1. December 2009 David Giandomenico DC Permanent Magnet Motors A tutorial winch design David Giandomenico Lynbrook High School Robotics FIRST Team #846 DGiandomenico@lynbrookrobotics.com (408)343-1183

2. December 2009 David Giandomenico

3. December 2009 David Giandomenico What We Want. Weight: Distance: Time (speed): 130 lbs 1.5 feet 5 seconds

4. December 2009 David Giandomenico What We’ve Got: Some of the Motors supplied in FIRST Robotics Kit

5. December 2009 David Giandomenico “CIM” Motor Specification

6. December 2009 David Giandomenico “CIM” Motor Performance

7. December 2009 David Giandomenico “CIM” Motor Performance Stall Current Stall Current Stall Torque Stall Torque No Load Current No Load Current No Load Speed

8. December 2009 David Giandomenico

9. December 2009 David Giandomenico Choosing a motor based on Maximum Output Power 1.Calculate Energy required to lift load. 2.Given the Time & Energy, calculate the mechanical Power required. 3.Boost Power requirement to adjust for Friction in the gearbox and elsewhere. 4.Choose a motor whose Maximum Output Power is at least 4/3 * (safety margin)

10. December 2009 David Giandomenico

11. December 2009 David Giandomenico

12. December 2009 David Giandomenico www.johnsonmotor.com

13. December 2009 David Giandomenico Fisher Price Motor Data 2004

14. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC

15. December 2009 David Giandomenico What is Torque? But isn’t that “Work”

16. December 2009 David Giandomenico Units of Work vs. Torque Work (Energy) Torque pound feet(lbf-ft), ft-lbf, oz-in, N-m … ft-lbf, Joules (=N-m), KWh, …

17. December 2009 David Giandomenico Work, Torque & Speed but

18. December 2009 David Giandomenico Power, Torque & Speed

19. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC (speed,torque)

20. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC

21. December 2009 David Giandomenico From FIRST_MOTOR_CALC.xls V=Rated Voltage

22. December 2009 David Giandomenico Speed & Torque in a DC PM Motor Let  ={0,100%} such that

23. December 2009 David Giandomenico From FIRST_MOTOR_CALC.xls V=Rated Voltage

24. December 2009 David Giandomenico Speed & Torque in a DC PM Motor Or, w/o calculus, Max occurs between two roots of quadratic, at  =0,  =1 that is,  =½ or equivalently, when  =50% Using calculus, Max Power occurs when:

25. December 2009 David Giandomenico From FIRST_MOTOR_CALC.xls V=Rated Voltage 75%

26. December 2009 David Giandomenico Max Power in a DC PM Motor

27. December 2009 David Giandomenico Fisher Price Motor Data 2004

28. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC

29. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC Current rises linearly with Torque

30. December 2009 David Giandomenico Motor Current Where α is the % No Load speed

31. December 2009 David Giandomenico Electrical Power

32. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC Input power is Current X Voltage

33. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC

34. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC

35. December 2009 David Giandomenico Fisher Price Motor 2004 From FIRST_MOTOR_CALC.xls V=12VDC

36. December 2009 David Giandomenico DC PM Motor Summary Max Power occurs at 50% No-Load Speed Best efficiency typically occurs at about 75%-85% No-Load Speed Most DC PM Motors will overheat if operated continuously at speeds less than 50% when full voltage is applied.

37. December 2009 David Giandomenico Gear Loss Estimate Suppose we have n=3 inline sets of gears, each with a 4:1reduction. What is the total efficiency if each gear set loses 4%?  T =  i n or  T = (100%-4%) 3 = 88.5%

38. December 2009 David Giandomenico When x is small,

39. December 2009 David Giandomenico

40. December 2009 David Giandomenico

41. December 2009 David Giandomenico Pascal’s Triangle 1 1 2 1 1 3 3 1 1 4 6 4 1 1 1 2 1 1 3 3 1 1 4 6 4 1

42. December 2009 David Giandomenico Binomial Theorem

43. December 2009 David Giandomenico Estimate of how many gear sets. Suppose we want a gear reduction of 1200. How many gear sets with a reduction of 3 do we need? Solve 3 N = 1200 N = ln(1200)/ln(3) = 6.45

44. December 2009 David Giandomenico Gear loss estimate We need 6.45 3:1 gear sets. Assuming a loss of 4% for each gear set,  T =  i n or  T = (1-4%) 6.45 = 76.8%

45. December 2009 David Giandomenico Putting it all together 1.Choose a winch drum size 2.Calculate the drum rpm 3.Choose the % motor operating speed 4.Calculate the required gear reduction to operate at that speed 5.Verify the output winch line force meets or exceeds the original specification, including gear box losses

46. December 2009 David Giandomenico Winch Design Specification

47. December 2009 David Giandomenico Winch Drum Speed

48. December 2009 David Giandomenico Determine the Gear Reduction

49. December 2009 David Giandomenico Gear Loss Estimate

50. December 2009 David Giandomenico Verify We Meet or Exceed Pull Strength Specification

51. December 2009 David Giandomenico Feat Accomplished! 171 lb exceeds required spec of 130lbs

52. December 2009 David Giandomenico More than you wanted to know about Robot Winch Design David Giandomenico Lynbrook High School Robotics FIRST Team #846 DGiandomenico@lynbrookrobotics.com (408)343-1183