1. Getting the Most From Your Motors
Kurt Heinzmann
DEKA Research & Development Corp.
January 2006

2. 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

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

4. 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

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

6. 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

7. 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

8. 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

9. Power loss in the motor
Power is lost in the motor due to friction, damping, and electrical resistance
Power loss is heat

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

11. 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

12. Basic Motor Theory Important motor parameters
Stall torque ( stall )
Stall current ( istall )
Free speed ( free )
Free current ( ifree )

13. Basic Motor Theory Important motor parameters
Torque constant ( Kt )
Torque is proportional to current
Units: (Nm/A)
newton-metres
ampere
Voltage constant ( Ke )
Motor internal voltage is proportional to speed
Units: V/(rad/s)
volts _
radian/second
Torque loss (loss)
We will derive this from free current
Unit: newtons (N)
Resistance (R)
Ohm’s law
Unit: ohm ()

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

15. 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.

16. Basic Motor Theory

17. Direct Current (DC), Permanent-Magnet (PM), Brush-Commutated Motor

18. Basic Motor Theory

19. Important motor parameters
Given these four parameters:
stall, istall, free, ifree and V,
Find these four parameters:
Kt, Ke, loss(free), and R.

20. Find torque constant Kt and voltage constant Ke

21. Find torque loss loss(free)

22. Find resistance R

23. Calculate current, speed, power and efficiency

24. stall = 0.65 Nm free = 2513 rad/s loss(free)
Fisher-Price Motor (2005)
stall = 0.65 Nm
From data sheet: From equation 3a: From equation 3b: From equation 4: From equation 5:
istall = 148 A
free = 2513 rad/s
ifree = 1.5 A
Kt = 0.65 Nm / ( ) A
= Nm/A
Ke = (12 V -1.5 A*0.081 )/ 2513 rad/s
= V/(rad/s)
loss(free)
= Nm/A x 1.5 A
= Nm
R = 12 V /148 A = 

25. Equations 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)

26. Fisher-Price Motor - Current

27. Fisher-Price Motor - Speed

28. Fisher-Price Motor - Power output

29. Fisher-Price Motor - Input Power

30. Fisher-Price Motor - Power loss

31. Fisher-Price Motor - Efficiency

32. Motor performance based on data sheet

33. Real World: Power loss 14 AWG wire: 3.0 m/ft. 12 AWG wire: 1.9 m/ft.
(Copper at 65 °C)

34. Fisher-Price Motor, stalled for approximately 2 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

35. Fisher-Price Motor, stalled for approximately 2 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

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

37. CIM motor (also known as Chiaphua and Atwood)

38. 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

39. CIM motor performance curves

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

41. 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

42. Performance curves re-calculated with R increased by 75%

43. "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%

44. Gear ratio Example: out = 1.5 Nm; out = 100 rad/s
Pmotor = Pout / g (12)

45. 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

46. 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

47. Gear ratio Fisher-Price Motor

48. Gear ratio - Fisher-Price Motor
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)

49. Gear ratio CIM motor

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

51. Gear ratio example Calculate current Choose motors based on
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

52. Summary of motors in the 2005 Kit of Parts Sorted by peak output power

53. Comparison of motors in the 2005 Kit of Parts

54. Keep batteries charged.
Delivered capacity was only one third of rated capacity.

55. Keep batteries charged.

56. 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