I've mounted a NEMA 34 on my mill z-axis. When idling, it generates a noise like white-noise.
Never heard this while the motor was on the bench, and the noise goes away when I loosen the mounting bolts. It also disappears if I change the code to disable the controller with no input commands.
So, I assume this is the PWM holding current in the windings, mechanically coupling to the mill structure. I have the holding current set to 50%.
No much. It's the nature of steppers. If You can You disable power to the stepper, else it's powered and pulsed to keep its position.
Maybe rubber dampers on the frame parts could do something.
Steppers require as much current to hold in place as they do to move. Obviously you are using some microstepping and the stepper controller is trying to hold that fractional step and it cannot do it with the low current setting.