Construction and validation of a theoretical model of the stiffness matrix of a linear ball guide with consideration of carriage flexibility

The stiffness matrices of joint elements, such as rotating and linear bearings, are essential for both static and dynamic analyses of mechanical systems employing such elements. However, few models of fully occupied stiffness matrices of linear guides are available. Here, we develop a comprehensive analytical model for calculation of the stiffness matrix of a linear ball guide. The model features five degrees of freedom (DOF) of loading, and displacement. Contacts between the balls and the rail/carriage are handled using Hertz contact theory. Carriage flexibility is considered using a new finite element model. A 5 x 5 stiffness matrix for a linear ball guide was derived and numerically validated under various loading scenarios using commercial software. Changes in stiffness elements by load, ball arrangement, and certain critical geometric parameters were evaluated. Finally, we built an experimental platform to further verify the model. The calculated displacement of a linear ball guide closely corresponded to the experimental data derived using varying external loads and preloads. (C) 2019 Elsevier Ltd. All rights reserved.