Maximum speed for 3 phase motor?

I have a 3450 rpm 3 phase motor on my drill press that I run up to 90 Hz (5175 rpm). It hasn't self destructed yet and the opinion around RCM is
that it's probably OK (it's not a VFD rated motor). But any higher would be pushing my luck.
In a thread here someone thought that a 1725 motor probably has the same mechanical structure as a 3450 & hence could be run at 120 Hz. My question is: if a 1725 motor is mechanically the same as a 3450 motor, do you think that it could be run at 5175 rpm?
Part B: this 1725 motor is on my lathe. If I push it to 5175 rpm, the max spindle speed will increase from 1000 rpm to 3000. Would that be a Bad Idea?
Thanks, Bob
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.