The effect of bearing properties on the eigenvalues of a rotordynamic system

Abstract

Natural frequencies and associated modal damping ratios are important in the diagnosis of rotating machinery problems. This work examines how the modal properties of a rotating shaft/disk system are affected by changes in rotation rate, lubricant viscosity, and bearing clearance. The system under analysis is a uniform, elastic, rotating shaft with a single, rigid disk concentrically mounted to the shaft away from mid-span. The shaft is supported by short-length, plain journal bearings. Standard lubrication theory is used to generate the stiffness and damping matrices for the bearings. The clearance and lubricant viscosity are independently adjustable at each bearing. A Ritz series expansion is used to generate the mass, stiffness, and gyroscopic matrices describing the shaft and disk. The combined action of the bearings and shaft/disk system is represented by stationary and rotational inertia, stiffness, and internal and external damping. A nonsymmetric generalized eigenvalue problem solver is used to calculate system eigenvalues from the system matrices over the speed range of interest. The behavior of the system is quantified in terms of dependence of the real and imaginary parts of system eigenvalues on the rotation rate. The real part of the eigenvalue is proportional to the modal damping ratio, and the imaginary part is the natural frequency. The analysis results include plots of natural frequency and damping ratio versus mode for varying bearing clearance and viscosity.