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Activity 1.2.6 Maximizing Motor Power – fischertechnik Introduction An engineer often must design a system to get the most out of limited resources. When designing a laptop or mobile phone, for example, an engineering team works to make the battery last as long as possible, for example. A vibrating cell phone uses a motor with an off-center load, and it needs to be designed with a gear train that delivers the most power or the highest efficiency. These design decisions can be made by making only four measurements of a motor. These four measurements describe the most important properties of a particular motor at a given voltage. In this activity you will learn how to make those four measurements. You will also learn how to choose a gear ratio to make a motor deliver maximum power or maximum efficiency for a given task. Equipment Fischertechnik 2 V micromotor Fischertechnik hubs and pulley DC power supply or one AA battery and holder Multimeter Timing device for timing to 0.01 s precision Vernier force sensor or other device able to measure ~200 mN Alligator jumper cables Thread Clamp © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 1 Procedure 1. Set the DC power supply to deliver constant voltage. This is accomplished by turning the current knob all the way clockwise. Then use the voltage knob to set the voltage to 1.0 V. Alternatively, provide power with one AA battery (one, not two as shown here.) 1.0 V 2. Connect the power source to the motor using alligator jumper cables. 3. Measure the no-load speed of the motor by counting the motor’s revolutions using a thread. a. Mount the motor to the table top using a clamp and fischertechnik parts. b. Attach a hub to the motor axle when the power is removed, and use the hub to anchor the end of a thread that is approximately 5 ft long. Hold the motor in a stalled position with the thread wrapped one to three times around the motor shaft © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 2 c. Start the timer as you release the thread. You will minimize tangles if you keep the thread relatively straight. It does not matter if the thread winds with slack in it; you are only counting revolutions. Since you want to know the motor’s speed with no load, do not slow the motor down by hanging onto the thread more than necessary. Stop the timer when the end of the thread reaches the motor. Unwind the thread, counting revolutions as you go. n = number of rotations = _______ Time for n rotations = _________ 4. Calculate the no-load speed = rotations/time. Using the fact that 2 radians = 1 rotation, convert the no-load speed to radians per second. This is the fastest that the motor will spin at this voltage. no-load = No-load speed = _________ rotations/second = _________ radians/second 5. Record the no-load current. The power supply displays current, but a multimeter should be used for accuracy. If current greater than the range setting of an ammeter passes through the meter, it blows the fuse of the meter and can damage the meter. Always start with ammeter range settings greater than the current can possibly be. The power supply gives a rough indication of the current, so you can go right to the correct range setting on the ammeter. Ino-load= No-load current = _________ A 6. Measure the stall torque of the motor. Accomplish this by affixing something to the shaft of the motor so that a force can be applied at a precise distance from the axis of rotation. You will actually calculate the torque by measuring a force and an off-axis distance. Use a caliper to measure the diameter of the shaft; the off-axis distance d is half of this diameter. d = distance from axis of rotation to point where force is applied = _______ m © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 3 F┴ = force to stall the motor = ______ N stall = stall torque = d × F┴ = ______ N·m 7. Record the stall current of the motor. If a current greater than the range setting of an ammeter passes through the meter, it blows the fuse of the meter and can damage the meter. Always start with ammeter range settings larger than the current could be. Istall = Stall current = _________ A 8. Congratualations! You have measured everything you need to measure to characterize your motor. You have all of the most important design parameters that describe the motor’s performance for operation at 3 V. Let’s put them in one place, creating a specification sheet, or spec sheet as it is commonly called. Specification Sheet Motor model: ________ For operation at 3 V: No-load current: ________ Stall current: ________ No-load speed: ________ Stall torque: ________ 9. Engineers make many design decisions by calculating important results from these specs. For example, what is the torque at which the motor delivers maximum power? Refer to the presentation Maximizing Motor Power if needed. =Motor torque for maximum power = ½ stall torque = ________ N·m © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 4 10. Engineers often want to select a component based on something they calculate from the specs. Suppose you are selecting a cell phone vibration motor and want at least 200 mW of power. Will this motor do the trick? Calculate the maximum output power of this motor. Note that the speed of the motor at half the stall torque is half the no-load speed. = Motor speed at maximum power = ½ no-load speed = ________ rad/s Pout = Motor output power at maximum power = × = ________ W 11. It is common for motor output power to be reported in horsepower. Convert the output power to hp. Show your work. Pout = ________ W × __________________ = _________ hp 12. Use the Internet to look up the power output of a power tool or air compressor on the market. Describe what you found out. Compare to your motor. 13. Because you characterized your motor, you can make a lot of design decisions. Suppose you want to use your motor to drive a robot that requires 0.05 N·m of torque on the drive axle. A gear train will transfer power from the motor to the drive axle. That 0.05 Nm will be the output torque from the gears. The motor will deliver the input torque to the gears. What gear ratio would you need to use to make this motor deliver maximum power to the drive shaft? = = 14. Because you measured the specs of your motor, you can predict how much electrical power it will consume. Let’s do that calculation for when the motor is exerting half of its stall torque – when it is working at maximum output power. How much electrical power is flowing into the motor? © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 5 Voltage = V = 1.0 V Current = I = halfway between stall current and no-load current = _______ A Electrical Power = Pin = I · V = __________________ = ___________ W 15. Sometimes engineers will design a device to be as efficient as possible instead of designing it to be as powerful as possible. How efficient is your motor? Calculate the efficiency of the motor when it is operating at maximum power. = = 16. It was easy to calculate the torque at which the motor would deliver maximum power. (Review: How did you calculate that torque? Look back at step 9.) It is not so easy to calculate the torque at which the motor will deliver power at maximum efficiency. But there is an algorithm for it. An algorithm is a procedure to follow. Steps 10, 14, and 15 walked you through the algorithm for calculating the efficiency for a given torque. What are the steps of the algorithm? 17. You could find the maximum efficiency by calculating the efficiency at many different torques and picking the highest efficiency. That would require many iterations of the algorithm! Computers are very good at automating that work. Open the spreadsheet 1.2.6 Motor Power at Constant Voltage and enter the specifications of your motor. © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 6 This spreadsheet is automated to calculate efficiencies for 100 torques between 0 N·m and the stall torque you enter. It automatically updates the two graphs to specify how four design parameters for your motor are dependent on the torque delivered by the motor. The first graph shows efficiency (in blue) and motor output power (in red). Discuss the graphs created by your spreadsheet with your lab partner. a. Paste images of your graphs here. b. What are the x- and y-axes for each curve? Notice two y-axes on each graph! Color: y-variable vs. blue: _____________ vs. ______________ red: motor power green: _____________ vs. ______________ purple: _____________ vs. ______________ vs. x-variable motor torque . © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 7 18. Find the point on the efficiency graph that is the maximum efficiency. Indicate this spot on the graph that you pasted into this document in step 17a above. You can indicate the spot on the graph by inserting a circle into this Word document using the following steps: a. Select: Insert > Shapes > select oval. b. Right click the oval. c. Change fill to “no fill.” d. Change the outline color to a setting that will effectively draw attention to a precise location on the graph. e. Change the line weight to be large enough to be obvious but small enough to be precise. 19. Based on your graphs, what is the maximum efficiency? = ___________ % max 20. At what torque does the maximum efficiency occur? max efficiency = ___________ N·m 21. Using the torque from step 20 as the x-coordinate on the second graph, find the current used by your motor when it is operating at maximum efficiency. Circle this point on your second graph following the method listed in step 18. max efficiency = ___________ A © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 8 22. How much electrical power does the motor use when it is operating at maximum efficiency? Pelec = I · V = ______________ = ________ W 23. The efficiency tells you what percent of the electrical energy is transformed to mechanical energy. The rest of the energy becomes heat energy, increasing the temperature of the motor. Power is the rate at which energy is transformed. At what rate is heat energy deposited into the motor when it is operating most efficiently? Pheat = ( 1 - ) Pelec = max © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 9 Conclusion 1. Explain what it means to “characterize” a component to be used in a system. 2. In this activity you used math and science to calculate how to use a motor in a design, instead of using trial and error. What are the advantages of using math and science in engineering design? What are the advantages of trial and error? 3. Explain how efficiency is related to electrical energy, mechanical energy, and heat energy. 4. The motor in the design shown at left has the specifications shown at right. What gear ratio should be used for maximum power? For operation at: 9V No-load current: 100 mA Stall current: 3A No-load speed: 20 rad/s Stall torque: 60 N·m © 2012 Project Lead The Way, Inc. Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 10