Probabilistic analysis of foundation forces for a class of unbalanced rotating machines

Abstract

This dissertation considers the problem of the foundation force of an unbalanced rotating machine from both deterministic and probabilistic viewpoints. The rotor-housing is modeled as a three degree-of-freedom system wherein the principal modes of vibration are a vertical translation in the direction of the machine supports and a rolling and pitching motion of the rotor. The equations of motion for the system are derived using analytical methods, solved and related to the foundation force. For a selected machine class all parameters are constant except for rotor mass eccentricity, the distance from the center of mass of the rotating mass to the bearing axis. The deterministic analysis requires the selection of some representative value of eccentricity from the data available for a number of rotors. The corresponding foundation force is calculated. No measure of the error associated with the foundation force is available. The probabilistic analysis requires the calculation of the mean value of the foundation force and includes some measure for its error. The classical probabilistic method accounts for foundation force error by employing the "propagation of errors" formula to calculate variance. This method is found to yield values too large for meaningful interpretation. Another method, the simulation method, considers a sufficient number of rotors individually, such that, when compared as the quantile function, the variability of the data is displayed. The sample variance for the rotors considered yields a satisfactory measure of rotor error.