Research Of Conicity Error Evaluating Algorithm Based On Area Hunting

Conical part is one of parts which is widely applied in machinery industry and aeronautics and astronautics industry. Conicity is a whole representation for form error of each geometric element of conical surface. The accurate assessment of conicity plays a crucial role in analyzing the causes of error and judging the qualitication of parts.In this dissertation, the research status on conicity error is introduced, and the typical evaluation algorithms and the mathematical models, such as genetic algorithm and simplex method, are explained. According to the definition of conicity error, two kinds of the area searching algorithms for conicity error evaluation are proposed. One was called as mesh searching algorithm, and another as geometrical optimization algorithm. These algorithms are all suitable for the situation of arbitrarily sampling. Using least square method and basic principle of three-point determine a circle, the selecting method of the initial axis during conicity error evaluation is determined, while sampling points are equal interval or unequal interval;taking the initial axis as a reference line and assigning the grid points and simple geometrical figures, the rules and procedures of changing position of assumed ideal conical axis are researched;taking the assumed ideal conical axis and the average radius of initial measured section and terminate measured section as main parameters, the assumed ideal cone was structured, and contrasting all values of maximum minus minimum between measured points and assumed ideal cone, the minimum zone conicity error of containing actual measured cone contour is obtained though calculation, comparison, corresponding judgement and circulation;the judging method of containing the minimum zone is discussed.The numerical simulation and comparison experiments were carried out to confirm the proposed algorithms. According to the results of numerical simulation and comparison experiments, the relationship between the conicity error evaluation precision and the partition rule of grid points in mesh searching algorithm is analyzed. The numeric area of grid points which match up to evaluation precision is also discussed;the principle of determining side of simple geometric figure in geometrical optimization algorithm is obtained, and the judging conditions of terminated optimizing circulatory which match up to evaluation precision is gained.The two algorithms which dissertation proposed adopt pure geometrical arithmetic,and the algorithm principle is simple and is easy to programme. First, layout of grid point,setting of geometric area and searching procedure are solved in the two algorithms. Then repeatedly calling distance formula of point or point and line to compare and judge, the area searching algorithms for conicity error evaluation can be used to evaluate conicity error accurately and effectively.