Electric Motor Selection

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 * w Velocity Torque servo servo Induction vector controlled Induction vector controlled induction V/F cost. induction V/F cost. time velocity

Motion Transmission 1) Gearboxes: J1 = (n1/n2)2 J2 Jtot = Jmot + J1 Moment of inertia to the motor shaft: J1 = (n1/n2)2 J2 Jtot = Jmot + J1 Motor n1 teeth n2 teeth

Motion Transmission (cont’d) v r w 2) Belt: J = m r2 = m (v/w) 2 3) Screw: J = m (s/(2p))2 m s

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 rotor with NdFeBo magnets

Motors Basic Equations Speed [rad/s] Electrical Equations: e = fcem = Kt w [V] C = Kt I [Nm] Mechanical Equations: P = dE/dt = C w = w dE/dq [Nm/s = W] C = J dw/dt [Nm] Current [A] Energy [J=Nm=Ws] Angle [rad]

Field-weakening (Deflussaggio) Increasing velocity the DC bus limit is reached (e = fcem = Kt w). For increasing furthermore the speed it is necessary to lower the statoric flux with 1/w (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 p/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 w = cost.

Field Weakening (cont’d) Torque fcem “e” velocity w

Torque characteristics of the different motor types DC brush motor Torque Torque Peak torque Universal Motors (motori serie) Nominal torque Nominal Work area Velocity Field weakening Velocity

Torque characteristics of the different motor types (cont’d) Stepper motor Torque pull-out torque Max speed possible to put as set point at speed zero Resonance zone Nominal Work area Load inertia Velocity (steps frequency) pull-in rate

Torque characteristics of the different motor types (cont’d) AC induction motor Pull-out torque Torque Torque brake Unstable zone const. power with Is max const. torque Torque follows pull-out torque Nominal Work area w 1/w 1/ w2 s = 1 s = 0 generator w B prop. to V/f = cost. V cost.

Torque characteristics of the different motor types (cont’d) AC brushless motor Torque Peak torque Nominal torque Nominal Work area Field weakening Velocity

Formulas Summary Rotational Case Linear Case E = C Da = P Dt [Nm=Ws=Am2T] P = dE/dt = C w = w dE/dq [Nm/s] C = F leverage = J dw/dt [Nm] F = I L B l ; B = F/ A [N] [T] F = LI = MMF/R ;MMF=NI [wb] [A] Linear Case E = F Ds = P Dt [J=Nm] P = dE/dt = F v [N m/s] F = m a [N=Kgm/s2]

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 = F 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 w prop. to N I: a little bigger due to Better slot filling It increases proportionally to number of windings

Shannon Sampling Theorem 45Hz < signal bw 55Hz > signal bw 50Hz fsample = 100Hz = 2fsignal fsample = 110Hz > 2fsignal fsample = 90Hz < 2fsignal

Servo digital control loop sampling time (tempo di campionamento): 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

Servo digital control loop (cont’d) lag error, following error (Errore 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.

DC Motors (motori in continua o motori a spazzole o motori a collettore) Simple drive electronics Cheap Possible problems with commutator and brushes

Ironless Motors (DC motor) B i F1 F2 (With integrated gear)

Ironless Motors (brushless)

AC 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.

AC induction motors (cont’d) 230VAC 230VAC Squirrel Cage (gabbia di scoiattolo) D-Connection (Connessione a triangolo) Y-Connection (Connessione a stella)

AC induction motors (cont’d) 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 slip (scorrimento).

AC induction motors (cont’d) 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.

Steppers (motori passo o passo-passo) 2 phases, 4 poles 6 rotor teeth Small loads No feed-back Cheap 2 phases, 8 poles 50 rotor teeth

Steppers Half Stepping: 1-phase-ON (FullStep): 4 poles * 6 teeth = 24 steps 1-phase-ON (FullStep): 4 poles * 6 teeth / 2 = 12 steps

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

Steppers Motor Types: Variable Reluctance (iron teeth) Permanent Magnets (PM teeth) Hybrid (rotor iron teeth misaligned axially, PM inside the rotor with N-S axially spaced) Direct Drive Variable Reluctance (ring-like rotor, double face stator) 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)