SIMULATION OF VIBRATIONS DUE TO BALL BEARING

滚珠轴承引起的振动模拟

• 批准号: 61550190
• 负责人: TAMURA Hideyuki
• 金额: $ 1.28万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1987
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61550190/
• 关键词: Vibration of Rotor; Ball Bearing; Machine Element; Running Accuracy; Computer Simulation; Random Vibration; カオス

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

众所周知，由滚珠轴承支撑的转子系统会发生复杂的振动，其原因可能是由于径向载荷与滚珠运动之间的相互作用而产生的特殊非线性弹簧特性和参数激励。 (1)提出了一种计算外环-球-内环之间弹簧特性的算法/程序，其中考虑了作用在球上的离心力。扩展到从隐式函数得到一般最优多项式的问题。（2）提出了一种基于直接积分计算稳态振动及其稳定性的算法/程序，例如，还提出了一种方案。提高精度并估计RKG方案的误差范围。(3)基于谐波平衡原理，提出了与上述相同的算法/程序，对方案(2)和(3)进行了比较。在计算方面(4) 研究了 Duffing 和 Helmholts 系统，以提供存在精确解的非线性自由振动的示例，并完成了一个程序，以便使用给定的系统参数和频率轻松、精确地获得数值结果。(5) 相关处理各种问题；a）幂级数的数值和算术回归，b）第一类完全椭圆积分的精确计算，c）隐函数的试解方案（超级牛顿拉夫森为(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(球体间)中的1.5幂指数法则推广到任意幂指数理论(7)对由内圈减质量的简单向心球轴承(转子)组成的系统的径向振动进行了计算机模拟，除了常见的简谐振动外，还出现了许多奇怪的现象。例如，在较宽的运行速度范围内会出现次谐波振动、几乎周期性振动和混沌现象。

项目成果

原要一郎: 日本機械学会論文集. 53. 2127-2134 (1987)

原阳一郎：日本机械工程师学会会议记录 53. 2127-2134 (1987)。

田村英之: 日本機械学会論文集. 52-475. 85-858 (1986)

Hideyuki Tamura：日本机械工程师学会会议记录 52-475（1986）。

田村英之: 日本機械学会論文集. 53. 2199-2207 (1987)

Hideyuki Tamura：日本机械工程师学会会议记录 53. 2199-2207 (1987)。

田村英之: 九州大学工学集報. 61. (1988)

田村秀幸：九州大学工学通报 61。（1988）

Hideyuki TAMURA: "Computation of a Complete Elliptic Integral of the First Kind Using q-Expansion" Technology Reports of the Kyushu University. 61. (1988)

Hideyuki TAMURA：“使用 q-Expansion 计算第一类完全椭圆积分”九州大学技术报告。