SIMULATION OF VIBRATIONS DUE TO BALL BEARING

众所周知，球轴承支承的转子系统会发生复杂的振动。一个特殊的非线性弹簧属性和参数激励之间的相互作用，径向负载和球的运动可能是一个合理的原因。利用计算机模拟的方法对相关现象进行了分析，并阐明了以下几点。(1)提出了一种计算外环-滚珠-内环间弹簧特性的算法/程序，其中考虑了作用在滚珠上的离心力。将其推广到由隐函数求最优多项式的一般问题。(2)本文提出了一种基于直接积分法（如RKG法）计算稳态振动及其稳定性的算法/程序。提出了一种提高RKG格式精度和估计误差界的方法。(3)基于谐波平衡原理，提出了一种与上述目的相同的算法/程序。方案（2）和（3） ...更多信息 在计算经济性方面进行了比较。(4)以Duffing系统和Helmholts系统为例，研究了存在精确解的非线性自由振动问题，并给出了在给定系统参数和频率的情况下，方便而精确地获得数值结果的方法。(5)有关杂项问题的治疗; a）逆转的幂级数数值和算术，B）精确计算的一个完整的椭圆积分的第一类，c）试验解决方案的隐函数（超级牛顿-拉夫逊以及超级Regula-法尔西计划）。(6)本文详细分析了圆柱滚子轴承的弹性特性，并将赫兹弹性接触理论（球与球之间）中的1.5次幂准则推广到任意次幂的理论。(7)应用计算机模拟计算了由内圈质量减小的简单径向球轴承（转子）组成的系统的径向振动。在很宽的转速范围内，除了常见的简谐振动外，还出现了亚谐振动、概周期振动和混沌等奇异现象。少

It is well known that a complicated vibrations occur in a rotor system supported by ball bearings. A peculiar non-linear spring property and a parametric excitation due to the interaction between radial load and the ball motion may be a plausible cause. The computer simulation is applied to analyse the relevant phenomena and the followings are clarified.(1) An algorithm/program is proposed to compute the spring property between outer ring-ball-inner ring, in which the centrifugal force acting on a ball is taken into account. It is extended to a problem to make generally an optimal polynomial from an implicit function.(2) An algorithm/program is proposed to compute the steady state vibrations and their stability based on the direct integral, e.g. RKG scheme. Also a scheme is proposed to improve the accuracy and to estimate the error bound of RKG scheme.(3) An algorithm/program is proposed to the same purpose to the above, based on the harmonic balance principle. Both schemes (2) and (3) … More are compared in terms of the computation economy.(4) Duffing and Helmholts systems are examined to serve example of non-linear free vibration whose exact solution exists, and a procedure is completed to obtain numerical results easily and precisely, using given system parameters and the frequency.(5) Related miscellaneous problems are treated; a)reversion of power series numerically and arithmetically, b)precise computation of a complete elliptic integral of the first kind, c)trial solution schemes of an implicit function (the super Newton-Raphson as well as super Regula-Falsi scheme).(6) Spring property of a cylindrical roller bearing is analysed in detail, and the 1.5 power index rule in the Hertzian elastic contact theory (between sphares) is extended to the theory with an arbitrary power index.(7) The computer simulation is applied to the radial vibration of a system composed of a simple radial ball bearing with a reduced mass (rotor) on the inner ring. Besides common harmonic vibrations, many strange phenomena e.g. subharmonic vibrations, almost periodic vibrations and the chaotics are found to occur in a wide range of operating speed. Less