| Paul Krause | Oleg Wasynczuk | Steven Pekarek | Timothy O'Connell |
The dc machine is not as popular as it was in the not-too-distant past; however, we will cover the permanent-magnet dc drive, since the brushless dc and induction motor drives are controlled to emulate the orthogonal position of the stator and rotor mmfs. Although we will briefly consider a torque-limiting dc drive, our beginning focus of this animation is to illustrate commutation.
$\;\;\;\;\;$ Perhaps the most challenging part of understanding how a dc machine works is the commutator. A 2-dimensional frontal view of a dc machine with 8 single-turn coils and an 8-segment commutator is shown in the animated Figure 1 below. Each rotor coil spans $180^{\rm o}$ and is drawn as two circles. A $\otimes$ indicates current flows into the page and a $\odot$ indicates current flows out from the page. Note that the connection from the primed to un-primed coil sides on the back side of the rotor is not visible in this frontal view. The coils are labelled $A_i - A_i^\prime$ and $a_i - a_i^\prime$ where $i = 1,2,3,4$. The commutator consists of 8 segments. Each segment is an arc-shaped piece of copper electrically insulated from the other segments. Each segment is electrically connected to two coil sides using copper wires as shown in the figure. The rotor coils and the commutator rotate in unison. A pair of stationary graphite brushes connects the external circuit, depicted as a current source, to the commutator segments. As the rotor rotates, the commutator segments "slide" relative to the stationary brushes.
$\;\;\;\;\;$ The field winding consists of 2 series-connected multi-turn coils. The field current $I_f$ is assumed herein to be constant giving rise to a stationary $N-S$ pole pair as depicted in Figure 1. The corresponding magnetic field is oriented downward through the rotor. The stationary $N - S$ pole pair can also be produced using permanent magnets instead of a field winding.
$\;\;\;\;\;$ In this animation, it is assumed that a dc current source injects a constant positive current into the top brush, which returns through the lower brush to the lower terminal of the current source. For the initial rotor position shown, there are two parallel paths of current flow. One path starting from top brush is $a_1 \rightarrow a_1^\prime \rightarrow a_2 \rightarrow a_2^\prime \rightarrow a_3 \rightarrow a_3^\prime \rightarrow a_4 \rightarrow a_4^\prime$ and out of bottom brush. The other path starting from top brush is $A_4 \rightarrow A_4^\prime \rightarrow A_3 \rightarrow A_3^\prime \rightarrow A_2 \rightarrow A_2^\prime \rightarrow A_1 \rightarrow A_1^\prime$ and out of bottom brush.
$\;\;\;\;\;$ Clicking the "Run" button in the animation will cause the rotor to rotate at a constant rotational speed $\omega_r$ in the counterclockwise direction. Plotted beneath the dc machine is the induced voltage that appears across the two stationary graphite brushes (i.e., the armature voltage) and the net electromagnetic torque (sum of torques produced by each of the 8 coils). At any rotor position in which the brushes do not overlap two segments, the armature voltage is the sum of the voltages induced in the 4 coils associated with each of the two paths of current flow. This voltage will be proportional to the product of $I_f$ and $\omega_r$. The proportionality constant is denoted as $L_{AF}$. The net electromagnetic torque is proportional to the product of $I_f$ and $I_a$. Conservation of power can be used to argue that the proportionality constant is also $L_{AF}$. The animation can be stopped at any point by clicking "Stop" and the rotor position can be manually increased or decreased by clicking the buttons labelled "CW" and "CCW".
$\;\;\;\;\;$There are several important observations that can be made. First, the action of the commutator directs the armature current to flow into the coil sides that are in the upper part of the rotor and out from the coil sides that are in the lower part. Thus, the armature current produces a more-or-less horizontal magnetic field oriented leftward, making the left surface of the rotor a $N$ pole and the right surface a $S$ pole. The interaction of the field and rotor poles is what produces torque proportional to $I_f I_a$, which does not vary significantly with respect to rotor position. Second, the induced voltage is also relatively constant under the assumptions of constant currents and speed.
$\;\;\;\;\;$If the number of coils and commutator segments are increased, the rotor current distribution approaches a continuum and, for constant $\omega_r$, $I_f$, and $I_a$, the torque and voltage approach constants independent of rotor position. This leads to the diagram of an "ideal" dc machine, shown in Figure 2. The corresponding equivalent circuit diagram and dynamic equations are given in the Equivalent Circuit tab of this animation, which can be accessed by clicking either the label to the left or at the top or bottom of this page.
