Geometry Searching Algorithm For Flatness Error Evaluation

Flatness error is an important content of mechanical parts form error, and is amajor technical index for processing of flat parts. The error size of it influence theservice life and usability of the mechanical system directly. Research the evaluationalgorithm of the flatness error which has high efficiency and high accuracy is of greatsignificance.According to the mathematic definition of flatness error and the minimumcondition criterion, the method to confirm the ideal plane when the measured plane iscontained by minimum area is researched in this paper, and the minimum zoneevaluation of the flatness error is realized by using geometric method. The researchcontents and results are as follows:1The minimum tolerance area criterion for flatness error evaluation and the leastsquare evaluation algorithm of flatness error are elaborated.2According to the geometric definition and the geometric characteristics of theflatness error, the traversal searching algorithm for flatness error evaluation isproposed. The effect rule of the different initial reference points and different extentedregions and different equipartition points on the flatness error is researched, and thedeterminating principle of the different initial reference points and different extentedregions and different equipartition points is given. The minimum conditionsverification for the results of the traversal searching algorithm has been done, andproves that the algorithm accords with the minimum tolerance area criterion.3The optimized analysis of the traversal searching evaluation algorithm forflatness error is made, and the geometric approximation searching algorithm forflatness error evaluation is proposed. The selection of initial reference points andauxiliary datum points and the optimization method for reducing the searching regionare researched, and the principle of optimal approximation and the base of judgementfor ending the approximation search are ascertained. The minimum conditionsverification for the results of the geometric approximation searching algorithm has been done, and proves that the algorithm accords with the minimum tolerance areacriterion.4The examples verification of the traversal searching algorithm and thegeometric approximation searching algorithm have been done. The examplesverification show that the evaluating results of the algorithms which have goodstypticity and stablity in this paper are agree with the results of representativemethods, and the algorithms can evaluate the flatness error effectively and accurately.