Induction motors are very particular about the voltage and frequency supplied to them.

Pure sine wave supply from a power grid or a Diesel Generator or a pure sine wave inverter maintains a constant voltage of 110 Volts AC RMS or 220 Volts AC RMS and a constant frequency of either 50 Hertz or 60 Hertz.

This is ideal for induction motors and they work normally.

However in case of conventional inverters like Square Wave, Trapezoidal Wave, Modified Sine Wave or Quasi Sine Wave, the voltage fluctuates a lot and the frequency fluctuates much more.

This results in excessive vibrations in the windings and reduced torque due to unstable voltage and frequency.

This is not at all healthy for the fan or any motorized device as the excessive current will be induced in the windings and excessive heating in the coils that will damage them and break them.

Thus, always get a pure sine wave inverter for any motorized device or inductive load otherwise it will result in permanent damage.

Why ceiling fan give a humming sound an square wave inverter

This one’s a bit academic; you’d use it in a teaching rather a training environment. It’s got all the analysis that you don’t really need outside of a lab on it, but the germane bits are there too.

The wiggly blue line wiggles at a constant rate going up and down at the same rate over time. On this diagram that’s on the x axis (time is always on the x axis by convention) and if this was a UK grid supply the period would be 1/50th of a second (or to put it another way, 50Hz). One thing many beginners get confused with is the concept of a cycle. Some think going up is a cycle and going down is a second cycle. Nope. A cycle occurs when it’s gone up from the considered point (we normally set that at zero) gone to zenith, gone back to the zero, down to a nadir, and then the second cycle starts when it gets back to the zero point again. On the Y axis we get the amplitude. For electrical, that’s the voltage at that point. The UK has a 230V (nominal) supply, and so you’d think that the zenith and nadir would be 230V, yes?