Download Getting_Most_From_Motors_2006

Getting the Most
From Your Motors
Kurt Heinzmann
DEKA Research & Development Corp.
January 2006
Getting the Most
From Your Motors
General Topics
•
•
•
•
•
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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
3.0
2.5
y = 0.11x + 0.53
Ifree, A
2.0
Current
Linear (Current)
1.5
Free current
per data
sheet
1.0
0.5
0.0
0
2
4
6
8
Voltage, V
10
12
14
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
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•
•
•
•
•
•
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 Theory
•
Important motor parameters
Torque constant ( Kt )
–Torque is proportional to current
– Units: newton-metres
ampere
(Nm/A)
• Voltage constant ( Ke )
–Motor internal voltage is proportional to speed
volts
_
– Units:
V/(rad/s)
radian/second
• Torque loss
(

loss)
– We will derive this from free current
– Unit: newtons (N)
• Resistance (R)
– Ohm’s law
– Unit: ohm ()
Units, Conversions
International System (SI) of units
Item
Force
Distance
Speed
Torque
Angle
Speed
Time
Voltage
Current
Power
Resistance
Energy
Pressure
Flow
Symbol
used
Comment
here
Mechanical effort
Mechanical displacement
Travelling speed
 Turning effort
Angular displacement
 Rotating speed
Don’t have much
V
Electrical effort
i
P
R
AbbrevSI unit
iation
newton
N
metre
m
metre/second m/s
newton metre Nm
radian
rad
radian/second rad/s
second
s
volt
V
Electrical flow
ampere
Rate of work
watt
Cause of power loss as heat ohm
Work
A
W
Alternate
unit
lb.
In.
mph
lb-in
degree
rpm
min., h
hp
Conversion
4.45 N = 1lb.
0.0254 m = 1 in.
0.45 m/s = 1 mph
2 rad = 360°
0.105 rad/s = 1 rpm
3600 s = 1 h
746 W = 1 hp

joule (Nm)
J
pascal (N/m2) Pa
Fluid effort
3
Fluid flow (at stated pressure) cubic metre/s m /s
ft-lb
psi
CFM
6900 Pa = 1 psi
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), BrushCommutated Motor
Basic Motor Theory
Important motor parameters
Given these four parameters:
stall, istall, free, ifree and V,
Find these four parameters:
Kt, Ke,
loss(free), and R.
Find torque constant Kt and
voltage constant Ke
Find torque loss
loss(free)
Find resistance R
Calculate current, speed, power and efficiency
Fisher-Price Motor (2005)
From data sheet:

stall
= 0.65 Nm
istall = 148 A

free
= 2513 rad/s
ifree = 1.5 A
From equation 3a: Kt = 0.65 Nm / (148.0-1.5) A
= 0.0044 Nm/A
From equation 3b: Ke = (12 V -1.5 A*0.081 )/ 2513 rad/s
= 0.0047 V/(rad/s)
From equation 4:
loss(free)
= 0.0044 Nm/A x 1.5 A
= 0.0066 Nm
From equation 5: R = 12 V /148 A = 0.081 
Equations 6 - 11 allow us to
calculate the following
performance curves as a function
of torque (with constant voltage):
•
•
•
•
•
•
current
speed
output power
input power
power loss
efficiency
(6)
(7)
(8)
(9)
(10)
(11)
Fisher-Price Motor - Current
Example motor
160
148 A
140
Current, A
120
100
80
60
40
20
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Fisher-Price Motor - Speed
Example motor
2500
Speed (rad/s)
2000
1500
1000
500
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Fisher-Price Motor - Power output
Example motor
2000
Power (W)
1500
1000
500
407 W
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Fisher-Price Motor - Input Power
Example motor
2000
1800 W
Output power, W
Input power, W
Power (W)
1500
1000
500
407 W
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Fisher-Price Motor - Power loss
Example motor
2000
Output power, W
1800 W
Power loss, W
Input power, W
Power (W)
1500
1000
500
407 W
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Fisher-Price Motor - Efficiency
Example motor
100
90
80
76%
Efficiency, %
70
60
50
40
30
20
10
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Motor performance based on data sheet
Fisher-Price motor
250
Output power, W
Speed, rad/s
Power loss, W
Current, A
Efficiency
2000
200
1800 W
148 A
1500
1000
150
100
76%
500
50
133 W
0
0.00
407 W
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0
0.70
Current (A); Efficiency (%)
Speed (rad/s); Power (W)
2500
Real World: Power loss
14 AWG wire:
12 AWG wire:
10 AWG wire:
6 AWG wire:
3.0 m/ft.
1.9 m/ft.
1.2 m/ft.
0.5 m/ft.
(Copper at 65 °C)
Fisher-Price motor, stalled for approximately 2 s
160
16
14
Fisher-Price Motor, stalled for approximately 2 s
~ Smoke ~
120
12
100
10
Motor winding temperature measurement
80
8
Current
Motor terminal voltage
60
Voltage, V
Current, A; Temperature, °C;
Resistance, mOhm
140
6
Battery voltage
40
4
20
2
0
0
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Time, s
Notes:
•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
Temperature, °C; Resistance, mOhm
160
140
Fisher-Price Motor, stalled for approximately 2 s
~ Smoke ~
120
100
Motor winding temperature measurement
80
Total circuit resistance
Motor resistance
60
Resistance of wires, connectors, breakers, etc.
40
Battery resistance
20
0
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Time, s
•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
Total circuit resistance increased to about
twice the initial motor resistance
Performance of the system compared with
motor performance based on data sheet
Fisher-Price motor
2500
250
Output power, W
Speed, rad/s
Power loss, W
Current, A
200
Efficiency
1500
150
1240 W
1000
100
95 A
500
68%
50
DATA SHEET
126 W
0
0.00
278 W
0.10
0.20
SYSTEM
0.30
0.40
Torque, Nm
0.50
0.60
0
0.70
Current (A); Efficiency (%)
Speed (rad/s); Power (W)
2000
CIM motor
(also known as Chiaphua and Atwood)
CIM motor data and curves
Stall torque

stall
= 347 oz-in = 2.4 Nm
Stall current istall = 114 A
Free speed

free
= 5342 rpm = 560 rad/s
Free current ifree = 2.4 A
CIM motor performance curves
CIM motor
1400
140
Output power, W
Speed, rad/s
1200
120
Current, A
1000
100
Efficiency
800
80
600
60
400
40
200
20
0
0
0.5
1
1.5
Torque, Nm
2
0
2.5
Current (A); Efficiency (%)
Speed (rad/s); Power (W)
Power loss, W
Comparison of power available from
Fisher-Price Motor and CIM motor
Comparison of power available from Fisher-Price motor and CIM motor
450
Fisher-Price motor
CIM motor
400
Output power, W
350
300
250
200
150
100
50
0
0
0.5
1
1.5
Torque, Nm
2
2.5
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
Performance curves re-calculated
with R increased by 75%
Comparison of power available from Fisher-Price motor and CIM motor
2500
500
Speed, Fisher-Price motor
Speed, CIM motor
Fisher-Price motor, R increased by 75%
CIM motor, R increased by 75%
2000
450
400
1500
300
250
<--- Stay to the left of the peak power point
1000
200
150
500
100
50
0
0
0
0.2
0.4
0.6
0.8
Torque, Nm
1
1.2
1.4
Output power, W
Speed, rad/s
350
"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%
Example:

Gear ratio
out = 1.5 Nm;
out = 100 rad/s
Pmotor = Pout / g
(12)
Gear ratio example
Output 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 example
Estimate 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
2500
500
Speed, Fisher-Price motor
Speed, CIM motor
Fisher-Price motor, R increased by 75%
CIM motor, R increased by 75%
4 stages
3 stages
2 stages
1 stage
1500
400
300
1000
200
0.1 Nm?
0.4 Nm?
500
100
0
0
0
0.1
0.2
0.3
0.4
Torque, Nm
0.5
0.6
0.7
0.8
Output power, W
Speed, rad/s
2000
Gear ratio
Fisher-Price Motor
Gear ratio - Fisher-Price Motor
Choosing operating point for Fisher-Price motor
2500
500
Speed, Fisher-Price motor
Power, Fisher-Price motor, R increased by
75%
Operating point
Speed, rad/s
1850 rad/s
400
1500
300
1000
200
Tw o stages: 185 W
500
100
0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Torque, Nm
Check: gear ratio Ng = motor/out = 1850 / 100 = 18.5:1 = 4.3 • 4.3
Operating point looks good (comfortably to the left of the peak power point)
Output power, W
2000
Gear ratio
CIM motor
Gear ratio - CIM motor
Choosing operating point for CIM motor
2500
500
Speed, CIM motor
Power, CIM motor, R increased by 75%
2000
400
1500
300
1000
200
One stage: 167 W
500
100
388 rad/s
0
0
0.1
0.2
0.3
0.4
0.43
Nm
Torque, Nm
0.5
0.6
0.7
Gear ratio Ng = motor/out = 388 / 100 = 3.9:1
Moderately heavy load for this motor (near peak power)
0
0.8
Output power, W
Speed, rad/s
Operating point
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
Number on
Supplier motor
Motor name
Fisher- 74550-0642 Power Wheels
Price
CIM
FR801-001 (Chiaphua,
Atwood)
Fisher- 74550-0642 Power Wheels
Price
Globe 409A586
2WD/4WD
transfer mtr.
Taigene 16638628 Sliding (van)
door
Globe 409A587
2WD/4WD
transfer mtr.
Nippon- E6DFWindow Lift
Denso 14A365-BB
Jideco
Window Lift
Mabuchi RS454SH
W/spur gear
ccw
Description
Motor only
Keyed output
shaft, ccw
Motor and
gearbox
Motor only
Peak
power,
Stall torque Stall Stall Free Free Free 10.5 V
(as from
torque current speed speed current supply
data sheet) (Nm) (A)
(rpm) (rad/s) (A)
(W)
Reference
Voltage on
data sheet Gear ratio
12
647 mNm
0.647
12
346.9 oz-in
2.45
114
77
12
180.8492308
12
Worm
Gearmotor
Planetary
Gearmotor
Worm
Gearmotor
Worm
Gearmotor
Spur pinion
on shaft
35 oz in
34 Nm cw,
30 Nm ccw
10.5
12
117
148 24000
2513
1.5
312
5342
559
2.3
261
148
133
13.9
2.5
203
0.247
21.5
9390
983
0.4
46
30
44
75
7.9
2.7
44
13
21.5
80
8.4
0.58
24
12.6
9.2 Nm
9.2
24.8
92
9.6
2.8
16
12
8.33 Nm
8.33
21
85
8.9
3
14
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
100000
Speed, rad/s
10000
Fisher-Price motor alone
1000
Globe motor alone
500 W
200 W
Mabuchi
CIM
100 W
100
50 W
20 W
10 W
10
5W
Nippon
Taigene
Jideco
Globe with
gearhead
1
0.01
0.1
1
Torque, Nm
10
FisherPrice with
gearbox
100
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
Discharged capacity, Ah; Voltage, V
16
14
12
10
Battery voltage
8
Discharged capacity
6
6.3 Ah
Panel voltage
4
2
0
0
5
10
Time, minutes
Delivered capacity was only one third of rated capacity.
15
Keep batteries charged.
Battery DC resistance during pulsed discharge.
Pulse: 50 A for 10 s, 0 A for 10 s
Resistance calculated from voltage drop and pulse current, at 1 s intervals throughout the pulse.
16
140
10 s
14
120
5s
12
4s
3s
Battery resistance
100
10
2s
Panel plus wire resistance
80
8
Battery open-circuit voltage
1 second
60
6
40
4
20
2
0
0
0.0
1.0
2.0
3.0
4.0
5.0
Discharged capacity, Ah
6.0
7.0
8.0
Battery open circuit voltage, V
DC resistance, milliohms
160
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