Block H - DC Motor

Objectives

1. Measure efficiency of a DC shunt motor.

2. Measure speed variation with load of a DC shunt motor.

Background

Direct current motors are widely used where high torque for low speed operation or variable speed operation are desired. The number of engineers who design DC motors is small, but most engineers will use DC motors at some point in their careers.

A simple circuit model for a separately excited DC motor is shown in Fig. 1. The field voltage V_f produces the field current I_f in the field winding. The terminal voltage V_t produces the armature current I_a in the armature winding. Both the armature and the field consist of coils of copper wire, possessing both resistance and inductance. In steady state, we are only concerned with DC flows so we can ignore the inductance. That is why we usually draw inductor symbols, but label them as resistors.

The field current I_f produces a flux which cuts the armature winding. The armature current I_a interacts with the flux to produce a torque, which causes the armature to rotate with a mechanical angular velocity _m. The movement of the armature winding through the flux produces a speed induced voltage E_a, which opposes the flow of current according to Lenz's Law. The basic equations of the motor are

T_d = K I_a ..........(2)

E_a = K _m ..........(3)

K has the same numerical value in both (2) and (3) if T_d is in Newton meters, is in Webers, I_a is in Amperes, E_a is in Volts, and _m is in radians per second. At the air gap between stator and rotor, the mechanical power is equal to the electrical power.

T_{d m} = E_a I_a..........(4)

The total power going into the DC motor is

Since this is a DC motor we do not have any phase angles or power factors to think about. The motor losses are

where P_rot refers to the rotational losses. The gap power is

The output power is

The output torque is less than the developed torque by the amount needed to overcome the rotational losses. It can be determined from the output power and the speed.

P_out = T_{out m} ..........(9)

where P_out is in watts, T_out is in Nm, and _m is in rad/sec.

The efficiency is given by

..........(10)

The speed characteristic equation is obtained by combining (1) and (3), and solving for _m.

..........(11)

This equation shows that the speed decreases as the armature current increases due to an increased load requirement. The speed regulation, analogous to the voltage regulation seen in the Block on transformers, is defined as

..........(12)

where NL and FL refer to no load and full load, respectively. Typical values of speed regulation for large DC shunt and separately excited motors are in the range of 5 to 12% , making the DC shunt and separately excited motors basically constant-speed machines.

(11) also shows that when the flux goes to zero, the speed goes to infinity. Actually, the machine has some residual magnetism, so there will be some flux even when V_f = 0. If the torque remains the same, the armature current must increase in the same proportion as the flux decreases, according to (2). So when the field voltage goes to zero, the armature current increases and the speed increases, probably to values well above rated for both quantities. The high current tends to overheat the motor, but this is not the major problem. The motor tends to fly apart under overspeed conditions, throwing large pieces of metal across the room with high velocity. A motor that has lost its field makes a very distinctive sound as it accelerates. If you are in the vicinity of such a motor, you have a few seconds at most to take appropriate action. If you did something to remove the field, try to undo what you just did. Throw the switch back to its original position or plug the wire back in where you just unplugged it. Otherwise you should take cover quickly.

The small DC motor being used in this experiment has enough rotational losses that it tends to self limit at a speed about three times rated speed without destroying itself. At least we have not lost any machines so far. Late in this experiment we will try removing the field voltage so we can hear the distinctive sound of acceleration. Once you have heard it, go ahead and restore the field voltage.

(9) gave the output power in SI units (Watts, Newton-Meters, etc.). Sometimes we have to deal with English units, which make the equation for power

P = 2 nT/33000 ..........(13)

where P is in hp, n is in rpm, and T is in ft-lb. Other convenient conversion factors follow.

Discussion and Calculations

1. Read Appendix D in the rear of this manual on the electrical machines used in this lab.

2. For the circuit in Fig. 1., both the field (excitation) and armature voltage are 120 V DC. The armature resistance is 10 and the field resistance is 750 . Rated armature current I_A is 1.7 A, rated speed is 3450 rpm, and rated shaft power out is 1/6 HP. Assume the motor is operating at rated conditions.
   a) What is K?

   b) What is the rated value of developed torque in Nm? In in-lb?

   c) What is the rated output mechanical power in Watts?

   d) What are the rotational losses in Watts?

   e) What is the overall efficiency of the motor? (at rated conditions)

Instructional Activity in Class

1. Locate the DC machine marked "B" and the dynamometer (a grey and yellow machine). Mount them on the baseplate as shown in Fig. 2. This allows you to read the dynamometer from the pulley end and also get at the banana sockets of the DC motor. Try the 19 inch timing belt (190XL037). Measure the resistance of the field winding.

2. Connect up the machines as shown in Fig. 3. Use the portable variable autotransformer from underneath the bench and the full wave single phase diode bridge supplied by the instructor. Switch the 120/140 switch on the variable autotransformer to 140.

3. Close the DC breaker and measure the voltage being supplied to the field winding. Compute the power being supplied to the field winding. Turn on the variable autotransformer and the AC breaker. Turn up the variable autotransformer and observe direction of rotation of the DC motor. Turn up the knob on the dynamometer and see if torque is increasing in the right direction. If the direction of rotation is wrong (so the dynamometer hits a stop immediately) turn all voltages off and reverse either the field or the armature connections to the DC motor. Turn voltages back on and verify correct direction of rotation.

   In this activity you will be measuring rpm with a GenRad Strobotac. This instrument is accurate to ±1 digit or ±0.1%, whichever is larger, but can still be improperly used to get wrong data. Intelligent use often requires a guess as to the approximate rpm. If you are operating a DC motor rated at 3450 rpm at 115 V, and you apply 120 V, you would look for the desired rpm between 3000 and 4500 rpm, and not at 600 rpm or 6000 rpm. If you do look at around 1/3 of the rated speed (3450/3 = 1150) you will also see a single image. This could lead to vastly inaccurate readings. If you apply 1/3 voltage to the motor, the speed will be about 1/3 of rated, so you would look between 800 and 1400 rpm. When you find the correct speed, doubling the strobe rate will give a double image on the rotating pulley. However, you cannot use this as your only criterion, because doubling the strobe rate from the 1/3 to 2/3 rates will also give a double image. Thus before you measure a speed with the Strobotac, be sure to check the machine ratings and determine the approximate speed!

   Prepare a table showing armature voltage, armature current, rpm, and torque. With the dynamometer field set to zero, adjust the variable autotransformer for 40 V DC on the panel meter. Record that voltage, current, rpm, and torque. Adjust the dynamometer field for I_a = 1 A and then 1.7 A, adjusting the variable autotransformer as necessary to maintain 40 V DC. Record current, rpm, and torque. Repeat the process for the variable autotransformer adjusted for 80 V DC and 120 V DC. You should have 9 rows of data.

   Compute during the laboratory the overall motor efficiency at full rated current and the speed regulation for V = 40, 80, and 120 V DC. How does this compare with the results of Prelab Activity 2?

4. Now we want to examine the effect of belt tightness on belt and bearing losses. Measure rpm and torque for the variable autotransformer adjusted for 120 V and the dynamometer field adjusted so the armature current is 1.7 A, for at least two belt tightnesses. Try one with the belt rather loose but not slipping, and another with the belt rather tight (try not to break anything). Compute the overall motor efficiency in each case and also compute the incremental power being supplied to the belt and bearings when it is excessively tightened.

5. Remove the belt from the motor, adjust the terminal voltage to about 100 V, and turn the field voltage off for a second or so to hear the motor accelerate. Don't leave it off very long. We are really not that curious to see if the speed will self limit without the motor self destructing.

Conclusion

1. Discuss the variation of performance of the DC motor with speed. Does the motor work `better' at low speeds or high speeds? Why do you suppose this is true?

2. Explain the philosophy of belt tightening like you were explaining it to a new employee of yours who needed to know how tight and why.

3. Explain the sound of a DC motor which has just lost its field to the same new employee and suggest appropriate action in your own words.