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王威, 王维民, 任映霖, 王珈乐, 李维博. 平行轴涡动黏性充液转子动力稳定性计算和影响因素分析. 力学学报, 2024, 56(3): 1-15. DOI: 10.6052/0459-1879-23-553
引用本文: 王威, 王维民, 任映霖, 王珈乐, 李维博. 平行轴涡动黏性充液转子动力稳定性计算和影响因素分析. 力学学报, 2024, 56(3): 1-15. DOI: 10.6052/0459-1879-23-553
Wang Wei, Wang Weimin, Ren Yinglin, Wang Jiale, Li Weibo. Dynamic stability investigation and influential factor analysis of parallel axis whirl rotor partially filled with viscous fluid. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 1-15. DOI: 10.6052/0459-1879-23-553
Citation: Wang Wei, Wang Weimin, Ren Yinglin, Wang Jiale, Li Weibo. Dynamic stability investigation and influential factor analysis of parallel axis whirl rotor partially filled with viscous fluid. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 1-15. DOI: 10.6052/0459-1879-23-553

平行轴涡动黏性充液转子动力稳定性计算和影响因素分析

DYNAMIC STABILITY INVESTIGATION AND INFLUENTIAL FACTOR ANALYSIS OF PARALLEL AXIS WHIRL ROTOR PARTIALLY FILLED WITH VISCOUS FLUID

  • 摘要: 超重力离心机转子系统在临界转速之上存在液-固耦合激振诱发的失稳区域, 该失稳区域的存在直接威胁充液类超重力离心机转子的安全稳定运行, 同时严重制约了离心机转子向高转速、大型化方向发展. 本研究旨在探究充液离心机转子的液-固耦合机理及减振措施, 通过建立黏性充液转子的流体动力学方程, 结合连续性方程以及边界条件并耦合转子的动力学方程, 开展超重力充液类离心机转子的动力稳定性的计算方法研究. 首先, 推导扰动形式的纳维-斯托克斯方程, 采用有限差分的数值计算手段求解上述扰动形式的流体动力学方程, 得到壁面处的流体压强与流体剪切力并进行数值积分; 其次, 将所求液体等效主刚度系数及交叉刚度系数与转子动力学方程进行耦合, 并采用状态空间法降阶求解动力学方程的阻尼衰减指数和涡动频率. 经过对比充液转子系统在变转速区间内的阻尼衰减指数变化瀑布图与交叉刚度变化瀑布图, 发现充液转子的稳定性是转子系统的阻尼、刚度、充液比和流体黏性等多个特性参数作用的结果, 具体表现为增加转子系统外阻尼以及降低系统交叉刚度对抑制转子失稳与振动具有明显效果.

     

    Abstract: The centrifuge rotor system filled with partial liquid has an unstable region caused by fluid-solid coupling excitation above the critical speed, which directly threatens the safe and stable operation of the liquid-filled super gravity centrifuge rotor and severely limits the development of the centrifuge rotor to high-speed and large-scale. This research attempts to understand the mechanics of fluid-solid interaction and vibration reduction measures in the rotor of a liquid-filled centrifuge. The dynamic stability of the liquid-filled centrifuge rotor is calculated using a method that takes into account the dynamic equation of the rotor, as well as the hydrodynamic equation, continuity equations and viscous liquid boundary conditions. First, based on the perturbation form of the Navier-Stokes equation, the above unsteady hydrodynamic equation is solved by the finite difference numerical method, and the fluid pressure and fluid shear force at the wall surface are obtained and numerically integrated. Then, the fluid equivalent principal stiffness coefficient and cross stiffness coefficient are coupled with the rotor dynamic equation, and the damping exponents and whirl frequency of the dynamic equation are solved by the state space method. By comparing the waterfall plots of the changes in damping exponents and cross stiffness in the variable speed range of a liquid-filled rotor system, the calculation results show that the stability of the liquid-filled rotor is the result of the damping, stiffness, liquid filling ratio and fluid viscosity of the rotor system. Increasing the external damping of the rotor system and reducing the cross stiffness of the system has obvious effects on suppressing the instability of the rotor. This study avoids the phenomenon of extreme gradients caused by analytical solutions by solving the Navier-Stokes equations numerically rather than analytically. Additionally, state-space downscaling is used to solve the eigenvalues, greatly increasing computational efficiency and saving time a crucial factor when performing multi-operating condition calculations.

     

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