The entire point of the VFD cable screen is to absorb the EMI from the VFD cables, and drain it to earth. Due the VFD cables carrying a fast switching AC signal, an AC signal will be generated in the screen.
The fact that there is a voltage present, tells me that's it not correctly grounded. And also that connecting it to the machine frame makes things worse, tells me the machine frame isn't grounded correctly. If the screen was correctly grounded, then there should be negligible voltage in it, as it should be getting drained to earth without causing any problems.

Which brings me back to my earlier question, are you sure your power supply earth is correctly earthed?