振动磨非线性碰撞振动的建模与分析

Simulation and Calculation of theNonlinear Collision of the Vibration Mill

振动磨系统的非线性主要来自散体介质的变质量碰撞，其中主碰撞和亚谐碰撞对系统动力学影响最为显著。主碰撞不但具有时变性，而且与空间坐标有关。基于研究的新进展，考虑到散体重心的动态偏移，提出了三自由度非线性振动模型，用平均法进行了求解分析，用时间序列分析的方法估计了变质量模型参数。分析求得机器振幅与实测值吻合较好，验证了所提出的理论和方法。

The nonlinearity of the oscillation system of the vibration mill is mainly due to the variable mass collision, where the principal and subharmonic collisions have the strongest influence on the system's dynamic behaviour. Moreover, the principal collision depends not only on time, but also on space. Therefore, the simulation of the system must be followed point by point. Based on the new research development and considering the dynamic displacement of the mass center of the grinding media, a threedegreeoffreedom nonlinear mathematical model is presented in this paper. A time series analysis procedure is introduced for the estimation of the mass parameter with subharmonic and an averaging method is used for the solution of the governing equations. The calculated amplitudes are in good agreement with the tested ones.