I have a 3 phase motor and 3 phase power supply (400V, 50Hz)
Currently this motor produces 1.5hp in torque and ~1750rpm. I need it to produce less.
My question is:
Is the best way to go about this, a rheostat or a VFD? The cheaper the better.
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The ONLY is going to be use a VFD. To vary the speed of a three phase motor, you need to change both the frequency and voltage. That is exactly what a variable frequency drive does. Using a rheostat to vary the voltage will cause the torque to drop off, but won't change the speed until except that it will drop when loaded due to reduced torque. It will also heat up more than it should.
The speed of rotation is going to be dependent on the line frequency. If you want to change the speed of rotation, at least with any reliability, you need a VFD.
The torque may imaginably be controllable just by adjusting the voltage, but I wouldn't make any guarantees about the motor lifetime in that configuration. With a rheostat, the losses will be substantial.
A VFD in the power range you're describing costs $300-$400. http://www.automationdirect.com/adc/Shopping/Catalog/Drives/GS2_%28115_-z-230-z-460-z-_575_VAC_V-z-Hz_Control%29/GS2_Drive_Units_%28115_-z-230-z-460-z-_575_VAC%29/GS2-42P0 http://www.automationdirect.com/adc/Shopping/Catalog/Drives/DURApulse_-GS3%28230_-z-_460_VAC_Sensorless_Vector_Control%29/DURApulse_-_GS3_Drive_Units_%28230_-z-_460_VAC_SLV%29/GS3-42P0
A rheostat rated for anything close to that power will cost comparable: https://www.digikey.com/product-search/en?pv2=130&pv2=532&FV=fff40004%2Cfff80540&k=rheostat&mnonly=0&newproducts=0&ColumnSort=0&page=1&quantity=0&ptm=0&fid=0&pageSize=500
A third approach is a variable transformer, or variac. That would let you adjust the voltage getting to the motor in a much more efficient way than using a rheostat. A viable unit can be had on eBay right now for $60, though of course that's going to change over time. And used variac vs. new VFD is not an apples-to-apples comparison, obviously.