Design Realization lecture 20

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Design Realization lecture 20

• John Canny
• 10/30/03

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Last time

• Real-time programming

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This time

• Mechanics Physics and Motors

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Review of physics

• Newtons 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.

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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.

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Physics of rotation

• Rotation is more complex Eulers 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.

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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 ?

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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.

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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)

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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

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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.

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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).

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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

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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.

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Synchronous AC Motors

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

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DC Motors

• DC motor types
• DC Brush motor
• DC Brushless motor
• Stepper motor

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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.

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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.

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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.

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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.

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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 ASteps are fixed size, so no need to
  sense the angle! (open loop control).

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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.

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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

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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 lt 10

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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

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Brushless DC Motors

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

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DC Motors gearing

• Gearing allows you to trade off speed vs. torque.
  
• An n1 reduction gearing decreases speed by n,
  but increases torque by n.
• Ratios from 101 to many 1000s 1 are available
  in compact gearheads that attach to motors.

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DC Motors gearing

• But gears cost efficiency (20 - 50)
• Gears decrease precision (due to backlash).
• Reduction gear train is normally not
  backdriveable (cant use for force control).

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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 100s (but maybeless as surplus).

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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.

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Linear movement

• There are several ways to produce linear movement
  from rotation
• Rotary to linear gearing

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Linear movement

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

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Linear movement

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

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True Linear movement

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

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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.