Generally, motor designs have a +-10% tolerance, but generallyyou see it the other way around; a motor will be designed for 4000V and connected to a 4160V source, because the lower design voltage makes allowances for some additional voltage drop when you have a long distance from the controller and the motor. If your motor is truly designed for 4160V and you truly have only a 4000V supply, then it might be OK, but you will have very little tolerance for any additional voltage drop.
So the real answer is; it depends on other factors. The best people to ask will be the motor mfr., and give them ALL of the information, i.e. motor lead length, conductor size etc.
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