Abstract
The purpose of this study is to investigate the stiffness of preloaded linear rolling ball guideway by method of FEA, experiment and theoretical approach, respectively. The stiffness of specific preload setting in the linear guideway was investigated by analyzing the relation between downward load and vertical displacement. The preload was determined by oversized balls which were interference fitted in the space between block and rail. FEA model was used to predict the stiffness of zero preload linear guideway (+0μm interference fitted) with only one rolling ball diameter of length of the guideway was used in modeling (1/12 length of the guideway). The results of this study were (1) prove that the stiffness provided by upper of 2 rows of rolling ball under downward load, not distributed from 4 rows equally. The deflection and contact angle change induced by ball rotating and compression under downward load. (2) Indicated a linear relation between the vertical load and the vertical displacement. Result shows a constant stiffness of the linear guideway under variable vertical loads. There were four parts of experiments developed in this study. In Part 1, the experimental fixture equipped with highly rigid frame, LVDT length measuring probe and load cell were used for stiffness measurement. The three types of test blocks （model U/R/A）with zero preload (+0 μm oversized ball fitted) were prepared to investigate the effect of varying the block geometry on stiffness. This result indicates that the variation in width and the variation in thickness at the block do not significantly affect the vertical stiffness in the experiments. In Part 2, the experimental setup for outward deformation of block (model R) with different oversized ball (+4/+8/+11 μm) were measured by two digital indicators, one on the vertical direction and another on the transverse direction. This result indicates that the deformations along the transverse direction are greater than those along the vertical direction. In Part 3, the measurements of the stiffness of preloaded linear guideways (model R block) were obtained from fixture of Part 1. The preload was determined by using four types of oversized balls that were interference fitted (+0/+4/+8/+11 μm). This result shows that the vertical displacement increases nonlinearly with an increase in the vertical load. The stiffness increases nonlinearly with an increase in the vertical load and oversized ball significantly affects stiffness. In Part 4, the experimental test rail equipped with opening notch design and micro load cell were used for internal force of preload measurements. The three types of test blocks (model U/R/A) and different oversized balls (the oversize amounts are from -10μm to +11μm) were prepared to investigate the effect of varying the block geometry on internal force of preload. This result indicates that the internal forces of preload increases nonlinearly and oversized ball significantly affects. The variation in thickness at the block is more significantly affect the internal forces than the variation in width in the experiments. For the theoretical approach, the contact angle equation of a steel ball based on Hertz’s contact theory and a deflection equation assuming a rigid block and rail were derived. An equation to calculate the preload of the preloaded linear guideway was also introduced for theoretical stiffness study. The preload was determined by using four types of oversized balls (+0/+4/+8/+11μm). There is a nonlinear relation between the vertical load and the vertical displacement for different preloads. The results show a non-constant stiffness of the linear guideway under variable vertical loads. In the zero preload linear guideway (+0μm interference fitted), the stiffness increased nonlinearity when vertical load increased. In the preload linear guideway (+4/+8+11μm interference fitted), at the begging the stiffness decreased nonlinearity and reveries increased nonlinearity when vertical load increased. At avertical load of around 6000 N, comparison of the measured vertical stiffness with the theoretical stiffness revealed relative differences ranging from 4.5% to 24.7%. The Pearson correlation coefficient between the transverse deformation and the difference between the experimental and theoretical stiffness is 0.959. The Pearson correlation coefficient shows that the correlation is significant. On the basis of these investigations, this study proposed an equation for modifying the theoretically calculated stiffness. The theoretical displacement was divided by to obtain the modified stiffness. A comparison of the measured vertical stiffness with the modified theoretically stiffness revealed relative differences ranging from 0.1% to 4.6%.