Reduced weight design of a flexible rotor with ball bearing stiffness characteristics varying with rotational speed and load

This paper presents an effective design approach for reducing the weight of a flexible rotor in ball bearings with rotational speed and load dependent stiffness characteristics under constraints on the system eigenvalues and bearing fatigue life. Design variables are chosen to be the inner radii of shaft elements, the positions of ball bearings, and the preloads on the bearings. The stiffness characteristics of high speed ball-bearings are completely described as functions of applied loads and spin speed, and applied to the dynamic behavior analysis of a rotor-bearing system. A transfer matrix method is used to obtain eigenvalues of the system and an augmented Lagrange multiplier (ALM) method is employed as art optimization technique. A multi-stepped rotor supported by two angular contact ball bearings is analyzed and designed to show the speed and load dependent stiffness effect on the system dynamic behavior and to demonstrate the effectiveness of the proposed optimum design approach. The results show that the effect of the stiffness on the system dynamic behavior is noticeable and that the suggested design approach is effective. [S0739-3717(00)00803-5].