1. Introduction to Motors Kurt Heinzmann DEKA Research & Development Corp. Christopher Mikus BAE Systems January 2005

2. 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?

3. Note These slides have been edited since the presentation on 7 Jan 2005. –Distinction has been made between torque constant K t and voltage constant K e, because, although in an ideal motor, K = K t = K e, K t and K e 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

4. 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

5. 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

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

7. 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

8. 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 Cooling a hot motor with snow or cold spray is not a suggested solution to heat generation. Changing the temperature of a motor’s components too quickly can cause permanent damage. Design your robot well to prevent motor overheating

9. 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

10. 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.

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 ( i stall ) Free speed (  free ) Free current ( i free )

13. Basic Motor Theory Important motor parameters Torque loss (  loss ) –We will derive this from free current –Unit: newtons (N) Resistance (R) –Ohm’s law –Unit: ohm (  ) Torque constant ( K t ) –Torque is proportional to current – Units: (Nm/A) ampere newton - metres volts _ radian/second Voltage constant ( K e ) –Motor internal voltage is proportional to speed – Units: V/(rad/s)

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 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.

16. Basic Motor Theory

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

18. Basic Motor Theory

19. Given:  stall, i stall,  free, i free and V, Find: K t, K e,  loss(free), and R. Important motor parameters 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

20. Find torque constant K t and voltage constant K e

21. Find torque loss  loss(free)

22. Find resistance R

23. Calculate current, speed, power and efficiency

24. From data sheet: From equation 3a: From equation 3b: From equation 4: From equation 5:  stall = 0.65 Nm i stall = 148 A  free = 2513 rad/s i free = 1.5 A  loss(free) = 0.0044 Nm/A x 1.5 A = 0.0066 Nm R = 12 V /148 A = 0.081  Example Motor K t = 0.65 Nm / (148.0-1.5) A = 0.0044 Nm/A Ke = (12 V -1.5 A*0.081  )/ 2513 rad/s = 0.0047 V/(rad/s)

25. Equations 6 - 11 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. Example Motor - Current

27. Example Motor - Speed

28. Example Motor - Power output

29. Example Motor - Input Power

30. Example Motor - Power loss Best operation is to the left of where these lines cross.

31. Example 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. 10 AWG wire: 1.2 m  /ft. 6 AWG wire: 0.5 m  /ft. (Copper at 65 °C)

34. 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

35. 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 Example motor, stalled for approximately 2 s

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

37. CIM motor (a.k.a. Chiaphua, a.k.a. Atwood) Be aware that a motor may have other names.

38. Stall torque  stall = 347 oz-in = 2.4 Nm Free speed  free = 5342 rpm = 560 rad/s Free current i free = 2.4 A Stall current i stall = 114 A CIM motor data and curves

39. CIM motor performance curves You will need to operate within the limits of the circuit breakers supplied with the kit! (20 A, 30 A, or 40 A)

40. Comparison of power available from example 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 P motor = P out /  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 P motor = P out /  g one stage: P motor = 150 W / 0.9 = 167 W two stages: P motor = 150 W / 0.9 /0.9 = 185 W three stages: P motor = 150 W / 0.9 /0.9 /0.9 = 206 W four stages: P motor = 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 Example motor

48. Gear ratio - example motor Check: gear ratio N g =  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 N g =  motor/  out = 388 / 100 = 3.9:1 Moderately heavy load for this motor (near peak power)

51. 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

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.

56. 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