In this paper, an axial flux coil assisted stator excitation BLDCM (CASEM) is designed. Because of the high magnetic saturation and strong coupling, the mathematical model of the motor has strong nonlinearity, and it is difficult to establish an accurate flux linkage model. Therefore, a three-dimensional flux linkage modeling method based on Fourier series is proposed in this paper, which considers multi-phase coupling and non-linear problems. Finally, a simulation model and an experimental platform are established to verify the correctness and effectiveness of the modeling method, which lays a foundation for further research on motor control to reduce torque ripple.