From Random Tolerances to Random Rotor Vibrations

Abstract

In the paper a statistical distribution of reaction forces in a vibrating rotor is traced back to assigned tolerances on components making up this rotor. First, the statistics of the unbalanced mass in an n-ring assembly is considered and an explicit expression for it is derived in terms of tolerances assigned to individual rings. As an illustrative example, the problem of vibrations of a rotor with two assembled disks is considered. The disks are manufactured to different specifications and the statistical distributions of reaction forces are found by Monte Carlo simulation. The latter allows to estimate the probability of vibrations or forces exceeding a specified level for a given accuracy of manufacturing. The methodology presented establishes a direct link between the manufacturing specifications for the components and the quality of performance of the equipment.