In order to solve the defects that the theory about air-gap flux density for field modulated permanent magnetic gear（FMPMG）is not perfect

and unable to deeply reveal its mechanism

based on the way of calculating the air-gap flux density and unilateral slotted air-gap permeance

the systematic mathematical model about air-gap flux density is deduced and established.In the light of the model

it can produce modulating effect to internal and external rotors

and make the modulated harmonic produced by one rotor match with the fundamental wave by another rotor

meanwhile the output rotational speed and torque of FMPMG is according to the gear ratio.The modulating effect of stationary steel polepieces depends on the magnetic number of pole pairs on the rotors

the more number of pole pairs

the more its modulating effect is obvious

on the other hand

is not obvious.