If you are running a motor from a VFD, it’s best to use a motor that was DESIGNED for that purpose. Yes, it is possible to use any 3 phase induction motor on a VFD, but just because you can, doesn’t mean you should.
Cooling is one of the main reasons. TEFC and ODP motors need a certain amount of air flow across them to keep from over heating. Slowing the motor slows the fan and reduces the cooling effect, while at the same time the harmonics on the output of the VFD is increasing the heating of the motor. “Inverter Duty” motors (although not a regulated term) typically have a “Speed Ratio” or “Turn Down Ratio” assigned to them, sometimes right on the nameplate but often just in the data sheets. So if the Speed Ratio says 4:1, that means it can handle being run at 25% speed from a VFD. If a motor was NOT designed for inverter duty, I would not use it at lower than 50% speed, if even that.
The “cube law” for centrifugal fans has to do with the POWER REQUIRED to run the fan at lower speeds. That means at 50% speed, the mechanical power needed to run the fan drops to .503 (cubed) or 1/8th power. The FLOW change, often called the “First Affinity Law”, states that the FLOW is directly proportional to the speed change, so 50% speed = 50% flow. From the standpoint of the motor fan keeping the motor cool, it’s the flow that we are concerned about.