# Hydraulic-Electric Analogies: DC Motors, Part 5

The analogous nature of hydraulic systems and their electrical counterparts can be compared and contrasted by examining motors and power conversion.

The conventional dc motor consists of stationary pole pieces, a rotor coil comprised of one or more turns of a conductor, a series of commutator segments (two for each coil on the rotor), and a pair of brushes to link current from the outside stationary world to the motor interior’s rotating world. Commutator segments are typically made of copper and the brushes consist of graphite. Both are conductors, plus the graphite provides a solid lubricant between the copper and graphite leading to longer brush life.

Figure 14 offers a very simplified drawing of a dc motor in its most basic form. Here, the rotor coil has only one turn. However,  making this type of motor operate requires many more turns to develop practical amounts of torque. The stator pole pieces are shown as permanent magnets, and, indeed, some small motors are built with a permanent magnet stator. In larger motors, controllable current through coils powers electromagnets. Later on, we’ll show that the stator coil current in the dc motor is perfectly analogous to the displacement adjustment in variable-displacement pumps and motors.

The dc motor of Figure 14 works as follows: The stator magnets provide a source of magnetic flux. When the rotor, through the brushes and commutator segments (collectively, the commutator segments are simply called the commutator), are connected to an external battery as shown, the right-hand side of the current-carrying rotor coil is immersed in the magnetic field. It subsequently experiences a force due the current being carried in a direction away from the viewer.

The right-hand rule leads to a force that is directed upward (recall that the direction of the stator magnetic flux is from the N pole to the S pole) on those conductors. As the current returns to the commutator on the left side of the rotor coil, it experiences the same magnetic flux, but the current direction now comes toward the viewer. The opposite direction of current, but with the same N-to-S field flux direction, causes a downward force on the left side of the rotor coil. The result is a torque that tends to turn the rotor in a counterclockwise direction.

The commutator keeps the current in the rotor coil going in the right direction in the two sides of the coil. Assume the rotor is in the position shown in Figure 14 and spinning in the counterclockwise direction. At that point, the coil experiences the greatest amount of flux from the stator magnets and therefore generates the greatest amount of torque. The breaks between the two commutator segments are situated at the 12 and 6 o’clock positions, as shown, and the current can freely enter and leave the coil through the fully contacting brushes and their respective commutator segments.

However, when the rotor turns 90 degrees counterclockwise from the position shown, three actions occur. First, the rotor coil sides move parallel to the stator flux, which doesn’t generate any voltage. Second, the brushes, which are wider than the gap that separates the commutator segments, create a short circuit across the battery and across the two ends of the rotor coil. Third, this is the point where the actual commutation takes place.

If the rotor turns, say, about 15 or 20 more degrees, the coil side that carried current away from the observer now begins to carry current toward the observer. In other words, the instantaneous current in the rotor coil is forced to change direction. The rotor is actually carrying alternating current even though it is a dc motor! This is perfectly analogous to a hydraulic motor in which the pistons, gears, or vanes, through their reciprocating actions, carry alternating flow while the port plate (hydraulic commutator) converts the incoming direct flow into internal alternating flow. The commutator in the dc motor converts the incoming direct current in internal alternating flow.

The short-circuit condition at the commutation point is clearly a problem. As the motor operates, the brushes and commutator create energy-wasting arcing. The brushes for the motor, as shown in Figure 14, are too wide for the separation gap, and would lead to excessive current. The gaps must be widened and/or the brushes have to be narrowed in order to be practical. The problems with commutation in the dc motor are almost perfectly analogous to the problems of crossover in a piston pump, when the piston diameter is greater than the separation between the kidney ports.

The flux-conductor-current condition, as stated previously, accounts for the rotor’s maximum torque in the position shown in Figure 14. It also results in the largest amount of induced counter voltage in the rotor.

Practitioners of electromechanical art and science call such induced voltage counter emf, reverting to the archaic electromotive force (emf) synonym for voltage. It’s called counter emf because it tends to “push” current back into the battery, counter to the battery, and it’s the same current that started the action in the first place. It doesn’t literally push current back into the battery; that would require the existence of perpetual motion or an overpowering load on the shaft. The motor generates a counter emf that will reduce the current as the rotor accelerates. Counter emf is also sometimes called back emf or speed voltage, because it’s a voltage induced by the relative speed between the magnetic flux field and a conductor.

Placing an external load on the motor output shaft will slow down the motor. As it slows down, the rotor coil moves more slowly through the stator field, reducing the induced voltage. As reduced counter emf fights against the battery voltage, the current rises, which increases the motor’s output torque so that it can try to overcome the load. At the same time, the higher battery current “tells the battery” that there’s an increased load on the motor.

This reveals one important concept of all energy-conversion machines: When the output load increases, the input-power side of the machine receives a “message” to deliver more input power to meet the rising load power requirement. It’s a manifestation of energy conservation. You can’t get more power out than you put in. You can’t have greater than 100% power efficiency. And you can’t achieve perpetual motion. Like hydraulic pumps and motors, electric motors—whether ac or dc—must obey this principle.

Determining DC-Motor Speed

The speed of ac motors is always linked to the frequency of the ac supply voltage. The synchronous motor has features that allow it to start from zero speed, and thus will lock onto the rotating field and run at synchronous speed. And the induction motor approaches the synchronous speed of the rotating field.

So, what determines dc-motor speed? Simply stated, it’s tied directly to the applied voltage and the strength of the stator magnetic field. However, it’s not easily calculated by the user of the motor. In fact, it can be difficult to nail down the stator-field strength, and requires nameplate data.

After external dc power is applied in the motor, the current results in torque, the rotor accelerates, and the speed voltage builds up. This causes the current to drop, thus reducing the torque and the acceleration. At some point—assuming no load is on the motor shaft—the counter emf approaches the applied voltage, the current nears zero, and acceleration stops. The motor reaches a steady-state no-load speed when the counter emf is approximately equal to the supply voltage. Increasing shaft load will reduce speed, as already discussed.

Controlling Motor Speed

It should be obvious that increased supply voltage can accelerate dc motor speed. But an interesting phenomenon occurs if the stator field is made variable. Consider a dc motor that’s equipped with an electromagnetic stator field. In other words, the magnetism doesn’t come from permanent magnets; rather, it comes from a coil wrapped around the iron stator pole pieces. The stator magnetic field is almost always referred to, simply, as the field. With controllable stator-field current, called field current, the strength of the stator magnetic field can also be controlled.

Consider the motor is operating at, say, 1500 rpm, at a particular supply voltage and field current, and then there’s an increase in field current. What happens? Greater field strength will produce a greater counter emf at the prevailing speed and the motor will slow down!

The field current, which makes the motor variable, is perfectly analogous to the displacement of a variable-displacement motor. At a given input flow, an increase in displacement will slow down the hydraulic motor. Decreasing field current speeds up the dc motor at a given shaft load and given supply voltage. Decreasing displacement of a hydraulic motor speeds up the hydraulic motor at a given flow and load torque. Again, the analogy is essentially perfect.