Download Three-Dimensional Elastic Bodies in Rolling Contact by J.J. Kalker PDF
By J.J. Kalker
This publication is meant for mechanicians, engineering mathematicians, and, quite often for theoretically prone mechanical engineers. It has its beginning in my Master's Thesis (J 957), which I wrote below the supervision of Professor Dr. R. Timman of the Delft TH and Dr. Ir. A. D. de Pater of Netherlands Railways. i didn't imagine that the skin of the matter had even been scratched, so I joined de Pater, who had by way of then turn into Professor within the Engineering Mechanics Lab. of the Delft TH, to jot down my Ph. D. Thesis on it. This thesis (1967) used to be weil bought in railway circles, that is due extra to de Pater's untiring promoting than to its advantages. nonetheless now not chuffed, I feit that i wished extra mathe matics, and that i joined Professor Timman's team as an affiliate Professor. This ended in the current paintings. Many thank you are as a result of G. M. L. Gladwell, who completely polished kind and contents of the manuscript. thank you also are because of my spouse, herself an engineering mathematician, who learn the manuscript via significantly, and made many beneficial reviews, to G. F. M. Braat, who additionally learn an criticised, and, moreover, drew the figures including 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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Extra resources for Three-Dimensional Elastic Bodies in Rolling Contact
Sample text
2Id) relative rigid slip or creepage; this expression holds only when V'" 0. 21f) A shilt is characterised by the fact that w is of the same order of magnitude as v. u. , and the slip becomes ) s. /at / (shift). 22a) In steady state rolling all dependence on explicit time vanishes, when the coordinate system is weIl chosen. The slip becomes s. = w. u .. / / ) I,) (steady state roIling). 21f) is retained. When v '" 0, we divide by the magnitude of the rolling velocity V. /V = wR/ vR . ;ax. 2Ie); vR .
45) 0 Note that the undeformed distance h equals h = undeformed distance = x l3 + x 23 . 46) The R , r = 1,2, are the principal radii of curvature Iying in the plane of x . They are ar ar taken to be positive if the corresponding center of curvature lies in the half -space x a3 ~ O. Assume that the angle that x al makes with x I equals wa ' see Fig. 9. 9 The intersection 01 the principal planes 01 curvature bodies in the undelormed state with the plane z = O. 48) x2 1,2. 48). 52) a and s . a If we define the axis of X in the manner of Fig.
13 Two counter/ormal (a) -con/ormal (b) bodies in near contact. see Fig. 7: Boundary Conditions for Same Applications We can add to this a displacement q. (i = x,y,z) of the entire body I with respect to the I body 2. 61) as since (n Ix,n Iy,n I z) = (O,-sin 0:, cos 0:), see Fig. 13. 56) remain valid. e. 0: is not constant. Suppose that we want to prescribe the total force components F , F , or F on body I. 63) The total forces in x,y,z-directions become (F ,F ,F ) = x y z JJ Contact (PI' P2 cos 0: - P3 sin 0:, P2 sin 0: + P3 cos 0:) For concentrated contacts, 0: is a constant.