test rig to measure dynamics response of angular contact ball bearing rotor system, and to evaluate the performance of angular contact ball bearings as a replacement to conventional journal bearings in turbocharger systems. A test rig was designed and developed to operate at speeds up to 70,000 rpm. The rotating components (i.e. turbine wheels) of the turbocharger test rig were made to be dynamically similar to an actual turbocharger. Proximity sensors were used to record the turbine wheel displacements while accelerometers were used to monitor the rotor vibrations. A radio telemetry based wireless temperature sensor was designed and installed on the bearing cage. The in-situ temperature sensor monitored and recorded the bearing condition in real time. The rotor dynamic results obtained from the turbocharger test rig were used to corroborate with an analytical model developed simulate the turbocharger rotor system. The turbocharger test rig was then used to examine the dynamic response of the turbocharger. The rotor displacements and bearing temperatures were recorded and analyzed to study the effects of bearing preloading and rotor imbalance on the turbocharger ball bearing rotor system.
We demonstrate for the first time a low-cost battery-free wireless telemeter integrated on a dynamically balanced ball bearing operating in a test setup that mimics the operating conditions of a two-compressor turbocharger. In this method we continuously monitor the bearing cage temperature and demonstrate the ability to detect rotor imbalance during operation even at low speeds below 5,550 RPM. The telemeter is based on a simple commercially-available temperature-sensitive capacitor coupled with an inductor that is mounted on the bearing cage and is able to operate at temperatures up to 150°C. Cage temperature is sensed wirelessly through a matched interrogator tuned to the natural frequency of the cage sensor at 13.1 MHz. A 5°C temperature differential is detected at 4,700 RPM between a balanced rotor and one with an applied 2.32 × 10-3 kg-m imbalance.
This paper examines the dynamic response of a rotating squealing disc brake subject to distributed nonlinear contact stresses where two brake pads are assumed to be stationary and rigid. The friction stresses produce high-frequency vibrations that exhibit standing or traveling waves on the disc surface. The wave pattern resulting from the binary flutter mechanism of one transverse doublet mode pair is studied here. The results show that the wave pattern is associated with mode-coupling character. For a steady-squealing mode, the stick zone of the contact area is determined by a smooth friction–velocity curve having both negative and positive slopes.
The current study investigates the disc brake squeal by using an annular disc in contact with two pads subject to distributed friction stresses. The disc and pads are modeled as rotating annular and stationary annular sector plates, respectively. Friction stress is described on the deformed disc surface as distributed non-conservative friction-couples and frictional follower forces. From disc doublet-mode and multiple-mode models, the mode-coupling mechanism influenced by disc rotation is examined. In automotive applications, the frictional mode-coupling resulting from friction couple is shown to be the major mechanism for dynamic destabilization, whereas the effects of disc rotation on flutter destabilization are found to be small. On the verge of stop, however, the rotation effects effectively stabilize the steady sliding. This comprehensive brake model has shown that there is a speed corresponding to maximum squeal propensity for each flutter mode.
This paper describes the mode-coupling-type squeal mechanism in a disc brake system. The mode shapes of a disc and a brake pad (an annular sector plate) are obtained using the component eigenvalue analysis and the Rayleigh–Ritz method, respectively. The disc–pad coupled system subject to friction-couple is discretized by the truncated set of system component modes. Mode-coupling instability is determined in closed form resulting from a reduced-order friction-coupling model, which subsequently defines the modal stability index. The proposed index parameter determines the necessary condition for flutter instability without solving system complex eigenvalues. The numerical investigation shows that the disc–pad modal interaction has a strong squeal tendency when two pads are not identical.
The mathematical formulation for determining the dynamic instability due to transverse doublet modes in the self-excited vibration of a thin annular plate is presented in this paper. An analytical approach is developed to obtain the stability results from the eigenvalue problem of a stationary disc with a finite contact area. The approach uses the eigenfunctions of transverse doublet modes in classical plate theory and establishes the formulation of modal instability due to the modal-interaction of a doublet mode pair. The one-doublet mode model of a disc and a discrete model equivalent to the one-doublet mode model are proposed for providing a more fundamental understanding of the onset of squeal. The analytical models are validated through a comparison of results from a modal expansion model obtained from finite element component models. Throughout the analytical investigation, the pad arc length is found to be a critical design parameter in controlling squeal propensity.
A brake system test rig was used to simulate braking operation and measure acoustic pressure, disc temperature and brake pressure during squeal events. Experimental results presented are the strong dependence of squeal frequency content on engagement pressure, the broadening of required brake pressure range for squeal existence as temperature increases, and a periodic squeal behaviour. A model was developed to analyse the stability for squeal prediction. This model is a reduced order modal model, based on component finite element modal properties. Additional support for the coupled mode instability is the correlation of experimental squeal frequencies with analysis.
A dynamic model for deep groove and angular contact ball bearings was developed to investigate the influence of race defects on the motions of bearing components (i.e., inner and outer races, cage, and balls). In order to determine the effects of dents on the bearing dynamics, a model was developed to determine the force-deflection relationship between an ellipsoid and a dented semi-infinite domain. The force-deflection relationship for dented surfaces was then incorporated in the bearing dynamic model by replacing the well-known Hertzian force-deflection relationship whenever a ball/dent interaction occurs. In this investigation, all bearing components have six degrees-of-freedom. Newton’s laws are used to determine the motions of all bearing elements, and an explicit fourth-order Runge–Kutta algorithm with a variable or constant step size was used to integrate the equations of motion. A model was used to study the effect of dent size, dent location, and inner race speed on bearing components. The results indicate that surface defects and irregularities like dent have a severe effect on bearing motion and forces. Furthermore, these effects are even more severe for high-speed applications. The results also demonstrate that a single dent can affect the forces and motion throughout the entire bearing and on all bearing components. However, the location of the dent dictates the magnitude of its influence on each bearing component.
Influence of race defects on the motions of bearing components (i.e. inner and outer races, cage, and balls) was investigated using a six degrees of freedom dynamic model for deep groove and angular contact ball bearings. Surface defects such as dents and bumps on bearing surfaces cause the elements (balls and cage) of bearings to vibrate and impact the inner and outer races. To model the effects of surface defects on bearing dynamics, the superposition principle was used to include the effects of a dent or bump on bearing dynamics. A bump having a general geometry was modelled as an equivalent ellipsoid in contact with the original bearing components geometry while a dent was modelled as an equivalent ellipsoidal depression on the bearing surface in contact with bearing component. Therefore, the net forces acting on the contacting body is superposition of forces acting on the bodies without any defect and forces corresponding to defect alone. This approach was also used to investigate and model the effects of debris contaminants on bearing performance. The effects of the debris are calculated similar to bumps with an exception that debris is free to move within the bearing component domain. The results indicate that surface defects and irregularities such as dents and bumps have a significant effect on bearing motion and forces. The results also demonstrate that a single defect can affect the forces and motion throughout the entire bearing and on all bearing components.
This article presents a new approach in which the explicit finite element method (EFEM) and the discrete element method (DEM) are coupled to investigate dynamics of flexible rotor systems supported by deep-groove ball bearings. In this investigation, DEM is used to develop the bearing (dynamic motion) model in which all of the components of the bearing (i.e., inner and outer race, balls, and cage) have 6 degrees of freedom. The flexible shaft is modeled with a full 3D elastic formulation using the EFEM rather than the reduced form, which implements component mode synthesis. The EFEM and DEM were combined to investigate the dynamics of flexible shaft rotor systems supported by ball bearings. Rotor and inner races of the bearings are fully coupled such that both translation and rotation of the flexible rotor are transmitted to the bearings. At each time step, the translational motion and rotation/tilt angle of the rotor cross section at the location of an inner race are applied to the inner race of the bearing. The resulting reaction forces and moments calculated in the dynamic bearing model are in turn applied to the nodes of the shaft. The combined model is used to investigate the motions of the inner races and the resulting reaction forces and moments from the supporting bearings due to an applied load on the shaft. In the current coupled modeling approach, the deformation of the shaft affects the internal components of the bearing by altering the orientation of the inner race, which results in ball spin and slip.
In this investigation, a three-dimensional (3D) finite element model (FEM) was developed to study fretting wear of Hertzian circular and line contacts. The wear law incorporated in this model is based on the accumulated dissipated energy (ADE). A stress-based damage mechanics finite element model using the ADE was developed to determine wear of non-conformal bodies in contact. Voronoi tessellation was used to simulate the microstructure of the materials during the fretting process. In order to simulate the wear area in fretting contacts, a material removal approach was developed and implemented in the model. The FEM was used to investigate partial slip regimes under various operating conditions. The normal and shear surface tractions for the circular and line contacts were applied to the domain in order to improve the computational efficiency. The calculated wear volume rate using the FE model is in good agreement with the wear coefficient available in the open literature. The influence of modulus of elasticity, hardness, and coefficient of friction on the partial slip fretting phenomenon were studied. In order to verify the model, several fretting wear tests were conducted using AISI 8620 steel and AISI 1566 steel in a partial slip regime of circular contact configuration. The properties for each material such as the modulus of elasticity, hardness, and the grain size were measured experimentally and compared with the model. For the defined load and displacement amplitude of the experimental fretting tests, both materials have shown a partial slip behavior in the initial cycles and then transition to a gross slip regime. The numerical model predicted the worn surface and wear-rate in partial slip regime which corroborated well with these experimental test results.
In this investigation, a finite element (FE) model was developed to study the third body effects on the fretting wear of Hertzian contacts in the partial slip regime. An FE three-dimensional Hertzian point contact model operating in the presence of spherical third bodies was developed. Both first bodies and third bodies were modeled as elastic–plastic materials. The effect of the third body particles on contact stresses and stick-slip behavior was investigated. The influence of the number of third body particles and material properties including modulus of elasticity, hardening modulus, and yield strength were analyzed. Fretting loops in the presence and absence of wear particles were compared, and the relation between the number of cycles and the hardening process was evaluated. The results indicated that by increasing the number of particles in contact, more load was carried by the wear particles which affect the wear-rate of the material. In addition, due to the high plastic deformation of the debris, the wear particles deformed and took a platelet shape. Local stick-slip behavior over the third body particles was also observed. The results of having wear debris with different material properties than the first bodies indicated that harder wear particles have a higher contact pressure and lower slip at the location of particles which affects the wear-rate.
In this investigation, the third body effects in fretting contact is modeled using the commercially available ABAQUS finite element (FE) software. A two dimensional Hertzian line contact model is simulated in the presence of third bodies at the contact interface. The third bodies are modeled using simplified geometry like cylinders. Elastic–plastic material properties are used to model both the first bodies and third bodies. The FE model is used to investigate fretting phenomena under different displacement amplitudesand the influence of third body particles on contact stress and contact slip. In addition, the effects of different factors such as material properties of the third bodies and number of third body particles on fretting are investigated. Fretting loops obtained from the model show notable differences in shear stress distribution when compared to smooth Hertzian line contacts in the absence of third body particles. The results indicate that the third bodies deformed to platelet like structures as observed in experiments. The obtained results also indicate that contact stress decreases with the increase in the number of third bodies. As the number of third bodies in contact is increased, the contact shear force between the first bodies decreases while the contact slip increases. Due to this phenomenon, the dissipated energy is not affected and therefore does not influence fretting wear rate significantly. Although fretting wear rate is not directly influenced by the presence of third bodies, plastic deformation of the first body surfaces influences contact parameters which in turn impacts fretting wear.
In this investigation, a new model for dry fretting wear of similar materials in Hertzian contact is proposed. The wear law which is dependent on material properties, applied load and sliding distance is proposed for similar materials under dry fretting wear conditions. Based on this law, a stress based damage mechanics equation for wear is formulated and a finite element model is developed to determine wear rates and wear coefficients. The modeling approach proposed is based on wear at the level of material microstructure and thus Voronoi tessellation is used to configure the microstructure of the bodies in contact. To simulate fretting wear, fatigue crack initiation and propagation along the grain boundaries, and grain removal technique is developed. Two distinct regions – wear initiation and wear propagation are observed from the results of the simulation. The results of the simulation are compared with the Archard wear law and the calculated wear coefficients are of the same order as suggested in the literature. Wear volume measurements for partial slip regime in fretting wear are obtained using the model and the effects of coefficient of friction, hardness and Young's modulus on fretting wear is studied. It is found that the wear rate is significantly influenced by hardness and Young's modulus while the applied coefficient of friction has little to no effect on the wear rate. A regression analysis of the results and a wear map technique to predict wear rates based on material parameters is also presented.
This paper studies the stick–slip oscillations of discrete systems interacting with translating energy source through a non-linear smooth friction curve. The stick–slip limit cycle oscillations of a single degree-offreedom model are examined by means of numerical time-integration and analytical methods. Similar approaches are also applied to the model of the coupled friction oscillator. Particularly, it is found that the steady-state response of the coupled oscillator can be divided into two different forms of oscillation (mode-merged and mode-separated oscillations) according to the frequency separation of two modes. The oscillation pattern of the steady-state response is shown to depend on system parameters such as detuning factor, energy source speed, and normal contact load.
A multi-degree-of-freedom (m.d.o.f.) system excited by a rough moving surface has been developed to study friction-induced oscillations. The normal degrees of freedom allow for oscillatory normal forces, while the normal–tangential coupling of friction produces parametric excitation in the slipping equations of motion. After a modal change of variables, first order averaging has been used to produce a set of autonomous equations of motion. Eigenvalue analysis of the averaged equations has produced stability predictions for the steady sliding position. Numerical integration of the original system of equations has verified the existence of locally unstable oscillations for a system excited by a rough surface input. The combination of velocity-dependent friction and a harmonically varying normal force have been shown to produce large-amplitude oscillations, in some cases leading to stick–slip responses.
A solution for the dry rolling/sliding contact of rough bodies under an applied normal load has been obtained. Both the deflection of the asperities and the bulk material are considered. The conservation of volume approach was used to model elastic-plastic deformation of the asperities. The bulk material was allowed to deform elastically. The stick-slip phenomenon of the rolling contact has also been investigated, including asperity deformation and wear as a function of time. The contact width between the two rough cylinders is shown to be approximately 20 percent larger than the width predicted for smooth surfaces by the Hertz equations for the same loading conditions. Similarly, the maximum surface pressure on the bulk material decreases approximately 25 percent when rough surfaces are considered.
In this investigation, a disc brake test rig was designed and developed to evaluate the friction and wear characteristics of pitch and poly-acrylonitrile based carbon-carbon composites subjected to different aircraft taxi energy fluxes and temperatures in air and nitrogen environment. The test rig was operated in drag configuration at a constant speed, and it was found that temperature of the disc, humidity of the surrounding environment, the supplied energy flux as well as the type of the composite play a critical role in determining whether coefficient of friction lies in the normal wear regime (<=0.2) or dusting wear regime (>=0.3). Results from these tests were compared with existing results in literature and a good agreement was found. Additionally, to quantify wear at different specimen temperatures and taxi energy fluxes, controlled tests were performed using an external thermal chamber, reaching temperatures up to 550 °C. It was found out that temperature and energy flux had a significant influence on friction and wear behavior depending on the type of composite and operating environment. Furthermore, optical and scanning electron microscopy were conducted to analyze the wear mechanisms. Matrix and interface cracking along with fiber breakage were observed from tests in air environment, whereas in nitrogen environment, particulate and layered debris played a prominent role.
The objectives of this study were to investigate the effects of temperature (750°C) on the coefficient of friction and wear rate of Inconel 617 in fretting wear in air and helium environments. An in-situ fretting wear measurement technique was developed to continuously monitor the change in wear depth during the fretting wear test. It was found that as the fretting wear progressed at room temperature and in air, the wear rate demonstrated a bilinear behavior including a severe running-in regime at the beginning followed by a mild steady state wear rate. The coefficient of friction decreased as the temperature was increased for both air and helium environments. In air environment, the wear rate decreased with increase in temperature. At 750 °C, helium environment showed more wear than in air environment. Scanning electron microscopy and energy dispersive X-ray spectroscopy were conducted to determine the morphology of the scar and relative proportion of oxygen on the specimens from both the helium and air environments. Oxides particles sintered to the contact surfaces were observed especially at 750 °C in air, which contributed to the lower friction and wear.
Ultrasmooth submicrometer carbon spheres are demonstrated as an efficient additive for improving the tribological performance of lubricating oils. Carbon spheres with ultrasmooth surfaces are fabricated by ultrasound assisted polymerization of resorcinol and formaldehyde followed by controlled heat treatment. The tribological behavior of the new lubricant mixture is investigated in the boundary and mixed lubrication regimes using a pin-on-disk apparatus and cylinder-on-disk tribometer, respectively. The new lubricant composition containing 3 wt % carbon spheres suspended in a reference SAE 5W30 engine oil exhibited a substantial reduction in friction and wear (10–25%) compared to the neat oil, without change in the viscosity. Microscopic and spectroscopic investigation of the carbon spheres after the tribological experiments illustrated their excellent mechanical and chemical stability. The significantly better tribological performance of the hybrid lubricant is attributed to the perfectly spherical shape and ultrasmooth surface of carbon sphere additive filling the gap between surfaces and acting as a nanoscale ball bearing.
Engineering surfaces with similar average or RMS roughness exhibit different values of skewness and kurtosis due to different machining processes. As the surfaces evolve during operation and the wear process, the roughness parameters undergo significant changes. To investigate the change in the roughness parameters and their effect on wear rate, it is of significant importance to investigate and simulate deep wear scars. In this study, a novel method to simulate wear on rough surfaces is proposed. The surface is treated as a collection of asperities of different radii at different heights. The method is applied to a linear elastic material model and the contact parameters are calculated using the Hertzian contact theory. Material removal is simulated by a simple truncation model and Archard's wear law is used at asperity level to evaluate wear depth. Surfaces with various values of RMS roughness, skewness and kurtosis are investigated and two distinct wear rates are obtained for each surface, running-in (severe) wear and steady state (mild) wear. It is also predicted that surfaces with high roughness, kurtosis and positive skewness exhibit higher wear rates. This investigation highlights the importance of studying the effects of surface parameters on wear rate and demonstrates that although a linear wear law is assumed at each asperity, a non-linear wear rate of rough surfaces can be obtained computationally, which are similar to trends observed in experiments.
In this investigation, the fretting wear phenomenon was investigated experimentally and analytically. For the analytical investigation, a combined finite discrete element model (FDEM) was developed to study the effects of displacement amplitude and normal force on fretting wear. The FDEM was used to investigate the wear of a fretting Hertzian line contact calculated using the Archard and dissipated energy wear theories. Although the FDEM results from each theory were in agreement, the dissipated energy approach more accurately predicted the wear volumes obtained from experimental measurements. A fretting wear test rig (FWTR) was used to verify and corroborate the results and conclusions of the numerical investigation. The results indicated that the dissipated energy equation better describes wear in fretting contacts than the Archard equation. An energy dissipation rate map was developed from the experimental results, showing the effect of normal force and displacement amplitude on frictional energy loss. The energy dissipation rate map was used to create a steady-state fretting wear map.
This paper presents a two-dimensional (2D) plane strain finite element model to simulate fretting wear in composite cermet coating. The coating considered in this investigation is High Velocity Oxy-Fuel (HVOF) sprayed Cr3C2–NiCr with 55% volume fraction of Cr3C2. The material microstructure is modelled using Voronoi tessellations with a log-normal variation of grain size. Moreover, the individual phases of the material in the coating were assigned randomly to resemble the microstructure from an actual SEM micrograph. The ceramic carbide phase is orthorhombic and the cubic matrix possesses a high anisotropy index. As a result, each grain was modelled with random orientation to account for material anisotropy. The RVE dimensions were chosen such that its elastic response represented the overall response of a poly-aggregate. In order to simulate debonding of the ceramic carbide phase from the matrix, cohesive elements were used at the grain boundaries. Damage mechanics was used to model degradation of cohesive elements resulting from repeated fretting cycles. A grain deletion algorithm was developed to simulate removal of material from fretting wear. The crack patterns predicted from the model match closely with the patterns observed in experimental studies on wear of HVOF Cr3C2–NiCr coating. The model also predicts carbide pullout, a major damage mechanism in HVOF Cr3C2–NiCr coating subjected to wear. Experiments were also conducted to evaluate and corroborate the wear rate of HVOF Cr3C2–NiCr coating. The wear rate from the model matches closely with experiments at a constant load and displacement amplitude. The results from the model were then extended to obtain a fretting wear map under a combination of various loads and displacement amplitudes.
The objectives of this investigation were to characterize the friction and fretting wear behavior of coated inlet ring and spring clip components used in land-based gas turbines at elevated (500 °C) temperature. In order to achieve the objective, a novel high temperature fretting wear apparatus (HTFWA) was designed and developed to simulate the conditions existing in a gas turbine. Sections of actual inlet ring and spring clip were cut from a gas turbine and used in the test apparatus. The test apparatus was used to investigate fretting wear of APS sprayed Cr3C2–NiCr (25% wt.), HVOF sprayed Cr3C2–NiCr (25% wt.), HVOF sprayed T-800 and APS sprayed PS400 coated inlet rings against HVOF sprayed Cr3C2–NiCr (25% wt.) coated spring clip. Fretting wear experiments were conducted with normal loads up to 400 N at a fixed displacement amplitude of 0.5 mm and frequency of 5 Hz. A proximity probe was used for in-situ wear depth measurement at the spring clip and inlet ring contact pair. The results indicate that the combination of PS400 coating on inlet ring and HVOF Cr3C2–NiCr on spring clip wear the least as compared to other combinations in both running-in condition and under steady state regime. PS400 also demonstrated a 50% reduction in coefficient of friction as compared to other coatings at 500 °C. Further, a theoretical approach was developed to estimate the evolution of wear depth with sliding distance for a cylindrical contact configuration using Archard's wear law. The experimental and theoretical results were found to be in good agreement with each other.
A new thermally cured polymer-graphene-zinc oxide-based solid lubricant is developed that reduces friction and wear significantly during the sliding wear of bearing steel under extreme contact pressure and long duration. The dry solid coating composite was made from a mixture of graphene, zinc oxide, and a specific industrial binder and then laminated on the surface of 52100 steel disks using the spin-coating technique. A ball-on-disk apparatus set to 1 GPa Hertzian pressure and a sliding distance of 500 m was used to examine the tribological properties of the coating. After ∼3000 cycles, the 15 μm thick coating created a significant reduction in the steel's coefficient of friction (approximately 82%) and wear loss compared to the uncoated surfaces. Following the triboligical examination, scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction, and Raman spectroscopy were conducted to determine the topography and morphology of the composite coating and resultant wear scars. It is revealed that the persistent protective coating on the disk surfaces was attributed to the adhesion influence of interfacial zinc oxide and graphene on the contact surfaces. Scratch testing of the new composite demonstrated a significant improvement in its adhesive properties on bulk interfacial surfaces compared to previously studied coatings.
In this investigation the combined finite discrete element method was used to analyze fretting wear of rough and smooth Hertzian contacts using the Archard wear equation and continuum damage mechanics. Surface roughness profiles were generated using the Voronoi tessellation procedure and scaled in order to analyze the effect of roughness on fretting wear. Using the Archard equation, wear loss increased with roughness in the partial slip regime. In contrast, in the gross slip regime roughness only played a role at the beginning of a test before all of the asperities had been removed. Using the damage mechanics, subsurface damage accumulation was found to be a linear function of cycles. In this approach, a long breaking-in period occurred before the first wear particles were detached from the surface; however, following initiation, wear loss was approximately a linear function of cycle number. The shape and evolution of fretting wear scars were in agreement with experimental results.
A new approach for modeling fretting wear in a Hertzian line contact is presented. The combined finite-discrete element method (FDEM) in which multiple finite element bodies interact as distinct bodies is used to model a two-dimensional fretting contact with and without coatings. The normal force and sliding distance are used during each fretting cycle, and fretting wear is modeled by locally applying Archard’s wear equation to determine wear loss along the surface. The FDEM is validated by comparing the pressure and frictional shear stress results to the continuum mechanics solution for a Hertzian fretting contact. The dependence of the wear algorithm stability on the cycle increment of a fretting simulation is also investigated. The effects of friction coefficient, normal force, displacement amplitude, coating thickness, and coating modulus of elasticity on fretting wear are presented.
This paper presents a numerical model that maps the evolution of fretting fatigue life of Hertzian rough contacting bodies in fretting wear. Effect of surface roughness parameters (i.e. root mean square, skewness and orientation) on fretting fatigue life is reported. Fretting fatigue life is calculated as the crack initiation period predicted by the Smith Watson Topper multiaxial fatigue theory. Fretting wear is also accommodated in the analysis and is calculated by local application of Archard's wear law. The results from this investigation indicate that wear initially improves resistance to fatigue cracking, and reduces fatigue life as it becomes dominant. The approach developed in this study allows for implementation of real rough surfacesand study the effects of various statistical surface properties on fretting fatigue life. The presence of surface roughness in the analytical model reduces predicted fatigue life significantly. Other statistical surface parameters such as skewness and orientation also have a major impact on fretting fatigue life calculations.
Sub-surface cracks can be initiated due to surface fatigue, which eventually reach the surface, leading to pitting, spalling and removal of material. In this investigation, a new approach based on shear stress reversal at the crack tips is implemented to propagate a subsurface initiated crack under fretting load. Hertzian line contact geometry is used to investigate the effects of different factors such as Hertzian pressure, coefficient of friction, displacement amplitude, and depth of the initial crack. Crack propagation paths and propagation life of the cracks under the surface are investigated in detail. Once the crack reaches the surface, it is assumed that the material enclosed is spalled and thus removed. Wear volumes and wear rates are calculated and effect of each variable on wear is analyzed. Wear rates increase with increase in maximum Hertzian pressure, displacement amplitude, coefficient of friction and depth of initial crack. The wear rates are also correlated to crack propagation rates and are in agreement with the dissipated energy wear coefficients obtained from literature.
Fretting is associated with the small amplitude relative oscillatory motion between two solid surfaces in contact. Fretting fatigue is a damage mechanism observed in a machine components subjected to fretting in tandem with fluctuating bulk stresses. This paper presents the results of an experimental investigation of the fretting fatigue behavior of AISI 4140 vs. Ti-6–4 in a cylinder-on-flat contact configuration, and a computational fatigue damage model of the same configuration. In the experimental investigation, a fretting test fixture was designed and developed which was coupled with an MTS machine to impose the fretting fatigue damage. Fretting fatigue experiments were conducted under completely (R=−1) reversed axial stress amplitudes, a constant maximum Hertzian Pressure (Ph) of 3 GPa and at a frequency of 5 Hz. The test rig was also used in a fretting wear configuration under gross slip conditions to determine coefficient of friction for the same contacting pair of materials. In the computational modeling, damage mechanics constitutive relations were incorporated in a finite element model to analytically investigate the fretting fatigue. Voronoi tessellation was used to account for the randomness of the material microstructure and its effects on the fatigue behavior. Material properties needed for the damage model were determined using the analytical solution for maximum fretting stress (σfretting) at the trailing edge of the contact which is assumed to drive the fretting fatigue failure. The critical damage value for AISI 4140 was extracted using the method of variation of elasticity modulus. Fretting fatigue lives predicted from the analytical model show good agreement with the measured experimental results.
A new approach was developed to estimate the crack initiation life of a fretting contact while accounting for the variability in the fatigue response. This was accomplished using a modified application of the Smith-Watson-Topper (SWT) fatigue criterion. A combined finite–discrete element model of a cylinder-on-flat configuration incorporating material randomness and disorder via a Voronoi tessellation was developed. The SWT equation was used with this model to predict the crack initiation lives for multiple material domains. The predicted crack initiation lives displayed a large degree of scatter and were less conservative than previous deterministic implementations of the SWT parameter. The scatter in the predicted initiation lives was quantified using Weibull statistics.
A new approach was developed for modeling the effect of the third body on fretting. This was accomplished using the combined finite-discrete element method (FDEM) in which the third body is analyzed as discrete elements while the first bodies are modeled using finite elements. This approach provides a link between large scale models which treat the mass of wear debris as a single or small number of bodies and small scale models which only study a control volume. The FDEM was used to analyze the behavior of third body particles between flat sliding surfaces. When the third body mass is composed of unconnected particles, it behaves as a Newtonian fluid, but this behavior ceases when the particles are connected into platelets. The FDEM was also used to study the behavior of third body particles inside a Hertzian line contact. As the number of particles and platelet size increase the load carried by the worn slip zone grows larger in relationship to the unworn stick zone.
A novel modular experimental apparatus was designed and developed to measure and visualize fretting wear and friction for Hertzian circular and elliptical contacts and flat on flat contacts. The experimental apparatus utilizes a magnetostrictive actuator to reciprocate a flat, ball, or cylinder between two fixed specimens. Two stationary flat or cylindrical specimens mounted on a rotary table clamp the reciprocating specimen from the top and bottom to generate the fretting contact. The two stationary test specimens installed on the rotary table perpendicular to the moving specimen form a crossed cylinder geometry which creates a well-defined circular contact. An elliptical contact with different aspect ratios can be obtained by varying the angle between the fixed and the moving specimens. Dead weights placed on top of the upper stationary specimen provide the normal load. A force sensor located in line between the actuator output shaft and the specimen is used to measure friction. The test rig’s modular design allows it to be configured for Hertzian circular (ball-on-flat, crossed cylinder), elliptical (crossed cylinder), and conformal (flat-on-flat) contacts. In the ball on flat configuration a steel flat or sapphire window is used in contact with the reciprocating ball. When the sapphire window is used a microscope and high speed camera is employed for in situ visualization and recording of the contact.
The fretting phenomenon was investigated experimentally in contacts between coated and uncoated steel rod and ball specimens generating a circular Hertzian contact. A fretting wear test rig equipped with a video camera was used to observe the effects of fretting on coated steel surfaces in both grease-lubricated and unlubricated environments. Tungsten carbide reinforced amorphous hydrocarbon (WC/a-C:H) and chromium nitride (Cr2N) coatings were tested and compared. Fretting wear volumes and surface profiles are presented for both grease-lubricated and unlubricated conditions. Videos of a coated ball fretting against a transparent sapphire flat were recorded and screen captures are presented. The role of normal load, lubrication, frequency, and amplitude of motion on the fretting wear of coatings is discussed. The lubricant released from the grease was observed to flow through channels in the stick zone of the fretting contacts. Both coatings were found to reduce fretting wear. WC/a-C:H was more effective at reducing wear under unlubricated conditions. WC/a-C:H decreased fretting wear more than Cr2N when delamination was avoided in grease-lubricated contacts.
The current study presents the results and effects of fretting wear on rolling contact fatigue (RCF) life of M50 bearing steel. A fretting wear test rig was designed and developed to induce fretting scars on the surface of standard M50 rods commonly used in a three ball and rod RCF testing machine. The fretting machine was used to induce fretting scars at a Hertzian contact pressure of 1.1 GPa, in the presence of MIL-L-23699 lubricant at a frequency of 10 Hz, slip amplitude of 21 µm for different number of cycles. The fretted rods were then evaluated at a contact pressure of 1.7 and 3.4 GPa in the three ball and rod RCF tester to determine the effect of fretted scar on fatigue life. The results indicate that a fretting scar can reduce the fatigue life at 3.4 GPa by an average of 30 per cent and fretted rods operating at 1.7 GPa behave very similar to an unfretted rod operating at 3.4 GPa.
Fretting phenomena operating in the presence of grease was investigated experimentally and analytically. A fretting test rig was designed, developed, and equipped with a microscope and high-speed video camera to observe the effects of the lubricant entrainment within the contact during the fretting phenomena. A mixed elastohydrodynamic lubrication model was used to analytically investigate lubricated fretting and corroborate with experimental results. An analytical approach is also presented to determine the amount of lubrication entrained within the fretting contact. The results of fretting wear operating in the presence of grease are presented for case-hardened steel in the crossed cylinder configuration and hardened steel ball-on-sapphire flat configuration. The roles of lubrication, oscillation amplitude, and cavitation in fretting are presented and discussed. Lubrication was found to mitigate the effect of fretting on a surface while the effect of oscillation amplitude on fretting was more complex. The results indicate that frequency increases the amount of material transfer between fretting surfaces. Gaseous cavitation was observed to occur in the trailing edge of the fretting contact and increased with speed. A closed form equation was derived to approximate the volume of the lubricant entering the fretting contact area during the fretting motion and explain the effect of test conditions on fretting wear.
An experimental apparatus and a numerical model have been designed and developed to examine the lubrication condition and frictional losses at the piston and cylinder interface. The experimental apparatus utilizes components from a single cylinder, ten horsepower engine in a novel suspended liner arrangement. The test rig has been specifically designed to reduce the number of operating variables while utilizing actual components and geometry. A mixed lubrication model for the complete ring-pack and piston skirt was developed to correlate with experimental measurements and provide further insight into the sources of frictional losses. The results demonstrate the effects of speed and viscosity on the overall friction losses at the piston and cylinder liner interface. Comparisons between the experimental and analytical results show good agreement.
The effect of viscoelastic layer on pressure, film thickness and friction coefficient in lubricated contacts has been investigated. The model consists of two elastic rollers coated with viscoelastic layers and separated by a thin film of lubricant. The results indicate that under low velocity conditions the friction coefficient monotomically reduces to a minimum and then increases as the speed increases. The results also indicate that for low velocities the contact characteristics are dominated by the properties of the viscoelastic layer and the elastic substrate and as the speed increases, the viscoelastic layer effect becomes negligible.
A model has been developed to investigate the effects of a rough elastic indenter in sliding contact with a viscoelastic layer bonded to an elastic semi-infinite plane. The viscoelastic layer is modeled as a one-dimensional Maxwell solid (small strain) while the substrate of the semi-infinite plane is modeled as a two-dimensional elastic half plane. The Fredholm integral equation of the second kind was obtained to determine the contact stresses. The results indicate that the viscoelastic properties of the layer and the velocity of the indenter significantly affect the contact pressure and internal stress distributions. The viscoelastic layer causes the pressure and internal stresses to become nonsymmetrical. High asperity densities reduce the amplitude of maximum shear stress at a fixed depth below the surface. Results are also presented for various coefficients of friction.
Analytic methods are developed for solving the contact problem of the rolling of an elastic cylinder along a visco-elastic layer bonded to an elastic base with the aim of studying the effect of the mechanical and geometric characteristics of their surface layers on the contact interaction parameters and the coefficient of rolling friction. A Maxwell model is used to describe the mechanical properties of the visco-elastic layer. The problem is treated assuming that there is partial siding in the contact area which makes it possible to treat the resistance to rolling as the overall result of the manifestation of the imperfect elasticity of the surface layers of the interacting bodies and sliding friction in the contact area. The solution of the problem of the total sliding of a cylinder on an elastic base covered with a thin visco-elastic layer is obtained as a special case.
The rolling or sliding contact of an elastic cylinder and a layered foundation has been investigated. The substrate of the foundation was modeled as a two-dimensional elastic half-space. The one-dimensional Maxwell model was used to describe the normal and tangential compliance of the viscoelastic surface layer bonded to the substrate. Conditions of partial and full slip within the contact area were considered. The Fredholm integral equation of the second kind was obtained to define the pressure distribution within the contact area. It has been established that the contact characteristics (i.e. pressure distribution, size and displacement of the contact zone and the indentation of the cylinder into the viscoelastic layer) depend on three non-dimensional parameters. Using these parameters the dependence of the contact characteristics upon the load, velocity, geometrical and mechanical properties of the contacting bodies was investigated. A model has also been developed to describe the traction at the contact interface of the elastic cylinder and the layered foundation. The model was used to analyze and determine the distribution and size of the slip and no-slip zones for different values of viscoelastic layer properties and sliding friction coefficients. As a result of the stress analysis, the rolling friction coefficient has been determined and investigated as a function of the non-dimensional parameters under consideration.
The objective of this study is to develop models to investigate the effects of contaminants(debris denting process) in heavily loaded rolling and sliding contacts. A dynamic timedependent finite element model (FEM) was developed to determine the elastic-plasticdeformation and contact force generated between the mating surfaces and a sphericaldebris as debris passes through the contact region. The FEA model was used to obtain theeffects of various parameters such as debris sizes, material properties, friction coefficients, applied loads, and surface speeds on the elastic-plastic deformation and contactforce of the system. The FEM was used to predict debris and mating surfaces deformations as a function of debris size, material properties, friction coefficient, applied load,and surface speed. Using the FEM, a parametric study demonstrated that material properties (i.e., modulus of elasticity, yield strength, ultimate strength and Poisson’s ratio) andfriction coefficients play significant roles on the height and width of dents on the matingsurfaces. For lower friction coefficients ~md,0.3! the debris and mating surfaces slipmore easily relative to one another and therefore the debris has lower aspect ratio. Asfriction coefficient is increased the debris and mating surfaces stick to one another andtherefore the debris deforms less and has higher aspect ratio. The results indicate that thepressure generated between the debris and mating surfaces is high enough to plasticallydeform the debris and mating surfaces and cause a permanent dent on the surfaces andcause residual stresses around the dent. Based on the FEM results, a dry contact model(DCM) was developed to allow similar analyses as the FEM, however, in significantlyshorter computational time.
This paper presents a novel approach to model the effects of surface roughness on fatigue of tensile specimens. Voronoi tessellation was employed to simulate material microstructure and generate rough surfaces. Continuum damage mechanics was utilized to model progressive material degradation due to fatigue loading. In order to evaluate and corroborate the results from the finite element fatigue damage model, an experimental investigation was conducted on 4130 steel specimens under fully reversed loading. SEM Imaging was performed to obtain grain morphology parameters to model microstructure accurately using Voronoi grains. Ra measured from optical surface profilometry was utilized to model roughness. Three levels of roughness were chosen for this study. Damage parameters for fatigue modeling were obtained from the experimental SN results of the smooth specimens having Ra = 0.1 μm. The same parameters were used to model fatigue of numerically generated rough domains and predict a reduction in fatigue lives with increase in Ra. The randomness originating from microstructure and surface profile predicts a scatter in fatigue lives. The fatigue failure mechanism predicted by the model is in close agreement with experimental observations. The reduction in endurance limit with increasing roughness level as predicted by the model provides better accuracy than the widely used empirical relationship for surface finish factor ka.
Non-metallic inclusions such as sulfides and oxides are byproducts of steel manufacturing process. When a component is subjected to repetitive loading, fatigue cracks can emanate from these inclusions due to stress concentrations that happen because of mismatch in elastic–plastic properties of inclusions and matrix. In certain applications such as gears and bearings, crack initiation from inclusions is accompanied with microstructural alteration. This paper employs a numerical as well an experimental approach to investigate these microstructural changes which are so-called “butterfly wings”. A 3D finite element model was developed to obtain the stress distribution in a domain subjected to Hertzian loading with an embedded non-metallic inclusion. A formerly introduced 2D model based on continuum damage mechanics (CDM) was developed to simulate the butterfly wing formation in 3D. Wingspan-to-inclusion ratios were observed at different cross sections following an analytical serial sectioning procedure. A closed form solution was suggested for the wingspan-to-observed-inclusion-diameter ratio and the results were corroborated with the data available in the open literature. On the experimental front, nonmetallic inclusions inside a sample made of bearing steel was detected using ultrasonic inspection method. Rolling contact fatigue (RCF) tests were run on the specimen and post-failure serial sectioning was conducted to understand the 3D shape of butterflies formed around an inclusion detected by ultrasound. Comparison of experimental and numerical serial sectioning of the wings showed a close correlation in the butterfly wings geometry.
This paper presents the results of torsion fatigue of widely used bearing steels (through hardening with bainite, martensite heat treatments, and case hardened). An MTS torsion fatigue test rig (TFTR) was modified with custom mechanical grips and used to evaluate torsional fatigue life and failure mechanism of bearing steel specimen. Tests were conducted on the TFTR to determine the ultimate strength in shear (Sus) and stress cycle (S-N) results. Evaluation of the fatigue specimens in the high cycle regime indicates shear driven crack initiation followed by normal stress driven propagation, resulting in a helical crack pattern. A 3D finite element model was then developed to investigate fatigue damage in torsion specimen and replicate the observed fatigue failure mechanism for crack initiation and propagation. In the numerical model, continuum damage mechanics (CDM) were employed in a randomly generated 3D Voronoi tessellated mesh of the specimen to provide unstructured, nonplanar, interelement, and inter/transgranular paths for fatigue damage accumulation and crack evolution as observed in micrographs of specimen. Additionally, a new damage evolution procedure was implemented to capture the change in fatigue failure mechanism from shear to normal stress assisted crack growth. The progression of fatigue failure and the stress-life results obtained from the fatigue damage model are in good agreement with the experimental results. The fatigue damage model was also used to assess the influence of topological microstructure randomness accompanied by material inhomogeneity and defects on fatigue life dispersion.
This paper presents the results of experimental and numerical investigation on fatigue of thin 304 stainless steel tensile specimens. In order to achieve the experimental aspects of this investigation a Micro Fatigue Test Rig (MFTR) was designed and developed to evaluate fatigue life and failure mechanism of tensile specimen. A 3D finite element model was also developed to investigate the fatigue damage of thin tensile specimen and to account for the effects of topological randomness of material microstructure on fatigue lives. The topology of the material grain structure was modeled using randomly generated 3D Voronoi tessellations corresponding to the measured grain size. Continuum damage mechanics was used to model the progressive material degradation. The damage parameters were obtained from the experimentally obtained S–N curve. A 3D mesh partitioning procedure was developed to consider both crack initiation and propagation stages considering the predominant transgranular, non-planar crack growth observed in the experiments. The stress–life results obtained from the fatigue damage model are in good agreement with the experimental data. The progression of damage and the proportion of life spent in crack initiation obtained from the model are consistent with empirical observations. The fatigue damage model was used to assess the influence of microstructure randomness accompanied by material inhomogeneity and internal voids on fatigue life dispersion.
This paper presents the results of a finite element model developed to investigate the effects of material microstructure topology on fatigue damage evolution in dog-bone tensile specimens. The Voronoi finite element model (VFEM) developed was used to study fatigue damage evolution in AISI 4142 steel under various loading conditions. An environmental scanning electron microscope (ESEM) coupled with an Instron fatigue testing machine was used to determine the strain and fatigue life of the dog-bone 4142 steel specimens at different mean stress levels. The damage variable was obtained using the method of variation of elasticity modulus. The experimental damage versus cycle curve was then used to determine the material properties (i.e. resistance stress σR and exponent m) needed for the VFEM fatigue damage model. The VFEM model was used to corroborate the analytical and experimental fatigue results. A comparison of the results obtained from the VFEM model and ESEM indicate that they are in good agreement.
This paper presents a fatigue damage model to estimate fatigue lives of microelectromechanical systems (MEMS) devices and account for the effects of topological randomness of material microstructure. For this purpose, the damage mechanics modeling approach is incorporated into a new Voronoi finite-element model (VFEM). The VFEM developed for this investigation is able to consider both intergranular crack initiation (debonding) and propagation stages. The model relates the fatigue life to a damage parameter "D" which is a measure of the gradual material degradation under cyclic loading. The fatigue damage model is then used to investigate the effects of microstructure randomness on the fatigue of MEMS. In this paper, three different types of randomness are considered: (1) randomness in the microstructure due to random shapes and sizes of the material grains; (2) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus; and (3) the randomness in the material properties considering a normally distributed resistance stress, which is the experimentally determined material property controlling the ability of a material to resist the damage accumulation. Thirty-one numerical models of MEMS specimens are considered under cyclic axial and bending loading conditions. It is observed that the stress-life results obtained are in good agreement with the experimental study. The effects of material inhomogeneity and internal voids are numerically investigated.
Fatigue initiation and failure of various microelectromechanical systems (MEMS) is of significant importance as they gain widespread acceptance in sensors and electronics. This paper presents an approach for utilizing available experimental fatigue data to evaluate the fatigue lives of MEMS components. The approach is based on a phenomenological discrete material representation in which a domain is represented by a collection of rigid elements that interacts via springs along their boundaries. The principles of continuum damage mechanics are used to degrade the spring stiffnesses as brittle damage occurs when the domain is subjected to fatigue loading. The model utilizes experimental stress-life data for LIGA Ni to identify the material properties used in the model. The proposed model captures the statistical distribution of material properties and geometrical randomness of the microstructure commonly observed in a wide variety of MEMS. Consequently, simulations that account for the variability in fatigue life can be readily performed. The model is applied to a dog-bone-shaped specimen to evaluate the influence of material heterogeneity and material flaws on fatigue crack initiation life and scatter. The ability of the model to predict the fatigue life of different types of MEMS devices and loading conditions is also demonstrated by simulating the fatigue stress-life behavior of a MEMS resonator support beam.
This work provides an alternative solution to the challenge of battery recycling via the upcycling of spent lithium cobalt oxide (LCO) as a new promising solid lubricant additive. An advanced solid lubricant mixture of graphene, Aremco binder, and recycled LCO was formulated into a spray with the use of excess volatile organic solvent. Numerous flat steel disks were spray-coated with the new lubricant formulation and naturally dried followed by curing at 180 °C. When tested on a ball-on-disk up to 230 m in distance, the composite new solid lubricant reduced the coefficient of friction (COF) by 85% between two steel surfaces compared to unlubricated surfaces under a constant 1 GPa Hertzian pressure in an ambient environment. The tribofilm composition, particle size, and type of contact are identified as important parameters in the improvement of the COF. Scanning electron microscopy was used to study its morphology, and energy dispersive X-ray spectroscopy was used to analyze the composition of pristine and tested tribofilms. Upcycled spent low value LCO powder was used as a lubricant additive in tribology for the first time with exceptional lubricious properties.
Submicrometer-sized carbon spheres coated with a MoS2 nanolayer (CS-MoS2) have been synthesized and investigated as a viable oil additive to enhance the tribological properties of conventional oil lubricants in both the boundary and mixed lubrication regimes. Submicrometer-sized carbon spheres (CS) are obtained by the rapid ultrasound-assisted polymerization of resorcinol and formaldehyde, and MoS2 is subsequently coated onto the CS particles via controlled heat treatment. The tribological performance of the proposed lubricant mixture was studied using a tribometer under the ball-on-disk and cylinder-on-disk configurations. The hybrid lubricant is comprised of 1 wt % CS-MoS2 particles dispersed in a standard engine oil (SAE 5W30) and demonstrated a significant reduction in friction and wear (15–35%) relative to the pristine reference oil under various disk speeds. Raman spectroscopic investigation of the wear scars following the tribological tests suggest high chemical stability of the CS-MoS2 particles. The enhanced tribological performance of the CS-MoS2 and oil mixture lubricant is attributed to both the spherical carbon particles and the superior lubrication of the MoS2 nanolayer. The combination of these tribological properties demonstrated by the secondary particle could prevent direct contact between sliding surfaces and act as a particulate ball bearing at the nanoscale.
In this study, the effect of adhesion on evolution of friction during the transition of the contact from pre-sliding into full sliding was investigated. In order to achieve the objectives, a micro optical friction (MOF) apparatus was developed to conduct dry sliding friction experiments and to allow for in situ visualization of the contact area for a sphere-on-flat configuration. MOF apparatus was used to measure friction under various load and speed combinations. The friction results exhibit the commonly observed behavior in friction (i.e., static friction is larger than dynamic friction). The results also demonstrated that the difference between static and dynamic friction forces increased with an increase in the applied normal load. We hypothesize and demonstrate that the difference between the measured maximum friction force commonly referred to as static friction force and the steady state or dynamic friction force divided by the dynamic coefficient of friction is the force of adhesion. The adhesion force results obtained from our experimental investigation corroborate well with the force of adhesion described by the DMT model. The reduction in friction force is attributed to the diminishing of adhesion force during full sliding of the contact.
This work presents a numerical model for normal engagement of two rough surfaces in contact. In this study, the Johnson translator system with a linear filter is used to transform a Gaussian white-noise input to an output surface with prescribed moments and autocorrelation function. The rough surface contact model employs influence coefficients obtained from finite element analysis of the contacting bodies. The contact solution accounts for the effects of macroscopic geometry and boundary conditions, and can be used to simulate engagement at a wide range of loads, including loads at which bulk effects dominate the response. A description of bulk deflection in terms of the displacement of the surface mean plane is also presented. The effects of surface topography on normal engagement stiffness are discussed.
Research in computer-aided design/engineering (CAD/E) has focused on enhancing the capability of computer systems in a design environment, and this work has continued in this trend by illustrating the use of the Dempster-Shafer theory to expand the computer’s role in a CAD/E environment. An expert system was created using Dempster-Shafer methods that effectively modeled the professional judgment of a skilled tribologist in the selection of rolling element bearings. A qualitative and symbolic approach was used, but access to simple quantitative models was provided to the expert system shell. Although there has been significant discussion in the literature regarding modification/improvement of the Dempster-Shafer theory, Shafer’s theories were found adequate in all respects for replicating the expert’s judgment. However, an understanding of the basic theory is required for interpreting the results.
MECHANICAL ENGINEERING TRIBOLOGY LABORATORY
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