Stuff to understand about motors:
Generally speaking, "standard" motors are *mechanically* designed to run to 3600 RPM, or maybe a little more. Roughly half the world runs on 50 Hz mains and the other half runs on 60 Hz, giving 3000 and 3600 RPM synchronous speeds for 2-pole motors, so designing for 3600 RPM effectively covers all the bases.
Within each motor frame, there are usually different windings that can be fitted to give different speeds at 60 Hz: 2-pole: 3600 RPM, 4-pole: 1800 RPM, 6-pole: 1200 RPM, 8-pole: 900 RPM, and so on. The windings are static and are bonded to the inside of the motor casing. All the rotating parts are the same, whichever windings are fitted. Since the bearings are designed for 3600 RPM, everything will hang together mechanically up to this speed.
The windings are effectively optimized for operation at around 50 Hz (European mains) to 60 Hz (US mains). Either side of this range, efficiency drops off. It's not linear: the further we go from the design range, the more drastic the drop-off. There are things that can be done to widen the range of frequencies a motor can run at, but they tend to be expensive and are only usually used when absolutely necessary. Most of the time, a relatively cheap standard motor can be used to get most jobs done.
The windings tend to be electrically good between "about" 10 Hz and "about" 100 Hz and this is the range over which both VFD manufacturers and motor manufacturers have tended to recommend operating 4-pole motors ( marked as 1800 RPM or 1500 RPM on 60 Hz or 50 Hz mains), certainly since I first started using VFDs in the late 1980s. 10 Hz to 100 Hz gives around 300 RPM to 3000 RPM speed range.
I've largely tended to stick to this: 4-pole motors with VFDs. However, about 13 years ago, a clearout at work put me in the wonderful position of having half-a dozen or so different 2.2 kW, 3HP, VFDs to play with for free, all single-phase-in. Some were just V/Hz drives and others were "Sensorless Vector" drives. Being slightly geeky, I set about testing them on my lathe (a pre-WW2 9" SouthBend that was in the waning years of a very hard life). I'd lucked into a 4-pole 1.1 kW, 1.5 HP 4-pole 3-phase motor through work and had fitted it when I moved the lathe, mainly because it was easy while the lathe was in pieces and would be almost impossible later.
All of the V/Hz drives worked equally well. Speed range was 10-100 Hz and I tried to reduce the minimum speed. Going much below 10 Hz, the motor felt "coggy" and by 7 Hz, all of them were showing a poor finish on machined surfaces. The Sensorless Vector drives (a Telemecanique Altivar 8, Telemecanique Altivar 11 and a Leroy Somer Digidrive) all gave a smooth finish down to 2 Hz or less.
"Sensorless Vector" is a system that allows a VFD to measure the phase angle between peak Current and peak Voltage, then vary the Voltage to maintain this angle at the design value for the motor (the power factor is the Cosine of this angle and is often marked on modern motors). For "our" purposes, its main benefit is that it allows the motor to run smoothly at lower speeds than a V/Hz drive.
I also played with the VFDs on a couple of belt grinders. These were based on 2" x 36" Multitool kits, originally intended to be fitted to bench grinders, but built onto 80-frame IEC metric motors using adaptor kits that were put together by a guy on the old British Blades forum. One was built on a 4-pole, 0.75 kW, 1 HP motor, with the other being built on a 2-pole 1.1 kW, 1.5 HP motor. Both motors were from the same manufacturer and used the same frame. At half the speed, the 4-pole produced less rated power than the 2-pole. The motor spec for the 2-pole gave a maximum frequency of 70 Hz for 4200 synchronous RPM and 4000 RPM at 1.1 kW, IIRC.
Mechanically, this would seem to mean I could take the 4-pole motor to 140 Hz. It worked really well to 100 Hz. By 120 Hz, it felt to be significantly down on power and by 140 Hz it was effectively gutless. This was regardless of which VFD I ran it on. I've since used a number of other VFDs, both big-name and generic Chinese. None will run a standard motor well much over 100 Hz. Only the SV drives will run well below 10 Hz.
I now use 2-pole motors with Sensorless Vector drives by default. The SV gives me the low-speed operation, while the 2-poles give me the high-speed operation.
I get the impression the 100 Hz upper limit still holds for drives used industrially and intended to run in the "constant power" range from rated Frequency (50 Hz or 60 Hz) on up. Going much above 100 Hz seems to cause the power to tail off pretty fast, which might be an issue with many machines. By 120 Hz, the power seems to be dropping quite fast. I think this would be a potential problem with a lot of machines, but a belt grinder has a much more sophisticated control system than many machines in the form of the person using it. The user can adjust pressure to maintain motor speed and removal rate, thanks to an array of sensors (eyes, ears, touch) and actuators (muscles) that are not normally available to Engineers designing/building automated machinery.
I'm pretty sure that by 140 Hz, anyone would notice the power tailing off and the OP has clearly found that 160 Hz is just too much.
The KBDA is listed as a Sensorless Vector drive, though I've not used one myself. My advice would be to buy a new 2-pole motor for the belt grinder and to build a disk grinder around the 6-pole (1200 synchronous RPM, 1140 RPM at rated load on 60 Hz mains).
