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I have found some 2.1kW servomotors who're cheaper than their 1.5kW version.
Do you know if an under powered servo driver can control a, for that driver, overpowered servomotor?

That is, if I...

My answer of connecting the motor directly to 50Hz was an error made by me.
It will go via the driver.

I understand that the driver will change the frequency and voltage. But the voltage will never be 460V only 380V max. What will be the effect of this, just a power loss like in a normal induction...

It's directly into the motor. 460V is what it says on the motor and in documentation.
Btw, I'm talking about this motor: Allen-Bradley-7032-05-4102 | hopmachines.nl.

What would the effect be when your connect a synchronous servomotor, built for 460V 60Hz 3 phase with 380V 50Hz 3 phase?

Would there be any negative effects for the lifetime of the motor?
What...