Fractal Prediction Model Research Articles

Fractal prediction model of thermal contact conductance of rough surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces, which has been widely studied since last few decades, and for predicting which many theoretical models have been established. However, the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity. In this paper, a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes: elastic, elastoplastic and fully plastic. Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model. The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area. The larger the fractal dimension, or the smaller the fractal roughness, the larger the thermal contact conductance is. The thermal contact conductance increases with decreasing the ratio of Young’s elastic modulus to the microhardness. The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface, which provide certain reference to the further study on the issue of heat transfer between contact surfaces.

Fractal Prediction Model for Tangential Contact Damping of Joint Surface Considering Friction Factors and Its Simulation

In order to accurately consider the influence of micro-morphology on the joint surface,the "solid-gap-solid" contact model of joint surface is proposed.The fractal prediction model of the tangential contact damping of joint surface is established based on the "solid-gap-solid" contact model,contact fractal theory and the Hertz theory.And the influence of relevant parameters on the tangential contact damping is revealed with the research of numerical simulation.All the work provides the preparation for follow-up dynamic modeling and dynamic analysis of joint surface.Simulation results show that tangential contact damping of joint surface increases with the increase of real contact area,reduces with the increase of normal load of joint surface and tends to be constant with the increase of friction coefficient between the joint surfaces.Real contact area influences the location of the turning point of the cte*-μ(critical friction coefficient μc).With the increase of the real contact area,critical friction coefficient μc increases at the same time.Big differences exist between the contact behaviors with the different fractal dimension values,especially on both sides of the fractal dimension critical value(D=1.55).

Fractal Prediction Model of Spontaneous Imbibition Rate

By utilizing fractal dimension as one of the parameters to characterize rocks, a mathematical model was derived to predict the production rate by spontaneous imbibition. This fractal production model predicts a power law relationship between spontaneous imbibition rate and time. Fractal dimension can be estimated from the fractal production model using the experimental data of spontaneous imbibition in porous media. The experimental data of recovery in gas-water-rock and oil–water–rock systems were used to test the fractal production model. The rocks (Berea sandstone, chalk, and The Geysers graywacke) in which the spontaneous water imbibition experiments were conducted had different permeabilities ranging from 0.5 to over 1000 md. The results demonstrate that the fractal production model can match the experimental data satisfactorily in the cases studied. The fractal dimension data inferred from the model match were approximately equal to the values of fractal dimension measured using a different technique (mercury-intrusion capillary pressure) in Berea sandstone.

Fractal Prediction Model of Friction Coefficient in Dry Friction Pair

To research the friction coefficient of rough surface under different contact loads. A mathematical model is proposed between the fractal parameters D and G and the non-dimensional real contact area based on M-B fractal contact model, surface profile curves are scanned by APE500 surface morphology, dimension change index k and size change index s are identified in tests, the model is verified on UMT-3 pin-on-disk wear apparatus. Results showed that the modeling method relying on limiting cases is feasible, this model could improve prediction accuracy of friction coefficient, and the experimental results are consistent with the theoretical prediction.