SIMULATION OF VIBRATIONS DUE TO BALL BEARING

众所周知，由球轴承支承的转子系统会发生复杂的振动。一种特殊的非线性弹簧特性和径向载荷与球运动之间的相互作用引起的参数激励可能是合理的原因。利用计算机模拟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-球-内环之间弹簧特性的算法/程序，其中考虑了球的离心力作用。将其推广到从隐函数求一般最优多项式的问题。(2)提出了一种基于直接积分的稳态振动及其稳定性计算算法/程序，如RKG格式。提出了一种提高RKG格式精度和估计误差界的方案。(3)基于谐波平衡原理，提出了一种与上述相同的算法/程序。(2)和(3)两种方案在计算经济性方面进行了比较。(4)以存在精确解的Duffing和Helmholts系统为例，在给定系统参数和频率的情况下，完成了简单而精确地得到数值结果的程序。(5)处理相关杂项问题；a)幂级数的数值和算术反演，b)第一类完全椭圆积分的精确计算，c)隐函数的试解格式（超级Newton-Raphson格式和超级regular - falsi格式）。(6)详细分析了圆柱滚子轴承的弹簧特性，将赫兹弹性接触理论中的1.5幂指数法则推广到任意幂指数理论。(7)对内圈减重的简单径向球轴承（转子）组成的系统的径向振动进行了计算机模拟。除常见的谐波振动外，在较宽的运行速度范围内，还会发生亚谐波振动、近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