I need to rotate a disk (around 20cm diameter of a lightweight material like aluminium) as fast as possible. It would need to stop momentarily between rotations. I'd like to reach speeds of 90 degrees turns every 1/4 second, and later perhaps even faster if possible (1/9th or 1/18 second?).
I've read about PM stepping motors but not clear whether they are fast enough.
Can anyone recommend a type of motor or a specific motor, please?
This is all doable by direct calculation:
First you need to calculate the moment of inertia of your disk - the mass by itself isn't enough here,
the MoI is all-important for rotation. For a 20cm diameter uniform disk of mass X kg the MoI will be X/200 (in kg m^2),
or 5X (in g m^2), or 50,000X (in g cm^2).
Moment of inertia goes up as radius squared, so it grows much faster mass when you increase dimensions.
The formula for angular acceleration is torque = MoI x angular acceleration.
So you then find out the angular acceleration (in radians / s^2) you want for the system to be
fast enough for what you want, calculate the torque needed.
No you know the minimum "hold-in" torque specification for your motor...
For instance to do 90 degrees in 50ms means pi/2 radians in 50ms, implying acceleration of 2500 rad/s/s
(using the formula s = 0.5 a t^2 in the angular domain).
So a 0.05kg disk would have MoI of 2.5e-4 kg m^2, torque = 2.5e-4 x 2500 = 0.625 Nm
This is the spec of a high-end NEMA 17 bipolar stepper (1.6A windings).
But that's not all, we need to know the max angular velocity to ensure this is in
the motor's range:
With the pi/2 in 0.05 s example again, thats an acceleration of 2500 for half the time (0.025s),
so omega = 62.5 rad/s, about 600rpm. That's quite a challenge for a NEMA 17.
angular velocity: rad/s
angular acceleration: rad/s^2
moment of inertia: kg m^2
MoI of uniform disc of mass m and radius r (kg, metres) is 0.5 m r^2
Equations of motion:
torque = MoI x angular acceleration
MoI = integral of mass x radius^2
angular distance = 0.5 x angular acceleration x time^2
rpm = 9.5 x angular velocity [ convert rad/s to rpm ]