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EXPERT SYSTEMS AND SOLUTIONS

Email: expertsyssol@gmail.com

expertsyssol@yahoo.com

Cell: 9952749533www.researchprojects.info

PAIYANOOR, OMR, CHENNAI

Call For Research Projects Final

 year students of B.E in EEE, ECE, EI,

M.E (Power Systems), M.E (Applied

Electronics), M.E (Power Electronics)

Ph.D Electrical and Electronics.

Students can assemble their hardware in our 

Research labs. Experts will be guiding the projects.

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Sizing Electric Motors for Mobile Robotics

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The Basics

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Unit Conversions

sec1

sec2

revrad !T 

sec11

m N W att 

!

sec111

CoulombV ol t  AmpereV ol t W att  !!

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Basics

The FORCE applied

by a wheel is alwaystangent to the wheel.

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

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Basics

The required

TORQUE to move amobile 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)

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Procedure for Sizing DC

Motors

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Information Needed Estimated Weight

Number of wheels and motors

Maximum incline

Desired maximum velocity at worst case

Push/Pull forces

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Procedure Step One: Determine total applied force

at worst case

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Friction Static Friction

 ± Used to determine traction failure

Rolling Friction

 ± Used to determine motor requirements

Kinetic Friction

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Rolling Friction

QR Is the coefficient of Rolling friction ± Using the coefficient of Static friction (QS)will typically be to high

To determine QR:

 ± Roll a wheel at a initial velocity, v, andmeasure the time, t, in which it takes tostop

 N  F   R R !

 g t 

v

 R

!

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Rolling Friction Some typical values for QR

 ± Steel on steel: 0.001

 ± Rubber on pavement: 0.015

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Other Forces

U

Usin!W  F  I 

Gravity

External

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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( UU Q !  RW  F 

 EX  R F W  F  ! )sincos( UU Q

W  F   R ! Q

 EX  R F W  F  ! Q

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Other Cases Tracks

 ± Set Qr =0

 ± Use a spring scale to determine the force requiredto pull the chassis in neutral and add that to the

worst case force

Gear Trains

 ± Bulky gear trains may significantly affect theoutcome

 ± If this is a concern, it may be best to test in the

same way as tracks

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Procedure Step One: Determine total applied force

at worst case

Step Two: Calculate power requirement

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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 thenumber of motors if more than onemotor is used

v F  P  !

RULE OF THUMB: 3 TIMES MARGIN

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Procedure Step One: Determine total applied force

at worst case

Step Two: Calculate power requirement

Step Three: Calculate torque and speed

requirement

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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 

r 

v![ 

Speed requirement

is in rad/sec

[ 

 P T  !

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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

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Spec Sheet

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Spec Sheet

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Torque vs. Speed Curve

Where T = Torque

TPK = Stall Torque

SNL = No Load Speed [  = Speed

[ !

 NL

 PK  PK 

S 

T T T 

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Torque vs. Speed CurveTorque vs. Speed

0.00 +00

1.00 -02

2.00 -02

3.00 -02

4.00 -02

5.00 -02

6.00 -02

7.00 -02

0 1000 2000 3000 4000 5000 6000 7000 8000

Speed, rpm

   T  o  r  q  u  e ,

   N  m

From this plot,

maximum speed canbe determined for a

given load.

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Power Power vs. Speed

0 00 +00

2 00 +00

4 00 +00

6 00 +00

8 00 +00

1 00 +01

1 20 +01

0 1000 2000 3000 4000 5000 6000 7000

Speed, rpm

       P  o  w  e  r ,  w  a   t   t  s

[ [ [  !  PK  NL

 PK 

T S 

T 

 P 

2

)(

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Power Power vs. Torque

0 00 +00

2 00 +00

4 00 +00

6 00 +00

8 00 +00

1 00 +01

1 20 +01

0 0 01 0 02 0 03 0 04 0 05 0 06

Torque, Nm

       P  o  w  e  r ,  w  a   t   t  s

T S T T 

S 

T  P   NL PK 

 NL

!

2

)(

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Power Power 

¡ 

¢ 

£ 

¤ 

eed

0 00¦ 

§ 

00

2 00¦ 

§ 

00

 ̈

00¦ 

§ 

00

6 00¦ 

§ 

00

© 

00¦ 

§ 

00

1 00¦ 

§ 

01

1 20¦ 

§ 

01

0 1000 2000 

000 ̈

000 

000 6000 

000

Speed, r pm

   P  o  w  e  r ,  w  a   t   t  s

Power vs. Tor   

e

0 00¦ 

§ 

00

2 00¦ 

§ 

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00¦ 

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6 00¦ 

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1 00¦ 

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1 20¦ 

§ 

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0 0 01 0 02 0 0 

0 0 ̈

0 0 

0 06

Tor    e, Nm

   P  o  w  e  r ,  w  a   t   t  s

max2

1T T  !

max2

1[ [ !

Peak power is obtained at half of 

maximum torque and speed

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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

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 A Few Extra Points

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Simple DC Motor Model

e R I V  ! [ !e

k e [ !e

k  R I V 

 I k T t !

2

max 1 ¹¹ º ¸©©

ª¨ !

 P 

 NL

 I  I L

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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)

dt 

di LV  !

Flyback voltages can be very high and damage

electronics, that is why a flyback diode in the

switching circuit is required.

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Winches Similar to drive motors

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Common Mistakes Using static or kinetic friction instead of rolling

friction

 ± If a wheel is rolling without slipping, the onlyenergy loss is due to deformations in thewheel/surface (rolling friction)

Using PWM to control a motor reduces theavailable torque

 ± The average power, speed and torque arereduced, however, effective torque is notsignificantly effected

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Questions?