Design Realization lecture 20 John Canny 103003 Last

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=ma F in Newtons, m in kg, a in m/s 2. § Acceleration a = dv / dt § Kinetic energy E = ½ m v 2 E in Joules, m in kg, v in m/s.

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.

Physics of rotation § Rotation is more complex; Euler’s equation: T=I + x. I T (torque) in N-m, in radians/sec 2, I in kg-m 2, = d / dt § I is a 3 x 3 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.

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

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.

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)

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

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.

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).

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 %

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.

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

DC Motors § DC motor types: § DC Brush motor § “DC” Brushless motor § Stepper motor

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.

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.

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.

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 “microstep” by activating both coils at once.

Driving Stepper Motors § Note: signals to the stepper motor are binary, onoff 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).

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.

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-cm 2 Weight: 1. 32 lb (0. 6 Kg. ) Length: 2. 13" (54 mm) Power output = 3 W § Precision stepper motor: 0. 02° /step, 1 rpm, 3 W

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

DC Motors – micro sizes § From Micromo: § Conventional (brush) DC motor: 6 mm x 15 mm § 13, 000 rpm § 0. 11 m Nm § Power 0. 15 W § V from 1. 5 to 4. 5 V

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

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 1000 s : 1 are available in compact “gearheads” that attach to motors.

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”).

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 maybe less as surplus).

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.

Linear movement § There are several ways to produce linear movement from rotation: § Rotary to linear gearing:

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

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

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.

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.