Activity 126 Maximizing Motor Power ndash fischertechnik

IntroductionAn 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 1

fischertechnik hubs and pulley

DC power supply or one AA battery and holder

Multimeter

Timing device for timing to 001 s precision

Vernier force sensor or other device able to measure ~200 mN

Alligator jumper cables

Thread

Clamp

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 2

Procedure1 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 10 V Alternatively provide power with one AA battery (not two as shown here)

2 Connect the power source to the motor using alligator jumper cables

3 Measure the no-load speed of the motor by counting the motorrsquos revolutions using a thread

a Mount the motor to the table top using a clamp and fischertechnik parts

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 3

10 V

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

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 motorrsquos 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 = rotationstime 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 = _________ rotationssecond

= _________ radianssecond

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 4

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

F = force to stall the motor = ______ N

stall = stall torque = d times F = ______ Nm

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 Congratulations You have measured everything you need to measure to characterize your motor You have all of the most important design parameters that describe the motorrsquos performance for operation at 3 V Letrsquos put them in one place creating a specification sheet or spec sheet as it is commonly called

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 5

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 = frac12 stall torque = ________ Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 6

10Engineers 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 = frac12 no-load speed = ________ rads

Pout = Motor output power at maximum power = times = ________ 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 times __________________ = _________ hp

12Use 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

13Because 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 005 Nm of torque on the drive axle A gear train will transfer power from the motor to the drive axle That 005 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

GR=τoutτ iquest

=iquest

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 7

14Because you measured the specs of your motor you can predict how much electrical power it will consume Letrsquos do that calculation for when the motor is exerting half of its stall torquemdashwhen it is working at maximum output power How much electrical power is flowing into the motor

Voltage = V = 10 V

Current = I = halfway between stall current and no-load current

= _______ A

Electrical Power = Pin = I V = __________________ = ___________ W

15Sometimes 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

η=PoutPiquest

=

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 8

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

fischertechnik hubs and pulley

DC power supply or one AA battery and holder

Multimeter

Timing device for timing to 001 s precision

Vernier force sensor or other device able to measure ~200 mN

Alligator jumper cables

Thread

Clamp

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 2

Procedure1 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 10 V Alternatively provide power with one AA battery (not two as shown here)

2 Connect the power source to the motor using alligator jumper cables

3 Measure the no-load speed of the motor by counting the motorrsquos revolutions using a thread

a Mount the motor to the table top using a clamp and fischertechnik parts

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 3

10 V

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

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 motorrsquos 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 = rotationstime 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 = _________ rotationssecond

= _________ radianssecond

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 4

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

F = force to stall the motor = ______ N

stall = stall torque = d times F = ______ Nm

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 Congratulations You have measured everything you need to measure to characterize your motor You have all of the most important design parameters that describe the motorrsquos performance for operation at 3 V Letrsquos put them in one place creating a specification sheet or spec sheet as it is commonly called

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 5

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 = frac12 stall torque = ________ Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 6

10Engineers 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 = frac12 no-load speed = ________ rads

Pout = Motor output power at maximum power = times = ________ 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 times __________________ = _________ hp

12Use 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

13Because 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 005 Nm of torque on the drive axle A gear train will transfer power from the motor to the drive axle That 005 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

GR=τoutτ iquest

=iquest

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 7

14Because you measured the specs of your motor you can predict how much electrical power it will consume Letrsquos do that calculation for when the motor is exerting half of its stall torquemdashwhen it is working at maximum output power How much electrical power is flowing into the motor

Voltage = V = 10 V

Current = I = halfway between stall current and no-load current

= _______ A

Electrical Power = Pin = I V = __________________ = ___________ W

15Sometimes 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

η=PoutPiquest

=

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 8

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

Procedure1 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 10 V Alternatively provide power with one AA battery (not two as shown here)

2 Connect the power source to the motor using alligator jumper cables

3 Measure the no-load speed of the motor by counting the motorrsquos revolutions using a thread

a Mount the motor to the table top using a clamp and fischertechnik parts

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 3

10 V

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

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 motorrsquos 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 = rotationstime 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 = _________ rotationssecond

= _________ radianssecond

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 4

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

F = force to stall the motor = ______ N

stall = stall torque = d times F = ______ Nm

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 Congratulations You have measured everything you need to measure to characterize your motor You have all of the most important design parameters that describe the motorrsquos performance for operation at 3 V Letrsquos put them in one place creating a specification sheet or spec sheet as it is commonly called

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 5

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 = frac12 stall torque = ________ Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 6

10Engineers 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 = frac12 no-load speed = ________ rads

Pout = Motor output power at maximum power = times = ________ 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 times __________________ = _________ hp

12Use 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

13Because 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 005 Nm of torque on the drive axle A gear train will transfer power from the motor to the drive axle That 005 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

GR=τoutτ iquest

=iquest

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 7

14Because you measured the specs of your motor you can predict how much electrical power it will consume Letrsquos do that calculation for when the motor is exerting half of its stall torquemdashwhen it is working at maximum output power How much electrical power is flowing into the motor

Voltage = V = 10 V

Current = I = halfway between stall current and no-load current

= _______ A

Electrical Power = Pin = I V = __________________ = ___________ W

15Sometimes 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

η=PoutPiquest

=

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 8

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

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

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 motorrsquos 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 = rotationstime 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 = _________ rotationssecond

= _________ radianssecond

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 4

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

F = force to stall the motor = ______ N

stall = stall torque = d times F = ______ Nm

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 Congratulations You have measured everything you need to measure to characterize your motor You have all of the most important design parameters that describe the motorrsquos performance for operation at 3 V Letrsquos put them in one place creating a specification sheet or spec sheet as it is commonly called

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 5

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 = frac12 stall torque = ________ Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 6

10Engineers 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 = frac12 no-load speed = ________ rads

Pout = Motor output power at maximum power = times = ________ 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 times __________________ = _________ hp

12Use 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

13Because 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 005 Nm of torque on the drive axle A gear train will transfer power from the motor to the drive axle That 005 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

GR=τoutτ iquest

=iquest

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 7

14Because you measured the specs of your motor you can predict how much electrical power it will consume Letrsquos do that calculation for when the motor is exerting half of its stall torquemdashwhen it is working at maximum output power How much electrical power is flowing into the motor

Voltage = V = 10 V

Current = I = halfway between stall current and no-load current

= _______ A

Electrical Power = Pin = I V = __________________ = ___________ W

15Sometimes 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

η=PoutPiquest

=

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 8

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

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

F = force to stall the motor = ______ N

stall = stall torque = d times F = ______ Nm

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 Congratulations You have measured everything you need to measure to characterize your motor You have all of the most important design parameters that describe the motorrsquos performance for operation at 3 V Letrsquos put them in one place creating a specification sheet or spec sheet as it is commonly called

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 5

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 = frac12 stall torque = ________ Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 6

10Engineers 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 = frac12 no-load speed = ________ rads

Pout = Motor output power at maximum power = times = ________ 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 times __________________ = _________ hp

12Use 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

13Because 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 005 Nm of torque on the drive axle A gear train will transfer power from the motor to the drive axle That 005 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

GR=τoutτ iquest

=iquest

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 7

14Because you measured the specs of your motor you can predict how much electrical power it will consume Letrsquos do that calculation for when the motor is exerting half of its stall torquemdashwhen it is working at maximum output power How much electrical power is flowing into the motor

Voltage = V = 10 V

Current = I = halfway between stall current and no-load current

= _______ A

Electrical Power = Pin = I V = __________________ = ___________ W

15Sometimes 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

η=PoutPiquest

=

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 8

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

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 = frac12 stall torque = ________ Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 6

10Engineers 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 = frac12 no-load speed = ________ rads

Pout = Motor output power at maximum power = times = ________ 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 times __________________ = _________ hp

12Use 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

13Because 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 005 Nm of torque on the drive axle A gear train will transfer power from the motor to the drive axle That 005 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

GR=τoutτ iquest

=iquest

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 7

14Because you measured the specs of your motor you can predict how much electrical power it will consume Letrsquos do that calculation for when the motor is exerting half of its stall torquemdashwhen it is working at maximum output power How much electrical power is flowing into the motor

Voltage = V = 10 V

Current = I = halfway between stall current and no-load current

= _______ A

Electrical Power = Pin = I V = __________________ = ___________ W

15Sometimes 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

η=PoutPiquest

=

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 8

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

10Engineers 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 = frac12 no-load speed = ________ rads

Pout = Motor output power at maximum power = times = ________ 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 times __________________ = _________ hp

12Use 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

13Because 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 005 Nm of torque on the drive axle A gear train will transfer power from the motor to the drive axle That 005 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

GR=τoutτ iquest

=iquest

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 7

14Because you measured the specs of your motor you can predict how much electrical power it will consume Letrsquos do that calculation for when the motor is exerting half of its stall torquemdashwhen it is working at maximum output power How much electrical power is flowing into the motor

Voltage = V = 10 V

Current = I = halfway between stall current and no-load current

= _______ A

Electrical Power = Pin = I V = __________________ = ___________ W

15Sometimes 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

η=PoutPiquest

=

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 8

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

14Because you measured the specs of your motor you can predict how much electrical power it will consume Letrsquos do that calculation for when the motor is exerting half of its stall torquemdashwhen it is working at maximum output power How much electrical power is flowing into the motor

Voltage = V = 10 V

Current = I = halfway between stall current and no-load current

= _______ A

Electrical Power = Pin = I V = __________________ = ___________ W

15Sometimes 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

η=PoutPiquest

=

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 8

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

17You 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 126 Motor Power at Constant Voltage and enter the specifications of your motor

This spreadsheet is automated to calculate efficiencies for 100 torques between 0 Nm 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 9

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

b What are the x- and y-axes for each curve Notice two y-axes on each graph

Color y-variable vs x-variable

blue _____________ vs ______________

red motor power vs motor torque _

green _____________ vs ______________

purple _____________ vs ______________

18Find 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 gt Shapes gt select oval

b Right-click the oval

c Change fill to ldquono fillrdquo

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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 10

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

19Based

on your graphs what is the maximum efficiency

max

= ___________

20At what torque does the maximum efficiency occur

max efficiency = ___________ Nm

21Using 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

22How much electrical power does the motor use when it is operating at maximum efficiency

Pelec

= I V = ______________ = ________ W

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 11

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

23The 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 - max

) Pelec

=

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 12

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

Conclusion Questions1 Explain what it means to ldquocharacterizerdquo 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

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 13

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14

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 9 V

No-load current 100 mA

Stall current 3 A

No-load speed 20 rads

Stall torque 60 Nm

copy 2012 Project Lead The Way Inc

Principles of Engineering Activity 126 Maximum Motor Power FT ndash Page 14