Static Stiffness Characteristics Analysis Of Five-Degrees-of-Freedom Linear Motion Ball Guide

Linear motion ball guide(LMBG)is a typical kind of sliding joint.It is widely used in CNC machine feed systems because of its high stiffness and low friction.The stiffness of the LMBG directly determines the rigidity of the machine tool.Therefore,it is of scientific significance and engineering value to study and establish the static stiffness model of the LMBG.However,the traditional 5-DOF static stiffness models of the LMBG ignore the flexible deformation in the non-contact area of the ball and raceway,resulting in a large deviation between the theoretical calculated stiffness value and the experimental test results.While the stiffness models considering the flexible deformation in the non-contact area of the joint are mostly used in calculation of linear stiffness,and the ones used in calculation of angular stiffness have not yet been reported.In this paper,the 5-DOF static stiffness modeling and analysis considering the flexibility outside the Hertz contact area is carried out for a typical linear motion ball guide,and the specific research work is as follows:1)5-DOF static stiffness rigid modeling of the LMBG:The physical equation of the ball-raceway deformation is established based on the Hertz contact theory.The deformation coordination equation is created based on the deformation coordination assumption.The equilibrium equation is created based on the force analysis of the carriage.Based on these equations,the static stiffness rigid model of five-degree-of-freedom LMBG is established.2)5-DOF static stiffness flexible modeling of the LMBG:The assumption of linearization of carriage and rail load-deformation is proposed,and the ball-raceway flexible contact model is established based on Hertz contact theory.The equivalent stiffness of carriage and rail is obtained using the FEM software.Then the static stiffness flexible model of five-degree-of-freedom LMBG is established based on the ballraceway flexible contact model,the deformation coordination equation and the equilibrium equation.Besides,a general calculation program based on MATLAB software is prepared to complete the solution of the flexible model.3)Static stiffness characteristics analysis of the LMBG:Using the established five-degree-of-freedom static stiffness model of the linear motion ball guide,numerical calculation is carried out on a specific linear motion ball guide as an example.Further analysis regarding the effects of loads and ball mounting method on the static stiffness of the guide system are conducted.The result of study suggests:1)The linear displacement of the carriage and rail shows a good linear relationship with the contact force,which indicates that it is reasonable to ignore the flexible deformation of the ball and linearize the stiffness outside the Hertz contact zone of the carriage and rail when modelling.Besides,compared with the deformation of carriage and rail,the deformation of ball under the contact force is extremely small,which can be neglected.2)For the LMBG of HGH45 CA type,the relative errors of vertical linear stiffness,rolling stiffness and yawing stiffness of the LMBG calculated by the flexible model are only 3.77%,9.03% and 41.73% respectively from the measured values,which are respectively 17.2%,11.58%and 16.73% lower compared to the rigid model.In addition,the 5-DOF static stiffness of the LMBG is affected by the external load,preload and initial contact angle,and the influence laws are different.