Sizing Electric Motors for Mobile Robotics

May 21, 2006

The Basics

May 21, 2006

Unit Conversionsrad rev 2 =1 sec sec N m 1Watt = 1 sec

Coulomb 1Watt = 1Volt Ampere = 1Volt sec

May 21, 2006

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

Force is measured in units of weight (lb, oz, N)May 21, 2006

BasicsThe required TORQUE to move a mobile robot is the force times the radius of the wheel.

May 21, 2006

Torque is measured in units of weight x length (lbft, oz in, Nm)

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 forcesMay 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 FrictionFR = R N 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 v stop

R =

May 21, 2006

tg

Rolling Friction Some typical values for R Steel on steel: 0.001 Rubber on pavement: 0.015

May 21, 2006

Other Forces Gravity

FI = W sin External

May 21, 2006

Total Force Calculate worst case Up hill with rolling friction

F = W ( R cos + sin )

Up hill with rolling friction, pushing Level ground with rolling friction

F = W ( R cos + sin ) + FEX F = R W

Level ground with rolling friction, pushingMay 21, 2006

F = R W + FEX

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 tracksMay 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 usedRULE OF THUMB: 3 TIMES MARGINMay 21, 2006

P = F v

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

v = r

Speed requirement is in rad/sec

Using the speed from above and the power per motor

May 21, 2006

P T=

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 requirementsMay 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 characteristicsMay 21, 2006

Torque vs. Speed CurveT = TPK TPK S NL

Where T = Torque TPK = Stall Torque SNL = No Load Speed = SpeedMay 21, 2006

Torque vs. Speed CurveTorque vs. Speed7.00E-02 6.00E-02

5.00E-02

Torque, Nm

4.00E-02

From this plot, maximum speed can be determined for a given load.

3.00E-02

2.00E-02

1.00E-02

0.00E+00 0 1000 2000 3000 4000 Speed, rpm 5000 6000 7000 8000

May 21, 2006

PowerT = TPK TPK S NL

= (TPKP = T

S NL T) TPK

TPK P ( ) = 2 + TPK S NL S NL 2 P (T ) = T + S NL T TPK

May 21, 2006

PowerPower vs. Speed1.20E+01 1.00E+01

8.00E+00 Power, watts

6.00E+00

4.00E+00

2.00E+00

TPK P ( ) = 2 + TPK S NL0 1000 2000 3000 Speed, rpm 4000 5000 6000 7000

0.00E+00

May 21, 2006

PowerPower vs. Torque1.20E+01 1.00E+01

8.00E+00 Power, watts

6.00E+00

4.00E+00

2.00E+00

S NL 2 P (T ) = T + S NL T TPK0 0.01 0.02 0.03 Torque, Nm 0.04 0.05 0.06

0.00E+00

May 21, 2006

Power vs. Speed1.20E+01

PowerPower vs. Torque1.20E+01

1.00E+01

8.00E+00 Power, watts

6.00E+00

4.00E+00

1.00E+01

2.00E+00 Power, watts

8.00E+00

0.00E+00 0 1000 2000 3000 Speed, rpm 4000 5000

6.00E+00 6000 4.00E+00

7000

1 = max 2

2.00E+00

0.00E+00 0 0.01 0.02 0.03 Torque, Nm 0.04 0.05 0.06

Peak power is obtained at half of maximum torque and speedMay 21, 2006

1 T = Tmax 2

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 characteristicsMay 21, 2006

A Few Extra Points

May 21, 2006

Simple DC Motor ModelV = I R+eT = kt I e = ke V = I R + ke

max

I NL = 1 IP

2

May 21, 2006

Motor Inductance The windings of a DC motor creates an Inductance, L Change in current through an di V =L inductance creates a voltage dt Switching current to a motor causes di/dt to spike (Flyback)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 effectedMay 21, 2006

Questions?

May 21, 2006