2663
« on: April 13, 2019, 01:30:43 AM »
Hi,
I cant find any specification from any manufacturer about the rotational inertia of the rotor of a 2.2kW asynchronous
spindle.
Rotational inertia is a specified parameter in servos and so I will use the servo data for a 2kW AC servo from Delta.
Its specified rotational inertia is:
0.00149 kg.m2 (more correctly called 'the first moment of inertia', usually given the symbol 'I')
Lets assume that if you had a direct coupled tool holder and smallish endmill that the rotational inertia would be approx:
0.002 kg.m2.
The kinetic energy of the rotor/toolholder/ tool combination at 3000 rpm is:
E(joules)=0.5 x I (kg.m2). w2 (rad/sec) (note w is the rotational speed in radians/second)
E=0.5 x 0.002 x (2 xPI x3000/60)2
E=98.7 joules
If the spindle were required to decelerate very quickly this kinetic energy would be fed back into the drive. In absence
of any braking resistance that energy would be added to the DC link capacitors. The voltage rise that would cause is:
E(Joules)= 0.5 X C (Farads, the capacitance of the link capacitors) x Vrise2
Rearranging and evaluating:
Vrise= (2 X 98.7/ 10000uF )1/2
Vrise=140.5V
Note for the purposes of this calculation I have assumed 10,000uF DC link capacitors, as is common in single phase
servo drives and VFDs.
Thus your DC links capacitors (on a 230V single phase driver) are normally charged to 320VDC, and because of the sudden
deceleration of the rotating component cause a voltage rise of 140.5V to a total of 460VDC. Note that the vast majority of
DC link capacitors, all aluminum electrolytic types, are rated to 450V. Thus your DC link capacitors are on the verge of blowing
up. This is exactly why braking resistors are required, to dissipate the kinetic energy WITHOUT the DC link capacitors
going over voltage.
My servo drive has a braking resistor threshold of 340VDC and a safety threshold of 380VDC. Thus if the voltage increased to
340VDC the braking resistor MOSFET is switched on and the braking resistor is now directly across the DC link. If the
voltage further increases, ie the braking resistor does not 'hold the voltage down' to 380VDC the servo drive faults
'over voltage' and switches off allowing the servo to coast to a stop.
If the deceleration is a matter of safety, ie the operator of the machine hit the Estop, we want the spindle to slow as quickly
as possible. If however you program a 'crash' stop the servo drive and braking resistor combination may not handle it and
shut down, allowing the servo to coast. This would be very bad design. In trying to decelerate we have caused the drive
to fault and therefore achieve a much lower deceleration than might have been possible had we allowed for the limited ability
of the driver/ resistor to absorb the energy.
Craig