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The calculation of the creep forces has always been one of the fundamental goals for a wheel-rail contact model. At the same time, a wheel-rail contact model has necessarily to consider the phenomena related to degraded adhesion because they deeply affect both creepages and creep forces. Degraded adhesion is extensively observed at the wheel-rail interface. However, the development of an accurate and efficient adhesion model is quite a challenge due to the complexity of the system and the difficulty in collecting detailed experimental data. In this framework, the paper presents a local degraded adhesion model (based on local slidings/creepages and local pressures inside the contact area) able to provide a more accurate description of the contact phenomena characterizing the wheel-rail degraded adhesion with respect to analogous global models (involving global sliding/creepages and forces). The new model is able to consider important phenomena like the energy dissipated at the contact and the consequent surface cleaning effect leading to an adhesion recovery between wheel and rail. To reach this goal, the Kalker's FASTSIM algorithm has been properly extended and improved to include the previous phenomena. Furthermore, the new model allows the achievement of a good trade-off between accuracy and numerical efficiency. Thank to its efficiency, the model can be implemented inside general railway vehicle multibody models to perform large scale dynamical simulations. The model has been finally validated through experimental data coming from on-field tests and consisting of specific braking maneuvers under degraded adhesion conditions.

Rolling resistance is a main consideration in quasi-static shear test simulations of particles via the discrete element method. However, not all rolling resistance models can satisfy the required objectivity and rate independence. A suitable model for spherical particles has been selected from five models in our previous works. In the current study, this model is combined with four normal and tangential contact models to confirm its applicability. After confirmation, the model is generalized to simulate direct shear tests on non-spherical particles. The stress–strain and dilatancy curves are rate-independent, and the relative rolling velocity between particles is objective. Furthermore, objectivity and rate independence for arbitrarily shaped particles are unchanged when normal stresses, volume fractions, or normal and tangential contact models are changed. Simulation results are also consistent with other experiment findings. For comparison, results are calculated for two other rolling resistance models; the shear curve at a single speed is consistent with the experiment, which has three stages: elastoplastic increasing, yielding, and keeping. However, the stress–strain curves at different shear rates do not coincide, which means that the models conflict with the rate independence of quasi-static granular systems. The virtues and defects of the five rolling resistance models are discussed from the perspectives of objectivity and rate independence. These two properties provide criteria for determining the appropriateness of a model, which has been rarely discussed in former studies.

Based on the fractal contact theory, the tangential contact stiffness of the plate joint surface is calculated by the performance parameters, the normal load, the tangential force and the fractal parameters of the plate surface. The tangential contact stiffness of the plate joint surface is calculated and its variation regularity is researched by numerical simulation, which is verified through the test. It is found that in the qualitative theoretical model, the fractal contact theory is correct, but the fractal theory has its scope of application, it is suitable for the smaller roughness and the larger normal load. In the experimental aspects, the contents of the research are a good supplement to the contact fractal theory.

This study provides some insights into the micro-slip behaviour of geological materials. The micromechanical experiments are conducted using a custom-built grain-scale apparatus on Leighton buzzard sand (LBS), which is a soil of relatively smooth and stiff grains, and completely decomposed volcanic (CDV) granules, which is a material composed of very rough and soft grains. It was observed that the CDV granules show more pronounced initial soft behaviour during normal loading, which might be due to their low apparent Young’s modulus and very high roughness. The results show that the micro-slip behaviour during inter-particle shearing can be related to the tangential stiffness degradation; this degradation is a function of the applied normal force, the surface roughness and the apparent Young’s modulus.

[EN] In this paper the two-dimensional contact problem is analysed through different mesh topologies and strategies for approaching equations, namely; the collocation method, Galerkin, and the polynomial approach. The two-dimensional asymptotic problem (linear theory) associated with very small creepage (or infinite friction coefficient) is taken as a reference in order to analyse the numerical methods, and its solution is tackled in three different ways, namely steady-state problem, dynamic stability problem, and non-steady state problem in the frequency domain. In addition, two elastic displacements derivatives calculation methods are explored: analytic and finite differences. The results of this work establish the calculation conditions that are necessary to guarantee dynamic stability and the absence of numerical singularities, as well as the parameters for using the method that allows for maximum precision at the minimum computational cost to be reached., The authors gratefully acknowledge the financial support of the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (project TRA2017-84701-R), as well as the European Commission through the projects 'RUN2Rail - Innovative RUNning gear soluTiOns for new dependable, sustainable, intelligent and comfortable RAIL vehicles' (Horizon 2020 Shift2Rail JU call 2017, grant number 777564) and 'PIVOT - Performance Improvement for Vehicles On Track' (Horizon 2020 Shift2Rail JU call 2017, grant number 777629).

The rolling resistance between a pair of contacting particles can be modeled with two mechanisms. The first mechanism, already widely addressed in the DEM literature, involves a contact moment between the particles. The second mechanism involves a reduction of the tangential contact force, but without a contact moment. This type of rotational resistance, termed creep-friction, is the subject of the paper. Within the creep-friction literature, the term “creep” does not mean a viscous mechanism, but rather connotes a slight slip that accompanies rolling. Two extremes of particle motions bound the range of creep-friction behaviors: a pure tangential translation is modeled as a Cattaneo–Mindlin interaction, whereas prolonged steady-state rolling corresponds to the traditional wheel–rail problem described by Carter, Poritsky, and others. DEM simulations, however, are dominated by the transient creep-friction rolling conditions that lie between these two extremes. A simplified model is proposed for the three-dimensional transient creep-friction rolling of two spheres. The model is an extension of the work of Dahlberg and Alfredsson, who studied the two-dimensional interactions of disks. The proposed model is applied to two different systems: a pair of spheres and a large dense assembly of spheres. Although creep-friction can reduce the tangential contact force that would otherwise be predicted with Cattaneo–Mindlin theory, a significant force reduction occurs only when the rate of rolling is much greater than the rate of translational sliding and only after a sustained period of rolling. When applied to the deviatoric loading of an assembly of spheres, the proposed creep-friction model has minimal effect on macroscopic strength or stiffness. At the micro-scale of individual contacts, creep-friction does have a modest influence on the incremental contact behavior, although the aggregate effect on the assembly's behavior is minimal.

In this paper, the debonding of a single fiber-matrix system of carbon fiber reinforced composite (CFRP) AS4/Epson 828 material is studied using Cohesive Zone Model (CZM). The effect of parameters namely, maximum tangential contact stress, tangential slip distance and artificial damping coefficient on the debonding length at the interface of the fiber-matrix is analyzed. Contact elements used in the CZM are coupled based on a bilinear stress-strain curve. Load is applied on the matrix, tangential to the interface. Hence, debonding is observed primarily in Mode II.Wide range of values are considered to study the inter-dependency of the parameters and its effect on debonding length. Out of the three parameters mentioned, artificial damping coefficient and tangential slip distance significantly affect debonding length. A thorough investigation is recommended for case wise interface debonding analysis, to estimate the optimal parametric values while using CZM.

Through the past years numerous theories regarding the contact between the wheel and the railway have been created with the purpose of resolving the interaction issues and improving the dynamical performances of the vehicle. In this context the paper comes with a three-dimensional approach of the contact between the wheel and the railway when there is a load transfer or a dual-contact. The analysis is done through the use of the CONTACT software which assimilates the contact the contact area through half-spaces and it divides it through the method the finite element [1]. In the contact area the linear elasticity theory is respected. CONTACT establishes the shape and size of the contact area between two elastically, deformable bodies found in tangential contact (normal loads). This thing is possible only if the form of the profiles found within the contact area is known. The analysis suggested through the paper validates the applicability of the CONTACT software for the profiles used by CFR and for the analysis of the dual-contact. Also, this approach allows the possibility for a tribological evaluation of the vehicle's behavior while traveling on a rail with excess as well with a rail with super-elevation deficiency.

The coefficient of earth pressure at rest $$K_{0}$$ of granular soils is revisited by discrete element method simulation. The effects of confining pressure, soil density and over-consolidation ratio (OCR) on the $$K_{0}$$ value are investigated. The coefficients of earth pressure at rest defined in the conventional form $$K_{0}$$ and in the incremental form $$K_{0}'$$ are compared. Most importantly, the microstructure of the soils (i.e. coordination number, anisotropies of contact normal and contact force) is monitored during the tests and it is used to explore the microscopic factors affecting the $$K_{0}$$ value of soils. The results suggest that $$K_{0}$$ and $$K_{0}'$$ generally approach a similar constant when the applied vertical stress is 6-10 times and 4 times of the initial isotropic stress, respectively. Meanwhile, the $$K_{0}$$ value decreases as the void ratio decreases and the vertical stress increases. The OCR has a significant effect on the $$K_{0}$$ value and for the same OCR the $$K_{0}$$ value is quite different during unloading and reloading. Better predictions are obtained by Jaky’s equation and Mayne and Kulhway’s equation if peak friction angle is used. The analyses indicate that the $$K_{0}$$ value depends on the coordination number of the soil, which is consistent with its density-dependent macroscopic behavior. The results also indicate that the $$K_{0}$$ value is closely related to the anisotropy coefficients of contact normal $$\alpha _{r}$$ , normal contact force $$\alpha _{n}$$ and tangential contact force $$\alpha _{t}$$ . During the initial $$K_{0}$$ -loading, $$\alpha _{r}$$ , $$\alpha _{n}$$ and $$\alpha _{t}$$ keep nearly constant and the evolution of $$K_{0}$$ during unloading and reloading is mainly resulted from the evolutions of $$\alpha _{n}$$ and $$\alpha _{t}$$ . It reveals that the particle rearrangement is negligible and the soil mainly adjusts the particle contact force to resist the external load during the $$K_{0}$$ loading and unloading.

To investigate the tangential contact stiffness of joint surfaces, the asperity contact of the joint surfaces is considered as an elliptically shaped contact, with the major and minor semi-axes of the contact areas assumed to follow a two-dimensional Gamma distribution. Hertz theory for the pressure distribution on an elliptical contact area is applied to solve for the tangential contact stiffness in a single asperity. Numerical results reveal a change in the tangential contact stiffness, with the influential factors being normal load, tangential load, eccentricity of elliptical asperities, correlation coefficient of asperity distribution, measured asperity height, and standard deviation of asperity distribution on joint surfaces. All of the results should provide theoretical guidance for evaluating or refining the tangential contact stiffness of joint surfaces.

A new theory is presented for predicting squat morphology on high and low rails of curves, based on tangential contact stress directivity for running bogies and local loading history. Notably, squats on high and low rails are predicted as distinct, with generally no branching on the latter. Field data confirm predictions, and illustrate three other aspects of squat growth: repetitive and transient tangential contact stress redistribution at the leading RCF-crack may explain branching; white etching material is found unrelated to crack initiation on head-hardened rails, and high-frequency dynamic wheel–rail interaction is shown incapable of explaining basic features of squat growth.

Adhesive wear and thermal degradation are the main aging mechanisms of paper-based friction materials. However, how these aging mechanisms affect the tribological characteristics of such materials is not fully understood. In this paper, the respective influences of the two aging mechanisms on the tribological characteristics of the friction materials are investigated through simulation. It is assumed that adhesive wear pre-dominantly affects the surface topography, while thermal degradation significantly affects the mechanical properties of the friction material. The simulation results show that the static friction coefficient and both normal and tangential contact stiffnesses increase due to adhesive wear, but decrease due to thermal degradation. These trends are qualitatively in agreement with experimental observations reported in the literature and our previous work.

One essential model necessary to model frictional contact between two surfaces accurately is a normal contact model. Many existing numerical applications base the normal contact between two surfaces on either a piecewise-linear penalty stiffness type model (designed to prevent excessive penetration of the two surfaces) or a material model that may not be applicable to the surfaces being studied (such as an elastic model when plastic deformation is present, or a Kelvin–Voigt type model that consists of piecewise-linear stiffness and damping to introduce damping for metallic contact). This chapter presents the current state-of-the-art for contact modeling between two metallic surfaces. The model is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. This assumption is validated to the extent that data is available and is a key assumption for coupling this normal contact model with different frictional models. In this chapter, the frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact.

A new tangential contact model between a rough surface and a smooth rigid flat is proposed in this paper. The model considers the contribution of both elastically deformed asperities and plastically deformed asperities to the total tangential load of rough surface. The method combining the Mindlin partial slip solution with the Hertz solution is used to model the contact formulation of elastically deformed asperities, and for the plastically deformed asperities, the solution combining the fully plastic theory of normal contact with the bilinear relation between the tangential load and deformation developed by Fujimoto is implemented. The total tangential contact load is obtained by Greenwood and Williamson statistical analysis procedure. The proposed model is first compared to the model considering only elastically deformed asperities, and the effect of mean separation and plasticity index on the relationship between the tangential load and deformation is also investigated. It is shown that the present model can be used to describe the stick–slip behavior of the rough surface, and it is a more realistic-based model for the tangential rough contact. A comparison with published experimental results is also made. The proposed model agrees very well with the experimental results when the normal load is small, and shows an error when the normal load is large.

Particle shape has been regarded as a key factor affecting mechanical behaviors of granular assemblies. The present work proposes a shape descriptor, i.e., asphericity, to isolate the effect of aspect ratio and angularity. A series of numerical triaxial compression tests are conducted on mono-disperse assemblies with different asphericities using a superball-based discrete element model. The corresponding mechanical behaviors are investigated from both macroscopic and microscopic points of view. Effects of particle asphericity are examined as well. It demonstrates that particle asphericity is able to enhance the particle–particle inter-locking with higher locked-in forces, showing an increasing proportion of sliding contacts, thereby making a granular assembly stiffer and stronger. In addition, weak contacts have a dominant proportion in the overall contact networks, positively correlated with asphericity. However, asphericity has an insignificant effect on the mean coordination number at the critical state. Furthermore, an established analytical stress–force–fabric relationship is verified using the present data. Anisotropy within an assembly is quantified in terms of several measures, i.e., contact normals, normal and tangential branch vectors, and normal and tangential contact forces. It is found that anisotropy of granular fabric is strongly determined by anisotropy sources in strong contact networks, where a larger asphericity results in a more anisotropic granular fabric.

In this paper, the normal contact problem between an elastic half-space and a cylindrical body with the axis parallel to the surface of the half-space is solved numerically by using the Boundary Element Method (BEM). The numerical solution is approximated with an analytical equation motivated by an existing asymptotic solution of the corresponding problem. The resulting empirical equation is validated by an extensive parameter study. Based on this solution, we calculate the equivalent MDR-profile, which reproduces the solution exactly in the framework of the Method of Dimensionality Reduction (MDR). This MDR-profile contains in a condensed and easy-to-use form all the necessary information about the found solution and can be exploited for the solution of other related problems (as contact with viscoelastic bodies, tangential contact problem, and adhesive contact problem.) The analytical approximation reproduces numerical results with high precision provided the ratio of length and radius of the cylinder are larger than 5. For thin disks (small length-to-radius ratio), the results are not exact but acceptable for engineering applications.

In a nonsliding tangential contact, vectors of tangential force and tangential displacement are related by the tensor of tangential stiffness. Using the boundary element method, we calculate the principal values of the tensor of tangential stiffness for a number of contact shapes. Of special interest for applications is that the anisotropy of the tensor of tangential stiffness is generally relatively small, even for extremely anisotropic contact shapes.

In the contact problems up to now, we have assumed that the contacting bodies have absolutely smooth, frictionless surfaces. According to this, there exist no shear forces in the contact area. If the contact point is also loaded in the tangential direction, then static and kinetic frictional forces become of interest. In this chapter, we investigate shear stresses in tangentially loaded contacts.

The problem of tangential contact between an elastic–plastic sphere and a rigid plane is studied analytically and numerically with the specific aim to derive force–displacement relations to be used in numerical simulations of granular materials. The simulations are performed for both ideal-plastic and strain hardening materials with different yield stresses and including large deformation effects in order to draw general conclusions. The results are correlated using normalized quantities pertinent to the correlation of indentation testing experiments leading to a general description of the tangential contact problem. Explicit formulas for the normal and tangential forces are presented as a function of the tangential displacement using data that are easily available from axi-symmetric analyses of spherical contact. The proposed model shows very good agreement when compared with the FE-simulations.

The dynamic tangential contact of rough surfaces of frictional elements of a stick-slip microdrive is theoretically investigated. By applying the method of dimensionality reduction, the contact areas of the frictional partners are modeled such that the physical properties of the contact can be fully considered and the influence of the roughness is taken into account. The dynamics of the microscopic rough contact is combined with a macroscopic movement of the drive’s runner in a hybrid dynamic simulation. The numerical results show a good agreement with experimental data. Furthermore, an analytical relation between maximal tangential contact displacement and normal force applied to the contact is analyzed, allowing the contact behavior to be theoretically predicted.

Digital image correlation (DIC) is a full field three dimensional measurement technique that can quantify displacements and strains of a surface. In this paper, digital image correlation is used as a slip measurement technique during coupon scale fretting fatigue experiments. Slip measured with the novel DIC technique is compared to conventional slip measurement techniques as clip gauges and modified clip gauge measurements proposed by Wittkowsky et al. Slip measurements with the DIC system show lower slip values and higher tangential contact stiffness’s compared to (modified) clip gauge measurements. Slip measured with DIC is obtained closer to the contact compared to clip gauges, eliminating the influence of elastic deformations or fitting parameters. During the fretting fatigue experiments are two equal contacts simultaneously tested. However, the slip of both contacts is not identical with outliers of more than 10% difference in slip amplitude.

Three-dimensional tire-pavement contact loads of two truck tires—a new-generation wide-base tire (WBT) and a dual tire assembly (DTA)—were measured and analyzed. Extreme and typical values of tire inflation pressure (552, 690, 758, and 862 kPa) and tire loading (26, 35, 44, 62, and 79 kN) were considered in the experimental program. The measurements were performed with the stress-in-motion Mk IV system at the Council for Scientific and Industrial Research in South Africa. Peak values in three directions were compared, and the importance of tangential contact stresses was highlighted. In addition, characteristic variations of the measurements in the longitudinal, transverse, and vertical directions were identified. A function depending on two regression parameters, applied load, and distance along the contact length was proposed to represent the contact load in the vertical and transverse directions. An analysis was performed on the measurements to obtain the regression parameters, and a simplified procedu...

In this paper, the energy dissipation in a mechanical lap joint is studied using the one-dimensional microslip friction model by incorporating the effect of interface tangential contact stiffness. A non-uniform pressure distribution of exponent law at the interface is considered and the resulted distinct stick-slip transitions along the contact interface are presented. Expressions of the critical slip loads giving rise to stick-slip transitions along the contact interface are determined. The loading force–displacement curves for different pressure distribution laws and different interface tangential stiffness are obtained and compared with each other. The hysteresis curves of the oscillating tangential contact forces versus tangential displacements and the dissipated energy at the contact are determined. It is shown that a classical power-law behavior is predicted between the energy dissipation and the applied tangential force. However, the exponents of the power-law are not the theoretical cubic but vary with interface stiffness and pressure distributions. The obtained results suggest that the joint interface tangential stiffness and interfacial pressure distribution are reasons for the varying exponent values obtained in experimental work.

In the past, contact model in the combined finite-discrete element method (FDEM) does not include the influence of the tangential contact interaction, and the deficient model associated with the contact force can seriously degrade the computing accuracy. In order to overcome this defect, an improved FDEM is developed in this work. The potential contact mechanism is implemented to calculate the normal contact force; meanwhile, the force-displacement law by coupling the classical Mohr–Coulomb type frictional algorithm and the rotation transformation algorithm is applied for the accurate computation of the tangential contact force. Consequently, a holonomic system of the calculation algorithm for the contact interaction is proposed, accounting for the influence of the tangential contact force. The performance of the approach is validated with well-known benchmarks including a frictional numerical test, the dynamic response of the block under the seismic excitation, a sliding/toppling test of a joint rock slope, a numerical simulation for joints structure affecting a sliding rock mass and the 2008 Donghekou Landslide trigged by the Wenchuan Earthquake. The results are compared against the experimental data and analytical solutions. Excellent agreements between the computational result and existing measurements show that the proposed approach has an outstanding ability to describe the complex mechanical properties among the separate entities.

Perspectival theory, related to Don Quixote by the many references in the corpus of Ortega, enables further research about the importance of the landscape and the physical description in order to understand the work of Cervantes. Similarly, it should be mentioned its relation with the development of literary theory. Such investigations give an interesting point of view under the framework called travel genre and its tangential contact with Quijote . On the other hand, and because of the publication of Obras Completas by Ortega, we find ourselves with a new order of the writings from the philosopher and an appropriate index for research.

An experimental method for estimating the tangential contact stiffness of contact interface with controlled contact asperities is discussed. The tangential contact stiffness is analyzed from the shift of certain eigenmode frequency of the system resulting from the changes in the density of contact asperities and the application of normal force. The results show that for the case of contact combination with 189 contact asperities, the corresponding eigenmode frequency shifted from 1.01 kHz at normal force of 19 N to 1.64 kHz at normal force of 148 N. This shift corresponds to the increase of tangential contact stiffness from 34.08 MN/m at normal force of 19 N to 67.44 MN/m at normal force of 148 N. It is found that the corresponding eigenmode frequency and its shift were affected by the density of contact asperities as well as the normal force. In the case of contact combination with 397 contact asperities, the corresponding eigenmode frequency shifted from 2.36 kHz at normal force of 49 N to 3.9 kHz at normal force of 153 N, indicating the increase of the tangential contact stiffness from 93.91 to 140.73 MN/m. A simple power relationship is proposed to explain the quantitative relationship between the eigenmode frequency shift and the tangential contact stiffness value.

All forces between wheel and rail (Fig. 3.1) act on a contact patch of a size of about 1.5 \(\mathrm{cm}^2\). The weight of the vehicle is translated through normal forces; the guidance through large-radius curves is provided by tangential forces; and during acceleration and braking, additional tangential forces in the circumferential direction of the wheel arise.

An investigation of the influence of constitutive friction laws on the damping behavior of dry friction joints is presented. The modeling starts at the micro- scale of the surface roughness leading to constitutive laws with regard to both the normal and tangential contact. These laws are used in a 3D finite element simulation of a simplified model joint. Numerical simulations show the influence of various levels of sophistication of the used contact laws. Here, the influence of high level contact laws proves to be limited in a spatially resolved joint model.

Until recently, the only way of solving contact problems was to applythree-dimensional contact theories. However, this presupposes higher mathematical and numerical knowledge, which usually only research groups possess. This has changed drastically with the development of the method of dimensionality reduction (MDR), which allows every practically oriented engineer an access to the solution of contact problems. The simple and contact-type dependent rules are summarized in the first part of the user manual; they require contacts between elastically homogeneous materials. The present paper forms the second part of the user handbook and is dedicated to the solution of contact problems between power-law graded materials. All the MDR-rules are listed with which normal, tangential and adhesive contacts between such high-performance materials can be calculated in a simple manner.

An analytical and numerical study of the tangential contact of a spherical particle under varying combined normal-tangential loading is presented. The normal and tangential contact is described by the Hertz and regularized Coulomb laws. This study is focused on the analysis of the tangential displacement of the particle’s contact point under variable normal force and reevaluation of the procedures for calculation of the tangential force. The incremental displacement-driven and force-driven constitutive relationships are developed. The importance of an adequate numerical treatment of the tangential component of the contact force is shown for the slide mode, and the recommendations for its evaluation are proposed. The performance of the algorithm is demonstrated by solving the problem of the oblique impact of the spherical particle on the wall. The suggested methodology allows us to analyse the elastic and sliding effects of the tangential interaction more precisely than existing methodologies. Besides, the issue of the direction of the tangential force, when the Coulomb limit is reached, was reconsidered in one-dimensional case by taking three versions of the unit direction vector, which are based on the tangential elastic displacement, tangential stick force, and tangential relative velocity of the contact point of the particle.

This paper describes the development of a 3D tyre–pavement interaction model to predict the tyre–pavement contact stress distributions for future use in the mechanistic analysis of pavement responses. The ribbed radial-ply tyre was modelled as a composite structure (rubber and reinforcement), and the tyre material parameters were calibrated through load-deflection curves. The steady-state tyre rolling process was simulated using an arbitrary Lagrangian Eulerian formulation. The model results are consistent with previous measurements and validate the existence of non-uniform vertical contact stresses and localised tangential contact stresses. The analysis results show that the non-uniformity of vertical contact stresses decreases as the load increases, but increases as the inflation pressure increases. However, vehicle manoeuvring behaviour significantly affects the tyre–pavement contact stress distributions. For example, tyre braking/acceleration induces significant longitudinal contact stresses, while ty...

In this study the tangential contact stiffness between two elastic bodies having nominally flat surfaces with different material combinations is investigated. The tangential contact stiffness between these two elastic bodies is first calculated based on the Greenwood-Williamson-McCool contact theory. Then, the tangential contact stiffness is determined by experimental investigation on a tribometer under the effect of different values of normal load and tangential displacement amplitude. The tangential contact stiffnesses obtained from the experimental data show a good agreement with the theoretical results, where the trends are similar and they are in the same order of magnitude.

Scanning coordinate metrology is largely based on recording the position of a spherical tip which is maintained in contact with the surface to be measured. The coordinate measuring machine (CMM) software converts these tip coordinates into coordinates of points on the measured surface, a process called probe radius correction. In order to investigate the probe radius correction accuracy of specific CMM software in scanning measurements, a surface probing simulator is developed. It calculates the coordinates of probe tip center points (virtual indicated measured points) as raw measurement data by numerically probing a known virtual surface. An iterative solution based on geometric criteria is used to achieve the necessary tangential contact conditions. Various sculptured surface profiles, probe radii, and scanning increments can then be simulated. These raw data are then fed to the CMM software where the probe radius correction is performed. The CMM results are then compared with the known surface to evaluate the probe radius correction accuracy of the CMM built-in algorithm. The simulator allows a rapid CMM software capability check for a variety of situations and may pinpoint shortfalls that may be avoided through alternative measurement procedures. It may also be used to motivate the development of new probe radius correction techniques and assist in their evaluation. Tests were conducted on a Zeiss and a Mitutoyo CMM to demonstrate the usefulness of the simulator.

Locking surfaces with a wet interface can enhance interactions between a grasped object and a soft pad. This paper presents a mechanical approach to understanding the role of morphological design in achieving wet adhesion for secure grasping by a soft pad. Two conditions were compared in modeling wet interfaces between an object and a soft pad: a pad with a flat surface, and a pad with a micropatterned surface. The latter was designed and analyzed based on the wet attachment between the surface of a tree-frog's toes and its substrate. In this model, we proposed a method to estimate the contact force in both normal and tangential directions between a soft pad with a micropattern surface and a rigid flat surface substrate. A square mold containing 3600 85 μm × 85 μm cells interspaced by grooves 15 μm wide and 15 μm deep was fabricated, using e-beam technology, as the micropattern pad. The generated normal and tangential contact forces of the pad with a micropattern surface, and a pad with a flat surface were measured in both normal and tangential directions under wet conditions. Experimental results showed good agreement with theoretical results, indicating that the micropattern significantly enhanced the contact force of the pad by approximately two-fold for the normal and 1.2- to 1.4-fold for the tangential force. This theoretical approach can be potentially utilized to investigate the association of soft pad morphology with wet adhesion, and enhance efficient grasping by soft robotic hands in wet and high-moisture environments.

Previous results, obtained using the load-scanning technique, indicate that the amount of plastic deformation of the contact surface contributes to a change in the global friction coefficient. This technique allows describing the friction from a local analysis method, since the normal and tangential contact forces to the sliding direction can be measured simultaneously, independently and precisely. It also allows maintaining a constant contact surface geometry [1].

The tangential contact stresses in the fretting fatigue of joints is studied. A model of the fatigue failure rate of joints permits estimation of their durability on the basis of the fatigue characteristics of a standard sample with a central hole.

Contact forces between workpiece and fixture define fixture stability during clamping and influence workpiece accuracy during machining. In particular, forces acting in the contact region are important for understanding deformation of the workpiece at the contact region. This paper presents a model that combines contact elasticity with finite element methods to predict the contact load and pressure distribution at the contact region in a workpiece-fixture system. The objective is to determine how much clamp forces can be applied to generate adequate contact forces to keep the workpiece in position during machining. The model is able to predict the normal and tangential contact forces as well as the pressure distribution at each workpiece-fixture contact in the fixturing system. Model prediction is shown to be in good agreement with known industry practice on clamp force determination. The presented method has no limits on the types of materials that can be analyzed.

This paper presents approximations to fatigue curves in fretting conditions with spherical contact in the alloy Al 7075. The curves are defined for a specific contact geometry and loads applied in the tests (axial load on the specimen, the normal and tangential contact forces). In order to obtain a curve of this type it is necessary to fix all parameters except for one and analyse its influence on life. The method used to estimate life in fretting fatigue combines initiation with propagation. Different approaches to the growth of short cracks are employed and in some cases a fretting fatigue limit is predicted. Various groups of fretting tests have been analysed, evaluating the suitability of each approximation.

This paper describes an experimental investigation to estimate the contact stiffness in normal and tangential directions. The static method was used to estimate normal contact stiffness and to study the effecting factors. In order to study tangential contact stiffness, dynamic methods were developed to estimate contact stiffness in both normal and tangential directions. That study is validated by the results of the static method in the identification of normal contact stiffness.

The rapid convergence of the tangential rolling contact parameters to their stationary values, combined with the high computational cost associated with calculations using instationary models, has meant that stationary models are usually employed in railway dynamics. However, the validity of stationary models when the applied contact conditions are subjected to rapid changes has not been sufficiently investigated. With the objective of deducing the effects of the evolution of the instationary process on the contact parameters, the tangential contact problem is solved for a set of reference conditions. For this purpose a calculation model is adapted, from which it is possible to analyse the evolution of the contact parameters when the forces exerted between rail and wheel are subjected to rapid changes. From the calculations made, situations impossible to simulate by means of stationary theories are obtained according to the frequency of variation in the forces, such as slip zones in the leading edge of the contact area and reverse contact (locally, the traction field is opposite to the direction of the external force transmitted to the contact).

It is shown that three-dimensional contacts have the same force–displacement law as in a simple one-dimensional model. This is valid both for normal and tangential contact problem. Under some additional assumptions these ideas can be used for adhesive contacts too. The above reduction makes it possible to develop effective simulation methods for contact and friction processes.

This paper presents a performance assessment of rotary end milling at the tangential contact. With this shape of the contact, process has been more stable. At the last decade due to the fact that cutting tools have a quenching problem, Turn-milling has been developing in manufacturing technology for processing hard steels, where in both the workpiece and the tool are given a rotary movement simultaneously. Thus, cutting edges have a time for quenching. The objective of present work is to investigate process of tangential turn-milling for machining of workpieces with in the normally available range of speed and feeds to explore its advantages. The investigations have been laid mainly on surface roughness and timing process. The experiments have been conducted for tangential turn-milling of mild steel workpiece.

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.

Plane normal contact of a rigid flat-ended hot punch and a thermoelastic half-space is considered under the assumption of finite friction between contacting surfaces. The problem is treated with the boundary integral methods. We consider independently normal and tangential contact problems. The rise of slip and stick regions under the punch is studied. The nonlinear equations for the unknown stick region size are obtained and solved numerically.