Research On Sampling Strategy And Profile Error Evaluation Algorithm For Free-form Surface

The parts made of highly precise free-form surface play an important role in thefield of aerospace, shipbuilding and automobile. Due to the complex process and highprocessing cost of free-form surfaces, the false rejection rate should be reduced,that isthe detection and evaluation methods must be improved. The free-form surface (FFS)sampling points distribution strategy, the mathematical definition of FFS profile toler-ance, profile error evaluation model and algorithm are studied in this paper.The sampling points distribution strategy is discussed firstly. The existed skillof centroidalVoronoi tessellation (CVT) generation is used for reference; thecurvature function of surface is studied and modified to satisfy the demand of densityfunction and the convergence of energy function is regarded as terminal condition ofalgorithm. A sampling method based on CVT is proposed. The adaptive distributionof the sampling points is realized by this method.Secondly, aiming at obtaining the error value with high precision, the tolerancesemanteme of profile in ASME_Y14.5.1is analyzed and the mathematical definitionof profile tolerance is discussed. And then the distance function from sampling pointsto FFS is deduced, on the basis, a mathematical model of error evaluation is proposedby bring the grid motion into the function. Thirdly, a profile error evaluationalgorithm, which combining Differential Evaluation algorithm and Nelder-Meadalgorithms, is developed to solve this model. The error which is evaluated by the newmethod satisfies the minimum zone principle.At last, the simulations are designed to confirm the algorithms. The results showthat the algorithms mentioned in the paper areefficiency and robustness. They canimprove the accuracy of sampling and evaluation by comparing them with commonmethods.