Transcript Introduction to Motors - FIRST Robotics Resource Center

Motors:
a System Approach
Kurt Heinzmann
DEKA Research & Development Corp.
January 2007
General Topics
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Example problems
Problem formulation and analysis
Manufacturers' torque curves and specification sheets
Temperature rise
Power loss in battery, wires and other components
Gear ratio
Review of motors from a previous Kit of Parts
Background
•
•
•
•
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Energy
Power
Power loss
Analysis
Test
Energy
• Work is energy.
• Example: “effort” times “displacement”
– Force is effort
– Distance is displacement
Power
• Power is how fast work gets done.
• Example: “effort” times “speed”
Power
• Power is a measure of how fast work gets done.
• POWER = EFFORT x FLOW (speed)
“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. Overloading will cause
excessive temperature rise. Use appropriate
gear ratio.
Analysis
• Example problems
• Important motor parameters
• Motor model revised to include other losses
(wires, battery, switches, fuses, etc.)
• Gear ratio
Basic Theory
• Torque is rotating EFFORT, speed is
rotating FLOW
– Torque = force x radius
• Voltage is electrical EFFORT, current is
FLOW of electrons
• Power = EFFORT x FLOW
– Mechanical power P(mech) = torque x speed
– Electrical power P(elec) = voltage x current
Units, Conversions
International System (SI) of units
Symbol
used
Item
Comment
here
Force
Mechanical effort
Distance
Mechanical displacement
Speed
Travelling speed
Torque
 Turning effort
Angle
Angular displacement
Speed
 Rotating speed
Time
Don’t have much
Voltage
V
Electrical effort
Current
i
Electrical flow
Power
P
Rate of work
Resistance
R Cause of power loss as heat
Energy
Work
Pressure
Fluid effort
Flow
Fluid flow (at stated pressure)
AbbrevSI unit
iation
newton
N
metre
m
metre/second m/s
newton metre Nm
radian
rad
radian/second rad/s
second
s
volt
V
ampere
A
watt
W
ohm

joule (Nm)
J
pascal (N/m2) Pa
cubic metre/s m3/s
Alternate
unit
lb.
In.
mph
lb-in
degree
rpm
min., h
Conversion
1 lb. = 4.45 N
1 in. = 0.0254 m
1 mph = 0.45 m/s
360 ° = 2 rad
1 rpm = 0.105 rad/s
1 h = 3600 s
hp
1 hp = 746 W
ft-lb
psi
CFM
1 psi = 6900 Pa
1 CFM = 0.00047 m3/s
Prefixes: m = milli- = one thousandth (mm, mNm)
k = kilo- = one thousand (km, kW)
Why use SI units?
• Fewer mistakes than when using U.S.
Customary units
• A motor converts electrical power to mechanical
power.
– If we express electrical power and mechanical power
in the same units (watts), we know what’s happening
at both ends of the motor, and inside it.
• Many are named after famous scientists
• Advice: Convert each parameter to SI units
before doing any other calculation.
• Consolation: you can always convert back to
US customary units.
Problem 1
Accelerate to a speed
Problem 1
Mass: m = 150 lb. = 68 kg
Speed: v = 6 ft./s = 1.8 m/s
Acceleration: a = 1.8 m/s per second = 1.8 m/s2
Force = m x a = 68 kg x 1.8 m/s2 = 122 N
Force from each wheel: F = 122 N / 2 = 61 N
Power: P = F x v = 61 N x 1.8 m/s = 110 W
Problem 2
Lift a weight a distance within a time
Problem 2
Gravitational constant: g = 9.8 m/s2
Weight: W = 14 lb. = 61 N
Force: F = W = 61 N
Height: h = 6 ft. = 1.8 m
Time: t = 4 s
Speed: v = 1.8 m/ 4 s = 0.45 m/s
Power: P = F x v = 61 N x 0.45 m/s = 28 W
Basic Motor Theory
Electrical Components
Basic Motor Theory
Basic Motor Theory
Important motor parameters
• Applied voltage ( V )
• Stall current
( stall )
( istall )
• Free speed
( free )
• Stall torque
• Resistance ( R )
Fisher-Price Motor
Fisher-Price Motor (2005)
From data sheet:
Stall torque

Stall current
istall = 148 A
Free speed
stall

= 0.65 Nm
free
= 2513 rad/s
Reference voltage V = 12 V
Calculate:
Resistance R = 12 V /148 A = 0.081 
Fisher-Price Motor – Current
(For detailed analysis, see " Getting the Most
From Your Motors" by Kurt Heinzmann, 2006)
Fisher-Price 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
Fisher-Price 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
Fisher-Price 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
Fisher-Price 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
Fisher-Price 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
Fisher-Price 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
Speed (rad/s); Power (W)
2500
Output power, W
2000
Speed, rad/s
1500
1000
500
407 W
0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Stall
Torque (Nm)
Peak power occurs when torque =
and when speed =

free
/2

stall
/ 2,
0.70
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)
Resistance of electrical
system components
Component (Resistance is
expressed in ohms)
Motor (nominal)
Hot motor (40% increase)
Battery
Wires (10 ft. of 12 AWG)
Breakers, connectors, switch
Total
Ratio
R(system)/R(motor nominal)
FisherPrice
JIDECO
Power
window lift
Wheels CIM
motor
motor
motor
0.570
0.081
0.105
0.798
0.030
0.019
0.020
0.867
0.113
0.030
0.019
0.020
0.182
0.147
0.030
0.019
0.020
0.216
1.5
2.3
2.1
Simplified electrical system
model
System model
Additional resistance reduces stall torque
proportionally.
Divide the stall torque on the torque/speed
diagram by the factor Rsystem/Rmotor(nominal)
Fisher-Price: stall = 0.65 Nm/2.3 = 0.28 Nm
Performance of the system compared with
motor performance based on data sheet
Fisher-Price motor
2500
Output power, W
Speed (rad/s); Power (W)
2000
Speed, rad/s
1500
1000
DATA SHEET
SYSTEM
500
(Was 407 W)
0
0.00
Stall: 0.28 Nm
173 W
0.10
(Was
0.65 Nm)
0.20
0.30
0.40
Torque, Nm
0.50
0.60
0.70
CIM motor
(also known as Chiaphua and Atwood)
CIM motor data and curves
Stall torque

stall
= 347 oz-in = 2.45 Nm
Stall current istall = 114 A
Free speed

free
= 5342 rpm = 560 rad/s
Free current ifree = 2.4 A
Rsystem/Rmotor(nominal) = 2.1
Comparison of power available from
Fisher-Price Motor and CIM motor
Motor power after including system losses
450
400
Fisher-Price in system
CIM in system
Output power, W
350
300
250
200
173 W
155 W
150
100
50
Stall: 2.45 Nm/2.1 = 1.2 Nm
0
0.00
0.50
1.00
1.50
Torque, Nm
2.00
2.50
Mechanical Components
Gear ratio Ng =
 /
in
out
Gear efficiency ηg = Pout/Pin

out
=

in
/ Ng;

out
= ηg x Ng x

in
"Gear" ratio:
Mechanical power transmission
efficiency is important
•
•
•
•
•
•
•
Spur gears: 90% per pair
Worm and gear: 10%-60%
Nut on a screw: 10%-60%
Twist cables: 30%-90%
Chain: 85%-95%
Wire rope (cables): up to 98%
Rack and pinion 50%-80%
System with gearbox
Gear ratio example
Fisher-Price motor with gear reduction
Given:
Gear ratio Ng = 4.6:1
Gear efficiency ηg = 90%
Calculate:
Output torque out = ηg x Ng x in = 4.14 x in
Output speed out = motor / Ng = 0.217 x motor
Is the little motor/gearbox combination the
same as the big motor?
Comparison of CIM (straight) with Fisher-Price geared down 4.6:1
(gear efficiency = 90%)
1000
200
CIM speed in system
900
Fisher-Price speed in system, 4.6:1
Fisher-Price power in system, 4.6:1
160
700
140
600
120
500
100
400
80
300
60
200
40
100
20
0
0
0.0
0.2
0.4
0.6
0.8
Torque, Nm
1.0
1.2
1.4
Output power, W
Output speed, rad/s
CIM power in system
157 W
800
180
The big (CIM) motor will not heat
up as fast as the small motor,
because it contains more material.
Problem 1
( v = 1.8 m/s; F = 61 N)
Motor speed: motor = free /2 = 559 rad/s/2 = 280 rad/s
We wish to try 8" wheels: Rwheel = 4" = 0.1 m
Wheel speed: motor = v / Rwheel = (1.8 m/s)/(0.1 m) = 18 rad/s
Gear ratio: Ng = motor / wheel = (280 rad/s)/(18 rad/s) = 16
Check torque and propulsion force:
Usual limit per stage is 5:1 - need two stages.
Gear efficiency: ηg = 0.9 x 0.9 = 0.81
Wheel torque:

wheel
= ηg x Ng x
Force: F =

wheel

stall
/2 = 0.81 x 16 x 1.2 Nm/2 = 7.8 Nm
/Rwheel = (7.8 Nm)/(0.1 m) = 78 N (OK)
Just right
CIM motor as wheel drive motor,
Geared 16:1 (81% gear efficiency)
100
200
CIM speed in system, 16:1
90
180
CIM power in system, 16:1
80
160
140
125 W
60
120
50
100
40
80
30
60
20
40
10
20
0
0.0
1.0
2.0
3.0
4.0
5.0
Torque, Nm
6.0
7.0
8.0
9.0
0
10.0
Output power, W
Output speed, rad/s
70
Problem 2
( v = 0.45 m/s; F = 61 N)
We wish to try a screw with Fisher-Price motor.
Screw speed = motor speed: screw = free / 2 = 2513 rad/s/2 =
1256 rad/s

screw
=(1256 rad/s)/(2π rad/revolution) = 200 rev./s
Screw pitch:
p = v/screw = (0.45 m/s)/(200 rev./s) = 0.00225 m/rev. = 0.00036 m/rad
(11 threads per inch).
Check torque and force:
Assume screw efficiency = 20%
Torque: screw = motor = stall / 2 = 0.28 Nm/2 = 0.14 Nm
Force:
F = ηg x

screw
/ p = (0.2 x 0.14 Nm)/(0.00036 m/rad) = 78 N (OK)
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
180.8
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
Resistance
(ohm)
2513
1.5
312
0.08
2.45
114
5342
559
2.3
261
0.11
77
148
133
13.9
2.5
203
0.08
0.247
21.5
9390
983
0.4
46
0.56
30
44
75
7.9
2.7
44
0.24
13
21.5
80
8.4
0.58
24
0.56
12.6
9.2 Nm
9.2
24.8
92
9.6
2.8
16
0.51
12
8.33 Nm
8.33
21
85
8.9
3
14
0.57
12
620 g-cm
0.061
5.2
4700
492
0.22
5.7
2.31
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
1
0.01
Globe with
its gearhead
0.1
1
Torque, Nm
10
Fisher-Price
with
its gearbox
100
Keep batteries charged.
Battery voltage with pulse load:
Discharge current: 50 A for 10 s, 0 A for 10 s (shared between two 30 A breakers).
Battery nominal capacity when discharged at 0.9 A (20 hour discharge rate): 18 Ah
Discharged capacity, Ah; Voltage, V
16
14
12
10
8
Battery voltage
6
Discharged capacity
6.3 Ah
4
2
0
0
5
10
Time, minutes
Delivered capacity was only one third of rated capacity.
15
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 used to do work. Include all losses in
analysis.
• Analyze, but test, too!
• Have fun