Static Stiffness Analysis Of Linear Motion Rolling Guides For Machine Tools

As a typical component,the linear motion rolling guide is widely used in machine tools.The static stiffness of the guide joint is an important performance index,which can not only reflect the bearing capacity of the guide,but also directly affect the dynamic performance of the machine tools.Therefore,it is very meaningful to establish the theoretical model for contact stiffness of the linear motion rolling guide.However,up to now,the angular stiffness of the linear motion ball guides system with four carriages is basically calculated by converting the linear stiffness of a single guide.In addition,no report can be found on the calculation of the five degrees-of-freedom static stiffness for the double-V roller guide and cross roller guide.Take these three types of linear motion rolling guides used in machine tools as the research objects,their static stiffness modeling and analysis are conducted.The specific research work is as follows:1)Based on the Hertz contact theory,the expression of the relationship between the ball-raceway contact force and contact deformation is derived.On this basis,a five degrees-of-freedom static stiffness model of a linear motion ball guides system with four carriages considering the table gravity is established,and then a test rig is set up to carry out the static stiffness test.Further analysis regarding the effects of loads,ball and raceway structural parameters on the static stiffness of the guides system are conducted.2)Based on the slicing method and elastic mechanics,the function expressions of the contact force and moment between roller and raceway are derived,and then the initial preload of raceways for the double-V roller guide under the combined action of table gravity and lateral preload is given.On this basis,a five degrees-of-freedom static stiffness model of the double-V roller guide is established.In addition,a stiffness test is carried out and the effects of loads and guide structural parameters on the static stiffness of double-V roller guide are analyzed.3)Using the established roller-raceway contact model,a five degrees-of-freedom static stiffness model of cross roller guide considering the arrangement of rollers is established,and then an experimental test is carried out using a cross roller guide,further study regarding the effects of loads,roller size and rollers arrangement on the five degrees-of-freedom static stiffness of the cross roller guide are conducted.The result of study suggests:1)Based on the Hertz contact theory or slicing method,the physical equations of contact between rolling element and raceway can be derived.Establish the deformation compatible equations,physical equations and force equilibrium equations of the guides joint,the static stiffness of the linear motion rolling guides with five degrees-of-freedom can be obtained by iteratively solving above equations using the Newton-Raphson method.2)The five degrees-of-freedom static stiffness of the linear motion rolling guides is affected by preload and external load,and different types of guides have different stiffness characteristics with load.In addition,the structural parameters of the rolling element and raceway have a significant influence on the static stiffness of the linear motion rolling guides,and the influence law is different.