Parametric Optimization of Linear Ball Bearing with Four-Point Connection in Steer-by-Wire Steering Column by Means of Genetic Algorithm

Abstract

This paper presents the process of the optimization of linear ball bearings with four-point connection using a genetic algorithm and the finite element method. Currently, modern steering systems without an intermediate shaft—steer-by-wire systems—are being developed. The focus of this paper was on the optimization of linear ball bearings with four-point connection, embedded between the outer and inner columns tube in terms of the number of balls in the bearing and the clearance between balls. The aim of the research was to maximize the first two natural frequencies in the steering system, which is crucial for improving the stability and efficiency of the system. Various factors influencing natural vibration such as bearing geometry, raceway and ball materials, and operating conditions (preload) were taken into account in the research. Preload is a major factor affecting not only linear motion but also natural frequency. In order to speed up the calculations, the author’s simplified model of a linear bearing with the use of a system of springs was proposed. The nonlinear properties of the spring were determined on the basis of Hertz’s theory. A genetic optimization process resulted in a linear bearing structure that meets the natural frequency criteria. In addition, the full reference model was numerically compared with the simplified one, which showed convergent results of natural frequencies.