Do we need constant frequency and constant voltage for AC motor forrunning it at constant speed?
No they don't need as such. in fact they are actually two great methods and most commonly used speed control methods other than changing direct rotor speed and others. Formula for frequency is N=120*(f/p) here N is speed and p are number of poles.
An AC motor will not work with DC applied. Some types of DC motors (particularly series wound ) can operate on either AC or DC. Any DC motor that reverses when the applied voltage is reversed (i.e. permanent magnet types) will not run on AC.
The Voltage and the Frequency are varied to adjust the speed. This method is incorporated in a Variable Frequency Drive (VFD). If you want to run at a constant speed it is like any other motor. Variations in voltage, frequency and load cause speed variations, so a control system is required to compensate for these effects. In principle, a tachometer is used to measure actual speed, and the difference between this and the desired speed are used to adjust the speed, using a VFD.
You can control the speed of induction motors by varying the frequency. To have the motor operate properly you must also vary the voltage so that the ratio of voltage to frequency is constant. This keeps the iron in the motor from saturating.
I would assume so, DC motors when the voltage is lowered the motor slows. If you're in the US your ac supply is going to be 60hz unless you're modifying it.
