Surface Forces and Surface Interactions

The third-body approach: A mechanical view of wear

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.

A Fast Algorithm for the Simplified Theory of Rolling Contact

Driven by recent empirical studies, we offer a new understanding of the degrees of freedom problem, and propose a refined concept of synergy as a neural organization that ensures a one-to-many mapping of variables providing for both stability of important performance variables and flexibility of motor patterns to deal with possible perturbations and/or secondary tasks. Empirical evidence is reviewed, including a discussion of the operationalization of stability/flexibility through the method of the uncontrolled manifold. We show how this concept establishes links between the various accounts for how movement is organized in redundant effector systems.

Toward a New Theory of Motor Synergies

A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques

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.

Survey of Wheel-Rail Rolling Contact Theory

Wheel-rail rolling contact theory

A 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.

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

In this paper, the variational principles of contact elastostatics, which were proposed and proved by Fichera (1964) and Duvaut & Lions (1972) are developed in an engineering fashion without use of functional analysis. The theory contains a number of new elements, but the elegant existence proofs of the French-Italian school are missing. A start is made by extending the principle of virtual work to normal and frictional contact in such a manner that it needs no longer be known beforehand whether—in the case of normal contact—actual contact is or is not established, or—in the case of frictional contact—slip does or does not occur. Then the principle of minimal potential energy is set up for a non-linear elastic body in contact with a rigid base. Uniqueness and minimality of the solution are proved under certain conditions, the Reissner principle is established, and the principle of minimal complementary energy is derived. Finally the principles are cast hi what is termed surface mechanical form, and two examples are given: the variational principle for normal half-space contact problems, and a new principle for time-dependent frictional half-space contact. Upon discretization, these principles provide a quadratic object function to be minimized under linear or quadratic inequality constraints. The positions of the contact area and of the regions of slip and adhesion appear as by-products of the calculation.

J. J. Kalker

Papers

A Fast Algorithm for the Simplified Theory of Rolling Contact

Survey of Wheel-Rail Rolling Contact Theory

Wheel-rail rolling contact theory

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

Variational principles of contact elastostatics