Download Intro_to_Motors Workshop

Introduction to Motors
Kurt Heinzmann
DEKA Research & Development Corp.
Christopher Mikus
BAE Systems
January 2005
Introduction to Motors
Topics
1. Manufacturers' torque curves and specification sheets
2. How to manage motor temperature rise
3. Gear ratio
4. Review of motors from the Kit of Parts
5. Which motor for which application on a robot?
Note
• These slides have been edited since the
presentation on 7 Jan 2005.
– Distinction has been made between torque
constant Kt and voltage constant Ke,
because, although in an ideal motor,
K = Kt = Ke, Kt and Ke differ significantly in
a gearmotor. Some of the motors in the kit
are gearmotors.
– New material was added
• Advice balloons
• Comparison of motors in the Kit
• Clarification of gear ratio selection
Steps
•
•
•
•
•
•
•
•
•
•
•
•
Assumptions and approximations
Power
Power loss in the mechanism
Power required at the motor
Power loss in the motor
Basic motor theory
Important motor parameters
Power loss in the motor
Power loss in other electrical components
Gear ratios
Comparison
Batteries
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)
Example motor
3.0
2.5
y = 0.11x + 0.53
Ifree, A
2.0
Current
1.5
Linear (Current)
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
Cooling a hot motor with
snow or cold spray is not a
– Contamination
suggested solution to heat
• Power loss is heat
generation. Changing the
temperature of a motor’s
components too quickly can
cause permanent damage.
Design your robot well to
prevent motor overheating
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
Design your robot’s drive
train such that it won’t
bind under stress and
add excessive friction to
your system. Reduce
friction and loading by
properly supporting axles
with bearings and pillow
blocks. Reduce side
loading by supporting
both ends of axles and
drive shafts.
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
• Electrical power gets converted to mechanical
power.
– If you express electrical power and mechanical
power in watts, you know what’s happening at both
ends of the motor.
– 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
FIRST rules do not
allow you to modify
the internal
components of a
motor. Read the
current year's rules
to understand how
you may modify gear
boxes if at all.
Basic Motor Theory
Important motor parameters
Given:
stall, istall, free, ifree and V,
Find: Kt, Ke,
loss(free), and R.
Some motors have an internal circuit breaker,
which will stop the motor, or PTC thermistor*,
which will stop or slow the motor by increasing its
electrical resistance, if the motor gets too hot.
After the motor cools, it runs normally again.
Examples:
Window motor
Sliding door motor
*PTC thermistor - resistor with a
positive temperature coefficient
Find torque constant Kt and
voltage constant Ke
Find torque loss
loss(free)
Find resistance R
Calculate current, speed, power and efficiency
Example Motor
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)
Example Motor - Current
Example motor
160
148 A
Speed (rad/s); Power (W)
140
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
Example Motor - Speed
Example motor
2500
Speed (rad/s); Power (W)
2000
1500
1000
500
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Example Motor - Power output
Example motor
Speed (rad/s); Power (W)
2000
1500
1000
500
407 W
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Example Motor - Input Power
Example motor
2000
1800 W
Speed (rad/s); Power (W)
Output power, W
Input 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
Example Motor - Power loss
Example motor
2000
1800 W
Output power, W
Speed (rad/s); Power (W)
Power loss, W
Input power, W
1500
1000
Best operation is
to the left of where
these lines cross.
500
407 W
0
0.00
0.10
0.20
0.30
0.40
Torque (Nm)
0.50
0.60
0.70
Example Motor - Efficiency
Example motor
100
90
Speed (rad/s); Power (W)
80
76%
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
Example motor
2500
250
Output power, W
Speed, rad/s
Power loss, W
Current, A
Efficiency
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)
2000
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)
Example motor, stalled for approximately 2 s
160
16
140
14
Example motor, stalled for approximately 2 s
120
12
100
10
Motor winding temperature measurement
80
8
Current
Motor terminal voltage
60
Voltage, V
Current, A; Temperature, °C;
Resistance, mOhm
~ Smoke ~
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
•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
Example motor, stalled for approximately 2 s
160
Temperature, °C; Resistance, mOhm
140
Example 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
Example motor
2500
250
Output power, W
Speed, rad/s
Power loss, W
200
Current, A
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
(a.k.a. Chiaphua, a.k.a. Atwood)
Be aware that a motor may
have other names.
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
You will need to
operate within the
limits of the circuit
breakers supplied
with the kit!
(20 A, 30 A, or 40 A)
Speed (rad/s); Power (W)
1200
140
Output power, W
Speed, rad/s
120
Power loss, W
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 (%)
1400
Comparison of power available from
example motor and CIM motor
Comparison of power available from example motor and CIM motor
450
Example 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 example motor and CIM motor
2500
500
Speed, Example motor
Speed, CIM motor
Example 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 example motor and CIM motor
2500
500
Speed, Example motor
Speed, CIM motor
Example 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
Example motor
Gear ratio - example motor
Choosing operating point for example motor
2500
500
Speed, Example motor
Power, example motor, R increased by 75%
2000
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
Operating point
1850 rad/s
Speed, rad/s
400
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
– 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,
Reference
Stall torque Stall Stall
Free Free Free
10.5 V
Voltage on Gear (as from
torque current speed speed current supply
data sheet ratio data sheet) (Nm) (A)
(rpm) (rad/s) (A)
(W)
12
647 mNm
12
346.9 oz-in
12
181
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
0.647
148 24000
2513
1.5
312
2.45
114
5342
559
2.3
261
77
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
6.3 Ah
6
Panel voltage
4
2
0
0
5
10
Time, minutes
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 planning up front will keep you alive in the heat
of the battle.
• Wisely choose the role that a motor will play on your
robot. Remember that most of these motors were
originally designed for applications other than a
competition robot.
• Test the conditions in which a motor is used and
calculate conditions when possible. If you operate
below the limits recommended here, your motors are
likely to be be trouble-free.
• Good Luck