In practice, multi-asperity contact problems are often solved as two dimensional (2D) plane problems rather than true three dimensional (3D) problems. This is accomplished by assuming that each peak on a 2D scanned profile is the pinnacle of a half sphere. Hertz contact equations are then used to solve for the radius of contact and pressure profile. In reality, the local maximum in the plane may not be the maximum in the unmeasured depth direction, creating inherent errors in the contact model. This error is shown to be significant in contact problems when estimating the area of contact and total contact force over a single asperity. The pressure corrected Sternberg-Turteltaub model is introduced, in which a cylinder is used to model a sphere in a plane. This model is shown to improve the contact area and total force estimates for a range contact parameters.
A Cylindrical Contact Model for Two-Dimensional Multiasperity Profiles
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Jagodnik, JJ, & Mu¨ftu¨, S. "A Cylindrical Contact Model for Two-Dimensional Multiasperity Profiles." Proceedings of the STLE/ASME 2003 International Joint Tribology Conference. Contact Mechanics. Ponte Vedra Beach, Florida, USA. October 26–29, 2003. pp. 73-78. ASME. https://doi.org/10.1115/2003-TRIB-0269
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