Narrow Results

In this paper, different types of fractal structures are generated to model the structures of nature porous media, an appropriate mathematical model is established for the heat conduction in fractal porous media, and the influence of various factors on the effective thermal conductivity of solid and fluid are analysed in detail, the relation between the characteristic size of the artificial fractal structures and the natural porous media is analysed. A lattice Boltzman model is developed to simulate fluid flow in fractal porous media. The results indicate that the flow field structures in fractal porous media exhibit fractal characteristics, the volume flow rate is proportional to the pressure drop, the relation of volume flow rate with porosity conforms to an exponential function.

High speed adaptive cutting experiment of high strength alloy steel based on fractal theory has been carried out. The impacts of cutting parameters on the cutting force, fractal dimension and surface roughness were analyzed. Based on the W-M function, the relationship between the fractal parameters and the traditional surface precision index is established. Meanwhile, the relationship between the cutting parameters and the fractal parameters of the cutting surface is also determined. Experimental results indicate that the main cutting force decreased by about 6% when the cutting speed increased from 100m/min to 240m/min under the condition of the cutting depth being 3.5mm and the feeding being 0.25 mm/r. The surface roughness decreases with the increase of the cutting speed, while it increases with the increase of the cutting feed and cutting depth. The biggest influence on the surface roughness is the cutting speed. The biggest influential factor is the cutting speed on the surface roughness. The impacts of cutting feeding and cutting depth are smaller.

Aiming at the nonlinear and non-stationary characteristics of rolling bearing fault vibration signals, feature correlation dimension (FCD) extraction method combining phase space reconstruction (PSR) and fractal theory is proposed. The method reconstructs high-dimension phase space from one-dimension vibration signals of different fault states of the rolling bearing so that deep data mining is achieved. Then through analysis of varying correlation dimension of phase space feature signals, FCD that corresponds to each fault state is extracted. The experiment shows that feature correlation dimension extracted by the method is effective to fault diagnosis of rolling bearing. The method can provide reliable feature information for condition monitoring and fault diagnosis of complicated rotating machinery, and has a broad application prospect.