Getting the Most From Your Motors

Kurt HeinzmannDEKA Research & Development Corp.

January 2006

Getting the Most From Your Motors

General Topics

• Manufacturers' torque curves and specification sheets• How to manage power loss and temperature rise• Gear ratio • Review of motors from a previous Kit of Parts • Which motor for which application on a robot?• Batteries

Introduction• Assumptions and approximations• Power• Power loss in the mechanism• Power required at the motor• Power loss in the motor

Assumptions and Approximations

• Steady operation– We will not discuss acceleration requirements

• Linear systems– We will represent nonlinear phenomena as linear

• Simple motor analysis– Study only two power loss parameters

• Loss due to electrical resistance• Loss due to friction and damping, combined in one fixed

value

Example: Simplify. Assume fixed free current(combine the effects of friction and damping)

Fisher-Price motor in 2005 Kit of Parts

y = 0.11x + 0.53

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 6 8 10 12 14

Voltage, V

Ifree

, A

Current

Linear (Current)Free current

per data sheet

Power• Power is a measure of how fast work gets done.• POWER = EFFORT x FLOW

“EFFORT”– force– torque– pressure– voltage– thinking

“FLOW”–travel speed–rotating speed–flow of fluid–flow of electrons–doing

Power Loss in the Mechanism

• Some power from the motor is lost due to friction in the mechanism– Gears, belts, cables– Bearings, guides– Tires, balls, or other deformable items– Damage– Contamination

• Power loss is heat

Power required at the motor• Power at the motor = power required at the point of use +

power lost in the mechanism• Power loss is heat

Power loss in the motor• Power is lost in the motor due to friction,

damping, and electrical resistance• Power loss is heat

Analysis

• Basic motor theory• Important motor parameters• Power loss in the motor• Power loss in other electrical components• Gear ratios• Comparison• Batteries

Basic Motor Theory

• Torque is rotating EFFORT, speed is rotating motion (“FLOW”)– Torque = force x radius

• Voltage is electrical EFFORT, current is FLOW of electrons

• Power = EFFORT x FLOW– Mechanical power P(out) = torque x speed– Electrical power P(in) = voltage x current

• Shaft power = power in – power loss– Power loss is sum of electrical loss and mechanical loss

Basic Motor Theory

Important motor parameters

• Stall torque ( stall )

• Stall current ( istall )

• Free speed ( free )

• Free current ( ifree )

Basic Motor TheoryImportant motor parameters

•Torque loss (loss)– We will derive this from free current– Unit: newtons (N)

• Resistance (R)– Ohm’s law

– Unit: ohm ()

• Torque constant ( Kt )–Torque is proportional to current

– Units: (Nm/A)ampere

newton-metres

volts _ radian/second

• Voltage constant ( Ke ) –Motor internal voltage is proportional to speed– Units: V/(rad/s)

Units, ConversionsInternational System (SI) of units

Item

Symbol used here Comment SI unit

Abbrev-iation

Alternate unit Conversion

Force Mechanical effort newton N lb. 4.45 N = 1lb.Distance Mechanical displacement metre m In. 0.0254 m = 1 in.Speed Travelling speed metre/second m/s mph 0.45 m/s = 1 mph

Torque Turning effort newton metre Nm lb-inAngle Angular displacement radian rad degree 2 rad = 360°

Speed Rotating speed radian/second rad/s rpm 0.105 rad/s = 1 rpmTime Don’t have much second s min., h 3600 s = 1 h

Voltage V Electrical effort volt V

Current i Electrical flow ampere APower P Rate of work watt W hp 746 W = 1 hp

Resistance R Cause of power loss as heat ohm Energy Work joule (Nm) J ft-lb

Pressure Fluid effort pascal (N/m2) Pa psi 6900 Pa = 1 psi

Flow Fluid flow (at stated pressure) cubic metre/s m3/s CFM 0.00047 m3/s = 1 CFM

Prefixes: m = milli- = one thousandth (mm, mNm) k = kilo- = one thousand (km, kW)

Why use SI units?

• Easier than U.S. Customary units• A motor converts electrical power to mechanical

power.– If you express electrical power and mechanical power in

watts, you know what’s happening at both ends of the motor, and inside it.

– Would you like to convert volts-times-amperes to horsepower?

• Advice: Convert to SI units before doing any other calculation.

• Consolation: you can always convert back.

Basic Motor Theory

Direct Current (DC), Permanent-Magnet

(PM), Brush-Commutated Motor

Basic Motor Theory

Given these four parameters:

stall, istall, free, ifree and V,

Find these four parameters:

Kt, Ke, loss(free), and R.

Important motor parameters

Find torque constant Kt and voltage constant Ke

Find torque loss loss(free)

Find resistance R

Calculate current, speed, power and efficiency

From data sheet:

From equation 3a:

From equation 3b:

From equation 4:

From equation 5:

stall = 0.65 Nm

istall = 148 A

free = 2513 rad/s

ifree = 1.5 A

loss(free)

= 0.0044 Nm/A x 1.5 A = 0.0066 NmR = 12 V /148 A = 0.081

Fisher-Price Motor (2005)

Kt = 0.65 Nm / (148.0-1.5) A = 0.0044 Nm/A

Ke = (12 V -1.5 A*0.081 )/ 2513 rad/s = 0.0047 V/(rad/s)

Equations 6 - 11 allow us to calculate the following

performance curves as a function of torque (with constant voltage):

• current (6)• speed (7)• output power (8) • input power (9)• power loss (10)• efficiency (11)

Fisher-Price Motor - Current

Example motor

0

20

40

60

80

100

120

140

160

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Torque (Nm)

Cur

rent

, A

148 A

Fisher-Price Motor - Speed

Example motor

0

500

1000

1500

2000

2500

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Torque (Nm)

Spe

ed (r

ad/s

)

Fisher-Price Motor - Power output

Example motor

0

500

1000

1500

2000

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Torque (Nm)

Po

wer

(W

)

407 W

Fisher-Price Motor - Input Power

Example motor

0

500

1000

1500

2000

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Torque (Nm)

Pow

er (W

)

Output power, W

Input power, W

407 W

1800 W

Fisher-Price Motor - Power loss

Example motor

1800 W

0

500

1000

1500

2000

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Torque (Nm)

Pow

er (W

)

Output power, W

Power loss, W

Input power, W

407 W

Fisher-Price Motor - Efficiency

Example motor

0

10

20

30

40

50

60

70

80

90

100

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Torque (Nm)

Eff

icie

ncy,

%

76%

Fisher-Price motor

1800 W

0

500

1000

1500

2000

2500

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Torque (Nm)

Spe

ed (r

ad/s

); P

ower

(W)

0

50

100

150

200

250

Cur

rent

(A);

Eff

icie

ncy

(%)

Output power, WSpeed, rad/sPower loss, WCurrent, AEfficiency

148 A

76%

407 W133 W

Motor performance based on data sheet

Real World: Power loss

14 AWG wire: 3.0 m/ft.12 AWG wire: 1.9 m/ft.10 AWG wire: 1.2 m/ft. 6 AWG wire: 0.5 m/ft. (Copper at 65 °C)

Fisher-Price motor, stalled for approximately 2 s

0

20

40

60

80

100

120

140

160

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time, s

Cu

rre

nt,

A;

Te

mp

era

ture

, °C

;

Re

sis

tan

ce

, mO

hm

0

2

4

6

8

10

12

14

16

Vo

lta

ge

, VMotor winding temperature measurement

Current

Motor terminal voltage

Battery voltage

~ Smoke ~

•This circuit was not properly protected (wrong circuit breaker)•Measuring thermocouple was inserted near windings (windings got hotter than thermocouple)•Brushes got hotter than windings

Fisher-Price Motor, stalled for approximately 2 s

Notes:

•Motor resistance increased from 67 m to 96 m (43%) in two seconds•Battery resistance = 18 m •Resistance of wires (5 ft. of 14 AWG), connectors, breakers, etc. = 25 m

Fisher-Price motor, stalled for approximately 2 s

0

20

40

60

80

100

120

140

160

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time, s

Tem

per

atu

re, °

C;

Res

ista

nce

, mO

hm

Motor winding temperature measurement

Total circuit resistance

Motor resistance

Resistance of wires, connectors, breakers, etc.

Battery resistance

~ Smoke ~Fisher-Price Motor, stalled for approximately 2 s

Total circuit resistance increased to about twice the initial motor resistance

Fisher-Price motor

0

500

1000

1500

2000

2500

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Torque, Nm

Sp

ee

d (

rad

/s);

Po

we

r (W

)

0

50

100

150

200

250

Cu

rre

nt

(A);

Eff

icie

nc

y (

%)

Output power, W

Speed, rad/s

Power loss, W

Current, A

Effic iency

68%

278 W126 W

1240 W

95 A

SYSTEM

DATA SHEET

Performance of the system compared with motor performance based on data sheet

CIM motor (also known as Chiaphua and Atwood)

Stall torque stall = 347 oz-in = 2.4 Nm

Free speed free = 5342 rpm = 560 rad/s

Free current ifree = 2.4 A

Stall current istall = 114 A

CIM motor data and curves

CIM motor

0

200

400

600

800

1000

1200

1400

0 0.5 1 1.5 2 2.5

Torque, Nm

Sp

eed

(ra

d/s

); P

ow

er (

W)

0

20

40

60

80

100

120

140

Cu

rren

t (A

); E

ffic

ien

cy (

%)

Output power, W

Speed, rad/s

Power loss, W

Current, A

Efficiency

CIM motor performance curves

Comparison of power available from Fisher-Price motor and CIM motor

0

50

100

150

200

250

300

350

400

450

0 0.5 1 1.5 2 2.5

Torque, Nm

Ou

tpu

t p

ow

er,

W

Fisher-Price motor

CIM motor

Comparison of power available from Fisher-Price Motor and CIM motor

Simple strategy

• Calculate (or read from data sheet) the motor resistance R

• Increase R by 50% - 100%

• Calculate power curve

• Operate at half of new peak power

Comparison of power available from Fisher-Price motor and CIM motor

0

500

1000

1500

2000

2500

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Torque, Nm

Sp

eed

, ra

d/s

0

50

100

150

200

250

300

350

400

450

500

Ou

tpu

t po

wer

, W

Speed, Fisher-Price motor

Speed, CIM motor

Fisher-Price motor, R increased by 75%

CIM motor, R increased by 75%

<--- Stay to the left of the peak power point

Performance curves re-calculated with R increased by 75%

"Gear" ratio: Mechanical power transmission

efficiency is important

• Spur gears: 90% per pair

• Worm and gear: 10%-60%

• Nut on a screw (not ball nut): 10%-60%

• Twist cables: 30%-90%

• Chain: 85%-95%

• Wire rope (cables): up to 98%

• Rack and pinion 50%-80%

Gear ratioExample: out = 1.5 Nm; out = 100 rad/s

Pmotor = Pout / g (12)

Gear ratio exampleOutput power = 1.5 Nm • 100 rad/s = 150 W

Try:Spur gears (assume 90% efficiency per stage)

Power required at motor Pmotor = Pout / g

one stage: Pmotor = 150 W / 0.9 = 167 W

two stages: Pmotor = 150 W / 0.9 /0.9 = 185 W

three stages: Pmotor = 150 W / 0.9 /0.9 /0.9 = 206 W

four stages: Pmotor = 150 W /0.9/0.9/0.9/0.9 = 229 W

Gear ratio exampleEstimate torque by inspection, then calculate an approximate gear ratio to determine how many gear stages are required.

Rule of thumb for spur gears: max. ratio per stage = 5:1

Comparison of power available from Fisher-Price motor and CIM motor

0

500

1000

1500

2000

2500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Torque, Nm

Sp

ee

d,

rad

/s

0

100

200

300

400

500

Ou

tpu

t p

ow

er,

W

Speed, Fisher-Price motorSpeed, CIM motorFisher-Price motor, R increased by 75%CIM motor, R increased by 75%4 stages3 stages2 stages1 stage

0.4 Nm ?

0.1 Nm ?

Gear ratioFisher-Price Motor

Gear ratio - Fisher-Price MotorChoosing operating point for Fisher-Price motor

0

500

1000

1500

2000

2500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Torque, Nm

Sp

ee

d,

rad

/s

0

100

200

300

400

500

Ou

tpu

t p

ow

er,

W

Speed, Fisher-Price motor

Power, Fisher-Price motor, R increased by75%Operating point

Tw o stages: 185 W

1850 rad/s

Check: gear ratio Ng = motor/out = 1850 / 100 = 18.5:1 = 4.3 • 4.3Operating point looks good (comfortably to the left of the peak power point)

Gear ratioCIM motor

Gear ratio - CIM motorChoosing operating point for CIM motor

0

500

1000

1500

2000

2500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Torque, Nm

Sp

eed

, ra

d/s

0

100

200

300

400

500

Ou

tpu

t p

ow

er,

W

Speed, CIM motor

Power, CIM motor, R increased by 75%

Operating point

One stage: 167 W

0.43

Nm

388 rad/s

Gear ratio Ng = motor/out = 388 / 100 = 3.9:1Moderately heavy load for this motor (near peak power)

Gear ratio example

• Calculate current– Should not exceed breaker current

• Choose motors based on– Power– Gearing required– Possibility of stalling and heating – small motors heat

up fast– Weight– All motor tasks

Summary of motors in the 2005 Kit of Parts

Sorted by peak output power

SupplierNumber on motor Motor name Description

Reference Voltage on data sheet Gear ratio

Stall torque (as from data sheet)

Stall torque (Nm)

Stall current (A)

Free speed (rpm)

Free speed (rad/s)

Free current (A)

Peak power, 10.5 V supply (W )

Fisher-Price

74550-0642 Power W heels Motor only 12 647 mNm 0.647 148 24000 2513 1.5 312

CIM FR801-001 (Chiaphua, Atwood)

Keyed output shaft, ccw 12 346.9 oz-in 2.45 114 5342 559 2.3 261

Fisher-Price

74550-0642 Power W heels Motor and gearbox 12 180.8492308 77 148 133 13.9 2.5 203

Globe 409A586 2W D/4W D transfer mtr.

Motor only 12 35 oz in 0.247 21.5 9390 983 0.4 46

Taigene 16638628 Sliding (van) door

W orm Gearmotor 10.5

34 Nm cw, 30 Nm ccw 30 44 75 7.9 2.7 44

Globe 409A587 2W D/4W D transfer mtr.

Planetary Gearmotor 12 117 13 21.5 80 8.4 0.58 24

Nippon-Denso

E6DF-14A365-BB

W indow Lift W orm Gearmotor 12.6 9.2 Nm 9.2 24.8 92 9.6 2.8 16

Jideco W indow Lift W orm Gearmotor 12 8.33 Nm 8.33 21 85 8.9 3 14

Mabuchi RS454SH W /spur gear ccw

Spur pinion on shaft 12 620 g-cm 0.061 5.2 4700 492 0.22 5.7

Comparison of motors in the 2005 Kit of Parts

Speed and torque at peak power with 10.5 V supply

1

10

100

1000

10000

100000

0.01 0.1 1 10 100

Torque, Nm

Sp

ee

d, r

ad

/s

5 W

10 W

20 W

50 W

100 W

200 W

500 W

Mabuchi

Jideco

Nippon

Globe with gearhead

TaigeneFisher-Price with gearbox

Fisher-Price motor alone

CIM

Globe motor alone

Keep batteries charged.Battery voltage and breaker panel voltage with pulse load:

Discharge current: 50 A (shared between two 30 A breakers); duty cycle: 10 s on, 10 s off.

Battery nominal capacity @ 20 hour discharge rate: 18 Ah

0

2

4

6

8

10

12

14

16

0 5 10 15

Time, minutes

Dis

char

ged

capa

city

, Ah;

Vol

tage

, V

Battery voltage

Discharged capacity

Panel voltage6.3 Ah

Delivered capacity was only one third of rated capacity.

Keep batteries charged.Battery DC resistance during pulsed discharge.

Pulse: 50 A for 10 s, 0 A for 10 sResistance calculated from voltage drop and pulse current, at 1 s intervals throughout the pulse.

0

20

40

60

80

100

120

140

160

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Discharged capacity, Ah

DC

resi

stan

ce, m

illio

hms

0

2

4

6

8

10

12

14

16

Bat

tery

ope

n ci

rcui

t vol

tage

, V

Battery resistance

Panel plus wire resistance

Battery open-circuit voltage 1 second

2 s

3 s4 s

5 s

10 s

Conclusion

• Proper motor selection, good wiring, an appropriate gear ratio, aligned mechanical components, and a full battery will keep you alive in the heat of the battle.

• Power loss is often a significant fraction of the power consumed. Include all losses in analysis.

• Analyze, but test, too!

• Have fun