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Unformatted text preview: Characteristics of DC Motor/Generators
M.D.Fox update 5 Oct. 2004; 3/14/06 Introduction
The purpose of this lab is to explore the characteristics of DC motors. DC motors are a form of electromechanical energy converters. Their efficiency depends on electrical losses due to armature resistance, unrecovered energy storage in magnetic fields and core losses including hysteresis and eddy currents, as well as mechanical losses due to friction, and vibration. The motors studied are Minertia permanent magnet DC motors with brushes. Since these motors were equipped with an attached rotary encoder it was easy to obtain exact shaft velocity. Two operating conditions were studied, an unloaded solitary motor, and a motor/generator pair in which a motor was shaft coupled to a paired generator, where the load could be varied in controllable fashion. Also examined was motor variability with respect to armature resistance, generator constant, and mechanical losses. The results, which generally follow theory, are presented below. While two of the motors studied were fairly similar, the third motor had significantly different characteristics. We start with some brief theory of permanent magnet DC motors and generators. Then we discuss materials and methods used in making the measuurements. A section is devoted to measurements on individual motors, followed by another section on measurements on motor/generator pairs. Finally we provide discussion and conclusions. 2 DcMotors051004-1.nb Theory; Permanent magnet DC Motor.
Figure 1 T RA + + VA EA
- + TM D wM
- The fundamental relationships for a DC motor include torque/speed relations on the mechanical side and voltage/current relationships on the electrical side as follows : T = TM - wM D VA = EA + IA RA From energy conservation, the electrical power input [after armature resistance losses] in Watt = Joule/Second must equal the mechanical power output [before frictional losses]. EA IA = TM wM Exercise: confirm that the units on both sides of Eq. 3 reduce to power. Under no external load conditions, @and neglecting other loss mechanismsD the total power utilized @dissipatedD will be IA 2 RA electrical loss in the armature and wM 2 D in the mechanical section. Model for permanent magnet DC motor. T = external torque @N mD, TM = torque in the air gap, wM = mechanical angular velocity @rad ê sD, D = mechanical damping factor @N m sD, VA = terminal voltage @J ê CD, Js C EA = induced voltage, @J ê CD, RA = armature resistance, A ÄÄÄÄÄÄÄÄÄÄ E, IA = input current A ÄÄÄÄÄÄ E. 2 C s TM Å Substituting EA = K wM into @3D above, or K wM IA = TM wM , we obtain IA = ÅÅÅÅÅÅÅÅÅÅÅÅ , K thus indicating that the armature current IA is linearly related to the mechanical torque and the constant of 1 proportionality @the torque constantD is K ' = ÅÅÅÅÅÅ or the inverse of the generator constant defined previously. K Typically the back emf EA is related to the angular velocity wM by the generator constant K, i.e. EA = K wM . EA is due to the generator activity of the motor. Assuming small armature resistance, so IA RA is negligible, a constant relationship should be obtained between the input voltage VA , and the angular frequency, w. This is the basis for using the input voltage to control speed in a DC motor. However, note that the speed will sag when a load is applied to the motor. DcMotors051004-1.nb 3 Permanent magnet DC Generator model.
IA T + wM D
- RA + + TM EA
- VA RL Figure 2
Model for a permanent magnet DC generator. Note the direction of the mechanical torque is changed,when the device is used as a generator. The fundamental relationships for the permanent magnet DC generator are as follows: T = TM + wM D VA = EA - IA RA When used as a generator, a torque T is applied at an angular frequency wM , generating an output voltage VA across a load RL . (4) (5) 4 DcMotors051004-1.nb Materials and Methods
Tek TDS 3012 Digital Scope GW Dual Tracking Lab DC supply GPC-185OD RPE out Minertia FA5MGS12 800783-3 DC Motor RiteTech 53408 Multimeter Figure 3
Experimental arrangement for obtaining measurements on DC motor. The Rite-Tech multimeter was used in ammeter mode, on the 200 mA scale. Some measurements were made with a Tektronix TDS 3032 digital scope. The experimental arrangement shown above in Fig. 3 was utilized to obtain data from the motors studied. For some studies we substituted a HP Harrison 6102 A DC power supply. DcMotors051004-1.nb 5 Power Supply R P E Motor Generator Load Scope Figure 4
Experimental schema. Left motor "A", model FA5MGS11, serial number: 700327-1; Right motor "B", model FA5MGS12, serial number W71213-1. Motors were connected by Imperial/Eastman poly-flo tubing, 44P-1/4. OD ~.25 " ID ~.175 ". Modeling clay was used to secure the motors on the stand. Load was a 100 Ohm Ohmite rheostat. Figure 5
Photo of motor/generator pair shown in Fig. 4. 6 DcMotors051004-1.nb Figure 6
Scope output of rotary pulse encoder [RPE] of Minertia FA5M-GS11 DC motor serial number: 700327-1, at about 10 Volt input. Ch1: White output, Ch2, Green output. Rated at 500 pulses per revolution. Figure 4 illustrates the arrangement used to obtain data for the motor generator pair. The load was an Ohmite Model G, 100 Ohm rheostat [.87 Amp maximum]. Scope images were obtained using WaveStar software on the TDS 3032, with a serial port link. Fig. 5 illustrates the motor/generator pair. Fig. 6 shows the two output channels from the rotary pulse encoder on the Minertia motors. CHARACTERIZATION OF INDIVIDUAL MOTORS
ü Obtain a Minertia DC motor in the laboratory. Be sure to record identifying numbers for the motor so you will be able to use the same one in subsequent laboratory sessions. For the single, unloaded motor, vary the armature voltage and measure the motor speed and armature current for each value of the armature voltage. Estimate the armature resistance by studying the offset in the speed/voltage plot. Plot the speed versus the armature voltage. Determine the motor constant (in Hz/V) by fitting to a straight line. 1 2 3 4 Vin,V 3.179 5.071 7.093 8.865 Iin,mA 50.5 54.1 56. 57.4 f ,kHz 2.016 3.609 5.277 6.947 DcMotors051004-1.nb 7 5 6 7 8 11.25 13.31 15.24 17.12 60. 62.4 64.4 66.6 8.888 10.69 12.34 14.04 Raw data for motor A. 2/17/04 Minertia FA5M-GS11,SN 700327-1. 1 2 3 4 5 6 7 8 Vin,V 3.12 5.07 7.09 9.15 11.2 13.16 15.09 17.15 Iin,mA 58.4 63.7 67.9 72.9 78.2 84. 94.2 96.6 Table 2 f ,kHz 1.842 3.444 5.047 6.682 8.331 10.01 11.87 13.51 Raw data for motor 2. 2/18/04 Minertia 800783-3. This motor had higher current draw, suggesting greater mechanical losses. f,Hz 15 12.5 10 7.5 5 2.5 5 10 Figure 7
Speed vs. armature voltage for motors 1 and 2 [800783,red]. Results are very similar. Plot was obtained by taking regressions of the curves from tables 1 and 2, determining the effective armature resistance, and then subtracting out the voltage drop across the armature to obtain the estimated speed/armature voltage curves. 15 20 Vin,V The regression for the first motor was; Ea = 0.00045633+0.878829 f . For the second motor, Ea = 105.459 Rev -0.067391+0.876757 f. For the first motor the slope was 878.829 Hz/Volt, or ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅ . The second motor ÅÅÅÅ Minute Volt had an effective armature R of 19 Ohm instead of 18 Ohm, for a 5.5 % difference. The speed [generator]constant was very close, about .12% difference. ü Plot the input power versus the speed. Plot the mechanical power loss versus the speed for the single motor. Repeat these procedures for a second Minertia DC motor. Are there significant differences in their characteristics? 8 DcMotors051004-1.nb Pin,W 1.5 1 0.5 f,kHz 2 4 6 8 10 12 14 Figure 8
Plot of Input power Vs. Speed for Minertia motors [motor 1=black, motor 2 =red]. Green = motor 1 mechanical losses only, blue = motor 2 mechanical losses only. To obtain mechanical power loss, subtract out electrical loss IA 2 R before plotting. Looking at only mechanical losses, the motors were close up to about 5 kHz, then diverged at higher speeds. The theory line is a regression of the form : 0.037791 + 0.0597616 x + 0.00134084 x2 for the first motor @blackD, 0.0417439 + 0.0679706 x + 0.00389151 x2 for the second motor @redD. The second motor had clearly greater power utiIization at higher speeds. I would call these differences significant. MOTOR/GENERATOR PAIR
ü Couple the two DC machines together. Vary the armature voltage to motor A, with no load connected to motor B. Measure the motor speed and the armature current for motor A for each value of the armature voltage. Using this information and that obtained for machine A alone, deduce the frictional losses in machine B as a function of the speed. 1 2 3 4 5 6 7 8 Vin,V 5.14 7.15 9.18 11.1 13.31 15.29 17.24 18.75 Iin,mA 127.5 134.9 138.4 141. 144. 148.8 152.8 155.4 Table 3
Data for unloaded Minertia motor ê generator pair shown in Fig. 4. f ,kHz 2.819 4.496 6.167 7.805 9.644 11.4 13.02 14.3 DcMotors051004-1.nb 9 Pin,W 3 2.5 2 1.5 1 0.5 2 4 6 8 10 12 14 f,kHz Figure 9
Power utilization by motor/generator pair compared to power use by Motor A alone [lower curve]. Significant additional mechanical power is used by connecting to the second motor/generator, shown as the red line in Fig. 9. 0.170913 + 0.0959693 f + 0.000977746 f 2 . The units will be Watts if f is in kHz. Subtracting the fits for the two curves, we obtain the expression for the mechanical power loss due to the generator load alone as a function of frequency : 0.208704 + 0.155731 f + 0.00231859 f 2 - H0.037791 + 0.0597616 f + 0.00134084 f 2 L = 10 DcMotors051004-1.nb ü Use machine A as a motor and machine B as a generator. Connect a resistor across the armature of machine B so that .5 Ampere flows in the generator when rated voltage is applied to the motor. (This situation will be referred to as “full load.” Take the 'rated' voltage to be 11 Volt. Figure 10
No load. Motor/generator mode with Vin = 10.14 Volt, Iin=137.1 mA, f=7.246 kHz. Motor is 700327-1. Output voltage [Ch. 1]is 8.917 Volt. No-Load Condition. DcMotors051004-1.nb 11 Figure 11
At 'Full Load', we have Iin = .430 A, Vin = 10.14 Volt, Vout = 2.000 Volt, I out = .41 A, f =4.633 kHz. ü Plot the speed versus the armature voltage for machine A under no-load and full load conditions. By what percentage does the speed decrease when full-load is applied at the rated armature voltage? Estimate the armature resistance of the generator. 1 2 3 4 5 6 7 8 Vin,V 5.08 14.47 7.16 9.08 11.03 12.19 13.04 14.04 Iin,mA 0.244 0.588 0.32 0.389 0.459 0.503 0.535 0.571 f ,kHz 1.921 6.858 3.021 4.139 5.104 5.714 6.051 6.638 Table 4
Raw data for full load motor/generator pair. Vout,V 0.762 2.93 1.22 1.75 2.06 2.35 2.59 2.85 Iout,A 0.18 0.65 0.29 0.39 0.49 0.55 0.59 0.64 12 DcMotors051004-1.nb Pin,W 8 6 4 2 f,kHz Assume rated armature voltage is 11 Volt, estimate the frequency to be 7.805 unloaded, 5.104 loaded. Then the loaded/unloaded speed ratio is about 65.4%. Data for unloaded and loaded motor ê generator pair. The loaded data is the upper set of points, showing larger power dissipation. The fit for the full load case was 0.45784 + 0.119715 f + 0.154252 f 2 . 2 4 6 8 10 12 14 DcMotors051004-1.nb 13 Discussion and Conclusions
In the present lab a number of measurements were carried out to determine various characteristics of small Minertia DC motors. Interestingly, while the first two motors analyzed were very similar, the third motor had significantly different characteristics. The Minertia 700327 had a generator constant of 878.829 Hz/Volt, while the second Minertia 800783 had a constant of 876.757 Hz/Volt. This represents a very close tolerance. The first Minertia had an estimated RA of 18 Ohm, while the second was 19 Ohm. Thus they were reasonably well matched. Power dissipation plots revealed the second motor suffered from significantly greater mechanical dissipation than the first,with the gap increasing to about 30% at higher speeds. The studies on linked motor generator pairs, revealed that loading the generator by placing a resistor on the output of the generator, had a significant effect on system performance, resulting in a much lower maximum velocity of 6.638 kHz, compared to maximum velocity of 14.3 kHz for the unloaded case. Also as expected the addition of the generator, even unloaded, added significantly to the input power dissipation of the pair due to increased mechanical loading. Interestingly, studies on the unit used as the generator in the motor/generator pair showed it to have an armature resistance of only 7.68461 Ohm, and a generator constant of 835.371 Hz/Volt, significantly different from the first two motors. The loaded/unloaded speed ratio at 11 Volt Va was 65.4%, with maximum load defined as .4 Ampere. Overall the Minertia motors appear to be handy, smooth running little motors. Since the ones in the lab have undoubtedly been subjected to harsh use, we should probably not be surprised to find some with differing characteristics, possibly due to wear or abuse. In addition, the meaning of the nomenclature is not totally clear, and some of the motors may well have been built to different specifications. References
1. ECE 214 course notes, Ayers. ...
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