Evaluation Of Machined Surface Topography By Means Of Fractional-order Statistics

Parts with complicated geometric characters has wide application requirements inhigh-performance in Optical Electro-Mechanical System, optical freeform surfaces is one of that.There have been some effective researches on evaluation of surface topography in theinternational academic community, but there are still issues needed to be studied to solve so far.These problems are:(1) The machined surfaces evaluated are mainly relatively simple surface shape, plane,cylindrical surface, sphere and rotationally symmetric surfaces, etc. Researches on evaluation ofmachined surfaces on non-rotationally symmetric workpiece are not deeply enough.(2) In most of current evaluation of machined surfaces, the measured surface topography isgenerally assumed to be a smooth Gaussian random process or random field, however, machinedsurfaces used in production rarely meet this assumption. Actual surface topography is usuallynon-smooth, non-Gaussian random process or random field, which depends not only on the shapeof machined surfaces but also on the processing method.(3) Most statistics used are still low integer order.Therefore, this thesis aims at turning of optical freeform surfaces, and uses fractional orderstatistics for the evaluation of surface topography with complicated geometric characters, whichcan provide basis for acquisition of new evaluation method of machined surfaces.Firstly, the thesis derives the mathematical expression of fractional statistics such asfractional moment, spectral moment and verifies them.Secondly, the thesis proposes the fractional statistics evaluation method of surface withcomplicated geometric characteristics. That is, take Fourier transform of the evaluated surfacetopography to generate its power spectrum, and then solve the fractional moment of the surfacetopography to generate the fractional spectral moment which we analyze and evaluate.Thirdly, the thesis researches the extraction of statistical characteristics from surfacetopography of optical freeform surfaces using fractional moment and fractional spectral moment.We find that the difference of surface topography with different machining parameters can berepresented by fractional spectral moment. The surface characters among height, slope andcurvature of surface topography can be generated in the evaluation of surface topography withcomplicated geometric statistics using fractional spectral moment.Fourthly, the thesis researches the extraction of statistical characteristics from surfacetopography of optical freeform surfaces using spectrum based on fractional Fourier transform. Wefind that the result of Fourier transform in one direction can be generated, and we can analyze thesurface topography in frequency field in one direction while analyzing the surface topography inspatial field in the other direction.Finally, the thesis researches the relation between the main frequency of surface topographyand machining parameters from changing the machining parameters and tool geometricparameters. The research indicates that evaluation of surface topography of turning surfaces of opticalfreeform surfaces using fractional statistics has its unique advantage to acquire statistical featurewhich cannot be represented with low integer order statistics.