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Bad gear geometry or lack of rigidity would be a reasonable worry for surface finish, not the phase of the motor.
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Single phase motors all rely on momentum to complete every single turn.
Even capacitor run motors are well known for not running as smoothly as a 3-phase motor.
Put some work from a single phase lath under a microscope.
I actually converted a single lath to 3-phase using a VFD, and checked the surface before and after.
The single phase had a noticeable pattern that was not present in the sa,e lath using a 3-phase motor.
VFDs produce 3-phase power as good as the stuff from the POCO.
A rotary phase converter generating the 'third phase' top use with 120/240 V single phase has always produced dirty power.
A full up motor generator 3-phase converter produces clean power, but is larger and costs more than the easily found rotary phase converters.