The Study On The Character Of Grounding Surfaces With Fractal And Wavelet Theory

It is well known that fractal and wavelet theory are two upsurge branches in math fields in recent years. They have been extensively applied to describe and process signals and many other fields. It has been an important interactive research branch in the field of mechanical surface to be united with fractal and wavelet theory. The dissertation makes a study on the character of grounding profiles with fractal and wavelet theory.The W-M function is the best model to describe the mechanical surface with fractal character. The fractal W-M function is introduced and the physical meaning of model parameters (D - G - gamma) is analyzed in the first part. The surfaces simulated with W-Mfunction can reflect the internal trait of mechanical surfaces.The fractal dimensions of real grounding profiles are calculated with the semi-variancemethod. The results show that the fractal dimension D can indicate the complexity of real surface. And with the increasing of the conventional evaluation parameters Ra, Rq and tp,the fractal dimension D increases. But the linear relation between them is not evident. The fractal dimension D is a compound parameter reflecting the character of mechanical surface.The beta criterion is proposed according to the character of W-M and wavelet function.The fractal dimensions of the simulated and real machined profiles are computed respectively with the beta criterion method. The results indicate the varying trend of Ddoesn't change though they have some difference with the results of semi-variance method. And the more complicated the profile is, the bigger the fractal dimension is.The semi-variance, power spectrum density and beta criterion method are used tocalculate the dimension of simulated fractal surfaces to have a compare between them. Experimental results show that the linear relation between log/z and logr(h) is veryclear in the bi-logarithm semi-variance figure. But in the power spectrum figure, the linear relation is not clear and the precision of semi-variance method is better than power spectrum density method. The precision of the beta criterion method is low when D is small. But in the field of revealing the fractal character, the beta criterion method is more dependable than the other two methods.Some application examples of fractal and wavelet theory in machinery field areintroduced in the last part.These results lay the foundation for further research on the fractal character of machined surface and the detecting the faults of machine system.