Motors: a System Approach

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Motors a System Approach

• Kurt Heinzmann
• DEKA Research Development Corp.
• January 2007

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• General Topics
• 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

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Background

• Energy
• Power
• Power loss
• Analysis
• Test

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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

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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

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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

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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

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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.

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Analysis

• Example problems
• Important motor parameters
• Motor model revised to include other losses
  (wires, battery, switches, fuses, etc.)
• Gear ratio

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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

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Units, Conversions
International System (SI) of units
Prefixes m milli- one thousandth (mm, mNm)
k kilo- one thousand (km, kW)
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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 whats
  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.

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Problem 1

• Accelerate to a speed

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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

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Problem 2

• Lift a weight a distance within a time

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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

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Basic Motor Theory
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Electrical Components
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Basic Motor Theory
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Basic Motor TheoryImportant motor parameters

• Applied voltage ( V )
• Stall torque ( ?stall )
• Stall current ( istall )
• Free speed ( ?free )
• Resistance ( R )

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Fisher-Price Motor
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From data sheet
Fisher-Price Motor (2005)
?stall 0.65 Nm
Stall torque Stall current Free speed Reference
voltage V 12 V
istall 148 A
?free 2513 rad/s
Calculate Resistance R 12 V /148 A 0.081 ?
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Fisher-Price Motor Current(For detailed
analysis, see " Getting the Most From Your
Motors" by Kurt Heinzmann, 2006)
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Fisher-Price Motor - Speed
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Fisher-Price Motor - Power output
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Fisher-Price Motor - Input Power
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Fisher-Price Motor - Power loss
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Fisher-Price Motor - Efficiency
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Motor performance based on data sheet
Peak power occurs when torque ?stall / 2, and
when speed ?free / 2
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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)
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Resistance of electrical system components
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Simplified electrical system model
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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

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Performance of the system compared with motor
performance based on data sheet
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CIM motor (also known as Chiaphua and Atwood)
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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
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Comparison of power available from Fisher-Price
Motor and CIM motor
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Mechanical Components

• Gear ratio Ng ?in / ?out
• Gear efficiency ?g Pout/Pin
• ?out ?in / Ng ?out ?g x Ng x ?in

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"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

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System with gearbox
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Gear ratio example
Fisher-Price motor with gear reduction
Given Gear ratio Ng 4.61 Gear efficiency ?g
90 Calculate Output torque ?out ?g x Ng x
?in 4.14 x ?in Output speed ?out ?motor / Ng
0.217 x ?motor
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Is the little motor/gearbox combination the same
as the big motor?
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• The big (CIM) motor will not heat up as fast as
  the small motor, because it contains more
  material.

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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 51 - need two stages.
• Gear efficiency ?g 0.9 x 0.9 0.81
• Wheel torque
• ?wheel ?g x Ng x ?stall /2 0.81 x 16 x 1.2
  Nm/2 7.8 Nm
• Force F ?wheel /Rwheel (7.8 Nm)/(0.1 m) 78
  N (OK)

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Just right
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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)/(2p 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 ?g x ?screw / p (0.2 x 0.14 Nm)/(0.00036
  m/rad) 78 N (OK)

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Summary of motors in the 2005 Kit of Partssorted
by peak output power
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Comparison of motors in the 2005 Kit of Parts
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Keep batteries charged.
Delivered capacity was only one third of rated
capacity.
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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