Hybrid dimension based modeling of part surface topography and identification of its characteristic parameters

Since the complete description of complex part surface is difficult to achieve using the existing integral dimensional or fractal dimensional approaches, the novel concept of hybrid dimension and its modeling method of part surface topography are proposed in this paper. The hybrid dimensional model of part surface topography is established based on the deflection method of surface correlation coefficient, which associates the integral dimensional and fractal dimensional surface topographies. Superimposing the normalized fractal dimensional surface altitude field on the B-spline surface, the hybrid dimensional model can express the integral dimensional information of part surface in macro level, and the fractal dimensional detail in micro level. And the correlation of part surface topographies among different scales and different dimensions is established by the Hybrid Dimensional Surface Correlation Coefficient. Moreover, the characteristic parameter identification method for the hybrid dimensional model of part surface topography is proposed. The component information of integral dimension and fractal dimension is separated and extracted by wavelet analysis, and hybrid dimensional characteristic parameters are identified by the generalized surface structure function method and the roughness mapping method. Finally, the proposed method is applied to design and manufacture of turbo expander.

► The concept of hybrid dimension is proposed based on integral and fractal dimensions. ► A hybrid dimensional modeling method is presented to describe the surface topography. ► Hybrid dimensional models preserve controllable regular shape and irregular detail. ► Characteristic parameters are constructed and identified to evaluate surface quality. ► Correlation is established between macro and micro surface topographies.