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Majumdar, A. et. al. “Characterization and Modeling of Surface.” Handbook of Micro/Nanotribology. Ed. Bharat Bhushan Boca Raton: CRC Press LLC, 1999 © 1999 by CRC Press LLC Characterization and Modeling of Surface Roughness and Contact Mechanics Arun Majumdar and Bharat Bhushan 4.1 4.2 4.3 Introduction Why Is Surface Roughness Important? How Rough Is Rough? • How Does Surface Roughness Influence Tribology? 4 Surface Roughness Characterization Probability Height Distribution • rms Values and Scale Dependence • Fractal Techniques • Generalized Technique for Fractal and Nonfractal Surfaces 4.4 4.5 Size Distribution of Contact Spots Observations of Size Distribution for Fractal Surfaces • Derivation of Size Distribution for Any Surface Contact Mechanics of Rough Surfaces Greenwood–Williamson. | Majumdar A. et. al. Characterization and Modeling of Surface. Handbook of Micro Nanotribology. Ed. Bharat Bhushan Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 4 Characterization and Modeling of Surface Roughness and Contact Mechanics Arun Majumdar and Bharat Bhushan 4.1 Introduction 4.2 Why Is Surface Roughness Important How Rough Is Rough How Does Surface Roughness Influence Tribology 4.3 Surface Roughness Characterization Probability Height Distribution rms Values and Scale Dependence Fractal Techniques Generalized Technique for Fractal and Nonfractal Surfaces 4.4 Size Distribution of Contact Spots Observations of Size Distribution for Fractal Surfaces Derivation of Size Distribution for Any Surface 4.5 Contact Mechanics of Rough Surfaces Greenwood-Williamson Model Majumdar-Bhushan Model Generalized Model for Fractal and Nonfractal Surfaces Cantor Set Contact Models 4.6 Summary and Future Directions References Appendix 4.1 Appendix 4.2 Appendix 4.3 Abstract Almost all surfaces found in nature are observed to be rough at the microscopic scale. Contact between two rough surfaces occurs at discrete contact spots. During sliding of two such surfaces interfacial forces that are responsible for friction and wear are generated at these contact spots. Comprehensive theories of friction and wear can be developed if the size and the spatial distributions of the contact spots are known. The size of contact spots ranges from nanometers to micrometers making tribology a multiscale phenomena. This chapter develops the framework to include interfacial effects over a 1999 by CRC Press LLC whole range of length scales thus forming a link between nanometer-scale phenomena and macroscopically observable friction and wear. The key is in the size and spatial distributions which depend not only on the roughness but also on the contact mechanics of surfaces. This chapter reexamines the intrinsic nature of surface roughness as well as reviews and develops techniques to .
