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

Abstract

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.

Research on nonlinear static and dynamic characteristics of linear guideway in machine tools considering carriage flexibility

“…The stiffness and displacement of the linear guideway have been extensively researched. Yang et al [6] analyzed the differences of the stiffness in different directions of the linear guideway, and discussed the multi-directional stiffness variation under the action of the complex loads. Cheng et al [7] established the stiffness matrix model of the roller linear guideway according to the energy balance equation, and discussed the influences of the external load and preload on the load distribution, energy loss and stiffness.…”

Effects of nonlinear behaviour of linear ball guideway on chatter frequency of lathe machine tool

“…Moreover, the preload applied to the LBG has a fundamental effect on the dynamic properties of the entire system and hence impacts the chatter stability of the tool [8,9]. Yang et al [10] showed that the contact stiffness of the groove in linear rolling guideways may vary by as much as 68-85% in different directions, depending on the type of load. Several studies have shown that the ball-groove contact behaviour, which represents the main source of nonlinearity in LBGs, can be well described by Hertzian contact theory [11,12].…”