关键词: 量词约束满足, Monte Carlo仿真, 小位移旋量理论, 公差分析, 凸壳化理论

Abstract: Aiming at the tolerance analysis problem in complex assembly,a new worst-case and statistical three-dimensional tolerance analysis method was proposed.The influence mechanism of quantifier notion(or)simulating geometrical deviations on geometrical behavior and the differentiation of diverse contact surfaces on the geometrical behavior were considered.By using Small Displacement Torsor(SDT)theory,the impact of geometrical deviations and contact types on the geometrical behavior was described.Through analyzing the convex hulls(compatibility hull,interface hull and functional hull)with three-dimensional parameter space,a mathematical quantifier expression was made for parts'admissible deviations,and the corresponding three-dimensional chains was formed.Based on the established Quantified Constraint Satisfaction Problem(QCSP),the mathematical tolerance analysis model was established,and simulation and testing were done by using worst-case method and Monte Carlo method.The effectiveness of proposed methods was proved with the feed system of TGK46100 CNC machine.

Key words: quantified constraint satisfaction problem, Monte Carlo simulation, small displacement torsor, tolerance analysis, convex hull theory