Vertical Stiffnesses of Preloaded Linear Guideway Type Ball Bearings Incorporating the Flexibility of the Carriage and Rail

This article deals with the vertical stiffnesses of preloaded linear guideway type ball bearings (linear bearings) incorporating the flexibility of the carriage and rail. First the vertical stiffnesses of light and medium preloaded linear bearings were measured, as well as the outward carriage deformations in the width direction. Compared with the stiffnesses calculated by the conventional rigid model (assuming the carriage and rail are rigid, except for the contact points with the balls), the measured stiffnesses were about 40% less. In preloaded linear bearings under a vertical load, the side faces of the carriage deformed outward. The deformations were minimal at the top, increased toward the bottom, and had a tendency to be greater under either a larger preload or a smaller vertical load. The measured stiffnesses and outward carriage deformations cannot be explained using the conventional rigid model. To overcome these problems with the conventional rigid model, a flexible model (taking into account the flexibility of the carriage and rail) is presented in this article. The flexible model deformations were estimated through finite element (FE) analysis. The Hertzian contacts between the balls and the carriage or rail also were considered. With relative errors of 9-21%, the calculated stiffnesses using the flexible model more closely matched the measured stiffnesses. Also, the calculated outward carriage deformations matched the measured deformations well. Clearly, there is a better match between the calculated results of the flexible model and the measurements than with the conventional rigid model.