Research On Filtering Technique Of Non-closed Circular Profile Measurement

With the development of advanced equipment manufacturing industry towards precision and ultra-precision tendency,an increasing demand of measurement accuracy for rotational parts arise.The accuracy of measurement can be affected by the performance of filter.Gaussian filter used in the current roundness evaluation is only applicable to full circular profiles,but it has boundary effect for some workpieces whose cross-sections contour is non-closed circular contour,such as bearings with holes,edged cylinder,and positioning shafts,etc.In addition,outliers in the measurement data caused by scratches and hard spots on the surface also can lead to distortion of filtering results.To solve the above problems,the following research has been carried out and completed:In order to solve the boundary effect problem of Gaussian filter,on the one hand,two modified Gaussian filters were studied.One is Gaussian filter based on extension of profile information which compensates the missing profile information by extension of profile information.The other is Gaussian regression filter that modify the Gaussian weight function by Gaussian regression method.On the other hand,spline filtering equation was derived by applying spline function.The effectiveness for suppressing boundary effect with three filters was verified by numerical simulation and experiments.The results show that Gaussian filter based on extension of profile information and Gaussian regression filter can suppress the boundary effect effectively,and spline filter can eliminate the boundary effect completely.To suppress the influence of outliers on filtering results effectively,robust estimation theory was introduced to filtering algorithm.Robust Gaussian regression filter model was constructed based on Gaussian regression filter,and a generalized robust spline filtering model is established based on spline filter.L1 norm and Tukey function in M-estimator were used in robust spline filter,respectively.And the algorithm of three robust filters was implemented by iterative re-weighted least squares(IRLS).The effectiveness for suppressing outliers distortion of three filters was verified by numerical simulation and experiments.The results show that robust Gaussian regression filter,robust spline filter based on L1 norm and M-estimator have obvious inhibition effect on outliers.The robust spline filter based on M-estimator has a good performance which can suppress the outlier of 12.4 ?m to0.1 ?m.Filtering software module for non-closed circular profile based on VisualStudio and C# language was developed,and it has been planted to roundness measuring instrument software.The main function of this software module is to collect,filter and evaluate data of non-closed circular profile,and the software module includes parameters setting interface,filter and output interface for non-closed circular profile also was tested.