Why the motor rotation speed is changeable?

r/min: motor rotation speed unit, the number of revolutions per minute, also can be expressed in rpm.
For example: 2-pole motor 50Hz 3000 r/min, 4-pole motor 50Hz 1500 r/min
Conclusion: The motor rotation speed is proportional to the frequency

Herein, the motor is induction AC motor which is used in most industries. AC induction motor rotation speed is approximate depend on the motor's poles and frequency. As we know, the motor poles constant. Since motor poles are not continuous numbers (multiples of 2, for example, the number of poles is 2,4,6), so it's not suitable to change this value to adjust the motor speed.

The frequency can be adjusted before supplying to the AC motor, then the motor rotation speed can be controlled freely. Therefore, frequency inverter is the preferred device for motor speed controls.

n = 60f / p
n: synchronous speed
f: power frequency
p: number poles

Conclusion: change frequency and voltage is the best motor control method.

But, if just change the frequency without changing the voltage, it will occur overvoltage (over-excitation) when frequency decreases and may cause AC motor damaged. So, the voltage should be changed while the frequency inverter outputs different frequency. If the inverter output frequency exceeds rated frequency, the voltage can not continue to increase, the maximum voltage only can be equal to the motor rated voltage.
For example: In order to reduce the motor rotational speed by half, the inverter output frequency change from 50Hz to 25Hz, then the inverter output voltage should change from 400V to about 200V.