An analytical model of static stiffness for linear rolling guideway considering the structural deformations of carriage

Abstract

To solve the deformations and stiffnesses changes of linear rolling guideway under different loads, and to provide reference for the structural design of the carriage, this paper presents an analytical model of three-degrees-of-freedom static stiffness for linear rolling guideway considering the structural deformations of the carriage. In this study, first, the contact loads and elastic deformations between balls and raceways caused by external loads and preload were obtained by Hertz contact theory. The elastic deformations between balls and raceways were described by the change of the curvature centers of the carriage raceways. Next, according to the constraints and loading conditions of the carriage, the elastic beam theory was introduced, and the structural deformations of the carriage under the contact loads were equivalent to the deformations of two cantilever beams. Then, the external loads and the displacements of the carriage were derived by the static equilibrium conditions of the carriage. At last, the proposed equivalent model of carriage structure deformations was validated by comparing the calculated deformations of the carriage with those from a commercial program under various loading conditions, and the accuracy of the static stiffness model proposed in this paper was further verified by the experimental results in the reference. The results show that the calculated structural deformations of carriage matched the deformations calculated by a commercial program well. Also, with relative errors of 4.4–17.5%, the calculated stiffnesses using the model proposed in this paper more closely matched the measured stiffnesses. Clearly, there is a better match between the calculated results of the proposed model and the measurements than with the conventional rigid model.