Modeling of Displacement of Linear Roller Bearing Subjected to External Forces Considering LM Block Deformation

Linear roller bearing (LRB) is an important mechanical element that is widely used in precise positioning systems that are subjected to large loads. This paper presents a new model for estimating the displacement of an LRB subjected to external forces. For this purpose, assuming that the linear motion block (LM block) is rigid, the equilibrium conditions for the LRB were obtained by solving the equilibrium equations of the rollers and the rigid LM block using the iterative Newton-Raphson method. The contact loads between the rollers and raceways were determined considering the profiled rollers. Then, the structural deformations of the LM block, subjected to the contact loads from the rigid LM block model, were computed using a finite element model for the LM block. The displacements of the LRB were then determined by superposition of the rigid LM block displacements on the induced displacements due to the structural deformations of the LM block. The proposed method was verified through comparison with a program by the bearing manufacturer.