Variable speed motor drives (VFDs) offer many benefits. But a frequently overlooked "gotcha" just might getcha.
A motor normally has a cooling fan mounted on its output shaft. The designers specify the fan size and blade pitch to move enough cooling air through the motor at the nameplate RPM. If your VFD slows the motor enough, the fan speed will be insufficient for adequate cooling.
If you're specifying a new VFD/motor installation, work with the manufacturer to arrive at a VFD/motor combination that has adequate cooling for the location in which it will be installed and the speed at which it will run. Don't be surprised if a gearbox is part of this.
For your existing VFD/motor installations: