Laboratory 2 - DSCL - Johns Hopkins University
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1. 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 Page 7 of 72. M E 530 420 Lab 2 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 6PM Tuesday September 20 2010 at 115 CSEB Reading CH 10 1 10 5 and 10 7 Your class lecture notes Pololu 2284 motor encoder gearbox specifications 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 Pololu 2284 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 Pre Lab 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 Questions 1 through 13 are pre lab questions For Q1 Include dynamic viscous friction and assume that static coulomb friction is negligible For Q2 Q13 Assume all friction is negligi
3. age 3 of 7 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 Rotate the motor shaft clockwise and counter clockwise manually 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 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 negative counterclockwise angular velocities Print an
4. ble 1 What is the equation of motion for a DC permanent magnet brush motor 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 This laboratory Louis L Whitcomb Page of 7 10 Define the efficiency of an electric motor 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
5. d annotate a scope screen shot for each data point Direction SPEED Angular Velocity Back EMF encoder pulse sec radians sec signed 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 Compute values for ke in units of Volts rad sec Note that in k in SI units of V rad sec is numerically equal to k in SI units of N m A Page 4 of 7 4 Mechanical Friction Parameters 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 Angular Velocity no external load encoder Motor Angular Velocity no external load rad sec Motor Current no external load Amps Motor Torque no external load N m pulse s
6. ec 24 Using the value for k that you determined experimentally in 22 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 Ttatic ks sgn and the motor dynamic friction Taynamic Kp a Give your experimentally determined value for ksin units of N m b Give your experimentally determined value for kp in units of N m rad sec Page 5 of 7 5 Visualizing Speed Torque Curves 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 28 The Y axis displays motor current Based upon your examination of this lab setup what is the scale factor of Amps per screen division 29 The X ax
7. function from the previous question Describe briefly what it tells you 13 Consider a hypothetical standard DC brush motor with the following motor parameters powered by a voltage power supply capable of delivering 0V 50V at up to 10 Amps Resistance R 5 0 Ohm Back Emf Constant K 0 5 Volt radian sec Torque Constant K 0 5 Newton Meter Amp Inductance L 200 u Henry Friction 0 zero Inertia 1 2 5 10 kg m For the operating condition of 2 5 Newton Meters of torque at 50 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 2 Newton Meters of torque at 50 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 3 Newton Meters of torque at 50 radians per second Explain why or why not Be specific Page 2 of 7 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 c
8. is displays tachometer voltage Based upon your examination of this lab setup what is the scale factor of radians per second per screen division 30 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 31 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 32 Use the spec sheet value of kt and the experimentally observed value for stall current from 37 to compute the stall torque 33 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 34 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 e Note your secret code on your lab report e Note your lab partner s secret code on your lab report e Note your workstation number on your lab report e Remember to show your work e Typed or hand written lab reports are OK Messy or ambiguous lab reports will be rejected e Please clean up your workstation to perfection when you are done Page 6 of 7 Cover Sheet for 530 420 Lab 2 DC Brush Motor Dynamic Parameters My Secret Code Fill in the secret code which was provided to you on your graded lab 1 My Lab Station
9. ommutator Record the lowest measured resistance value 15 Determine the manufacturer s specification for winding resistance from the Spec Sheet for this model of motor Note that the winding resistance is not listed explicitly but you can compute one from the specified stall current and specified nominal operting operating voltage 16 Compare your measured motor resistance value to the resistance value you computed from the sheet for this motor 3 Motor Back EMF and Torque Constant Parameters 17 Read from the Pololu spec sheet e Hook up the motor s encoder CH A output to the oscilloscope s CH1 input Recall that this involves the following steps Verify the pin connection specification in the motor sheet Note in your writeup the pin number and associated signal for each of the device s six electrical pin connections www pololu com MOTOR CONNECTIONS Black motor power positive Red motor power negative ENCODER CONNECTIONS Blue Hall sensor Vcc 5V Supply Green Hall sensor GND Yellow CH A Hall sensor A output White CH B Hall sensor B output Figure 1 Pinout detail from motor datasheet Connect the encoder pin labeled Vcc to the power supply s fixed 5V output lug using a banana to clip test lead c6 99 Connect the encoder pin labeled GND to the power supply s fixed 5 output lug using a banana to clip test lead P
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