On the stiffness of linear roller bearings

Abstract

This thesis creates and validate a model for predicting the static stiffness of a linear crossed roller bearing as a function of its key design variables within a range of 20%. Linear crossed roller bearings play an essential role in the high-tech industry, this kind of bearing is used for precision applications such as microscopes, optical systems, and semiconductor production equipment. The performance of all these systems is related to the ability to produce and control a certain motion of a body. Bearings facilitate this motion, they are designed such that the resistance in the direction of movement is minimal. Generally, in all other directions, the bearing should be as stiff as possible as a high bearing stiffness is beneficial for controlling the motion. Stiffness is beneficial as it contributes to achieving a high control bandwidth and minimizes sensitivity to external forces or vibrations. Mechatronic systems have to meet very strict targets in terms of positioning accuracy and settling times. The dynamics of mechatronic systems is dominantly dependent on the performance of their bearings. Nowadays, the performance of a machine is predicted before building the physical machine through virtual prototyping. Virtual prototyping is becoming increasingly important: an accurate model in an early stage of a development project minimizes the risk of not achieving specifications in a later stage. For accurate modelling of precision machines using linear cross roller bearings, reliable data on the stiffness characteristics of these bearings is required. This thesis performs a step-by-step validation of models. Starting with an empiric determination of the load-stiffness relation for an individual cylindrical roller-rail contact as this is not affected by the uncertainties present in bearing assemblies. This is followed by an analysis of the tangential effects that come into play when a roller is loaded at 45°. Once the roller-rail model at 45° is validated, this empirical roller-rail model is used to develop a model that predicts the stiffness of linear roller bearing assemblies.