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

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To determine the motor shaft RPM using a tachometer, the formula is RPMs = RPMt * (dt/ds), where RPMs is the shaft RPM, RPMt is the tachometer RPM, dt is the tachometer diameter, and ds is the motor shaft diameter. In this case, with a tachometer RPM of 1400 and diameters of 31.5mm for the tachometer and 12mm for the motor shaft, the calculation yields a motor shaft RPM of 3675. This calculation reflects the principle similar to gear ratios, confirming that the tachometer's reading does not directly equal the motor shaft RPM. The discussion emphasizes the importance of understanding the relationship between the diameters and RPMs for accurate measurements. Overall, the correct calculation reveals that the motor shaft runs significantly faster than the tachometer indicates.
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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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