A couple of questions about a 3 phase motor

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I knew a chap a few years ago who was looking to replace the knackered original variator on a Chip master with one of the roller type ones taken from a twist and go scooter.
No idea whether he managed it, but an interesting idea.
I had considered that. There's also the strange segmented metal belt system used by (I think) Nissan. A quick bit of searching didn't give me any answers for the efficiency of those CVTs, but a Reeves Drive appears to be in the same region as the Kopp Variator (80-90%).
 
A small amount of variation from a motors rated speed isn’t really an issue. However, if an induction motor is rotated at a speed higher than its rated speed, it will experience a significant decrease in torque due to a reduction in the magnetic flux within the motir, potentially causing the motor to overheat; this is because the motor's design is optimised for operating within its rated speed range, and exceeding that limit can lead to issues with current draw and overall performance.
Lower than rated speed can also cause issues with cooling due to the fan not pushing enough air over the motor fins leading to the motor over heating.
I think your plan is likely to head to problems.
 
A small amount of variation from a motors rated speed isn’t really an issue. However, if an induction motor is rotated at a speed higher than its rated speed, it will experience a significant decrease in torque due to a reduction in the magnetic flux within the motir, potentially causing the motor to overheat; this is because the motor's design is optimised for operating within its rated speed range, and exceeding that limit can lead to issues with current draw and overall performance.
Lower than rated speed can also cause issues with cooling due to the fan not pushing enough air over the motor fins leading to the motor over heating.
I think your plan is likely to head to problems.
The Alpak II motor in my current lathe is rated for a huge speed range (2.5 to 100Hz); though there's no spec of that range (that I know of) for the Brook motor. For the majority of (what I use the lathe for) the Brook should be running between 40 and 60Hz; so hopefully pretty safe.

Based on some drilling operations it may be in the 20 to 30Hz range occasionally; but only for a few minutes at a time.
 
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