Laboratory 3 - DSCL - Johns Hopkins University
Contents
1. 13 Consider a hypothetical standard DC brush motor with the following motor parameters powered by a voltage power supply capable of delivering OV 75V at up to 30 Amps Resistance R 2 5 Ohm Back Emf Constant K 0 5 Volt radian sec Torque Constant K 0 5 Newton Meter Amp Inductance L 100 u Henry Friction 0 zero Inertia I 1 5 10 kg m For the operating condition of 7 5 Newton Meters of torque at 75 radians per second compute the following a Motor Voltage b Motor Current c Electrical power into the motor d Mechanical power out of the motor via the output shaft e Power lost in the motor itself What happens to this lost power f Efficiency g Can you use this motor and power supply to provide a continuous shaft output of 7 Newton Meters of torque at 75 radians per second Explain why or why not Be specific h Can you use this motor and power supply to provide a continuous shaft output of 8 Newton Meters of torque at 75 radians per second Explain why or why not Be specific Page 2 of 9 Part 2 Lab Work 2 D C Motor Winding Resistance 14 Use your DMM to measure the resistance of your motor the resistance between the motor s red and black leads Make your measurement with the shaft NOT moving Observe that the resistance values will vary with motor position due to variation in the internal resistance of the brush commutator Record the lowest measured resistance value 15 Determine the2. manufacturer s specification for winding resistance from the Pittman Spec Sheet for this exact model of motor 16 Compare your measured motor resistance value to that listed in the Pittman specification sheet for this motor 3 Motor Back EMF and Torque Constant 17 Read from the Pittman spec the values of the torque constant k and the back emf constant k If necessary convert these constants to SI units of N m Amp and V rad sec respectively Show your work Hint In the ST units suggested k and k have identical numerical values e Hook up the motor s encoder CH A output to the oscilloscope s CH1 input Recall that this involves the following steps Carefully insert the free end of the encoder ribbon cable into your breadboard Find the pin connection specification in the HEDS 9100 Data sheet Note the pin number and associated signal for each of the device s five electrical pin connections a lt 6 Cz 852525 8 1 8 gt otour I 0 07 2 9 6 9 0 27 f om eG 11 9 0 47 i t i i i 1 T as 4 75 0 10 58 0 347 0 187 0 004 45 0 23 ALIGNING R CESS 4 2 44 2 41 X 2 79 ALIGNING RECESS 0 096 0 095 X 0 110 2 44 2 41 DIA 2 16 0 085 DEEP 0 096 0 095 2 16 0 085 DEEP OPTICAL ta 4 11 0 162 CENTER gt 6 35 0 250 REF Figure 1 Pinout detail from HEDS 9100 encoder datasheet Connect the encoder pin labeled Vcc to the power supply s fixed 5V ou
3. mode add a third scope probe to measure the power supply voltage Create a MATH trace which plots the product of the motor current signal voltage across the 0 1 Ohm resistor and the power supply voltage It may be convenient to set your scope time axis to ROLL mode a b c d e What physical quantity does this MATH trace represent What are SI unit scale factors of the derived unit for each of the three traces e g rad sec div for motor speed amps div for current and XXX div for the math trace With a 5V power supply voltage manually vary the load on the motor output shaft At what motor velocity or velocities is the MATH trace minimum Does this observation agree with motor theory Why or why not Print and annotate scope plot s at each condition At what motor velocity or velocities is the MATH trace maximum Does this observation agree with motor theory Why or why not Print and annotate scope plot s at each condition Note your secret code on your lab report Note your lab partner s secret code on your lab report Note your workstation number on your lab report Remember to show your work Typed or hand written lab reports are OK Messy or ambiguous lab reports will be rejected Please clean up your workstation to perfection when you are done Page 8 of 9 Cover Sheet for 530 420 Lab 3 Use this cover sheet for your lab writeup My Secret Code Fill in the secret code which was provided to you
4. M E 530 420 Lab 3 DC Brush Motor Dynamic Parameters Louis L Whitcomb Department of Mechanical Engineering G W C Whiting School of Engineering The Johns Hopkins University Laboratory Due Date 5PM Wednesday September 22 2010 at 115 CSEB Reading CH 10 1 10 5 and 10 7 Your class lecture notes Pittman GM9234C212 R3 2C1533 Spec Sheet available on the course homepage https dscl lesr jhu edu ME530420_2010_Fall_ Term Spec sheets for Maxon 43 032 000 22 00 146 motor tachometer available on the course homepage comprised of Maxon motor model 2332 967 51 236 200 identified as 967 in the spec sheet Maxon tachometer model 118910 TDS3014 Oscilloscope User Manual available on the course homepage TDS3014 Oscilloscope Training Manual available on the course homepage Apparatus Pittman GM9234C212 R3 2C1533 motor assembly Maxon 43 032 000 22 00 146 motor assembly Tektronix power supply scope and DMM Show your work In derivations and computations be sure to circle your final answer The questions in this lab are numbered You must use these numbers in your lab writeup to identify your derivations and answers Part 1 Computational and Modeling Questions 1 Motor Theory DC Permanent Magnet Brush Motors Pre Lab Questions Answer the following in advance of doing the lab Assume the motor is connected to a voltage power supply Vs 1 What is the equation of motion for a DC permanent magnet brush mot
5. eter voltage Based upon your examination of this lab setup what is the scale factor of radians per second per screen division 36 The instructor will show you how to plot a speed torque curve for two motor supply voltages 5V and 10V Print and annotate scope plots of each 37 From the scope plots determine a the stall current and b no load speed in SI units of the motor for both motor supply voltages 38 Use the spec sheet value of kt and the experimentally observed value for stall current from 37 to compute the stall torque 39 From the motor spec sheets determine a the stall torque and b no load speed in SI units of the motor for both motor supply voltages 40 Compare the experimentally observed values 37 38 with the derived from specification values 39 How do they compare Give your answer as a difference in SI units and as a percent difference 7 Visualizing Speed Torque Curves For 530 620 Students e Review the spec sheet for for the Maxon 43 032 000 22 00 146 motor tachometer comprised of Maxon motor model 2332 967 51 236 200 identified as 967 in the spec sheet and tachometer model 118910 to a power supply and an oscilloscope e Design a simple circuit consisting of a 0 1Q resistor in series with the motor power lead such that you can monitor the motor current by measuring the voltage across the 0 1Q resistor with your oscilloscope e Read the scope manual section on XY mode Configure t
6. he scope in XY mode e Connect the the 0 1 to the scope channel that drives the Y axis i e so that the Y axis displays a voltage proportional to motor current which as you will recall is proportional to torque Increasing current should result in increasing Y position of the scope trace i e up e Connect the motor tachometer output leads such that they drive the X axis of the scope display i e so that the X axis displays the tachometer voltage which is proportional to motor angular velocity Increasing angular velocity should result in increasing X position of the scope trace i e to the right 41 w Give a complete circuit diagram showing your circuit its connection to the power supply and how your scope s two leads each lead has TWO connections are connected to the circuit Be specific on which lead is CH1 and which is CH2 42 The Y axis displays motor current Based upon your examination of this lab setup what is the scale factor of Amps per screen division 43 The X axis displays tachometer voltage Based upon your examination of this lab setup what is the scale factor of radians per second per screen division 44 Use your setup to capture and plot a speed torque curve for two motor supply voltages 5V and 10V Print and annotate scope plots of each 45 From the scope plots determine a the stall current and b no load speed in SI units of the motor for both motor supply voltages 46 Use the spec
7. negative counterclockwise angular velocities Print and annotate a scope screen shot for each data point Direction SPEED encoder pulse sec Angular Velocity radians sec signed Back EMF volts 21 Plot your data for back emf in Volts versus signed angular velocity in rad sec 22 Use your experimental data to compute an experimental value for the motor s back emf constant ke e Compute values for ke in a units of Volts krpm and b units of Volts rad sec e How does your experimentally determined value compare to the manufacturer s spec Page 4 of 9 4 Mechanical Friction With CH2 still connected to the motor leads now also connect the motor power leads to the variable output of your power supply in series with your DMM Use your DMM to measure the DC current use the DMM s 0 400 mA setting if available supplied to the motor by the power supply Set the current limit of the variable output power supply to maximum i e a 2A current limit when the current knob is turned fully clockwise 23 Set the power supply output to 1 0V Note the exact voltage the motor rotation velocity from the encoder trace on CH1 of your scope and the average motor current from your DMM Repeat this measurement for the supply voltages listed in the following table Motor Motor Angular Motor Angular Motor Current Motor Torque Supply Velocity no external Velocity no external
8. no external load no external load Voltage load encoder load rad sec Amps N m pulse sec 24 Using the manufacturer s specification for k and your measured values for motor current i compute a fourth column in your table for the motor torque T k i at each of these data points 25 Plot a graph of motor torque on the Y axis as a function of motor angular velocity on the X axis 26 Discuss your graph of motor torque versus motor velocity Discuss the curious feature of this plot What is going on here 27 From your graph determine approximate experimental values for the motor static friction Tstatic ks sgn and the motor dynamic friction Tdynamic kp o 28 Compare your experimentally determined friction coefficients to those listed in the Pittman spec sheet for your motor Note that motor static friction is labeled motor friction torque in the Pittman spec sheet and motor dynamic friction is labeled viscous damping factor in the Pittman spec sheet Page 5 of 9 5 Motor Speed Torque Curves 29 Use your DMM to measure the DC current use the DMM s 10A setting supplied to the motor by the power supply Carefully immobilize the motor output shaft with the supplied knob and note the stall current at each of the supply voltages given in the following table Motor Supply Voltage Motor Angular Velocity no external load rad sec Motor Current stall current Amps Mot
9. on your graded lab 1 My Lab Station My Partner s Secret Code Lab Station Clean TA s Signature amp Date Your TA will sign here after you have finished your lab cleaned up your lab station to perfection and shown your lab station to your TA Note We grade labs anonymously Please do not include personal identity information within you lab name etc Use your secret code in place of personal identity information Page 9 of 9
10. or Torque stall torque N m 30 Using the manufacturer s specification for k and your measured values for motor current i compute a fourth column in your table for the motor torque T k i at each of these data points 31 Plot the data points from the 3 0V rows of your two tables for speed and torque at a no load and b stall on a graph showing angular velocity in radians per second on the X axis and torque in Newton Meters on the Y axis Graph paper is fine Connect the two data points with a line 32 Discuss the relation indicated by this line 33 On the same graph plot the points and corresponding lines for the remaining supply voltages you tested Discuss this family of curves Page 6 of 9 6 Visualizing Speed Torque Curves For 530 420 Students Your lab instructor will set up a Maxon 43 032 000 22 00 146 motor tachometer comprised of Maxon motor model 2332 967 51 236 200 identified as 967 in the spec sheet and tachometer model 118910 to a power supply and an oscilloscope The scope is set up in XY mode The Y axis displays a voltage proportional to motor current which as you will recall is proportional to torque The X axis displays the tachometer voltage which is proportional to motor angular velocity 34 The Y axis displays motor current Based upon your examination of this lab setup what is the scale factor of Amps per screen division 35 The X axis displays tachom
11. or when the input is a voltage i e it is driven by a voltage power supply Use symbolic constants for motor parameters Is this a differential equation or algebraic equation What is its order How many degrees of freedom does it have What is the state vector of this system 2 Derive the expression for the steady state stall torque of the motor 3 Derive the expression for the steady state no load speed of the motor 4 Derive the expression for steady state in N m torque as a function of steady state angular velocity in rad sec 5 Sketch and label a plot of your function from the previous question Describe briefly what it tells you 6 Derive the expression for the steady state electrical power input of the motor as a function of steady state angular velocity 7 Sketch and label a plot of your function from the previous question Describe briefly what it tells you 8 Derive the expression for the steady state mechanical power output of the motor as a function of steady state angular velocity 9 Sketch and label a plot of your function from the previous question Describe briefly what it tells you 10 Define the efficiency of an electric motor This laboratory Louis L Whitcomb Page 1 of 9 11 Derive the expression for the steady state efficiency of the motor as a function of steady state angular velocity 12 Sketch and label a plot of your function from the previous question Describe briefly what it tells you
12. sheet value of kt and the experimentally observed value for stall current to compute the stall torque Page 7 of 9 47 From the motor spec sheets determine a the stall torque and b no load speed in SI units of the motor for both motor supply voltages 48 Compare the experimentally observed values 45 46 with the derived from specification values 47 How do they compare Give your answer as a difference in SI units and as a percent difference 49 Configure your scope back in normal Y T mode Create a MATH trace which plots the product of the motor current signal voltage across the 0 1 Ohm resistor and the motor speed tachometer output It may be convenient to set your scope time axis to ROLL mode 50 a b c d e What physical quantity does this MATH trace represent What are SI unit scale factors of the derived unit for each of the three traces e g rad sec div for motor speed amps div for current and XXX div for the math trace With a 5V power supply voltage manually vary the load on the motor output shaft At what motor velocity or velocities is the MATH trace minimum Does this observation agree with motor theory Why or why not Print and annotate scope plot s at each condition At what motor velocity or velocities is the MATH trace maximum Does this observation agree with motor theory Why or why not Print and annotate scope plot s at each condition With you scope still in normal Y T
13. tput lug Connect the encoder pin labeled GND to the power supply s fixed 5V output lug Set up the oscilloscope Be sure to check each channel to verify that it is functioning properly as per Laboratory 1 Verify that the probe type is set to 10X and that the trigger is set to CH1 Connect the encoder output pin labeled CH A to CH 1 of your scope Hook up the scope s CH 1 ground appropriately Connect the motor s red and black leads directly to CH 2 and CH 2 ground respectively of your oscilloscope As you turn the motor by hand verify that you can see both the motor back emf voltage on CH 2 and the encoder square wave output on CH 1 18 Comment on the relation you observe between the motor s shaft speed magnitude and sign and the corresponding voltage magnitude and sign you observe on the oscilloscope It may be convenient to have the scope time axis set to roll mode i e 1 0 or 0 5 seconds per division for this exercise Page 3 of 9 19 With help from the laboratory instructor use a variable speed drill drill to carefully rotate your motor at an approximately constant angular velocity Use the scope to measure the motor back emf voltage on CH 2 and the encoder output frequencey on CH 1 Note these values Print and annotate the scope screen 20 Repeat to collect at least four data points i e two different positive clockwise angular velocities and two different
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