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中文摘要：
当软轴型单晶炉提拉系统工作在某一转速附近时,其重锤摆动量会显著增大,严重影响单晶生长质量。为解决此问题,需要建立该系统的数学模型来研究提拉系统的动力学特性。本文在对提拉系统工作原理分析的基础上,应用Lagrange第二类方程建立了考虑该系统面内、面外振动的四自由度非线性振动微分方程。导出了该非线性模型的近似线性模型,对非线性模型响应与线性模型响应做了比较。进一步分析了系统的稳定性,应用Campbell图得到了考虑回转惯性效应后系统的临界转速。通过数值仿真定量说明了减小对中误差和增大阻尼可以减小重锤系统最大摆动幅值。
英文摘要：
When the pulling system of single-crystal growth furnace runs near a certain speed,the oscillation in the end of pulling system increases significantly,which seriously affects the growth quality of single crystal.In order to solve this problem,the mathematical model of pulling system is required for studying its dynamic characteristics.In this work,first,the four degrees of freedom nonlinear dynamic equations considering the rotation inertia of single-crystal object were built by Lagrange equation.Then,a linear approximation model was deduced from the nonlinear model,the responses of linear model were compared with that of nonlinear model by means of the implicit Runge-Kutta integration.The system＇s stability was analyzed,and the critical speed of the system was obtained with Campbell diagram when the gyroscopic effect was taken into account.Finally,the numerical simulations showed that the maximum amplitude of oscillation could be allayed by reducing the center error and increasing the damping.
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A new method for the determination of the zero velocity region of the Karnopp model based on the sta
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