Hertzian contact mechanics

Railway vehicle running behavior is mainly determined by the forces that exist
between wheel and rail surfaces. These forces are influenced by the nonlinear wheel/rail
contact. Furthermore, for better organization of condition monitoring and repair of railway
vehicles, better understanding of wheel/rail contact is essential. In this study, analysis of
wheel/rail geometrical properties is given along with a detailed explanation of search of
contact points and solution of normal problem. The commonly used wheel/rail pair,
S1002-UIC60E1, is given as an example. The methodology given in this work is same as
the methodology followed by most of the commercial software for dynamical analysis of
vehicles.

The equilibrium shape of plain weave fabric, accounting for yarn to yarn contact and incorporating the transverse compressibility, is presently investigated, relying on an energetic analysis of the textile. Each yarn is modeled as an undulated beam at a mesoscopic level, with a shape modeled by a Fourier series. In order to get an accurate description of the contact between yarns, we have considered the contact occurring on a surface (distributed contact) of finite extent according to Hertz contact theory. This method allows evaluating the reaction forces between weft and warp from the pressure distribution in the contact zone between yarns, and the evolution of the contact area versus the applied tension. The overall response of fabric under uniaxial and biaxial tension is computed as the minimum of the total potential energy of the set of interwoven yarns, including the work of reaction forces on the contact zones. The calculated nonlinear response for two important materials (glass, carbon) is due to the change of the geometry, namely the crimp variation and the change of contact area during increased loading. The contact area increases with the applied tensile force and is comparable to the yarn diameter. Only the contribution of the displacement due to flexion is shown to be sensitive to the distribution of the forces on the contact surface. A good agreement between the model predictions and tensile measurements of the response of plain weave fabric has been obtained.

A novel method for measuring the interfacial coefficient of friction between two solids which avoids sliding is described, and sample results are given. The technique makes use of the fact that a carefully controlled sequence of partial slip states between contacting bodies may be used to produce relative motion whose extent is a strong function of the coefficient of friction. It is argued that this approach induces much less surface damage in the components, and therefore yields a value for the coefficient of friction which is much more representative of their unmodified condition.

The contact of two bodies is found in many engineering applications. Some of the best examples are Hardness Testing, contact between ball bearings in races, Head-Disk interaction in storage devices, Impact of dust and other particles on Fan blades in a gas turbine and in Sports, especially where ball contact is dominant (like Golf, Hockey, Snooker etc.). The major characteristics of the problem are the localized deformation and the variation in the contact area with the contact force. The contact force-displacement relationship is nonlinear and high stresses are often generated. Therefore, plastic deformation is likely to occur for most engineering contact problems. This paper tries to simplify and concise the hertz contact behaviour under both Elastic and Plastic regime, which helps for better understanding in designing various contact parts.

Indentation size effects have been observed in both polymers and metals but, unlike in metals, the origin of size effects in polymers is not well understood. To clarify the role of second order gradients of displacements, a model polymer is examined with spherical and Berkovich tips at probing depths between 5 and 25 μm. Applying different theories to determine the elastic modulus, it is found that with a pyramidal tip, the elastic modulus increases with decreasing indentation depth, while tests with the spherical tip yielded essentially constant values for the elastic modulus independent of indentation depth. The differences between these tips are attributed to second order displacement gradients, as they remain essentially constant with a spherical tip while they increase in magnitude with decreasing indentation depth applying a Berkovich tip.

We present a newly developed approach for the calculation of interfacial stiffness and contact area evolution between two rough bodies exhibiting self-affine surface structures. Using spline assisted discretization to define localised contact normals and surface curvatures we interpret the mechanics of simulated non-adhesive elastic surface-profiles subjected to normal loading by examining discrete contact points as projected Hertzian spheres. The analysis of rough-to-rough contact mechanics for surface profiles exhibiting fractal structures, with fractal dimensions in the regime 1-2, reveals the significant effect of surface fractality on contact mechanics and compliance with surfaces having the same mean roughness but higher fractality showing lower contact stiffness in conditions of initial contact for a given load. The predicted linear development of true contact area with load was found to be consistent with diverse existing numerical and experimental studies. Results from this model demonstrate the applicability of the developed method for the meaningful contact analysis of hierarchical structures with implications for modelling tribological interactions between pairs of rough surfaces

English translation of Eberhard Contius' classic original PhD dissertation in German from 1929 on The Influence of Total Pressure and Area on Contact Resistance. This was the first monumental work in the research of electrical contact resistance.

Various claims have been made about the influence of Heinrich Hertz's on Wittgenstein's work. I consider some such recent claims, made by Allan Janik, to the effect that Hertz exercised a very strong influence on Wittgenstein, early and late. I suggest they are ill-founded, in virtue of misinterpretations either of Hertz, or of Wittgenstein, or of both. I try to set the record straight on issues such as the three criteria Hertz suggests for evaluating scientific 'representations' [] or 'images' [], his conception of philosophy, the nature of Hertz's project and its relation to philosophy, the extent to which he agrees and disagrees with Ernst Mach, and his influence on the .

The place of Heinrich Hertz"s The Principles of Mechanics in the history of the philosophy of science is disputed. Here I critically assess positivist interpretations, concluding that they are inadequate. There is a group of commentators who seek to align Hertz with positivism, or with specific positivists such as Ernst Mach, who were enormously influential at the time. Max Jammer is prominent among this group, the most recent member of which is Joseph Kockelmans. I begin by discussing what Hertz and Mach had to say about one another, and I specify certain respects in which their views are indeed similar. I then go on to detail their differences, looking at Hertz"s attitude to the atomic theory, to the mechanical world-view, to simplicity, to unobservables and metaphysics, and his objections to Newtonian forces. I conclude that the positivist interpretation of Hertz"s mechanics significantly overplays its similarities to Mach"s views.

Railway vehicle running behavior is mainly determined by the forces that exist between wheel and rail surfaces. These forces are influenced by the nonlinear wheel/rail contact. Furthermore, for better organization of condition monitoring and repair of railway vehicles, better understanding of wheel/rail contact is essential. In this study, analysis of wheel/rail geometrical properties is given along with a detailed explanation of search of contact points and solution of normal problem. The commonly used wheel/rail pair, S1002-UIC60E1, is given as an example. The methodology given in this work is same as the methodology followed by most of the commercial software for dynamical analysis of vehicles.