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I have a motor that rotates at 1800 RPM at 60 Hz. It then runs through a 15:1 gearbox that spins a 4" work roll. How do I calculate the FPM of the work roll based on different frequencies and work roll diameters? I not only want to know the formula, but also how the formula is derived. Its been driving me crazy!!!

I have a motor that rotates at 1800 RPM at 60 Hz. It then runs through a 15:1 gearbox that spins a 4" work roll. How do I calculate the FPM of the work roll based on different frequencies and work roll diameters? I not only want to know the formula, but also how the formula is derived. Its been driving me crazy!!!

Work roll turns at 1800 RPM/15 = 120 RPM

Each revolution advances the work the circumference of roll, pi*d
4" = (1/3) ft so
120 rev x pi x (1/3) ft/rev = 40*pi ft/min ~ 125.66 FPM

There is not necessarily a simple connection. At 60 Hz, a sybchronous motor with two poles turns at 3600 RPM, 4 poles 1800 RPM, etc. An induction motor always slips a little (depending on load) with respect to the electrical frequency, so a four pole induction motor might only be around 1600-1700 RPM.

The electrical field rotation rate is 60 Hz times the number of pole pairs (poles/2) times 60 seconds per minute, for two pole winding 3600 cycles per minute, for four pole 1800 cycles per minute.

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