How do you calculate actual r.p.m. from a reading on the outside of shaft on an electric motor?

Question

The motor is coupled to a gearbox and the only rpm reading I can get is by putting a tach on the side of the 1.75" shaft and not the center of the shaft. Anyone know what formula to use to get actual rpm's? It's a variable speed DC motor so the 1160 rpm rating on the motor nameplate is no help.

Answer 1

I'm not sure here, how your tachometer setup is actually working, mechanically.....

I'm going to make a shot in the dark and guess that you are just using a small friction idler wheel, against the side of the shaft.

That being the case, it's the same problem as that of different sized pulleys.

The idea is that the *linear* speed of the outside of either pulley has to be the same. The circumference of a wheel is

C = 2π R;

Then, if the wheel makes "N" revolutions per second, the linear speed of the outside of the wheel is

V = 2π R N.

Therefore, since the linear speed of the outside of the two wheels or pulleys must be the same:

2π R1 N1 = 2π R2 N2.

Solving,

N2 = (R1 N1) / R2.

With gears, the formula is the same, except you use the number of *teeth* on each gear, instead of the radii of the wheels.

Hope I guessed right,
~W.O.M.B.A.T.