J. J. Kalker

Three-Dimensional Elastic Bodies in Rolling Contact

1 The Rolling Contact Problem.- 2 Review.- 3 The Simplified Theory of Contact.- 4 Variational and Numerical Theory of Contact.- 5 Results.- 6 Conclusion.- Appendix A The basic equations of the linear theory of elasticity.- Appendix B Some notions of mathematical programming.- Appendix C Numerical calculation of the elastic field in a half-space.- Appendix D Three-dimensional viscoelastic bodies in steady state frictional rolling contact with generalisation to contact perturbations.- Appendix E Tables.

A Fast Algorithm for the Simplified Theory of Rolling Contact

SUMMARY An algorithm “Fastsim” for the simplified theory of rolling contact is described which is 15-25 times as fast as the existing programs Simrol (Kalker), and 3 times as fast as Rolcon (Knothe). The relative total force computed with Fastsim differs at most 0.2 from that calculated with Simrol, Simcona (Goree & Law), Rolcon, and the “exact” program Duvorol (Kalker). Descriptions and lists of an Algol 60, and HP 67 program version are available upon request: the Fortran IV version is given in the paper.

Survey of Wheel—Rail Rolling Contact Theory

SUMMARY This paper describes the theory of frictional rolling contact as far as it is significant for the wheel-rail system. It is divided into two parts. The first part, mostly non-mathematical, contains a historical survey from the times of Carter and Fromm (1926) to the present day, in which all aspects of rolling contact theory are discussed. Included are a quantitative account of the results of Hertz theory (Section 3), and a table of the creepage and spin coefficients. The second part gives a present day account of the simplified theory (Section 4), and of the exact linear and non-linear theory (Section 5). The paper closes with some recommendations for future research, of which the most pressing is a thorough investigation of the accuracy of simplified theory.

A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems

SummaryA variational principle governing the frictionless contact between two elastic bodies is established, which is valid both for linear and for non-linear elasticity. In the case of linear elasticity it appears to lead to an infinite dimensional convex quadratic programming problem. It is applied to the half-space geometry in linear elasticity and it is established that non-Hertzian normal half-space contact problems are physically meaningful.A Hertzian and a non-Hertzian normal contact problem are investigated numerically, to which end the principle is discretised on a triangular network. In the case of the Hertz problem it is found that the exact relationships between penetration, maximum pressure, and total normal force are well satisfied. The form of the contact area is given only crudely, unless the discretisation network is considerably refined. It appeared that such a refinement is only necessary close to the edge, in which case passable results will be obtained.

Wheel-rail rolling contact theory

Abstract In this paper the theory of rolling contact is surveyed after a development of over 60 years. Six theories are significant at present: (1) the two-dimensional theory of Carter (1926); (2) the linear theory (Kalker 1967); (3) the complete theory (CONTACT, Kalker 1983–1990); (4) the British Rail Table Book (ca. 1980); (5) the theory of Shen, Hedrick and Elkins (1984); (6) the simplified theory (Kalker, 1973–1989). Their operation, scope and limitations will be discussed, and it will be indicated to which problem(s) of wheel-rail technology each of these theories is best suited.

The hand of the musician: The kinematics of the bidigital finger system with anatomical restrictions

Tendons of the fingers are frequently interconnected by anatomic structures that limit the displacements of these tendons relative to each other. In this paper a bidigital finger system in which such interconnections between tendons are present is kinematically modelled. Using this model, an exhaustive description of the effects on finger movement of connections between the different tendons of the fingers is given. The study provides a context for the interpretation of typical difficulties of finger coordination in musicians, especially in pianists and string players.

The Mechanics of the Contact Between Deformable Bodies

A recommendation to hold a symposium on contact problems in mechanics, sponsored by the International Union of Theoretical and Applied Mechanics (IUTAM), was made by the Engineering Mechanics Group of the Department of Mechanical Engineering, Delft University of Technology. In order to outline the scope of the Symposium and select the place and date IUTAM appointed a Study-group of seven members in 1971. Following an interchange of views between these members the Study-group proposed to IUTAM to organise an International Symposium on the Mechanics of the Contact between Deformable Bodies on August 20-23, 1974, at Twente University of Technology, Netherlands, with a number of participants restricted to about 60, the outline of scope being as follows: Theoretical and fundamental experimental studies on the mechanical aspects of the contact between solid bodies: solid surfaces, area of contact, mechanics of friction in the broadest sense. Mathematical analysis of the normal contact and tangential contact (pure sliding, steady and unsteady rolling) between two (elastically, plastically and viscoelastically) deformable solid bodies on the basis of simplified models of the contact mechanism. Problems involving hydrodynamic lubrication as the main phenomenon should be excluded. IUTAM accepted this proposal and appointed in December, 1972, a scientific committee consisting of the following members: N. H. Arutjunjan (USSR), H. Buffer (BRD), L. E. Goodman (USA), A. Ju. ISIinskij (USSR), K. L. Johnson (UK), W. Nowacki (Poland), A. D. de Pater (Chairman, Netherlands) and D. Tabor (UK). Their main duty was the selection of lecturers and other participants.

Rolling Contact Phenomena

In this paper, we treat the rolling contact phenomena of linear elasticity, with special emphasis on the elastic half-space.

Biomechanics of the finger with anatomical restrictions - The significance for the exercising hand of the musician

Exercise and teaching of musicians presupposes in the individual the constitutive ability to freely execute the finger movements required in the playing of the instrument. However, in the hand anatomical restrictions may exist that limit the mobility of the fingers and, thereby, the possibility to determine their movements voluntarily. In this article we investigate the kinematics of a monodigital system in which restrictions are present.

Rail Quality and Maintenance for Modern Railway Operation

Rail Developments and Future Requirements.- Future Rail Requirements.- Rail Developments and Requirements for Heavy Haul Railways.- Rail Metallurgy and Processing.- Rail Metallurgy and Processing.- A Review of Bainitic Steels for Wheel/Rail Contact.- An Off-Line Heat Treatment Process Results in Quality DHH Rails at Sydney Steel Corporation.- Residual Stresses in Rail.- Rail Maintenance.- Strategies for Maximizing Rail Life.- Noncontact Ultrasonic Inspection of Train Rails for Stress.- Experiences in Ultrasonic Measurements of Stresses in Rails.- Rail Side Wear Problem on Chinese Railways.- Rail Rectification Specifications and Modern Grinding Stone Technology.- In Track Quality Control and Assessment of Rails.- Contact Phenomena.- Computational Contact Mechanics of the Wheel-Rail System.- Dynamic Models of the Track and Their Uses.- Rail Service Load Environment by Measurement and Modeling.- Analytical and Numerical Treatment of Flange Contact.- On an Approach to Prediction of Contact Loading of Rail for Two-Point Contact Between Wheel and Rail.- Experimental Tribo-Analysis of Rail/Wheel Interface.- Shakedown, Residual Stress and Plastic Flow in Repeated Wheel-Rail Contact.- Residual Stresses.- How Residual Stresses can Affect Rail Performance.- Predication of Residual Stress in Rails: Practical Benefits from Theoretical Approach.- A New Approach to Enhancement of Experimental Data.- Effect of Grinding Strategy on Residual Stress in the Rail Head.- Residual Stress Measurements in Rails by Neutron Diffraction.- Neutron Diffraction Measurements of Residual Stress in Rails.- Residual Stresses and Catastrophic Rail Failure.- Beneficial Residual Stresses at Bolt Holes by Cold Expansion.- Residual Stress Analysis in Rolling Contact.- Crack Propagation.- Fatigue Crack Growth in Rail Steels.- Crack Behaviour under Rolling Contact Fatigue.- Numerical Analysis of 3D Cracks Propagating in the Rail-Wheel Contact Zone.- Modelling of 3D Rail Head Rolling Contact Fatigue Cracks.- Tribological Investigations of Crack Development on the Rail on an Energetical Basis.- The Effect of Head Checking on the Bending Fatigue Strength of Railway Rails.- Rolling Contact Fatigue Cracks on S.N.C.F. Conventional Tracks.- List of Participants.