Research On The Mathematical Models And Visualization For Form And Position Errors Based On Radius Measurement

Form and position errors of parts are the key to performance of machine, especially in mechanical products of high precision. Therefore, at home and abroad, measuring and evaluating accuratly for the form and position errors of parts has been a general concern problem. Based on radius measurements, the theory of evaluation for the form and position errors is not particularly perfect.In this thesis, in accordance with national standards for the definition and evaluation method about the form and position errors, the mathematical model of the straightness error is established by least squares and minimum zone methods. The mathematical model of the flatness error is established by least squares and minimum zone methods. The mathematical model of the roundness error is established by least squares circle, minimum zone circle, minimum circumscribed circle and maximum inscribed circle methods. The mathematical model of the cylindrical error is established by least squares cylinder,minimum zone cylinder, minimum enclosing cylinder and maximum inscribed cylinder. The mathematical model of spatial straightness error is established by least squares and minimum zone methods.The mathematical model of the concentricity error is established by least squares and minimum zone methods.The graphics and contour map of the objective function is ploted used a large number of experimental data by MATLAB.It is fully demonstrated that all objective functions are continuous and convex function, the minimum value is unique,and any local minimum point is the global minimum point.In visualization,the simulation about the error graphic of the actual measured surface is realized by interpolation calculation and graphical display capabilities of MATLAB.We can see micro-geometry of the actual measured surface intuitively.It can provide valuable information for causing the errors and improving the processing.A evaluation system of the form and position errors is developed by Lab Windows/CVI based on the least squares method in this thesis. Select a specific evaluation of the system in the start screen.The rapid and accurate error evaluation for the sampling data can be made after inputting the necessary sampling parameters to the panel. Assessment results can be automatically saved.