Mechatronics

Electric Motor

Selection

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Servosystem Selection• “Servo” generally is used as a synonymous of “brushless”. • Brushless motors are generally defined in terms of torque, not power, since the torque is available from zero to nominal speed, while P = C *

Velocity

time

servo

Induction vector controlled

inductionV/F cost.

Torque

velocity

servoInduction vector controlled induction

V/F cost.

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Motion Transmission

1) Gearboxes:Gearboxes:

Moment of inertiato the motor shaft:

J1 = (n1/n2)2 J2

Jtot = Jmot + J1

Motor n1 teeth

n2 teeth

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Motion Transmission (cont’d)

2) Belt:Belt:

J = m r2 = m (v/) 2

3) Screw:Screw:

J = m (s/(2))2

mv

r

m

s

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Motor’s poles number

Brushless can technically be built with any pole pair number.

A high pole pair number generally gives high torques.

The limit given by permanent magnets distance on the rotor and from the diameter of the motor.

AHR190J8 rotorwith NdFeBo magnets

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Motors Basic Equations

Electrical Equations:e = fcem = Kt [V]

C = Kt I [Nm]

Mechanical Equations:P = dE/dt= C = dE/d[Nm/s =

W]

C = J d/dt [Nm]

Speed [rad/s]

Current [A]

Angle [rad]Energy [J=Nm=Ws]

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Field-weakening (Deflussaggio)Increasing velocity the DC bus limit is

reached (e = fcem = Kt ).

For increasing furthermore the speed it is necessary to lower the statoric flux with 1/and doing so also Kt will be lowered and so also C = Kt Iq).

(The effect can be obtained changing the phase of is beyond /2 with respect to the rotor position; the current thus staying maximum and thus avoiding quantization effects due to small digital vectors).

We thus have P = C = cost.

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Field Weakening (cont’d)

Torquefcem “e”

velocity

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Torque characteristics of the different motor types

DC brush motorDC brush motorTorque

Velocity

Peak torque

Nominal torque

Field weakeningNominal

Work area

Universal MotorsUniversal Motors((motori seriemotori serie))

Torque

Velocity

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Torque characteristics of the different motor types (cont’d)

Stepper motorStepper motorTorque

Velocity(steps frequency)

NominalWork area

Resonance zone

pull-out torqueMax speed

possible to put as set point

at speed zero

pull

-in

rate

Load

inertia

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AC induction motorAC induction motorTorque

const. torque const. powerwith Is max

B prop. to V/f = cost.

V cost.

Pull-out torque

Torque follows pull-out torque

Torque characteristics of the different motor types (cont’d)

Torque

Unstable zone

NominalWork area

brake

generator

s = 0s = 11/1/ 2

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AC brushless motorAC brushless motorTorque

Velocity

Peak torque

Nominal torque

Field weakeningNominal

Work area

Torque characteristics of the different motor types (cont’d)

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Formulas Summary

Rotational Case

E = C = P t [Nm=Ws=Am2T]

P = dE/dt= C = dE/d[Nm/s]

C = F leverage= J d/dt [Nm]

F = I B l ; B= / A [N] [T]

= LI = MMF/R ;MMF=NI [wb] [A]

Linear Case

E = F s= P t [J=Nm]

P = dE/dt= F v[N m/s]

F = m a [N=Kgm/s2]

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Rewinding (Riavvolgimento cave statoriche)

For increasing Kt with the same motor is

sufficient to rewind stator slots with smaller section cable so to make more windings:

Kt = Srot N / A will be thus increased.

With the same motor, I will thus have more torque C = Kt I with the same current I,But with a smaller max. speed since e = Kt

prop. to N I: a little bigger due toBetter slot filling

It increases proportionally to number of windings

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Shannon Sampling Theorem

signalsample ff 2

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.005 0.01 0.015 0.02 0.025

45Hz < signal bw

55Hz > signal bw 50Hz

fsample = 100Hz = 2fsignal

fsample = 110Hz > 2fsignal

fsample = 90Hz < 2fsignal

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Servo digital control loop• sampling time (sampling time (tempo di tempo di campionamentocampionamento):): to avoid z-transform analysis (that would mean to work at the control system limits) it is necessary to sample 5-10 times faster than Shannon theorem says.Generally we have:

Load Response Bandwidth = 10-50Hz

Sample&Update Rate > 1KHz

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•lag error, following error lag error, following error ((Errore di inseguimentoErrore di inseguimento):): each control block introduces a delay (integral action plays an important role in this respect) that leads to a lag error naturally different from zero. To minimize it the feed-forward could be useful: it bypasses closed loops regulating blocks (and thus it does not load the integral actions). The feed-forward action it is dependent from: velocity, inertia, acceleration, viscous friction, that thus have to be known with good accuracy.

Servo digital control loop (cont’d)

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DC Motors DC Motors (motori in continua o motori a spazzole

o motori a collettore)

•Simple drive electronics

•Cheap

•Possible problems with commutator and brushes

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Ironless Motors

(DC motor)

(With integrated gear)B

iF1

i F2

B

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Ironless Motors

(brushless)

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AC induction motorsAC induction motors (a induzione o in alternata o a gabbia di

scoiattolo)Frequency-controlled asynchronous (induction) motors are mostly used for simple drive functions, without feed-back. For example to regulate the speed. The motor is a squirrel-cage asynchronous motor, and the control unit a frequency converter.The squirrel-cage asynchronous motor is the absolutely most commonly used AC induction motor:

• it is CHEAP,• it is VERY RELIABLE,• it is a STANDARD PRODUCT within the IEC std.

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AC induction motors (cont’d)

D-Connection(Connessione

a triangolo)

Y-Connection(Connessione

a stella)

Squirrel Cage(gabbia di scoiattolo)

230VAC

230VAC

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The synchronous speed is the rotation speed of the magnetic field, generated in the field windings when supplied with a three-phase AC voltage:

The actual, true, speed of the rotor is determined also by how great a load the motor is driving. This speed is called the asynchronous speed, and the difference between the two is termed slipslip ((scorrimentoscorrimento).).

AC induction motors (cont’d)

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Note that the AC induction motor (asynchronous) has always a physiological slip (in speed), while the AC brushless motor (synchronous) has always a physiological lag error (in position).

From a construction point of view the stator of an AC induction motor and the one of an AC brushless are quite similar (both has a winding lay-out so to obtain a single sinusoidal rotating field from 3 sinusoidal pulsating fields).

Often an AC brushless drive can also control (with Vector Control techniquies) an induction motor.

AC induction motors (cont’d)

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SteppersSteppers(motori passo o passo-passo)2 phases,

4 poles6 rotor teeth

2 phases, 8 poles50 rotor teeth

• Small loads• No feed-back• Cheap

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Steppers

Half Stepping:4 poles * 6 teeth = 24 steps

1-phase-ON (FullStep):4 poles * 6 teeth / 2 = 12 steps

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Distribuzione del campo magnetico al traferro di un motore passo-passo

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Steppers Motor Types:

1. Variable Reluctance (iron teeth)

2. Permanent Magnets (PM teeth)

3. Hybrid (rotor iron teeth misaligned axially, PM inside the rotor with N-S axially spaced)

4. Direct Drive Variable Reluctance (ring-like rotor, double face stator)

5. Multi-Stack (rotor divided axially in 3 parts with teeth misalingned of 1/3; stator also divided in 3 parts each energized in sequence: only 1/3 of Fe used at the same time)

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