An electromechanical coupling model for an inclined drum washing machine vibration system based on Euler-Lagrange theory

Washing machines are typical systems with electromechanical coupling vibration. A novel approach is presented for modeling of an inclined drum washing machine system in this paper. Its Lagrangian function and Rayleigh dissipation function are obtained firstly. Then, its detail electromechanical coupling model is established based on Euler-Lagrange theory and variational principles. Notation that the model both in abc and dq coordinate frame are proposed corresponding to the model of permanent magnet synchronous motor in different coordinate frames. At last, some results of simulation and experiment operating at the same conditions are achieved, which can verify the correctness and effectiveness of the proposed approach. This paper provides a theoretical basis for further work on how to analyze, design and control vibration of the system. In addition, the proposed method also can give a novel way for the researches of other electromechanical coupling systems.