Probabilistic Design and Analysis of Foundation Forces for a Class of Unbalanced Rotating Machines

Abstract

Rotors of rotating machinery inherently have mass eccentricities that transfer forces to the bearings, housing, and foundation of the machine. This paper considers, from a probabilistic viewpoint, ways to determine the foundation forces and their probabilities. A rotor-housing system is modeled with three degrees-of-freedom, a translation in the direction of the machine supports, a roll, and a pitch. Equations are presented for the motion of the model and the expression for maximum foundation force is developed. All parameters are constant except for rotor mass eccentricity, which is introduced into the problem as a random variable. The probabilistic analysis includes the calculation of the mean value of the foundation force and some measure for its error or variance. An approximate calculation for variance yields values too large for meaningful interpretation. However, a simulation method using a sufficient number of individual rotors leads to a quantile function that displays the variability of the foundation force data in useful form, and allows determination of foundation force probabilities. A numerical example illustrates how the equations can be applied to a sample taken from a population of mass-produced rotors.