60Hz motor running on 50Hz power supply or vice versa

Electric motors, both single and three phase, are designed for running on a specified power frequency. But sometimes we may use a 'wrong' motor on the power supply.

The basic, RPM is in direct proportion to Hz. If you decrease the power supply frequency, the motor will slow down. On the contrary, if you increase the frequency, the motor will speed up. The RPM change is proportional to the Hz change.

60Hz motor will run 20% slower on 50Hz power supply
This also results in 20% less power. Basically, running the electric machine slower usually means it will be demanding less power. That's good, as the motor also decrease 20% of its power, and the cooling fan is slow down too. But the critical factor here is the V/Hz ratio. It goes up 20%! Not good. This means that during parts of every power line cycle the magnetic structure of the motor will probably be overloaded.

The only recourse here is to correct the V/Hz with the variable value that is easy to change – V the voltage. Lower the voltage with a transformer to correct the V/Hz ratio.

50Hz motor will run 20% faster on 60Hz power supply
AC motor kilowatt is proportional to Torque times RPM. As the motor's torque is not going to change significantly with the increase of frequency, it will now output 20% more power. A 10kW 50Hz motor will be a 12kW motor on 60Hz power source.

Running a machine 20% faster is very likely going to increase its power demand by at least 20%! If the machine cyclically accelerates or decelerates in operation it will be subject to greater mechanical forces. If the motor is driving centrifugal loads their demand may even go up by the square of the speed increase.

Case 1: You have 60Hz power for a 50Hz equipment
Let's say you just got a great deal on an equipment. As it's being wired up you realized that it has 50Hz on its nameplate and you have 60Hz power supply.

The equipment will be running 20% faster! Is this going to be a problem? If it is, can the speed be returned to design speed by changing a pulley size to drop the speed 20% back to where it was?

Once this assessment has been done and sheaves are changed or other modifications are done to help mitigate the speed/power issues, move on to the next step. Read the nameplate to get the Full Load Amperage commonly known as the FLA rating for the motor at the voltage you'll be running it with.

Using a clamp-on ammeter, run the machine and check to see the amperage is below the FLA. If it is you can proceed with running the equipment as desired. Do check to see that it's still under FLA when fully loaded. If it's over FLA you must do some sort of load mitigation.
 
Case 2: You have 50Hz power for a 60Hz appliance
You receive an appliance and since you are in 50Hz power source, the 60Hz label is bothering you. As well it should!

Again, realizing the appliance will run 20% slower, will it get the job done? In this case you can not change pulley sizes to correct the speed because the motor just lost 20% of its horsepower nameplate rating. If you change pulleys it will likely be overloaded - seriously.

If the appliance can run 20% slower there may still be hope. Even though it is going to lose cooling with its internal fan running more slowly, running the load slower and with a 20% less powerful motor will likely even out. The V/Hz increase may still get you.

At this point if your assessment shows you will probably be alright with the slower speed, again check the nameplate for the FLA. Run the appliance and quickly check the running current with an ammeter. If it's below FLA proceed to load the appliance while closely monitoring things. If you stay below FLA it will probably be OK.

But! Running at FLA now that the cooling fan has reduced ability is still possibly going to be a problem. You should monitor the motor's temperature and assure yourself that after extended running time, under load, it remains below the nameplate temperature rise.

If even unloaded you're seeing FLA or more you will need to reduce the voltage because the motor is probably saturating. Before going to the bother of adding buck transformers, seriously consider changing out the motor for the correct 50Hz power supply. Remember you may need to up the rated kilowatt if you're going to change gear ratios to return the equipment back to its original speed.