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Basic Mechanics Presentation
Basic Mechanics – Physics and Motors
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Motion Control RequirementsMotion Control Applications must be:1. Predictable2. Verifiable 3. Controllable
Design Considerations:• Accuracy
– Stiffness– Environment
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Design Considerations
•Accuracy
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4
Accuracy Accuracy vs. Precision
• Accuracy doesn’t mean Precision
• Accuracy represents the ability to get closest to a defined point.
• Precision is the ability to execute a move and return to the same point (regardless of accuracy).
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5
Accuracy Accuracy vs. Precision
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Accuracy ResolutionWhile Resolution is not Accuracy…
It is part of what makes up Accuracy
Two parts of Resolution1. Electrical Resolution2. Mechanical Resolution
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Design Considerations
•Accuracy– Stiffness
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What Exactly is Stiffness?SE
RVO
STIFFNESS
MOTOR
MECHANICALELECTROMATE
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StiffnessSE
RVO
STIFFNESS
MOTOR
MECHANICALELECTROMATE
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Stiffness Motor
• Motor Stiffness– Mechanical stiffness
– Ability to respond to commanded motion
– Flux pattern (Magnetic Servo)
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Stiffness Mounting / Drive location
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Stiffness Mounting / Drive location
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Design Considerations
•Accuracy–Stiffness–Environment
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Environment Position Feedback Control Schemes
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Environment Position Feedback Control Schemes
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Environment Position Feedback Control Schemes
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Environment Position Feedback Control Schemes
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Environment Position Feedback Control Schemes
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Environment External forces
• Side Loading
• Motor resonance
• System harmonicsELECTROMATE
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Vibration – Nearby Conditions
• Other machinery
• Road traffic
• Building sway
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Review of physics• Newton’s law for translation:
F = m a F in Newtons, m in kg, a in m/s2.
• Acceleration a = dv / dt
• Kinetic energy E = ½ m v2
E in Joules, m in kg, v in m/s.ELECTROMATE
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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; Euler’s equation:
T = I α + ω x I ω T (torque) in N-m, ω in radians/sec, α in
radians/sec2, I in kg-m2, α = dω / dt
• I is a 3x3 matrix, not necessarily diagonal.
• If T = 0, then I α = - ω x I ω
which is usually non-zero. So α is non-zero, ω changes with time, and the object wobbles.
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Physics of rotation• Angular momentum is q = I ω
• The rotation equation simplifies to T = dq / dt because
dq/dt = I dω/dt + dI/dt ω = I α + ω x I ω
• So even though an object wobbles when there is no external force, the angular momentum is conserved: q = I ω
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Physics of rotation• Kinetic energy of rotation is ½ ωT I ω
• 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 θ (Joules) ELECTROMATE
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Power• Power is rate of doing work.
• Power of a force = F v (Watts).
• Power of a torque = T ω (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 ??ELECTROMATE
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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 this ideal well are called DC servo motors.
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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 (2 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 activating both 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 A…Steps are fixed size, so no need to sense the angle! (open loop control). ELECTROMATE
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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. ELECTROMATE
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Stepper Motor example• 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)
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DC Motors – micro sizes• 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 • 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 n:1 reduction gearing decreases speed by n, but increases torque by n.
• Ratios from 3:1 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 (can’t 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 $100’s
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Feedback• 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• > 10 g acceleration• 6 lbs weight• 500 Hz corner
frequency.
• Used for precision vibration control.ELECTROMATE
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Summary• AC motors are good for inexpensive high-
power applications where fine control isn’t 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.ELECTROMATE
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