Nippon Pulse Basic Mechanics Presentation

Basic Mechanics
– Physics and Motors

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Motion Control Requirements
Motion Control Applications must be:
1. Predictable
2. Verifiable
3. Controllable

Design Considerations:
• Accuracy
– Stiffness
– Environment Sold & Serviced By:

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Design Considerations

• Accuracy

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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). Sold & Serviced By:

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4

Accuracy
Accuracy vs. Precision

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5

Accuracy
Resolution
While Resolution is not Accuracy…

It is part of what makes up
Accuracy

Two parts of Resolution
1. Electrical Resolution
2. Mechanical Resolution Sold & Serviced By:

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• Accuracy
– Stiffness

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What Exactly is Stiffness?

M
O

OT
RV

OR
SE

STIFFNESS

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Stiffness

M
O

OT
RV

OR
SE

STIFFNESS

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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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• Accuracy
–Stiffness
–Environment

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Environment
Position Feedback Control Schemes

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Environment
External forces

• Side Loading

• Motor resonance

• System harmonics Sold & Serviced By:

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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=ma
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. Sold & Serviced By:

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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. Sold & Serviced By:

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Physics of rotation
• Rotation is more complex; Euler’s equation:
T=Iα + ωxIω
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=Iω

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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. Sold & Serviced By:

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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) Sold & Serviced By:

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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 Sold & Serviced By:

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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 ?? Sold & Serviced By:

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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. Sold & Serviced By:

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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. Sold & Serviced By:

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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. Sold & Serviced By:

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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). Sold & Serviced By:

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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. Sold & Serviced By:

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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 Sold & Serviced By:

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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) Sold & Serviced By:

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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. Sold & Serviced By:

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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”). Sold & Serviced By:

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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. Sold & Serviced By:

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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. Sold & Serviced By:

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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. Sold & Serviced By:

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Nippon Pulse Basic Mechanics Presentation

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Nippon Pulse Basic Mechanics Presentation