Research Of Form Errors Based On The Genetic Algorithm

Form errors of parts have a crucial impact on the performance of the machine, especially in mechanical products of high precision. Therefore, at home and abroad, measuring and evaluating accurately for the form and position errors of parts has been a general concern problem. Establish the mathematical model of form errors and research its corresponding algorithm in the Cartesian coordinate system is of great significance.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 errors 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 errors is established by least squares circle, minimum zone circle, minimum circumscribed circle and maximum inscribed circle method. The mathematical model of the sphericity errors is established by least squares sphere, minimum zone sphere, minimum circumscribed sphere and maximum inscribed sphere methods. The mathematical model of the cylindrical errors is established by least squares cylinder, minimum zone cylinder, minimum enclosing cylinder and maximum inscribed cylinder methods. The mathematical model of the spatial straightness errors is established by least squares and minimum zone methods.The assessment method of form errors based on genetic algorithm was studied systematically. The specific steps of the assessment methods of form and position errors based on genetic algorithm were given.The basic nature of the objective function about the mathematical models was studied systematically. The graphics and contour map of the objective function is plotted by a large number of experimental data. It is proved by experiment that the minimum values of the objective function for the minimum zone method. The objective functions are continuous and convex function, the minimum value is unique.Finally, the ability of genetic algorithm for the form errors was proved by examples and analysis of results. Its accuracy is very high. It can be infinitely close to the real values.in theory. It applies to the form and position errors of the coordinate measuring machine data processing.