In order to explore the non-linear resonance characteristics of the mechanical-piezoelectric system of the harmonic piezoelectric motor, an electromechanical integrated harmonic piezoelectric motor is designed that integrates piezoelectric driving, harmonic drive and movable tooth drive.The electromechanical coupling equations of the driving system are set up based on the non-linear piezoelectric effect and non linear elastic effect. The primary resonance equations are deduced using the Linz Ted-Poincaré method. Then, the amplitude frequency curves are obtained, and the impact of different non-linear effects on primary resonance is analyzed. Finally, the accuracy of the analytical solution is verified with the Runge-Kutta numerical method. The results show that the influence of the non-linear piezoelectric effect on primary resonance dominates the non-linear elastic effect. The primary resonance of the piezoelectric stack occurred far from natural frequencies. Moreover, the jumping phenomenon appeared with frequency changes. The numerical response aligns well with the analytical response.