If I had a motor with no nameplate, how could I determine whether it were designed for 50Hz or 60Hz operation? (I don't have another motor like it to compare it to).
In my opinion, unless you have a well equipped motor test laboratory (including variable voltage and frequency power supply may be a dynamic load dynamometer) beside of solid knowledge of electric motors, you will not be able to define the voltage and frequency. You need to get the nameplate data.
After a little more thought, may I suggest the following checks.
1> Determine the frame size.
If it is a metric or IEC frame size it was probably designed for 50 cycle. If it was used or rated for 60 Hz. it was probably a 50 Hz motor that was re-rated for 60 Hz.
If it is an inch or NEMA frame it is probably a 60 Hz. design, but it still may have been re-rated for 50 Hz.
2> Apply a variable 3 phase voltage. Increase the voltage until the speed is stable. Determine the speed. Increase the voltage further until saturation is reached. That is the point where the current starts to increase disproportionately. Rated voltage will be about 15% or 20% below the saturation voltage. If the motor is a 60 Hz NEMA motor the rated voltage will be a multiple of 115 volts, 200 volts or 400 volts.
3> Now from the Frame size, rated voltage, speed and cooling method you should be able to locate a similar motor in a manufacturers literature and determine rated power and rated current.
4> Load the motor to about 80% or 90% and check the temperature.
respectfully
I assume that you know the voltage rating and just want to determine the frequency.
If this is the case, then you could run it open shaft on the correct voltage and the supply frequency that you have available.
Once the motor is operating at full speed, measure the current drawn (open shaft current). If this current is significantly higher than the expected magnetizing current for a motor of this size and speed, then the applied frequency is too low. If the magnetizing current is significantly lower than the magnetizing current for a motor of this rating and poles, then the frequency is too high.
If you do not know the voltage rating, then I would suggest that you need to apply a variable voltage at your local supply frequency and slowly increase the voltage till you get an open shaft current that would be reasonable. This is not particularly accurate, but it would give you a good indication. The voltages at 50Hz are pretty well defined, and the voltages at 60Hz are different.
This test will give you an indication of the V/Hz ratio and you can determine the operating voltage a t 50Hz and at 60Hz.
The magnetizing current for large two pole machines is typically in the order of 20 - 25% while small low speed machines may be closer to 40 - 50%
Thanks for filling in the gaps that I left in my post, Mark.
The frequency is not that important to a motor, but the dimensions are the best way to distinguish an IEC or metric motor at 50 Hz from an NEMA or inch motor at 60 Hz. You may use the frequency that is most readily available to determine the approximate Volts per Hertz ratio. use the ratio 5/6 or 6/5 to convert the voltages from 50 Hz to 60 Hz and vice versa.
respectfully