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Abstract: Based on the finite element method (FEM) and the Lagrange equation, a novel nonlinear model of a double disc rotor-seal system, including the coupled effects of the gravity force of the discs, Muszynska’s nonlinear seal fluid dynamic force, and the mass eccentricity of the discs, is proposed. The fourth order Runge-Kutta method is applied to solve the motion equations of the system and numerically determine the vibration response of the center of the discs. The dynamic behavior of the system is analyzed using bifurcation diagrams, time-history diagrams, axis orbit diagrams, Poincaré maps, and amplitude spectrums. With the rotor speed increasing, the system presents rich forms including periodic, multi-periodic, quasi-periodic, and chaotic motion. We also discuss the effects of the distance between the two discs, the mass of the discs, seal clearance, seal length, and seal drop pressure on the dynamic behavior of the system. The numerical results demonstrate that a symmetrical disc structure, small disc mass, proper seal clearance, long seal length and high seal drop pressure can enhance the stability of a double disc rotor-seal system. The results provide a theoretical foundation for the design of multi-stage sealing systems.

非线性双圆盘转子-密封系统的数值分析

研究目的：求解双圆盘转子-密封系统的非线性振动特性和运动响应
创新方法：采用有限元法（FEM）和拉格朗日方程求解双圆盘转子-密封系统，进而为研究多级转子系统的非线性振动问题提供有效方法。
研究手段：基于有限元法（FEM）和拉格朗日方程，得到包含Muszynska非线性密封流体力和圆盘重力作用下的双圆盘转子-密封系统的运动方程。同时利用四阶龙格-库塔法求解系统动特性运动响应情况，利用分岔图、时间历程图、轴心轨迹图、庞加莱映射和幅值谱等分析图研究双圆盘转子-密封系统的非线性振动特性。
重要结论：随着转速的增大，双圆盘转子-密封系统呈现丰富的非线性运动形式，包括周期性运动、多周期运动、准周期运动以及混沌运动。在右端圆盘不平衡质量小于34 kg、密封间隙范围为0.376 mm–0.54 mm、密封长度大于0.13 m或者密封压差高于0.104 MPa的情况下均有利于提高双圆盘转子-密封系统的稳定性。

关键词：非线性；转子-密封系统；有限元法；流体激励

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