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. |
Contents
IV | 1 |
V | 4 |
VI | 6 |
VII | 10 |
VIII | 18 |
IX | 20 |
X | 22 |
XI | 23 |
LXV | 133 |
LXVII | 134 |
LXVIII | 137 |
LXIX | 138 |
LXXI | 148 |
LXXII | 150 |
LXXIII | 154 |
LXXIV | 156 |
XIII | 24 |
XVI | 25 |
XVIII | 28 |
XXII | 35 |
XXIII | 41 |
XXIV | 44 |
XXV | 45 |
XXVI | 47 |
XXVII | 48 |
XXVIII | 49 |
XXIX | 50 |
XXX | 51 |
XXXI | 52 |
XXXII | 56 |
XXXIII | 59 |
XXXVI | 64 |
XXXVII | 66 |
XXXVIII | 67 |
XXXIX | 68 |
XL | 69 |
XLI | 71 |
XLII | 73 |
XLIII | 74 |
XLIV | 78 |
XLV | 80 |
XLVI | 82 |
XLVII | 84 |
XLVIII | 94 |
XLIX | 95 |
L | 99 |
LI | 100 |
LII | 101 |
LIII | 103 |
LV | 107 |
LVI | 112 |
LVIII | 117 |
LIX | 119 |
LX | 120 |
LXI | 122 |
LXIII | 123 |
LXIV | 126 |
LXXV | 157 |
LXXVI | 158 |
LXXVII | 159 |
LXXVIII | 160 |
LXXIX | 168 |
LXXX | 172 |
LXXXI | 181 |
LXXXIII | 182 |
LXXXIV | 183 |
LXXXV | 184 |
LXXXVII | 185 |
LXXXVIII | 186 |
LXXXIX | 188 |
XC | 193 |
XCI | 202 |
XCII | 203 |
XCIV | 205 |
XCV | 206 |
XCVI | 207 |
XCVII | 213 |
XCVIII | 214 |
XCIX | 215 |
C | 216 |
CI | 218 |
CII | 219 |
CIII | 221 |
CIV | 224 |
CV | 229 |
CVI | 231 |
CVIII | 233 |
CX | 235 |
CXI | 237 |
CXII | 239 |
CXIII | 245 |
CXIV | 255 |
CXV | 265 |
CXVI | 285 |
295 | |
307 | |
Other editions - View all
Common terms and phrases
adhesion area algorithm Appendix area of adhesion areas of slip axes calculated Cartesian coordinate system Cattaneo circular contact area coefficient of friction consider constant constraints contact area contact ellipse contact formation convex convex function coordinate system Coulomb's Law creepage and spin deformed discretisation displacement difference elastic field elliptic integrals equations exact theory FASTSIM Figure finite finite element method frictional contact goto half-space half-space approximation Hertz Hertzian influence functions integral Johnson KOMBI Lagrange multipliers lateral creepage linear theory load longitudinal creepage method minimiser modulus of rigidity non-quasiidentical normal pressure normal traction P₁ P₂ Panagiotopoulos process parameter particle plane Poisson's ratio potential contact pure spin rectangle rolling direction simplified theory solution steady state rolling stress surface traction tangential traction three-dimensional total force traction bound traction distribution two-dimensional u₁ undeformed distance vanishes viscoelastic x₁
Popular passages
Page 298 - Amsterdam, 1962. 7 Hailing, J., "The Microslip Between a Rolling Element and Its Track Arising From Geometric Conformity and Applied Surface Traction," Journal of Mechanical Engineering Science, Vol. 6, 1964, pp. 64-73. 8 Ollerton, E., "Stresses in the Contact Zone," Proceedings, Institution of Mechanical Engineers, London, Convention on Adhesjon, 1964.
Page 300 - A Fast Algorithm for the Simplified Theory of Rolling Contact.
Page 302 - The Contact Problem of a Rigid Cylinder on an Elastic Layer," Applied Science Research, Vol.
Page 301 - The elastic stress and the displacement on the surfaces of two rubber-clad steel cylinders between which paper is led Kalker.
Page 304 - Friction and Wear of Materials, John Wiley and Sons, New York.
Page 297 - Journal of Applied Mechanics. ASME. 5 1 5-522. Kalker, JJ 1970. Transient phenomena in two elastic cylinders rolling over each other with dry friction. Journal of Applied Mechanics. ASME.