SIMULATION OF VIBRATIONS DUE TO BALL BEARING

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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