基于双摆模型的单晶炉提拉系统摆动现象动力学分析

Dynamic Simulation of Oscillation Phenomenon of Single-Crystal Growth Furnace Lifting System Based on Double Pendulum Model

针对单晶炉旋转提拉系统在运行中出现的摆动现象进行了建模和数值仿真。将该旋转提拉系统简化为在支座简谐激励下的双摆力学模型,模型中考虑了提拉软轴及提拉头的质量,以及系统的阻尼。应用拉格朗日方程导出了该系统的非线性振动方程并加以线性化,通过模态分析将耦合的双自由度振动方程化为两个单自由度方程。应用Matlab平台进行数值仿真,模拟出了提拉系统振动幅值随旋转频率的变化关系。理论分析结果与实际中观察到的现象一致。研究结果为改善提拉系统的动态性能,减小提拉系统的摆动幅值提供了理论方法和依据。

Modeling and numerical simulation of oscillation phenomenon of single-crystal growth furnace rotating - lifting system is studied. The rotating - lifting system of single-crystal growth furnace is simplified into a double pendulum model under harmonic excitation of supporting. The masses of lifting soft axis and lifting head, and the system＇s damping are taken into account in this model. The nonlinear oscillation equation of this system is established by means of the Lagrange ＇ s equation, and is linearized under the assumption of micro-oscillation. The equation of two-degree freedom system is decoupled into two single equations by means of modal analysis. The relationship between oscillation magnitude and rotation frequency is simulated using Matlab software. The results of theoretical analysis are in agreement with the reality phenomenon. The research provides basis for improving the dynamic properties and diminishing oscillation magnitude of this system.