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Design Realization lecture 20

Design Realization lecture 20. John Canny 10/30/03. Last time. Real-time programming . This time. Mechanics – Physics and Motors. Review of physics. Newton’s law for translation: F = m a F in Newtons, m in kg, a in m/s 2 . Acceleration a = dv / dt

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Design Realization lecture 20

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  1. Design Realization lecture 20 John Canny 10/30/03

  2. Last time • Real-time programming

  3. This time • Mechanics – Physics and Motors

  4. Review of physics • Newton’s law for translation: F = m aF in Newtons, m in kg, a in m/s2. • Acceleration a = dv / dt • Kinetic energy E = ½ m v2E in Joules, m in kg, v in m/s.

  5. Physics of translation • Momentum p = m v and so F = dp / dt • In the absence of force, momentum is conserved. • Momentum conservation implies energy conservation.

  6. Physics of rotation • Rotation is more complex; Euler’s equation:T = I  +  x I T (torque) in N-m,  in radians/sec,  in radians/sec2, I in kg-m2,  = d / dt • I is a 3x3 matrix, not necessarily diagonal. • If T = 0, then I  = -  x I  which is usually non-zero. So  is non-zero,  changes with time, and the object wobbles.

  7. Physics of rotation • Angular momentum is q = I  • The rotation equation simplifies to T= dq / dt becausedq/dt = I d/dt + dI/dt  = I  +  x I  • So even though an object wobbles when there is no external force, the angular momentum is conserved: q = I 

  8. Physics of rotation • Kinetic energy of rotation is ½ T I  • In the absence of external torque, kinetic energy of rotation is conserved. • But angular momentum conservation does not imply energy conservation.

  9. Work • Work done by a force = F x (Joules) where x is the distance (m) through which the force acts. • Work done by a torque = T  (Joules)

  10. Power • Power is rate of doing work. • Power of a force = F v (Watts). • Power of a torque = T  (Watts). • Power often expressed in horsepower = 746 Watts

  11. Motors • Motors come in several flavors: • DC motors • Stepper motors • (AC) induction motors • (AC) Single-phase motors • (AC) Synchronous motors • The first two are highly controllable, and usually what you would use in an application. But we quickly review the others.

  12. 3-phase AC • Three or four wires that carry the same voltage at 3 equally-spaced phases: • Single phase AC requires two wires (only 1/3 the current or power of 3-phase).

  13. AC induction Motors • Induction motors – simple, cheap, high-power, high torque, simplest are 3-phase. • Speed up to 7200 rpm: speed ~ 7200 / # “poles” of the motor. • Induction motors are brushless (no contacts between moving and fixed parts). Hi reliability. • Efficiency high: 50-95 %

  14. Single-phase AC Motors • Single-phase (induction) motors – operate from normal AC current (one phase). Household appliances. • Single-phase motors use a variety of tricks to start, then transition to induction motor behavior. • Efficiency lower: 25-60% • Often very low starting torque.

  15. Synchronous AC Motors • Designed to turn in synchronization with the AC frequency. E.g. turntable motors. • Low to very high power. • Efficiency ??

  16. DC Motors • DC motor types: • DC Brush motor • “DC” Brushless motor • Stepper motor

  17. DC Brush Motors • A “commutator” brings current to the moving element (the rotor). • As the rotor moves, the polarity changes, which keeps the magnets pulling the right way. DEMO • Highly controllable, most common DC motor.

  18. DC Brush Motors • At fixed load, speed of rotation is proportional to applied voltage. • Changing polarity reverses rotation. • To first order, torque is proportional to current. • Load curve: • Motors which approximate thisideal well arecalled DC servomotors.

  19. DC Brushless Motors • Really an AC motor with electronic commutation. • Permanent magnet rotor, stator coils are controlled by electronic switching. DEMO • Speed can be controlled accurately by the electronics. • Torque is often constant over the speed range.

  20. Stepper Motors • Sequence of (3 or more) poles is activated in turn, moving the stator in small “steps”. • Very low speed / high angular precision is possible without reduction gearing by using many rotor teeth. • Can also “micro-step” by activatingboth coils at once.

  21. Driving Stepper Motors • Note: signals to the stepper motor are binary, on-off values (not PWM). • In principle easy: activate poles as A B C D A… or A D C B A…Steps are fixed size, so no need to sense the angle! (open loop control).

  22. Driving Stepper Motors • But in practice, acceleration and possibly jerk must be bounded, otherwise motor will not keep up and will start missing steps (causing position errors). • i.e. driver electronics must simulate inertia of the motor.

  23. Stepper Motor example • From Sherline CNC milling machine: • Step angle: 1.8° • Voltage: 3.2 V • Holding torque: 0.97 N-m • Rotor inertia: 250 g-cm2 • Weight: 1.32 lb (0.6 Kg.) • Length: 2.13" (54 mm) • Power output = 3W • Precision stepper motor: 0.02° /step, 1 rpm, 3W

  24. DC Motor example • V = 12 volts • Max Current = 4 A • Max Power Out = 25 W • Max efficiency = 74% • Max speed = 3500 rpm • Max torque = 1.4 N-m • Weight = 1.4 lbs • Forward or reverse (brushed) • Many DC motors of all sizes available new and surplus for < $10

  25. DC Motors – micro sizes • From Micromo: • Conventional (brush)DC motor: 6mm x 15mm • 13,000 rpm • 0.11 m Nm • Power 0.15 W • V from 1.5 to 4.5 V

  26. Brushless DC Motors • From Micromo: • Brushless DC motor: 16mm x 28mm • 65,000 rpm • 50 m Nm • Power 11 W • V = 12 V

  27. DC Motors – gearing • Gearing allows you to trade off speed vs. torque. • An n:1 reduction gearing decreases speed by n, but increases torque by n. • Ratios from 10:1 to many 1000s :1 are available in compact “gearheads” that attach to motors.

  28. DC Motors – gearing • But gears cost efficiency (20% - 50%) • Gears decrease precision (due to backlash). • Reduction gear train is normally not backdriveable (can’t use for “force control”).

  29. DC torque motors • Some high-end motors are available for direct drive servo or force applications (no gears). • They have low speed (a few rpm), high precision (with servo-ing), and moderate torque. • Typically have large diameter vs. length, and use rare-earth magnetic material. • Cost $100’s (but maybeless as surplus).

  30. Sensors • Shaft encoders can be fitted to almost any DC motor. They provide position sensing. • Many motor families offer integrated encoders. • Strain gauges can be used to sense force directly. Or DC brush motor current can be used to estimate force.

  31. Linear movement • There are several ways to produce linear movement from rotation: • Rotary to linear gearing:

  32. Linear movement • Ball screws: low linear speed, good precision • Motor drives shaft, stages move (must be attached to linear bearing to stop from rotating).

  33. Linear movement • Belt drive: attach moving stage to a toothed belt: • Used in inkjet printers and some large XY robots.

  34. True Linear movement • There are some true linear magnetic drives. • BEI-Kimco voice coils: • Up to 1” travel • 100 lbf • > 10 g acceleration • 6 lbs weight • 500 Hz corner frequency. • Used for precision vibration control.

  35. Summary • AC motors are good for inexpensive high-power applications where fine control isnt needed. • DC motors provide a range of performance: • DC brush: versatile, “servo” motor, high speed, torque • DC brushless: speed/toque depend on electronics • Stepper: simple control signals, variable speed/accuracy without gearing, lower power • Direct-drive (torque) motors, expensive, lower torque • Linear actuation via drives, or voice coils.

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