Dispense del Corso 7/10

Motor
Sizing
Sizing
Transmission Selection:
•The Velocity Accuracy is almost load-independent and
completely motor-independent: it does depend only on the
position sensor and regulator tuning
•The reaction times of a brushless can be as low as few
ms: the limits is now the mechanics attached to it
•A resonance can grow, due to load elasticity that cause
oscillations that behave as high-noise vibrations (the
motor over-heat in this case is due to accelerationsdecelerations)
•Solutions: higher load stiffness or lower response time
(lower gains with lower performances…)
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Sizing
Transmission selection (cont’d)
rotation-rotation :
•Belt (cinghia dentata): low cost, band-width<10Hz
•Gearbox (riduttori): high cost, low backlash is necessary <10-15 arcmin
•Ball-screw (vite senza fine): efficiency very low at high speeds, high static
friction (attrito di primo distacco): not good for varying speed applications
rotation-linear:
•Belt (cinghia dentata): low cost
•Ball-screw (vite senza fine): good if speed <1m/s
•Pinion-rack (pignone-cremagliera): big backlashes, band-width <5Hz
•Metallic tape: high band-width but with limited loads
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Sizing
Transmission selection (cont’d)
Power applications (mandrels, traction, avvolgitori): not relevant
kinematic performances, motor cost is important. It’s useful a transmission with a
reduction-adaptation stage (that allows for smaller motor).
Positioning applications (position profiles): high kinematic
performances. With high reduction ratio, the load inertia become less important,
but the motor inertia becomes more important. The optimal ratio (with respect
to the motor’s torque) is the one with same load inertia (to the rotor’s side) and
rotor inertia (inertial ratio), or the direct-drive solution.
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PLANETARY GEARBOXES
solar wheel
Basic parts of an
epicyclical gearbox stage:
planetary
wheel
• solar wheel (or pinion)
• planetary wheel
• internal crown
internal crown
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When the planetary rollers turn they describe a
geometrical profile called epicycloid, here shown:
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Parts of an epicyclical gearbox
with one stage
Carcassa con
dentatura interna
pignone
Planetari
(3*120°)
Albero di
uscita
Albero di
ingresso
Planetari
(3*120°)
Carcassa con
dentatura interna
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Scomponiamo un riduttore nelle sue parti….
Cuscinetto
Guarnizione
Albero d’uscita con
chiavetta
Cuscinetto
2° stadio
1° stadio
Cannotto calettatore
:
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Parts of an epicyclical gearbox
with two stages
Ring gear of first stage
is connected with the
planetary carrier of the
second stage
(rotating with output)
ring gear = housing
(fix)
Planetary
gears
3x120°
Planetary carrier
of the second stage
(output flange)
pinion of the
first stage
(input)
1-stage
2-stage
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ANGULAR BACKLASH / ACCURACY
Angular Backlash:
1 to 10 arcmin in
gearboxes for servos
Transmission selection (cont’d)
Indeed:
J = JM + JL/N2 ; C = J dw/dt
with: qM = N qL
Sizing
And I look for the minimum of
CM = (N JM + JL/N) d qL /dt
deriving with respect to N and equaling to 0 we get:
N2 = JL / JM that is: JL/N2 = JM
but ATTENTION: this “inertia weighing” is for determining optimal N
only; but if I can reduce JL/N2 and/or JM working directly on them, still
having them different, I have to do it! It is not convenient to increase the
rotor’s inertia!
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Rotor-Load Inertia Ratio
Sizing
Il classico criterio di progetto per servoazionamenti prescrive di scegliere un
insieme motore + trasmissione tale da ottenere un’inerzia del carico (ridotta
all’albero motore) circa uguale all’inerzia del rotore stesso o di poco superiore.
Tale impostazione è legata a problematiche distinte:
– 1. scegliere il rapporto N di trasmissione ottimale (derivata rispetto ad
N) per massimizzare l’accelerazione del carico, una volta fissati il
motore ed il carico
– 2. ottenere una sufficiente insensibilità delle prestazioni al variare delle
condizioni operative (“robustezza del controllore” ottenuta appunto
trovando il minimo e quindi con derivata che cresce lentamente da
entrambi i lati)
– 3. ottimizzare le prestazioni dinamiche dell’asse controllato (avere
deformazioni modeste tra sensore e carico)
E’ chiaro che, a fronte di condizioni dinamiche, l’adozione di un motore con
grande inerzia ne ridurrà gli effetti negativi, ma in generale ciò renderà anche
più difficile e costoso raggiungere prestazioni elevate già nelle condizioni
nominali.
Una possibilità alternativa, è invece quella di cercare di stimare la variazione
del comportamento dinamico istante per istante e modificare di conseguenza
guadagni o strategie di controllo (ad esempio col feed-forward).
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Rotor-Load Inertia Ratio
Vel.mot.
Coppia
Sizing
Bassa inerzia Jmot+carico
Log
w = 2pf
Log
Log
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Sizing
Rotor-Load Inertia Ratio
Nel caso rotativo vi è di solito una risonanza (in generale a frequenze
abbastanza basse) dove motore e carico si muovono in direzione opposte,
deformando il collegamento motore-carico. Sopra la frequenza di risonanza la
risposta in frequenza continua a scendere lungo una linea che rappresenta
l’inerzia del solo rotore, fino alle frequenze più elevate dove si vede il limite
della banda passante dell’anello di corrente (circa 1 kHz) dove potrebbero
essere visibili le risonanze legate a deformazione della struttura che collega
motore e sensore.
L’adozione di motori lineari permette di superare le limitazioni legate alla
presenza delle catene cinematiche tradizionali (cedevolezza tra motore e
sensore di posizione, attrito variabile lungo la corsa, inerzia, …) e sviluppare
quindi applicazioni con elevate prestazioni dinamiche.
Per poter raggiungere tali prestazioni è però necessario mantenere sotto
controllo diversi aspetti, di natura elettrica, elettronica e meccanica. Un utile
strumento per fare ciò è costituito dall’analisi meccatronica, che permette,
tramite modelli che uniscono una descrizione della struttura meccanica,
tipicamente ottenuta tramite modelli agli elementi finiti, ad una descrizione
dell’azionamento, di stimare i principali indici prestazionali e verificare se,
durante il funzionamento, insorgano limitazioni legate ai specifici componenti
scelti, quali l’azionamento ed i sensori di posizione.
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Sizing
Transmission selection (cont’d)
•The gearbox cost is typically similar to the motor’s cost, thus the
optimal motor dimensioning is not the optimal system dimensioning,
considering the gearbox problems.
•Every gearbox ratio N2 > JL / JM is wrong because it reduces the
bandwidth and increases the motor’s energy consumption.
•The ideal case is thus WITHOUT GEARBOX
•An important exception is when JL >> JM so that the inertia rotor cannot
compensate the load mechanical resonances.
Cymex SW tool link
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Sizing
Transmission selection (cont’d)
• Long and thin motors have low inertia: high accelerations are
possible
• Short and thick motors have high torsional stiffness: OK with
high inertia loads
Shaft diameter
Steel shaft length
Torsional Stiffness : S = p D4 78.5 109 /(32L)
Resonance Frequency: F = SQR(S/JL)/(2p)
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Servo-System
Sizing:
Sizing
1) Draw velocity/time diagram through the cycle
2) Port inertias and loads to the rotor’s side
3) Calculate accelerations and torques
4) Add 2) e 3)
5) Calculate: torque RMS, velocity RMS, average torque,
max.torque duration, torque at the max.speed, max.torque
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Servo System Sizing (cont’d)
Sizing
• Max torque verification:
The max torque required from the motor cannot be bigger than the motor’s peak torque (di
targa).
• Motor temperature verification:
With the motor thermal model, the torque over the nominal torque have to be maintained for
intervals below 0.3s with 1.0s cycle, typically.
The excessive temperature is the ONLY good reason to increase the motor’s size
•DC bus voltage verification:
Vmax-speed < Emin
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Servo System Sizing
•Drive size verification:
Imax < Cpeak motor / Kt
(for not burning the motor)
IRMS > CRMS / Kt
(for profile following)
Imax > Cpeak profile / Kt
(for profile following)
• Power-on (in-rush) verification:
At the power-on the electronics absorbs more than double current
for 0.3s for charging internal capacitors
In-Rush Resistors
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Needed Mechanical Inputs
for Motion Book:
1.
Position or Speed or Torque
or machine
2. Inertias and/or Masses and Distances from
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d
Electro-Magnetic Compatibility
(EMC):
Sizing
The PWM has square waves with edges at 5000V/ms that in turn generates
frequency spectrum that, coupling with cable and winding capacitances,
produce radio emissions at 10KHz-100MHz.
Useful hints:
• Ground the motor, drive and shield and keep this ground separate from
signal ground
• Power and signal separated, with shielded cables, with 90deg
intersection
• Ferrites where necessary
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Sizing
EMC: Frequency spectrum example
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Sizing
Trouble-Shooting in
First Rig Installation
•
•
•
•
•
Insufficient Motor Torque: increase current limit or motor size
Motor get hot: increase motor size
Motor is noisy: lower Kp and/or Kd of the PID
Motor is unstable: lower Kp and/or Kd of the PID
Motor follows the cycle but is noisy: reduce mechanical backlashes and/or
lower Kd
• Motor doesn’t turn or does it intermittently: wrong U,V,W, cabling or
feedback cabling
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