What is the calculation for determining motor shaft RPM using a tachometer?

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SUMMARY

The calculation for determining the motor shaft RPM using a tachometer involves understanding the relationship between the tachometer's RPM and the diameters of both the tachometer and the motor shaft. Given a tachometer RPM of 1400 and diameters of 31.5mm for the tachometer and 12mm for the motor shaft, the formula used is shaft RPM = tachometer RPM * (tachometer diameter / motor shaft diameter). This results in a calculated motor shaft RPM of 3675. This method effectively applies the principles of gear ratios to rotational speed measurements.

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I am trying to figure out the speed that a motor shaft is running at but i have no reference materials to work with. I had to place a tachometer on the outside of the shaft as there was no centre drilled hole to work from. I got the following results:

Diameter of tachometer: 31.5mm
Diameter of motor shaft: 12mm
RPM of tachometer: 1400rpm

What calculation would i need to work out the rpm of the motor shaft?
 
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wouldn't the rpm of the shaft be 1400 rpm unless I am missing something , or are you wanting the angular velocity
 
If the tachometer is of the type that uses a contact wheel to pick up rotation, then the shaft RMPs = RPMt * dt/ds, where subscript s is for shaft and t for tachometer. With the values you gave, the 1400 tachometer RPM then corresponds to 3675 shaft RPM.
 
Filip Larsen said:
If the tachometer is of the type that uses a contact wheel to pick up rotation, then the shaft RMPs = RPMt * dt/ds, where subscript s is for shaft and t for tachometer. With the values you gave, the 1400 tachometer RPM then corresponds to 3675 shaft RPM.


Yeh that's the answer I had as well. I just thought it seemed too simple to be the same principle as gear ratio's. Thanks for your help.
 

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