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

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**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

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**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

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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 rotor with NdFeBo magnets

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**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]

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**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.

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**Field Weakening (cont’d)**

Torque fcem “e” velocity w

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**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

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**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

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**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.

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

AC brushless motor Torque Peak torque Nominal torque Nominal Work area Field weakening Velocity

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**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]

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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 = 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

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**Shannon Sampling Theorem**

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 (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

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**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.

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**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)**

B i F1 F2 (With integrated gear)

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**Ironless Motors (brushless)**

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**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.

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**AC induction motors (cont’d)**

230VAC 230VAC Squirrel Cage (gabbia di scoiattolo) D-Connection (Connessione a triangolo) Y-Connection (Connessione a stella)

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**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).

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**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.

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**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

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**Steppers Half Stepping: 1-phase-ON (FullStep):**

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: 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)

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