悬臂式箔片气体动压轴承的稳定性分析
发布时间：2018-10-22 10:39
【摘要】：悬臂式箔片气体动压轴承是一种以悬臂式弹性元件作为支承的自作用式气体动压轴承,其特殊的结构使得此类轴承具有自适应力强、低摩擦损耗、高转速以及良好的运转稳定性等突出的优点,此轴承有着非常深远的发展前景。随着当今科学技术的快速发展,对于提高机械设备转速的要求也日益强烈,而此问题的关键就在于解决气体轴承的高速稳定性问题。本文对悬臂式箔片气体动压轴承的稳定性问题,提出了比较系统的理论研究方法。 本论文主要研究内容： (1)运用了柱形薄壳的有矩理论,联合求解柱壳的几何方程、物理方程和平衡微分方程,得到并求解了柱壳非线性大挠度弹性变形偏微分方程组,对轴承的弹性箔片变形问题进行分析；利用流体润滑理论知识,推导出等温条件下动压气体润滑Reynolds方程,是研究的基础方程。 (2)建立了含有气体可压缩性和弹性箔片变形等因素影响的气膜厚度模型,将有限差分法(FDM)和Newton-Raphson迭代法耦合使用,利用Matlab编写程序完成压力控制Reynolds方程和气膜厚度方程的耦合求解,计算了气体轴承的压力分布、承载力、摩擦力矩以及偏位角等静态特性,分析了宽径比、轴承数、偏心率等参数对悬臂式箔片动压气体轴承静态特性的影响。 (3)在静态分析的基础上,建立了气膜厚度和压力关于扰动微量的十个关系方程,并利用耦合求解的方法实现该轴承润滑气膜动态特性的研究,分析了偏心率、扰动频率、转速、长径比、箔片弹性系数等参数对动态特性系数的影响。 (4)采用“八个动态特性系数”法,结合动力学运动方程,介绍了两种稳定性判别方法：临界质量、临界涡动比判别法和基于Routh-Hurwitz(劳斯-霍尔维茨)准则的特性方程系数矩阵各阶子行列式法。同时,建立了悬臂式箔片气体动压轴承的轴承—转子系统模型,利用后一种方法初步计算并验证该模型的稳定性。 本文的结果为研究悬臂式箔片气体动压轴承的稳定性提供系统的理论方法,还可以对此类轴承的动力学设计提供理论和数据参考。
[Abstract]:The cantilever foil gas dynamic bearing is a kind of self-acting gas dynamic bearing supported by cantilever elastic element. Its special structure makes this kind of bearing have strong self-adaptability and low friction loss. High speed and good running stability and other outstanding advantages, this bearing has a very far-reaching development prospects. With the rapid development of science and technology, the demand for increasing the rotational speed of mechanical equipment is increasingly strong, and the key to this problem is to solve the problem of high speed stability of gas bearings. In this paper, a systematic and theoretical study method is presented for the stability of the cantilever foil gas dynamic bearing. The main contents of this thesis are as follows: (1) the theory of moment of cylindrical thin shell is used to solve the geometric equation, physical equation and equilibrium differential equation of cylindrical shell. The partial differential equations of nonlinear large deflection elastic deformation of cylindrical shell are obtained and solved, the elastic foil deformation of bearing is analyzed, and the Reynolds equation of hydrodynamic gas lubrication under isothermal condition is derived by using the theory of fluid lubrication. (2) the film thickness model with the effects of gas compressibility and elastic foil deformation is established, and the finite difference method (FDM) and Newton-Raphson iterative method are used together. The coupling solution of pressure control Reynolds equation and gas film thickness equation is accomplished by using Matlab program. The static characteristics of gas bearing such as pressure distribution, bearing capacity, friction moment and offset angle are calculated, and the ratio of width to diameter and bearing number are analyzed. The influence of eccentricity and other parameters on the static characteristics of cantilever foil dynamic gas bearing. (3) on the basis of static analysis, ten relation equations of film thickness and pressure to disturbance trace are established. The dynamic characteristics of the bearing lubricating film are studied by coupling solution. The eccentricity, disturbance frequency, rotational speed and aspect ratio are analyzed. The influence of foil elastic coefficient and other parameters on the dynamic characteristic coefficient. (4) using the "eight dynamic characteristic coefficients" method and combining with the dynamic motion equation, two methods of judging stability are introduced: critical mass, and dynamic motion equation. The critical vorticity ratio method and the determinant method of coefficient matrix of characteristic equation based on Routh-Hurwitz (Laws-Holwitz) criterion are presented in this paper. At the same time, the bearing-rotor system model of the cantilever foil gas dynamic bearing is established, and the stability of the model is preliminarily calculated and verified by the latter method. The results of this paper provide a systematic theoretical method for the study of the stability of the cantilever foil gas dynamic bearing, and can also provide theoretical and data reference for the dynamic design of this kind of bearing.
【学位授予单位】：山东理工大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH133.3
本文编号：2286925
[Abstract]:The cantilever foil gas dynamic bearing is a kind of self-acting gas dynamic bearing supported by cantilever elastic element. Its special structure makes this kind of bearing have strong self-adaptability and low friction loss. High speed and good running stability and other outstanding advantages, this bearing has a very far-reaching development prospects. With the rapid development of science and technology, the demand for increasing the rotational speed of mechanical equipment is increasingly strong, and the key to this problem is to solve the problem of high speed stability of gas bearings. In this paper, a systematic and theoretical study method is presented for the stability of the cantilever foil gas dynamic bearing. The main contents of this thesis are as follows: (1) the theory of moment of cylindrical thin shell is used to solve the geometric equation, physical equation and equilibrium differential equation of cylindrical shell. The partial differential equations of nonlinear large deflection elastic deformation of cylindrical shell are obtained and solved, the elastic foil deformation of bearing is analyzed, and the Reynolds equation of hydrodynamic gas lubrication under isothermal condition is derived by using the theory of fluid lubrication. (2) the film thickness model with the effects of gas compressibility and elastic foil deformation is established, and the finite difference method (FDM) and Newton-Raphson iterative method are used together. The coupling solution of pressure control Reynolds equation and gas film thickness equation is accomplished by using Matlab program. The static characteristics of gas bearing such as pressure distribution, bearing capacity, friction moment and offset angle are calculated, and the ratio of width to diameter and bearing number are analyzed. The influence of eccentricity and other parameters on the static characteristics of cantilever foil dynamic gas bearing. (3) on the basis of static analysis, ten relation equations of film thickness and pressure to disturbance trace are established. The dynamic characteristics of the bearing lubricating film are studied by coupling solution. The eccentricity, disturbance frequency, rotational speed and aspect ratio are analyzed. The influence of foil elastic coefficient and other parameters on the dynamic characteristic coefficient. (4) using the "eight dynamic characteristic coefficients" method and combining with the dynamic motion equation, two methods of judging stability are introduced: critical mass, and dynamic motion equation. The critical vorticity ratio method and the determinant method of coefficient matrix of characteristic equation based on Routh-Hurwitz (Laws-Holwitz) criterion are presented in this paper. At the same time, the bearing-rotor system model of the cantilever foil gas dynamic bearing is established, and the stability of the model is preliminarily calculated and verified by the latter method. The results of this paper provide a systematic theoretical method for the study of the stability of the cantilever foil gas dynamic bearing, and can also provide theoretical and data reference for the dynamic design of this kind of bearing.
【学位授予单位】：山东理工大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH133.3
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