Date of Award

Fall 1992

Document Type


Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)


Mechanical and Industrial Engineering

First Advisor

M. C. Leu

Second Advisor

Denis L. Blackmore

Third Advisor

E. S. Geskin

Fourth Advisor

Nouri Levy

Fifth Advisor

Zhiming Ji


Two methods, namely the conventional and fractal geometry methods, are developed for surface topography characterization. The conventional method utilizing statistical and random process techniques is used to study waterjet machined surfaces. In the study the waterjet surfaces are separated into smooth and striation zones, where striation influence is negligible in the smooth zone. It is found that the smooth zone has a random, moderately isotropic texture, with the height distribution nearly Gaussian. In the striation zone the major frequencies of the surface profile power spectra are independent of cutting parameters, while the amplitudes of these frequencies monotonically increase with cutting speed or depth of cut. The effects of cutting speed, depth of cut, orifice diameter, and abrasive size on the surface topography are also studied. This provides useful information for controlling process parameters to obtain smooth finished surfaces. The spectral analysis is used to investigate the structure dynamics of the waterjet machining system. It is found that the vibration of the abrasive waterjet machining system plays an important role in the striation formation.

Manufactured surfaces which have random texture, such as those produced by electrical discharge machining, waterjet cutting, and ion-nitriding coating, can be characterized by fractal geometry. A Gaussian random fractal model coupled with structure functions is used to relate surface topography with fractal geometry via fractal dimension (D) and topothesy (L). This fractal characterization of surface topography complements and improves the conventional statistical and random process methods of surface characterization, especially in the study of contact mechanics and wear processes. The Gaussian fractal model for surface topography is shown to predict a primary relationship between D and the bearing area curve, while L affects this curve to a smaller degree. Several experiments are performed, and the results support the predicted effects of D and L on the bearing area curve.

Fractal characterization of surface topography is further applied to the study of contact mechanics and wear processes. A fractal geometry model is developed, which predicts the wear rate in terms of fractal parameters D and L for wear prediction. This model shows that the wear rate Vr and the true contact area Ar have the relationship Vr?(Ar)m(D), where m(D) is a function of D and has a value between 0.5 and l. Next the optimum (i.e. the lowest wear rate) fractal dimension in a wear process is studied. It is found that the optimum fractal dimension is affected by contact area, material properties, and scale amplitude. Experimental results of wear testing show good agreement with the predictions based on the model.