Linear bearings are important components that support the machine weight and load, as well as assist in precise transfer. Linear bearings consist of guide rails, carriages, and rolling elements. Among them, linear roller bearings are mostly used for systems that must support large loads, e.g., large...
Linear bearings are important components that support the machine weight and load, as well as assist in precise transfer. Linear bearings consist of guide rails, carriages, and rolling elements. Among them, linear roller bearings are mostly used for systems that must support large loads, e.g., large machine tools. Because the displacement and stiffness of linear bearings are directly related to the machine accuracy, it is very important to predict the bearing stiffness characteristics in advance at the design stage. This thesis presents a novel five degrees-of-freedom (DOF) model for the static analysis of linear roller bearings subjected to external loading. In this study, first, a rigid analytical model was developed to obtain the roller contact loads and displacements of carriage caused by the elastic deformation at the roller-carriage and roller-rail contact points. The non-Hertzian contact loads between the rollers and raceways were utilized to take into account the profiled roller and/or profiled guide rail. Next, the structural deformations of the carriage owing to the contact loads were computed using the finite element method (FEM). The associated displacements of the carriage top were derived systematically. Then, the total displacements of the carriage top were obtained by summing the displacements estimated from the rigid model and the induced structural displacements obtained by FEM. The proposed model was validated by comparing the calculated displacements of the carriage with those from a commercial program under various loading conditions. Further investigation regarding the effect of preload on displacements of the linear roller bearing was conducted. The simulation results showed the dependence of carriage rigidity and internal load distribution on the linear roller bearing characteristics.
On the other hand, the characteristics of linear roller bearings with guide rail error were investigated. For linear bearings, the guide rails are mainly fixed on the floor and the carriages moves along the guide rails, so that errors in the guide rails inevitably affect the motion error of the carriages. These guide rail errors can be caused from many sources such as uneven floor surface, guide rail machining error, deformation by heat, and deformation by bolt tightening. To obtain the motion error of the carriage on the erroneous rail, an analytical model was developed, which took into account the flexibility of the carriage under loading by using the finite element (FE) model. The motion error was obtained through the estimation of the bearing displacement during moving on the erroneous rail. To verify the accuracy of the proposed model for motion error estimation, it was compared with the data available in a reference. Then, the effect of rail waviness parameter such as wave length, error amplitude on the motion error of the carriage was investigated. The simulation results showed that the magnitude of motion error was very sensitive to the ratio of bearing length and rail error period.
Linear bearings are important components that support the machine weight and load, as well as assist in precise transfer. Linear bearings consist of guide rails, carriages, and rolling elements. Among them, linear roller bearings are mostly used for systems that must support large loads, e.g., large machine tools. Because the displacement and stiffness of linear bearings are directly related to the machine accuracy, it is very important to predict the bearing stiffness characteristics in advance at the design stage. This thesis presents a novel five degrees-of-freedom (DOF) model for the static analysis of linear roller bearings subjected to external loading. In this study, first, a rigid analytical model was developed to obtain the roller contact loads and displacements of carriage caused by the elastic deformation at the roller-carriage and roller-rail contact points. The non-Hertzian contact loads between the rollers and raceways were utilized to take into account the profiled roller and/or profiled guide rail. Next, the structural deformations of the carriage owing to the contact loads were computed using the finite element method (FEM). The associated displacements of the carriage top were derived systematically. Then, the total displacements of the carriage top were obtained by summing the displacements estimated from the rigid model and the induced structural displacements obtained by FEM. The proposed model was validated by comparing the calculated displacements of the carriage with those from a commercial program under various loading conditions. Further investigation regarding the effect of preload on displacements of the linear roller bearing was conducted. The simulation results showed the dependence of carriage rigidity and internal load distribution on the linear roller bearing characteristics.
On the other hand, the characteristics of linear roller bearings with guide rail error were investigated. For linear bearings, the guide rails are mainly fixed on the floor and the carriages moves along the guide rails, so that errors in the guide rails inevitably affect the motion error of the carriages. These guide rail errors can be caused from many sources such as uneven floor surface, guide rail machining error, deformation by heat, and deformation by bolt tightening. To obtain the motion error of the carriage on the erroneous rail, an analytical model was developed, which took into account the flexibility of the carriage under loading by using the finite element (FE) model. The motion error was obtained through the estimation of the bearing displacement during moving on the erroneous rail. To verify the accuracy of the proposed model for motion error estimation, it was compared with the data available in a reference. Then, the effect of rail waviness parameter such as wave length, error amplitude on the motion error of the carriage was investigated. The simulation results showed that the magnitude of motion error was very sensitive to the ratio of bearing length and rail error period.
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