Stiffness Analysis of Linear Guideways Without Preload

Abstract

AbstractTheoretical and experimental investigations of the stiffness of non-clearance linear guideways without preload were conducted. A theoretical approach that applied Hertz's contact theory to steel balls to derive the contact angle equation was proposed. The theoretical analysis showed that the stiffness of the linear guideway under variable vertical loads changes nonlinearly with the external load. Therefore, an experimental setup was proposed in which the stiffness curves of three blocks, differing in geometrical shape and assembled with steel balls, were measured under increased vertical load until the guideway began to plastically deform. The results showed that variation in both the width and the thickness of the block does not significantly affect stiffness. A comparison of the theoretical and experimental results revealed a relative error of 4.5%, indicating the correctness of the theoretical model. Based on theoretical equations, the main parameters that affect stiffness are conformityfm, coefficient of contact deformationcδ, reference diameter of the ballDw, number of load-carrying rowsi, number of load-carrying balls in one rowZ, and initial contact angle α0. The results are useful for determining the static/dynamic behavior and rigidity of linear guideways in the design stage.