Mechatronics
Electric Motor
Selection
Mechatronics
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.
Mechatronics
Motion Transmission
1) Gearboxes:Gearboxes:
Moment of inertiato the motor shaft:
J1 = (n1/n2)2 J2
Jtot = Jmot + J1
Motor n1 teeth
n2 teeth
Mechatronics
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
Mechatronics
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
Mechatronics
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]
Mechatronics
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.
Mechatronics
Field Weakening (cont’d)
Torquefcem “e”
velocity
Mechatronics
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
Mechatronics
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
Mechatronics
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
Mechatronics
AC brushless motorAC brushless motorTorque
Velocity
Peak torque
Nominal torque
Field weakeningNominal
Work area
Torque characteristics of the different motor types (cont’d)
Mechatronics
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]
Mechatronics
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
Mechatronics
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
Mechatronics
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
Mechatronics
•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)
Mechatronics
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
Mechatronics
Ironless Motors
(DC motor)
(With integrated gear)B
iF1
i F2
B
Mechatronics
Ironless Motors
(brushless)
Mechatronics
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.
Mechatronics
AC induction motors (cont’d)
D-Connection(Connessione
a triangolo)
Y-Connection(Connessione
a stella)
Squirrel Cage(gabbia di scoiattolo)
230VAC
230VAC
Mechatronics
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)
Mechatronics
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)
Mechatronics
SteppersSteppers(motori passo o passo-passo)2 phases,
4 poles6 rotor teeth
2 phases, 8 poles50 rotor teeth
• Small loads• No feed-back• Cheap
Mechatronics
Steppers
Half Stepping:4 poles * 6 teeth = 24 steps
1-phase-ON (FullStep):4 poles * 6 teeth / 2 = 12 steps
Mechatronics
Distribuzione del campo magnetico al traferro di un motore passo-passo
Mechatronics
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)
Mechatronics