Motor Running Speed

I have changed the existing winding with a different winding scheme. I have also changed the shaft of the rotor and bearing. Original shaft has been replaced with a new longer shaft and accordingly supported by a different bearing at the end of the shaft. Two touchdown bearing has also been used near the end plate to protect the winding. The question is that I know natural frequency of the rotor and if we bypass that frequency quickly then we can achieve higher speed. So what are the constraints in achieving higher speed with respect to electrical engineering, forget mechanical constraints. We can assume that rotor and bearing will never fail, then till what speed can we go?

There are three choices.
Case 1: the volt/hertz will remain constant, in an attempt to maintain torque. This means that the winding insulation must withstand the proportional voltage increase that comes along with the frequency increase. (10x voltage for 10x frequency, for example). Internal clearances between "live" and "grounded" parts will necessarily also have to increase by approximately the same proportion to avoid discharging inadvertently to a ground plane (like the motor frame, the shaft, or some luckless bystander). And at least one bearing should be insulated - preferably all, if you're looking to reach up into the hundreds of hertz. The grounding method for the machine becomes tougher as well - with higher frequencies (including those that are part of the "switching frequencies" of the drive used to raise the line frequency) the cross-section required is significantly larger and much shorter in length. Typically, at around 200 Hz I'd be suggesting a cross-section of roughly 200 mm^2 and a maximum length of 3 m - with each end solidly connected (i.e. welded, not bolted) to its respective termination point.

Case 2: the voltage is held constant, but the frequency increases. In this case, torque is going to go WAAYYY down if the line frequency becomes high enough. Potentially, it will get to the point where the machine is no longer able to overcome the friction at standstill and will only "hum" a little - no motion.

Case 3: a compromise between the two previous cases. The line voltage is raised somewhat as frequency increases, but not at the rate of Case 1. Ultimately, it will be the same result as Case 2 - just at a higher speed point before there is no longer sufficient torque developed to break away from the standstill condition.

If you're raising the voltages at all, the ideas in Case 1 about clearances need to be addressed. If you're raising the frequencies at all, the ideas regarding grounding cross-section and length need to be taken into account.

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