Research On Digital Inspection And Assessment Algorithm Of Three-dimensional Circularity Errors

With the development of computer technology, precision and ultra-precisionmachining technology, digital processing technology and detection technology, thequality requirements of mechanical parts are becoming more stringent in engineeringpractice. The circularity error which is one familiar form errors produces an effect onthe parts with fit precision, tightness, wear resistance and service life directly. Thetwo-dimensional circularity error evaluation methods which has a few limitationscannot be used directly for inclined holes and tilted shafts in space anywhere.Although the research on evaluation methods of three-dimensional circularity errorexists, it is still immature. Since the new generation Geometrical ProductSpecifications and Verifications is put forward, it has great theoretical significanceand engineering value for a systematic study on digital detection and evaluation of thethree-dimensional circularity error.Firstly, the operation and operator technology of the three-dimensionalcircularity error detection were described, according to the new generation GPS.Considering that the measurement error exists during the actual detection process, thefact that the measured points set of circularity errors is not precisely distributed in thesame plane was pointed out, the mathematical model of the Least Squares Plane Basedon the Center point of arithmetic average of the measured points set(LSPBC) wasestablished, the least square fitting plane as well as the projective points set wereobtained. The digital experimental results show that the measurement error existsduring the detection process of the three-dimensional circularity error.Secondly, in the least square plane of the measured points set, according to thenew generation GPS, taking the projective points set for research object, thethree-dimensional circularity error evaluation methods with the minimumcircumscribed circle method, the maximum inscribed circle method, the minimumzone circle method, and the improved method of the first two methods-thecircumscribed circle method and the inscribed circle method were discussed, themathematical models of the five kinds of evaluation methods were established, theassessment processes and flow charts were provided.Thirdly, taking the superiority of the particle swarm optimization algorithm forsolving nonlinear optimization problems into consideration, applying the particle swarm optimization based on time-varying inertia weight, taking the projective pointsset as the research object, the mathematical models of the three-dimensionalcircularity error evaluation methods with the least square circle method, theChebyshev fitting circle method, the minimum circumscribed circle method, themaximum inscribed circle method and the minimum zone circle method wereestablished, the assessment processes and flow charts were provided.Finally, the detection experiment which is about the three dimensional circularityerror of a cylinder was done according to operation techniques of the new generationGPS. Aiming at the experimental data, applying three-dimensional circularity errorevaluation methods based on the new generation GPS and the particle swarmoptimization, the circularity error and the information about the center and the radiusof the fitting circle were obtained. The three-dimensional circularity error evaluationsystem was designed by using MATLAB GUI. Experimental results show that thethree-dimensional circularity error evaluation methods of the new generationGPS-based and the PSO-based are correct and effective.The following conclusions can be drawn from this thesis. The Chebyshev fittingcircle method can be used to close substitute the minimum zone circle method whenthe accuracy requirement is not high. The minimum zone circle methods of the newgeneration GPS-based and the PSO-based which could meet the requirements ofprecision and ultra-precision machining can effectively achieve three-dimensionalcircularity error evaluation with higher evaluation accuracy.