maximum speed of a motor

The speed of an electric motor is limited only by the size of your budget.

The point to the responses is that you are asking the question in a vague way, so there are going to be responses that will fit your query.

If what you meant was , why can't we have for example an AC SQUIRREL CAGE INDUCTION MOTOR that spins 50,000RPM, then that is a different issue. Speed in an SCIM is dependent upon the line frequency and the number of magnetic poles, S(rpm) = F (hz) X 120 / P (number of poles).

So from that you can extrapolate that the fewer the poles, the faster it spins. But on for instance a 50Hz motor, 2 poles will make it spin at 3000RPM, and you cannot have fewer than 2 poles, so that is the base speed limit. What you CAN do however is to make a motor that will accept a higher frequency, and then use an inverter drive to provide that higher frequency. So working backward if you want 50,000RPM from a 2 pole motor, the frequency must be 833Hz, and there are no inverter drives that I am aware of that will put out 833Hz (although someone may do it).

But at 50,000RPM the bearings and motor balancing had better be damed good! Hence the comment on the opnly practical limitation being the amount of money wou are willing to spend.

Now that said, if you remove the limitation of it being an AC SCIM and allow for other technilogies, then there already are motors that spin that fast.

If you need 50,000rpm this is possible of course. I have been asked to accelerate motors up to 100,000 rpm+.

So, you need to select a motor that meets this and other needs (torque profile, balance, ripple (smoothness) etc) that you have, and couple this to the relevant supply (VFD, I have supplied up to 1667Hz as a standard) and so there you are. I suppose more specialised higher frequency is available, no problem.

As mentioned elsewhere, we can - so can you expand on your question with more information?