Three-Dimensional Elastic Bodies in Rolling ContactThis book is intended for mechanicians, engineering mathematicians, and, generally for theoretically inclined mechanical engineers. It has its origin in my Master's Thesis (J 957), which I wrote under the supervision of Professor Dr. R. Timman of the Delft TH and Dr. Ir. A. D. de Pater of Netherlands Railways. I did not think that the surface of the problem had even been scratched, so I joined de Pater, who had by then become Professor in the Engineering Mechanics Lab. of the Delft TH, to write my Ph. D. Thesis on it. This thesis (1967) was weil received in railway circles, which is due more to de Pater's untiring promotion than to its merits. Still not satisfied, I feit that I needed more mathe matics, and I joined Professor Timman's group as an Associate Professor. This led to the present work. Many thanks are due to G. M. L. Gladwell, who thoroughly polished style and contents of the manuscript. Thanks are also due to my wife, herself an engineering mathematician, who read the manuscript through critically, and made many helpful comments, to G. F. M. Braat, who also read an criticised, and, in addition, drew the figures together with J. Schonewille, to Ms. A. V. M. de Wit, Ms. M. den Boef, and Ms. P. c. Wilting, who typed the manuscript, and to the Publishers, who waited patiently. Delft-Rotterdam, 17 July 1990. J. J. |
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adhesion area algorithm Appendix area of adhesion areas of slip axes calculated circular contact area coefficient of friction consider constant constraints contact area contact ellipse convex function Coulomb's Law creepage and spin deformed discretisation displacement difference elastic field elliptic integrals equations error exact theory FASTSIM Figure finite frictionless goto half-space Hertz Hertzian influence functions integral J.J. Kalker KOMBI Lagrange multipliers lateral creepage linear theory load method minimiser modulus of rigidity non-quasiidentical normal pressure normal traction P₁ P₂ Panagiotopoulos process parameter perturbed Poisson's ratio potential contact pure spin quasiidentical rectangle rolling direction simplified theory slip and adhesion solution steady state rolling stress surface traction tangential traction theory of rolling three-dimensional total force traction bound traction distribution two-dimensional u₁ undeformed distance vanishes viscoelastic Young's modulus α α Ιτ