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May 21, 2006 Sizing Electric Motors for Mobile Robotics

# Sizing Electric Motors for Mobile Robotics

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May 21, 2006

Sizing Electric Motors for Mobile Robotics

May 21, 2006

The Basics

May 21, 2006

Unit Conversions

sec1

sec

11 mNWatt

sec111 CoulombVoltAmpereVoltWatt

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)

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)

May 21, 2006

Procedure for Sizing DC Motors

May 21, 2006

Information Needed

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

case• Push/Pull forces

May 21, 2006

Procedure

• Step One: Determine total applied force at worst case

May 21, 2006

Friction

• Static Friction– Used to determine traction failure

• Rolling Friction– Used to determine motor requirements

• Kinetic Friction

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

May 21, 2006

Rolling Friction

• Some typical values for R

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

May 21, 2006

Other Forces

sinWFI

• Gravity

• External

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

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

May 21, 2006

Procedure

• Step One: Determine total applied force at worst case

• Step Two: Calculate power requirement

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

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

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

PT

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

May 21, 2006

Spec Sheet

May 21, 2006

Spec Sheet

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

May 21, 2006

Torque vs. Speed Curve

• Where T = Torque• TPK = Stall Torque

• SNL = No Load Speed = Speed

NL

PKPK S

TTT

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

May 21, 2006

Power

NL

PKPK S

TTTPK

NLPK T

STT )(

TP

PKNL

PK TSTP 2)(

TSTTSTP NLPK

NL 2)(

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)(

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)(

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

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

May 21, 2006

A Few Extra Points

May 21, 2006

Simple DC Motor Model

eRIV eke ekRIV

IkT t 2

max 1

P

NL

II

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.

May 21, 2006

Winches

• Similar to drive motors

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

May 21, 2006

Questions?