Research On The Approach Theory And Algorithm For Evaluating Geometrical Errors

Geometrical errors of parts are often the key factors that influence the complete appliance's working quality. On the basis of analyzing the characters and research states of the new generation geometrical product specifications, this dissertation focus on geometrical tolerances whose tolerance zones take on turning characteristic. In this dissertation, the mathematic definitions of geometrical tolerances are presented and the mathematical models for evaluating geometrical errors are created; To the principle of measuring coordinate values, an extensive study on how to solve the exact values of various errors is carried out, such as sphericity error,straightness error of median line,roundness error,cylindricity error,composite positional error and so on.Firstly, the basic conceptions based on the new generation geometrical product specifications are presented and the restraint relationships among different geometrical tolerances of the same factor are analyzed. The unified mathematical model for evaluating geometrical errors is created with the theory of point set topology.According to the meanings of form tolerances in correlative criterions and the mathematic definition theroies of tolerances, the mathematic definition of sphericity tolerance is presented and the mathematical model for evaluating sphericity error is created. The geometrical approximation theory of evaluating geometrical errors is put forward and modeled. The whole sphericity error approximation process is created and the data processing flow is presented. The simulation results indicate that the geometrical approximation algorithm have obvious predominance in evaluating accuracy , iteration times and otherwise .It researches how to select the optimal sample size when measuring geometrical errors in three-coordinates measurement machine. Taking measuring sphericity error with evenly distributed dot as an example, this dissertation brings forward the method of confirming the optimal sample size which is based on regression analysis. The result indicates the optimal sample size determined by this method is only the half of the usual sample size.The method determining the optimal sample size is studied aiming at the...