The modeling and prediction of gravity deformation in precision machine tool assembly

The variation propagation in mechanical assembly is an important topic in several research fields, such as computer aided tolerancing (CAT) and product quality control. Mathematical models and analysis methods have been developed to solve this practical problem. Tolerance analysis which is based on the rigid hypothesis can be used to simulate the mass manufacturing and assembly. The state space model and stream of variation theory are mainly applied in flexible part assembly. However, in precision machine tool assembly, both tolerance design and process planning critically impact the accuracy performance, mainly because of the fact that the gravity deformation, including the part deformation and the variation in the joint of two connecting parts, cannot be ignored in variation propagation analysis. In this paper, based on the new generation GPS (Geometrical Product Specification and Verification) standards, the verification and modeling of key characteristics variation due to gravity deformation of single part and adjacent parts are discussed. The accurate evaluation of position and orientation variation taking into account form errors and gravity deformation can be solved from this model by FEM. A mathematical model considering rail error, stiffness of bearings is introduced to simulate the motion error in gravity effect. Based on this work to more accurately calculate the variation propagation considering gravity impact, a state space model describing the assembly process of machine tools is proposed. Then, in any assembly process, the final accuracy can be predicted to find out whether the accuracy is out of design requirement. The validity of this method is verified by a simulation of the assembly of a precision horizontal machining center.