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DC Permanent Magnet Motors A tutorial winch design

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Presentation on theme: "DC Permanent Magnet Motors A tutorial winch design"— Presentation transcript:

1 DC Permanent Magnet Motors A tutorial winch design
David Giandomenico Lynbrook High School Robotics FIRST Team #846 FIRST robots have drive trains, arms, winches, lifts…operated by DC permanent motors. In describing how to use motors, this tutorial lecture will discuss motor characteristics, efficient (and inefficient!) use of motors, gearbox friction, and general physics concepts such as torque, work, and power. December 2009 David Giandomenico D.Giandomenico D.Giandomenico

2 2004 FIRST Competition;Attach to 10ft high bar and
lift robot off ground. What is the design criteria? December 2009 David Giandomenico D.Giandomenico D.Giandomenico

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

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

5 “CIM” Motor Specification
Complicated. What do we look for? December 2009 David Giandomenico D.Giandomenico D.Giandomenico

6 “CIM” Motor Performance
Key data. All graphs can be determined from 4 numbers. In order, No Load speed (aka free speed), December 2009 David Giandomenico D.Giandomenico D.Giandomenico

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

8 How to get started? Which motor is most suited for our application?
December 2009 David Giandomenico D.Giandomenico D.Giandomenico

9 Choosing a motor based on Maximum Output Power
Calculate Energy required to lift load. Given the Time & Energy, calculate the mechanical Power required. Boost Power requirement to adjust for Friction in the gearbox and elsewhere. Choose a motor whose Maximum Output Power is at least 4/3 * (safety margin) Typical operating output power is no more than ¾ or 75% ( 1 over 4/3) of the Max Out power – which we will see later. Gearbox friction may be around 60-80%, depending on the # of gears among other factors. December 2009 David Giandomenico D.Giandomenico D.Giandomenico

10 December 2009 David Giandomenico D.Giandomenico D.Giandomenico

11 December 2009 David Giandomenico D.Giandomenico D.Giandomenico

12 www.johnsonmotor.com December 2009 David Giandomenico D.Giandomenico

13 Fisher Price Motor Data 2004
December 2009 David Giandomenico D.Giandomenico D.Giandomenico

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

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

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

17 Work, Torque & Speed but December 2009 David Giandomenico

18 Power, Torque & Speed December 2009 David Giandomenico D.Giandomenico

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

20 Fisher Price Motor 2004 V=12VDC
Area of boxes results in inverted parabola. December 2009 From FIRST_MOTOR_CALC.xls David Giandomenico D.Giandomenico D.Giandomenico

21 V=Rated Voltage Curve may be normalized December 2009
From FIRST_MOTOR_CALC.xls David Giandomenico D.Giandomenico D.Giandomenico

22 Speed & Torque in a DC PM Motor
Let ={0,100%} such that Speed indicated as N; Torque indicated by T December 2009 David Giandomenico D.Giandomenico D.Giandomenico

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

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

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

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

27 Fisher Price Motor Data 2004
December 2009 David Giandomenico D.Giandomenico D.Giandomenico

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

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

30 Motor Current Where α is the % No Load speed
Simple linear Model for Current. December 2009 David Giandomenico D.Giandomenico D.Giandomenico

31 Electrical Power With fixed 12V applied, then input power simply follows the current. December 2009 David Giandomenico D.Giandomenico D.Giandomenico

32 Fisher Price Motor 2004 Input power is Current X Voltage V=12VDC
Note: Io is commonly a few percent of I stall. Question: If we plotted the output power on the same graph, how would it look? Input power is Current X Voltage December 2009 From FIRST_MOTOR_CALC.xls David Giandomenico D.Giandomenico D.Giandomenico

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

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

35 Fisher Price Motor 2004 V=12VDC
Power out / Power In; Because we can write the output power and the input power as equations, we can also write an equation for the efficiency. With a little calculus it is also easy to write a formula for the speed that yields the Max Efficiency. December 2009 From FIRST_MOTOR_CALC.xls David Giandomenico D.Giandomenico D.Giandomenico

36 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. December 2009 David Giandomenico D.Giandomenico D.Giandomenico

37 Gear Loss Estimate or T = (100%-4%)3 = 88.5%
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 = in or T = (100%-4%)3 = 88.5% December 2009 David Giandomenico D.Giandomenico D.Giandomenico

38 When x is small, Answer: Why adding losses can be a reasonable approximation. Following slides have more detail why this is true for anyone who just has to know!  December 2009 David Giandomenico D.Giandomenico D.Giandomenico

39 Binomials: Note the binomial coeffients for 1st order y terms
Binomials: Note the binomial coeffients for 1st order y terms. In our case, x=1 December 2009 David Giandomenico D.Giandomenico D.Giandomenico

40 Yet more! Is there a way to easily determine the binomial coefficients?
December 2009 David Giandomenico D.Giandomenico D.Giandomenico

41 Pascal’s Triangle 1 1 1 1 1 1 December 2009 David Giandomenico D.Giandomenico D.Giandomenico

42 Binomial Theorem December 2009 David Giandomenico D.Giandomenico

43 Estimate of how many gear sets.
Suppose we want a gear reduction of How many gear sets with a reduction of 3 do we need? Solve 3N = 1200 N = ln(1200)/ln(3) = 6.45 …Back to the task at hand. We need a winch that can turn fairly slowly. How can we determine gearhead efficiency when we don’t know what the gearing arrangement will be? December 2009 David Giandomenico D.Giandomenico D.Giandomenico

44 Gear loss estimate We need :1 gear sets. Assuming a loss of 4% for each gear set, T = in or T = (1-4%)6.45 = 76.8% Clearly, we can’t have 6.45 gear sets, a non-integer quantity. But as an estimate, this number is sufficient. December 2009 David Giandomenico D.Giandomenico D.Giandomenico

45 Putting it all together
Choose a winch drum size Calculate the drum rpm Choose the % motor operating speed Calculate the required gear reduction to operate at that speed Verify the output winch line force meets or exceeds the original specification, including gear box losses Other methods are possible, and perhaps preferable. This is straightforward, requiring a bit of trial and error, but without the complexity of completely analyzing all the tradeoffs. December 2009 David Giandomenico D.Giandomenico D.Giandomenico

46 Winch Design Specification
December 2009 David Giandomenico D.Giandomenico D.Giandomenico

47 Winch Drum Speed December 2009 David Giandomenico D.Giandomenico

48 Determine the Gear Reduction
December 2009 David Giandomenico D.Giandomenico D.Giandomenico

49 Gear Loss Estimate December 2009 David Giandomenico D.Giandomenico

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

51 Feat Accomplished! 171 lb exceeds required spec of 130lbs
Did we overdesign the winch? How will the winch respond when lifting 130 lbs, if it is pulling with 171 lbs? How do we build this winch? December 2009 David Giandomenico D.Giandomenico D.Giandomenico

52 More than you wanted to know about Robot Winch Design
David Giandomenico Lynbrook High School Robotics FIRST Team #846 (408) December 2009 David Giandomenico D.Giandomenico D.Giandomenico

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