Static condensation in modeling roller guides with preload

This article presents the methodology for modeling the stiffness of a machine tool load-bearing system using the finite element method. A new, simplified model of stiffness of the linear guide with a preload based on equivalent contact model was proposed. An equivalent contract model was developed where the ball was replaced with four rod elements of equivalent stiffness, interconnecting the opposite ends of the face of cuboidal finite elements. To shorten the computation time and facilitate modeling reduction and substructuring methods was used. The accuracy of the proposed model was compared with experimental results. In addition, the computation times were evaluated by comparing the simplified model with the full model and other equivalent models. Then, the model was used to determine the stiffness of the machine load-bearing system on the example of a machining table using the aforementioned methods and the obtained results were compared in terms of accuracy (less than 1% difference in maximum displacement value) and computation time with the classic approach (up to 97% in time reduction). This paper demonstrated the validity of the proposed model, allowing accurate and fast determination of the stiffness of machine tool load-bearing system.