| With the development of production technology and the progress of science and technology,people have higher and higher requirements for the surface quality of products.Surface micro-morphology can reflect a lot of information about the surface quality.Among them,surface roughness is an important index to reflect the surface micro geometry error of mechanical parts.It has an impact on the fitting,corrosion resistance,contact stiffness,fatigue strength,sealing and appearance of parts.Therefore,the accurate extraction and evaluation of surface roughness plays an important role in predicting the performance of the workpiece,monitoring the performance of the parts,improving the production process and controlling the machining process.In the field of surface metrology,how to establish the evaluation mean line is the key problem to evaluate the surface roughness,which has developed from the early least square method and polynomial fitting method to today’s filtering technology.It can be seen that the theory and method of establishing the evaluation mean line are becoming more and more perfect and mature.Filtering technology can separate different wavelength components into well-defined bandwidth,which is very important to extract information needed to provide process feedback and establish functional correlation.Therefore,the international standard ISO 16610 has published a series of filtering techniques.However,there are many disadvantages in the standard.For example,there is a contradiction between the transmission characteristics and the end effect of the spline filter.The two-dimensional spline filter has the anisotropic amplitude frequency characteristics.The calculation error of the robust spline filter is large,and the calculation cost of the robust Gaussian regression filter is high.In order to solve the above problems,this paper mainly does the following research work:（1）Research on the transmission characteristics and end effects of the Approximating Spline filter: This thesis first conducts a detailed study on the design principle of the spline filter in the international standard.The standard gives the cubic spline filter and approximating spline filter（β=0.625242）two mathematical models,the study found that the standard spline filter has the contradiction that the transmission characteristics and end effects cannot be unified.In order to solve the above problems,the design principle of approximating spline filter is given in this thesis.A new approximating spline filter is constructed by adding the first derivative term to the cubic spline filter.The maximum deviation of transmission characteristics between the approximating spline filter and Gaussian filter is 4.263%.In order to further reduce the deviation from the transmission characteristics of the Gaussian filter,a cascade approximating spline filter is constructed.When the two-cascade approximating is applied,the maximum deviation is reduced to 0.92%,and the approximating accuracy is improved by one level.However,the cascaded approximating spline filter also has a certain degree of end effect.This thesis solves this problem by introducing new boundary conditions,thereby realizing a cascaded approximating spline filter that takes into account the transmission characteristics and end effects.Finally,this thesis superimposes the one-dimensional approximating spline filter in the orthogonal direction to realize the isotropic approximating spline filter,which lays the foundation for the wide application of the spline filter in the three-dimensional surface roughness.（2）Research on filtering algorithm of approximating spline filter: The computational efficiency and filtering accuracy of the filter affect the effective evaluation of surface roughness.Therefore,it is very important to study the implementation algorithm of approximating spline filter.In this paper,we design four methods to realize approximating spline filter: Gaussian elimination,LU decomposition,LDLT decomposition and Thomas.Based on two-dimensional profile and three-dimensional surface filtering,the computational efficiency and filtering accuracy of the four algorithms are compared,and relevant suggestions are given.（3）Research on the robustness of approximating spline filter: Approximating spline filter also has the disadvantage of poor robustness.Although the international standard recommends robust Gaussian regression filter and robust spline filter to suppress the influence of outliers.However,the calculation time of robust Gaussian regression filter is long,the cost is high,the calculation error of robust spline filter is large,the output result is not ideal,and the evaluation difference between the two is large,so it is unable to realize the comparison of measurement results.In order to solve the above problems,based on M-estimation theory,this paper introduces 6 classical robust weight functions and constructs a robust approximating spline filter.Based on two-dimensional profile and three-dimensional surface filtering,the filtering performance of 6 robust approximating spline filters is studied,and relevant suggestions are given.（4）Research on filter and parameter selection method: Although international standards form a systematic filtering technology system,and give the sampling length and cutoff wavelength in the two-dimensional profile filter parameters selection specifications.However,the method of selecting the three-dimensional surface parameters is not specified.As there are many types of filters,it is very important to choose a suitable filter for surface roughness evaluation.Therefore,this thesis summarizes the application range of common filters,and studies the influence of sampling length and cutoff wavelength selection on regional roughness parameters.In this thesis,the performance of approximating spline filter is studied and improved.Firstly,the cascade approximating spline filter is constructed to realize the transmission characteristics of high precision approximating Gaussian filter.And new boundary conditions are introduced to solve the end effect.Secondly,the algorithm of approximating spline filter is proposed,which improves the computational efficiency and filtering precision of the approximating spline filter.Thirdly,the robust weight function is introduced to improve the robustness of approximating spline filter and solve the shortcomings of robust Gaussian regression filter and robust spline filter in international standard.Finally,the application scope of filters commonly used in international standards is summarized,and the relevant suggestions of filter parameter selection in areal filtering are given. |
