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May 21, 2006 Sizing Electric Motors for Mobile Robotics
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Sizing Electric Motors for Mobile Robotics

Aug 15, 2014

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Page 1: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Sizing Electric Motors for Mobile Robotics

Page 2: Sizing Electric Motors for Mobile Robotics

May 21, 2006

The Basics

Page 3: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Unit Conversions

sec1

sec2 revrad

sec

11 mNWatt

sec111 CoulombVoltAmpereVoltWatt

Page 4: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Basics

The FORCE applied by a wheel is always tangent to the wheel.

Force is measured in units of weight (lb, oz, N)

Page 5: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Basics

The required TORQUE to move a mobile robot is the

force times the radius of the wheel.

Torque is measured in units of weight x length (lb·ft, oz ·in, N·m)

Page 6: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Procedure for Sizing DC Motors

Page 7: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Information Needed

• Estimated Weight• Number of wheels and motors• Maximum incline• Desired maximum velocity at worst

case• Push/Pull forces

Page 8: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Procedure

• Step One: Determine total applied force at worst case

Page 9: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Friction

• Static Friction– Used to determine traction failure

• Rolling Friction– Used to determine motor requirements

• Kinetic Friction

Page 10: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Rolling Friction

R Is the coefficient of Rolling friction– Using the coefficient of Static friction (S)

will typically be to high• To determine R:

– Roll a wheel at a initial velocity, v, and measure the time, t, in which it takes to stop

NF RR

gtv

R

Page 11: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Rolling Friction

• Some typical values for R

– Steel on steel: 0.001– Rubber on pavement: 0.015

Page 12: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Other Forces

sinWFI

• Gravity

• External

Page 13: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Total Force

• Calculate worst case– Up hill with rolling friction

– Up hill with rolling friction, pushing

– Level ground with rolling friction

– Level ground with rolling friction, pushing

)sincos( RWF

EXR FWF )sincos(

WF R

EXR FWF

Page 14: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Other Cases

• Tracks– Set r=0– Use a spring scale to determine the force required to

pull the chassis in neutral and add that to the worst case force

• Gear Trains– Bulky gear trains may significantly affect the outcome– If this is a concern, it may be best to test in the same

way as tracks

Page 15: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Procedure

• Step One: Determine total applied force at worst case

• Step Two: Calculate power requirement

Page 16: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Power Requirement

• Determine velocity, v, requirement under maximum load (worst case force)

• Using the worst case force and velocity, calculate the power requirement

• This is the total power, divide by the number of motors if more than one motor is used

vFP

RULE OF THUMB: 3 TIMES MARGIN

Page 17: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Procedure

• Step One: Determine total applied force at worst case

• Step Two: Calculate power requirement• Step Three: Calculate torque and speed

requirement

Page 18: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Speed/Torque Requirements

• Using the velocity requirement, v, and the radius of the wheel, r

• Using the speed from above and the power per motor

rv

Speed requirement is in rad/sec

PT

Page 19: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Procedure

• Step One: Determine total applied force at worst case

• Step Two: Calculate power requirement• Step Three: Calculate torque and speed

requirement• Step Four: Find a motor that meets

these requirements

Page 20: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Spec Sheet

Page 21: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Spec Sheet

Page 22: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Procedure

• Step One: Determine total applied force at worst case

• Step Two: Calculate power requirement• Step Three: Calculate torque and speed

requirement• Step Four: Find a motor that meets these

requirements• Step Five: Plot motor characteristics

Page 23: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Torque vs. Speed Curve

• Where T = Torque• TPK = Stall Torque

• SNL = No Load Speed = Speed

NL

PKPK S

TTT

Page 24: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Torque vs. Speed CurveTorque vs. Speed

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

0 1000 2000 3000 4000 5000 6000 7000 8000

Speed, rpm

Torq

ue, N

m

From this plot, maximum speed can be determined for a

given load.

Page 25: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Power

NL

PKPK S

TTTPK

NLPK T

STT )(

TP

PKNL

PK TSTP 2)(

TSTTSTP NLPK

NL 2)(

Page 26: Sizing Electric Motors for Mobile Robotics

May 21, 2006

PowerPower vs. Speed

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

0 1000 2000 3000 4000 5000 6000 7000

Speed, rpm

Pow

er, w

atts

PKNL

PK TSTP 2)(

Page 27: Sizing Electric Motors for Mobile Robotics

May 21, 2006

PowerPower vs. Torque

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

0 0.01 0.02 0.03 0.04 0.05 0.06

Torque, Nm

Pow

er, w

atts

TSTTSTP NLPK

NL 2)(

Page 28: Sizing Electric Motors for Mobile Robotics

May 21, 2006

PowerPower vs. Speed

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

0 1000 2000 3000 4000 5000 6000 7000

Speed, rpm

Pow

er, w

atts

Power vs. Torque

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

0 0.01 0.02 0.03 0.04 0.05 0.06

Torque, Nm

Pow

er, w

atts

max21TT

max21

Peak power is obtained at half of maximum torque and speed

Page 29: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Procedure

• Step One: Determine total applied force at worst case

• Step Two: Calculate power requirement• Step Three: Calculate torque and speed

requirement• Step Four: Find a motor that meets these

requirements• Step Five: Plot motor characteristics

Page 30: Sizing Electric Motors for Mobile Robotics

May 21, 2006

A Few Extra Points

Page 31: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Simple DC Motor Model

eRIV eke ekRIV

IkT t 2

max 1

P

NL

II

Page 32: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Motor Inductance

• The windings of a DC motor creates an Inductance, L

• Change in current through an inductance creates a voltage

• Switching current to a motor causes di/dt to spike (Flyback)

dtdiLV

Flyback voltages can be very high and damage electronics, that is why a flyback diode in the

switching circuit is required.

Page 33: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Winches

• Similar to drive motors

Page 34: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Common Mistakes

• Using static or kinetic friction instead of rolling friction– If a wheel is rolling without slipping, the only

energy loss is due to deformations in the wheel/surface (rolling friction)

• Using PWM to control a motor reduces the available torque– The average power, speed and torque are

reduced, however, effective torque is not significantly effected

Page 35: Sizing Electric Motors for Mobile Robotics

May 21, 2006

Questions?