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Yes, the MMF (Magnetomotive Force) of the damper windings in synchronous machines does depend on the pole pitch as well as other factors such as the current in the damper windings and the number of turns. The damper windings, placed in the pole faces of the rotor or around the poles, act to damp rotor oscillations during operation, especially under transient conditions. These windings are short-circuited, and their main role is to provide a path for induced currents when the rotor speeds up or slows down relative to the synchronous speed.
As the pole pitch affects the physical dimensions of the machine and the distribution of the magnetic field, it inherently impacts the characteristics of the MMF produced by the damper windings. A larger pole pitch signifies a larger physical machine size, which can alter the distribution and intensity of the magnetic flux, thereby affecting the induction in the damper windings and the resulting MMF. The MMF is crucial in generating the necessary reaction to counteract rotor oscillations and maintain stability during machine operation.