Hybrid modeling and analysis of multidirectional variable stiffness of the linear rolling guideway under combined loads

In the working process of high-speed multiaxis machine tools, inertial loads due to high feed acceleration and time-varying gravity loads due to changing configuration of multiaxis structure result in time-varying complex loads applied to linear rolling guideway. Existing models cannot efficiently represent the effect of complex loads on multidirectional stiffness variation of linear rolling guideway. In this paper, a hybrid model of multidirectional stiffness of linear rolling guideway and the solving algorithm are proposed. The complex loading conditions of linear rolling guideway in high-speed multiaxis machine tool structure are considered. And contact flexibilities between rolling balls and grooves are modeled with the effect of elastic deformations of runner block and rail. The proposed model can calculate the multidirectional stiffness with high accuracy. Meanwhile the differences between the stiffness characteristics in different directions are represented correctly. The variations of multidirectional stiffness of linear rolling guideway under time-varying combined loads are analyzed. This study provides an effective way to comprehensively evaluate the stiffness characteristics of linear rolling guideway which can contribute to the dynamic analysis and active design of high-speed machine tool structure.