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This paper introduces a new technique that enables considering the impact of soil fabric on microstructure of internally unstable gap-graded soil. The influence of soil fabric on erodibility of fine particles was studied by transferring the real soil fabric from a micro-computed tomography (μCT) image to discrete element method (DEM) using a new image processing workflow. The pair correlation function (PCF), a two-point correlation between particles in images, was used as a microgeometrical parameter to assess the impact of image filters on the quality of the μCT image. Comparison between PCF and particle size distribution of the raw μCT and reconstructed images suggest that anisotropic diffusion and non-local mean filters reproduce the real soil fabric samples most effectively. DEM results showed lower coordination number but slightly higher stress reduction factor for the real fabric, indicating that the real contact geometry results in having fine particles more involved in force network.

The Hertz contact law for two linear elastic spheres plays a very important role in the discrete element method (DEM). Within the classic Hertz contact theory, the contact strain energy distribution in the two contacting spheres is analytically derived, which states that the ratio between the strain energies stored in the two spheres is solely dependent on their material properties, regardless of their radii. This strain distribution law is generally valid for non-spherical and other contact cases, provided that the two surfaces in contact can be reasonably treated as two elastic half-spaces and that the deformation is small. The independence feature of the law from the contact geometry also greatly facilitates the computation of the contact strain energy stored at particle level. As a direct consequence of this law, the contact point between two particles in DEM could also be determined. The numerical simulations demonstrate good agreement between the theoretical prediction and the numerical results for the tested cases involving spheres and ellipsoids with varying sizes and material properties.

Gears are important motion and power transmission components and enhancing their machining accuracy and performance. In this work, a novel processing of ultrasonic vibration-assisted forming grinding gear (UVAFGG) is proposed, which involves the superimposition of ultrasonic vibration on the gear, and the thermo-mechanical coupling effect on surface residual stress is explored as well. Firstly, based on the local contact geometry relationship for forming grinding, the three-dimensional (3D) distribution model of the heat flux density along the tooth profile is established. In addition, the mathematical relationship models between the grinding force, grinding heat, residual stress, and grinding parameters are also given. Then, the effect of grinding parameters such as spindle speed and ultrasonic amplitude for the characteristics of residual compressive stress accumulation is obtained by comparing the single factor experimental and finite element simulation results. It is found that under the action of ultrasonic vibration, the grinding heat and grinding force reduce by 38.7% and 40.5 % and 40.5 %, respectively. The surface residual compressive stress gradually decreases with the increase in spindle speed, while with the increase in ultrasonic amplitude, it increases first and then decrease. Comparing with the conventional grinding gear (CGG), the average rate of increase of the surface residual compressive stress under the both parameters is 17.8 %–31.3 % and 20 % respectively. Meanwhile, the residual compressive stress along involute shows a negative correlation with the increase in the rolling angle. At the same time, the experimental and simulation results agree well with the theoretical model. In conclusion, the results of this study provide a novel process technology for gear machining, and a reference for the investigation on residual stress during UVAFGG.

A calculation model of grinding temperature during full tooth groove form grinding (FTGFG) was established through the simplification of the three-dimensional (3D) heat conduction process and based on the theoretical analysis of the transient moving heat source temperature field. The proposed model calculated the grinding temperature distribution of the gear surface and also described the coupling effect of two adjacent grinding heat sources at the junction of the tooth groove. Based on the grinding principle and the contact geometry relationship between the formed grinding wheel and the workpiece, the distributions of grinding parameters, grinding wheel geometry parameters, the actual contact arc length between the grinding wheel and the workpiece, tangential grinding force, and the heat partition to the workpiece were analyzed. A 3D non-uniform heat flux distribution model was also developed based on the actual tangential grinding force distribution, the linear velocity distribution of the grinding wheel, the heat partition ratio along the cross-section of the tooth groove, and the triangular heat flux model in the direction of the contact arc for the contact zone during FTGFG. Finally, a test method for form grinding temperature measurement was designed, and the theoretical model was verified by experimental results. Test results revealed that the temperature distribution on the tooth groove surface during form grinding was non-uniform. Due to the coupling effect of two adjacent heat sources, the temperature increased sharply, and a steep peak was formed at the flange where the bottom plane and the transition arc intersected or the transition arc and the involute intersected. A comparison between experimental and theoretical results on the ground surface and in the transverse section revealed that the analytical model had better prediction accuracy and that the relative error was within 15 %.

We propose a system containing a single pyrene molecule sandwiched between two metallic electrodes. The transport properties of the single pyrene molecule with four configurations are investigated using a steady-state theoretical model. We calculate the transmission probability and the electric current for the structure (1, 8), the structure (1, 7), the structure (1, 5) and the structure (1, 4). By applying a gate voltage on the pyrene molecule, we calculate the thermoelectric properties. The thermoelectric and electron transport properties can be controlled by quantum interference, the contact geometry and the gate voltage. The asymmetric behavior and the splitting of resonances in the transmission spectrum occur due to applying a gate voltage on the pyrene molecule. As a result, the structures (1, 5) and (1, 7) have a maximum value of the figure of merit reaching to 0.8 at the Fermi level. According to the results, the structures (1, 5) and (1, 7) can be act as promising thermoelectric applications in molecular electronics.

This paper studies the instantaneous second-order total freedom of two smooth objects initially in contact at a single point. The analytical determination of the set of physically allowed second-order motions is formulated in the Euclidean space using the screw theoretic concepts of twist and twist-derivative. Mathematical expression that characterizes the nature of second-order motion for an arbitrary contact geometry is derived in terms of twist coordinates, twist-derivative coordinates and the principle normal curvatures of the two surfaces at the point of contact. It is shown that the characteristic of this expression is equivalent to that of the derivative of reciprocal product of the instantaneous twist and contact normal line. The efficacy of the theory developed is demonstrated through two illustrative examples.

Studies on the eutectic reaction of core materials are important for more accurate evaluation of progression of a reactor severe accident since such reactions provide significant input to the followed in- and ex-vessel phenomena. In this study, motivated to obtain some knowledge and database for enhanced understanding on this reaction, a series of simulated experiments was performed using the Pb-Sn couple due to their lower eutectic point. The experiments were conducted in a self-designed experimental system, which mainly consists of a sample holder and a visible resistance furnace. To acquire relatively comprehensive understanding, different experimental parameters such as the reaction temperature (463–483 K), contact pressure (0.43–1.15 MPa) and the contact geometry (square, upright and inverted isosceles trapezoids) were varied. Based on the experimental observation and quantitative data obtained, influence of experimental conditions on the reaction rate as well as the chemical composition and specific heat capacity of reaction product was analyzed. It is found that the reaction temperature and contact pressure have noticeable impact on the reaction rate, while the role of contact geometry seems to be insignificant. As for the composition of reaction product, despite an evident effect of reaction temperature and contact geometry, non-remarkable impact of the contact pressure is found. Although the composition of reaction product is varied at different conditions, the change in macroscopic specific heat capacity of the reaction product is confirmed to be limited over present scope of experimental parameters. The obtained results in this work to some degree have confirmed the good applicability of our experimental system developed, thus providing us with promoted confidence for future investigations on eutectic interaction using actual reactor materials. Knowledge and fundamental data from our work might be also utilized for the future development and verifications of eutectic-reaction models in reactor severe accident analysis codes.

Secondary air systems of civil aircraft engines require labyrinth seals with a minimum gap clearance for optimal functioning. In the case of high speed contact during the engine running-in period, an abradable material is deposited on the stationary part of the seal to limit the damage of the rotating shaft, which is made of a titanium alloy. Such situations are potentially critical for the seal; hence, the present study aims to observe the material behaviour during these contact conditions and to establish the tribological circuit of a third body through the interface. A high-speed contact test rig was developed to recreate contact conditions occurring in an aircraft engine. Two contact configurations occurring in different locations of the engine, with different materials and surface areas were explored. Thermal and mechanical instrumentation were used in each test. The influence of the contact geometry and the test conditions show that material flows through the contact determine the life cycle of the contact (by establishing a balance between the source, internal and material flow) and allows for the control of the thermomechanical constraints in a high-speed contact.

Lubrication is often employed in fretting contacts to reduce wear and stresses associated with high friction. Owing to the very small displacements associated with fretting, penetration of lubricating oils into the contact may not be effective. The efficacy of the penetration of the lubricant into the contact is very difficult to observe experimentally, and accordingly, this paper presents a numerical simulation of a lubricated fretting contact using a Coupled–Eulerian–Lagrangian (CEL) finite element method. Meso-scale CEL finite element models are developed to simulate the cylinder-on-flat arrangement used experimentally at the University of Nottingham in which the roughness of contact surfaces is characterized as fractal geometry by the Weierstrass-Mandelbrot (W-M) function. The fluid–solid and solid–solid contact in the lubricated fretting contact are simulated, and from these, wear and friction coefficients are determined. The effects of contact geometry on lubricated fretting contacts and lubricant on fretting wear are modelled and compared with experimental observations. Results indicate that oil lubrication reduces fretting wear and friction effectively in the less-conforming contacts but has little effect in the more-conforming contacts.

Gear hone is a special tool used for roll finishing of lateral faces of hardened gear teeth. Over time, penetration of abrasive grains into the metal, wear and breaking in of the hone material, contact and bending deformation of the hone teeth, especially if an elastic binding agent is used, lead to changing the tooth contact geometry, i.e. a point contact turns into an elliptical contact. The gear hone tooth deformation is a function of the contact point height, i.e. for contact points closer to the tooth top, the deformation is many times larger than that occurring for contact points closer to the tooth bottom. It affects the specific sliding ratio between the meshing hone and the workpiece. Meanwhile, slight equalization of the specific sliding along the tooth height occurs. Comparable deformations, errors and metal removal rates applicable to the gear hone and the workpiece would contribute to the effectiveness of the error reduction measures. The elasticity of the tool’s composite material must be duly considered in calculating the geometry, selecting the compound composition and assessing the applicability of gear hones.

Laser induced transient current technique (LI-TCT) was proven to be a successful tool for measuring at the same time carrier lifetime, carrier mobility , and electric field distribution in X- and gamma ray detectors with plain contacts on opposite surfaces. Unfortunately, the most performing detectors exploit more complicated contact geometries that, hindering hole contribution to signal formation, allow a much better spectroscopy . In this paper, a LI-TCT based method is presented, for the determination of transport parameters as well as electric field distribution directly in single carrier devices. The method’s validity is demonstrated in twin CdZnTe detectors having similar material properties, but different weighting potentials.

This study investigates the thermal response of titanium alloy fretting sliding through a numerical approach with the consideration of the friction dissipation, plastic dissipation, surface roughness and wear. The fretting sliding of a cylindrical pad on a specimen with surface roughness is modeled to predict the temperature distribution, the evolution of the wear profile, and the fields of surface and subsurface stresses. Specifically, a thermo-elasto-plastic constitutive model considering the thermal-induced softening of material properties is developed to evaluate the contact pressure and the tangential stress on the surfaces as well as the subsurface stresses in the contacting components. The friction and plastic energy dissipations function together as the heat source to cause the temperature rise in the contact zone. A modified Archard model is used to predict the wear profile of the contact surface and change the contact geometry. The models are then incorporated in the finite element analysis of the fretting sliding to evaluate the thermal response. The influences of the plastic dissipation and the surface roughness on the temperature rise in the fretting sliding are discussed.

Dynamic contact resistance measurement (DRM) is an effective technique to evaluate the contact conditions of high voltage SF 6 circuit breaker. However, the relations between DRM characteristics and contact performance remain ambiguous, the influence of the electrical stress on the DRM curves is equivocal as well, and there is no contact erosion evaluation method based on DRM. To investigate the relations between DRM characteristics and contact erosion, the DRM results of high voltage SF 6 circuit breaker at various degrees of erosion obtained from the designed experiments are presented. The experiments demonstrate that with the degradation of the contacts, the average arcing contact resistance ( R a ) increases, and the arcing contact wipe ( D a ) decreases. Then, the simulation of the erosion test is performed to analyse the relations between R a and D a and the contact performance. The results show that with the decrease of R a , the threshold of D a to ensure the success of the current commuting from the main contacts to the arcing contacts becomes shorter. Moreover, the influence of the electrical stress on R a and D a are investigated. Results demonstrate that R a reflects the influence of arc by-products and contact geometry caused by electrical stress, and that D a reflects the influence of the interrupted current, the arcing time, the contact geometry, and the contact material. Finally, an evaluation method of the contact erosion for SF 6 circuit breaker based on DRM is proposed.

Riemannian and contact geometry formalisms are used to study the fundamental equation of electromagnetic radiation-like systems, obeying a Stefan–Boltzmann’s-like law. The vanishing of metric determinant is used for classifying what kind of systems cannot represent a possible generalization of blackbody-like systems. In addition, thermodynamic curvature scalar R is evaluated for a thermodynamic metric, giving R = 0 , which validates the non-interaction hypothesis stating that the scalar curvature vanishes for non-interacting systems.

The friction behavior of soft, aqueous, biotribological contacts depends on contact geometry, speed, and pressure. Previous efforts to measure the surface profile of soft sliding contacts have been stymied by the matching index of refraction of aqueous materials submerged in water. Here, hydrogel surface deformations were imaged using confocal microscopy to experimentally investigate the contact geometry as a function of sliding speed. In situ fluorescence confocal microscopy measurements of the contact deformation during unidirectional friction experiments revealed the existence of a front/back asymmetry that increased with increasing sliding speed. A polyacrylamide hydrogel disk (96.5% water) was polymerized with fluorescent dyes and used as a rotating countersample below a polished glass hemispherical pin (1 mm radius of curvature). All experiments were performed submerged in a dilute (0.7 wt%) suspension of 1 μm red fluorescent microspheres in ultrapure water. Imaging of the contact was performed using a confocal microscope in situ with unidirectional sliding at 0.1, 1, 10, and 100 mm/s. The friction coefficient increased monotonically with increasing speed from μ ~ 0.04 at 0.1 mm/s to μ ~ 0.20 at 100 mm/s. All imaging was performed relative to the stationary glass probe under steady-state conditions. The contact line measured by connecting the leading and exiting contact points was nearly perpendicular to the loading direction at 0.1 mm/s sliding speed, but distorted as sliding speed increased. Consistent with the theories of viscoelastic contributions to polymer friction, the tangent of the contact-line angle correlated with friction.

A new framework which describes the role of three key processes in fretting wear of metals is proposed, with these three processes being: (i) oxygen transport into the contact; (ii) formation of oxide-based wear debris in the contact and (iii) ejection of the wear debris from the contact. Based upon a physical understanding, rate equations for the three key processes are proposed, which provide a basis for the influence of test parameters (such as contact geometry, applied load, slip amplitude, fretting frequency etc) on the three rates to be understood. To maintain system equilibrium in steady-state fretting, the three processes must operate at the same rate as each other (debris cannot be ejected from the contact faster than it is formed, and debris cannot be formed faster than it is ejected). Accordingly, the observed wear rate is the rate of the process with the lowest rate of the three processes, with this process being termed the rate-determining process. The effect of test parameters on the three key processes differs, and thus the effect of changes in any test parameter on the observed rate of wear will itself be dependent upon which of the three processes is rate-determining. A number of assumptions have been made in deriving the equations which describe the key processes and it is recognised that these equations themselves may be refined in light of future research; however, any such revised equations can simply replace those proposed as part of the rate-determining process framework. The framework can be applied to both conforming and non-conforming contact geometries. In tests with non-conforming contact geometries, the contact size increases with wear; since it is proposed that the rates of two of the three processes (oxygen transport and debris ejection) are dependent upon the size of the contact, the rate determining process can change during such a test and the rate of wear will continually fall when either of these processes are rate-determining. This complexity means that the evolution of the wear volume can only be evaluated numerically through the use of a time-marching analysis in such cases. In contrast, in tests with conforming contact geometries, the contact size does not change as wear occurs, and so there will be no changes in the rate-determining process as wear proceeds. It is recognised that this framework addresses wear under steady-state conditions and does not consider the initial period of exposure where steady-state conditions are being developed. In the case of conforming contacts where the contact size is large, the duration of the initial transient period may be substantial and may form a significant proportion of the test duration or component lifetime. This needs to be recognised both in the design of tests and in the application of this framework.

This paper presents an experimental investigation into the effects of contact conformity, contact pressure and displacement amplitude on the gross-slip fretting behaviour grease-lubricated cylinder-on-flat contacts in the context of flexible marine riser pressure armour wire, and compares behaviour with that observed in unlubricated conditions. Characterisation of friction and wear is critical to fretting fatigue life prediction in flexible risers since friction directly controls trailing-edge fretting stresses and hence fatigue crack initiation, on the one hand, and on the other hand, directly affects wear via relative tangential slip (displacement). Wear can have a beneficial or detrimental effect on fatigue crack initiation and propagation, depending on relative slip and slip regime. It is shown that friction and wear are higher for dry conditions than for grease-lubricated conditions. For grease-lubricated conditions, behaviour is determined by whether grease can be retained in the contact (as opposed to being extruded out). Retention (or replenishment) of grease in the contact results in low rates of wear and low coefficients of friction; these conditions are favoured by fretting displacements above a critical value, by low contact conformity, and by low applied loads. The authors would like to thank the Irish Research Council and Wood Group Kenny for funding of this project through the Enterprise Partnership Scheme (EPSPG/2013/638), the National University of Ireland for funding through a NUI Travelling Scholarship. We also wish to acknowledge the help and support we have received from Dr. Adrian Connaire and Mr. Kieran Kavanagh (Wood Group). The authors also wish to acknowledge the support of the Faculty of Engineering at the University of Nottingham where this research was conducted. peer-reviewed

Different origination theories for squat-type rail defects are examined and confronted with experimental evidence. Based on the morphology of the three-dimensional defect crack pattern, with a leading crack directivity governed by the tangential stress history, it is shown that theories assuming dynamic wheel-rail interaction as a direct initiation mechanism of the double-lobed defect violate the causality principle. Rail surface anomalies of three categories increase the tangential stress exposure and thus the risk of defect development: pertaining to the material properties, contact geometry (including both the global scale, involving the dynamic stress level transmitted by the contact area, and the local scale, involving transient stress redistribution within this area), and contact stiffness. Both detection measures focusing on geometrical surface deviations giving rise to dynamic wheel-rail interaction (such as axle-box acceleration measurements) and the idea of a critical diameter for such imperfections are inadequate. Instead, and apart from the surface geometry, steel micro-cleanliness and chemical composition, phase transformation mechanisms of surface material (due to operational conditions or treatment by grinding or milling) and welding deserve attention. Fluid entrapment remains a potentially contributing factor in early growth, while crack face oxidation and corresponding volumetric expansion may contribute at any stage after initiation.

Vertical dynamic vehicle-track interaction in the through route of a railway crossing is simulated in the time domain based on a Green's function approach for the track in combination with an implementation of Kalker's variational method to solve the non-Hertzian, and potentially multiple, wheel-rail contact. The track is described by a linear, three-dimensional and non-periodic finite element model of a railway turnout accounting for the variations in rail cross-sections and sleeper lengths, and including baseplates and resilient elements. To reduce calculation time due to the complexity of the track model, involving a large number of elements and degrees-of-freedom, a complex-valued modal superposition with a truncated mode set is applied before the impulse response functions are calculated at various positions along the crossing panel. The variation in three-dimensional contact geometry of the crossing and wheel is described by linear surface elements. In each time step of the contact detection algorithm, the lateral position of the wheelset centre is prescribed but the contact positions on wheel and rail are not, allowing for an accurate prediction of the wheel transition between wing rail and crossing rail. The method is demonstrated by calculating the wheel-rail impact load and contact stress distribution for a nominal S1002 wheel profile passing over a nominal crossing geometry. A parameter study is performed to determine the influence of vehicle speed, rail pad stiffness, lateral wheelset position and wheel profile on the impact load generated at the crossing. It is shown that the magnitude of the impact load is more influenced the wheel-rail contact geometry than by the selection of rail pad stiffness.

A customized 2D computational tool has been developed to simulate bifacial rear local contact PERC type PV structures based on the numerical solution of the transport equations through the finite element method. Simulations were performed under various device material parameters and back contact geometry configurations in order to optimize bifacial solar cell performance under different simulated illumination conditions. Bifacial device maximum power output was also compared with the monofacial equivalent one and the industrial standard Al-BSF structure. The performance of the bifacial structure during highly diffused irradiance conditions commonly observed in the Middle East region due to high concentrations of airborne dust particles was also investigated. Simulation results demonstrated that such conditions are highly favorable for the bifacial device because of the significantly increased diffuse component of the solar radiation which enters the back cell surface.

Numerous studies have reported on the tibiofemoral articular cartilage contact kinematics, however, no data has been reported on the articular cartilage geometry at the contact area. This study investigated the in-vivo tibiofemoral articular cartilage contact biomechanics during a dynamic step-up motion.Ten healthy subjects were imaged using a validated magnetic resonance and dual fluoroscopic imaging technique during a step-up motion. Three-dimensional bone and cartilage models were constructed from the magnetic resonance images. The cartilage contact along the motion path was analyzed, including cartilage contact location and the cartilage surface geometry at the contact area.The cartilage contact excursions were similar in anteroposterior and mediolateral directions in the medial and lateral compartments of the tibia plateau (P0.05). Both medial and lateral compartments were under convex (femur) to convex (tibia) contact in the sagittal plane, and under convex (femur) to concave (tibia) contact in the coronal plane. The medial tibial articular contact radius was larger than the lateral side in the sagittal plane along the motion path (P0.001).These data revealed that both the medial and lateral compartments of the knee experienced convex (femur) to convex (tibia) contact in sagittal plane (or anteroposterior direction) during the dynamic step-up motion. These data could provide new insight into the in-vivo cartilage contact biomechanics research, and may provide guidelines for development of anatomical total knee arthroplasties that are aimed to reproduce normal knee joint kinematics.

Based on the random theory of the probability density evolution method (PDEM), a refined random wheel/rail contact model for train-track-bridge systems is proposed. The trace line method with the law of equal slopes is developed to determine the wheel/rail contact locations, which are described by probability density functions on the wheel/rail surface. The number theoretic method (NTM) and stochastic harmonic functions (SHFs) are employed to generate the representative random track irregularities. Considering the excitation of random track irregularities and the wheel/rail contact geometry, the wheel/rail normal contact force and the tangential creep force are accurately calculated and analyzed using the proposed wheel/rail contact model. A high-speed railway case study is presented to reveal the random dynamic characteristics of a train-track-bridge system and the wheel/rail interaction. The results show that the time-varying probability density evolution functions of the wheel/rail contact points can effectively indicate both the phenomenon of wear on the rail surface and its distribution characteristics. Additionally, some significant conclusions are obtained.

This paper describes the outcomes of a series of laboratory ice crushing experiments that was performed (Sopper, 2016) to investigate the effects of external boundary condition and indenter contact geometry on ice load magnitude under crushing conditions. Four boundary conditions were considered: dry cases, submerged cases, and cases with the presence of snow and granular ice material on the indenter surface. Indenter geometries were a flat plate, wedge shaped indenter, (reverse) conical indenter, and a hemispherical indenter. These were impacted with artificially produced ice specimens of conical shape with 20° and 30° cone angles. All indenter – ice combinations were tested in dry and submerged environments at 1 mm/s and 100 mm/s indentation rates. Additional tests with the flat indentation plate were conducted at 10 mm/s impact velocity and a subset of scenarios with snow and granular ice material was evaluated. The tests were performed using a material testing system (MTS) machine located inside a cold room at an ambient temperature of –7 °C. Data acquisition comprised time, vertical force, and displacement. In several tests with the flat plate and wedge shaped indenter, supplementary information on local pressure patterns and contact area were obtained using tactile pressure sensors. All tests were recorded with a high speed video camera and still photos were taken before and after each test. Thin sections were taken of some specimens as well. Ice loads were found to strongly depend on contact condition, interrelated with pre-existing confinement and indentation rate. Submergence yielded higher forces, especially at the high indentation rate. This was very evident for the flat indentation plate and spherical indenter, and with restrictions for the wedge shaped indenter. No indication was found for the conical indenter. The presence of snow and granular ice significantly increased the forces at the low indentation rate (with the flat indentation plate) that were higher compared to submerged cases and far above the dry contact condition. Contact area measurements revealed a correlation of higher forces with a concurrent increase in actual contact area that depended on the respective boundary condition. In submergence, ice debris constitution, ice extrusion, as well as crack development and propagation were impeded. Snow and granular ice provided additional material sources for establishing larger contact areas. The dry contact condition generally had the smallest real contact area, as well as the lowest forces. The comparison of nominal and measured contact areas revealed distinct deviations which were dependent on the boundary conditions. The incorporation of those differences in contact process pressures-area relationships indicated that the overall process pressure was not substantially affected by changes in true contact area.

This contribution reports on an ongoing research project aimed in developing a unified theoretical framework for the description of interconnected thermo-mechanical systems with a particular emphasis on thermodynamic engines. We analyse from the geometrical viewpoint the structure of thermodynamic and mechanical interconnection and propose an approach to the unified description of thermo-mechanical systems. The theoretical results are illustrated by a physical example.

It is well known that mechanisms and rates of fretting wear of many metals are dependent upon the temperature of the environment; specifically, it is known that a transition temperature exists, above which the debris forms a protective bed in the contact which results in very low rates of wear being observed. This paper seeks to investigate the influence of contact geometry and slip amplitude on the transition temperature of a high strength alloy steel, and to understand these effects in terms of debris retention in (or expulsion from) the contact. Cylinder-on-flat fretting tests were performed at temperatures between 25 °C and 250 °C with two displacement amplitudes (25 μm and 100 μm) and two cylinder radii (6 mm and 160 mm). It was found that for the smaller cylinder radius, the transition temperature increased as the fretting displacement amplitude was increased. However, it was found that whilst the contacts with 6 mm radius cylinders and 160 mm radius cylinders exhibited very different mechanisms of wear at low temperature, the temperature at which the transition to forming of the protective debris bed was not strongly influenced by the contact geometry; moreover, at the higher temperature, the protective bed is formed irrespective of contact geometry. It is proposed that the reduction in wear rate at higher temperatures is associated with the retention of oxide debris within in the contact area for long enough that it sinters to form a protective ‘glaze’ layer. By increasing the displacement amplitude, the rate at which the oxide is ejected from the fretting contact increases and this reduces the ability to form a protective layer; as such, a higher temperature is required to form the protective glaze as the displacement amplitude is increased.

Fretting can lead to surface wear and/or crack nucleation depending on the sliding condition and contact geometry. To formalize this aspect, Ti-6Al-4V cylinder/plane and punch/plane contacts were investigated. The experimental crack nucleation domains in partial and gross slip conditions were established and simulated combining SWT cumulative damage analysis with FEM surface wear simulations. Good correlations were achieved if the experimental boundary conditions including system tangential accommodation and micro-rotations measured using DIC analysis, were considered. Fretting maps were simulated by predicting partial slip and gross slip displacement amplitudes above which cracks were respectively nucleated and removed by surface wear. Finally, it was shown that whatever the contact geometry, the gross slip cracking domain was inversely proportional to the surface wear rate.

Water-lubricated ceramic bearings are currently being used in engineering applications like water pumps, air compressors and marine systems, due to their higher efficiency, reduced environmental impact and simpler constructive designs. In search of low-cost and high-performance tribosystems, bearings made of dissimilar ceramics are not frequently studied, but have potential to show good tribological compatibility. In this study, tribological behavior of two dissimilar ceramic pairs, ZrO2-Al2O3 and ZrO2-ZTA (10 vol% ZrO2), was investigated. Water-lubricated ball-on-disc tests under loads ranging from 6.0 to 24.6 N and sliding speeds from 0.1 to 2.0 m/s were performed. Worn surfaces were characterized by optical microscopy, SEM and contact-type profilometry. Thermal (Sc,t) and mechanical (Sc,m) severity of contact models explained the mild to severe wear transition as function of tribosystem's variables such as load, speed, distance, materials’ properties, contact geometry and environment. During mild wear regime, wear rates were smaller than 10⁻⁷ mm³/Nm, friction coefficients remained low (0.1

Thanks to a result of Lisca and Matic and a refinement by Plamenevskaya, it is known that on a 4-manifold with boundary Stein structures with non-isomorphic Spin c structures induce contact structures with distinct Ozsvath–Szabo invariants. Here we give an infinite family of examples showing that converse of Lisca–Matic–Plamenevskaya theorem does not hold in general. Our examples arise from Mazur type corks.

In a dynamic radial shaft sealing (RSS) system good wear resistance is crucial for proper functionality. This contribution is dedicated to the analysis of wear in radial shaft seal applications in a sealing system itself and on a tribologically equivalent system. To make elastomers more wear resistant, new and innovative material concepts and compounds have to be evaluated. To do so a simple tribologically equivalent system, the ring-cone-tribometer (RFT), consisting of an elastomer ring and a coned shaft, was used. Two different radial shaft seal types were compared under identical test conditions on a multi-shaft test bench, to the results generated on the RFT. This was done to evaluate and compare the tribological properties of the RFT towards RSS. To avoid ageing or batch-to-batch influences the slabs for the production of the ring samples were molded from the same elastomer material batch as the radial shaft seals. Initial differences in terms of wear, friction, contact width and hardness between RSS and RFT were reduced step by step using an optimized, stiffer test setup on the RFT and a FE-simulation model to optimize the contact geometry. Data scattering on the RFT was reduced to a minimum so that the higher scatter within the results of the RSS test population was in a similar dimension as the deviation in both systems. To determine the wear during a test run, an online-wear measurement system, based on eddy current sensors, was developed that allows for the online estimation of seal wear progress on the RFT at any time. This process is based on a geometrical approach using the initial contact width and the axial displacement during the operation. The online-wear measurement correlates very well with the post-mortem wear measurement. All results form a set of tools which constitutes a solid foundation for online evaluation of rubber and seals in the future.

Musculoskeletal models of the hand rarely include fingerpad contact mechanics, thereby limiting our ability to simulate and examine hand-object interactions. The objective of this study was to evaluate whether two common contact models (Hunt-Crossley and Elastic Foundation) can accurately represent the fingerpad. Two musculoskeletal models of the index finger were created by adding fingerpad contact geometry using either the Hunt-Crossley or Elastic Foundation contact models. Key contact parameters (target force, contact area, and stiffness) were then systematically varied through 432 forward dynamic simulations to examine how these parameters influenced estimation of finger-tip forces. Across all simulations, variation in target force, contact area, and stiffness parameters impacted the computation time required to complete the simulations and the accuracy of the predicted finger-tip force. Computation time was over three times longer in simulations with high versus low values of contact area and stiffness in both contact models. For both contact models, larger contact area and stiffness values resulted in simulations that more closely predicted target force. However, across all simulations, the Hunt-Crossley model produced a greater proportion of accurate finger-tip force simulations than the Elastic Foundation model, suggesting that the Hunt-Crossley contact model may be preferable for modeling the fingerpad. Overall, our study demonstrates how the Hunt-Crossley and Elastic Foundation contact models behave in low-force biomechanical scenarios, such as those experienced during hand-object manipulation, and provides a foundation for incorporating contact mechanics into musculoskeletal models of the hand.

The defining property of every three-dimensional ε-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is also K-contact and η-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity. As an example we analyze S3 equipped with a contact structure together with an associated metric tensor such that the canonical generators of the contact distribution are null. The resulting Lorentzian metric is shown to be a vacuum solution of three-dimensional massive gravity. Moreover, by coupling the New Massive Gravity action to Maxwell-Chern-Simons we obtain a class of charged solutions stemming directly from the para-contact metric structure. Finally, we repeat the exercise for the Abelian Higgs theory.

For the thermal modeling of cup wheel grinding process, most previous studies ignored the effect of wheel-work contact geometry on the amplitude and distribution of heat flux and grinding temperature, which oversimplifies the heat transfer condition when compared with that in the real grinding process, as a cup wheel typically has a rounded edge, due to the rapid wear during the initial grinding passes. In this paper, the relationships among the wheel-work contact geometry, the local material removal pattern at the grinding zone and the grinding temperature distribution have been investigated. A comprehensive 3D analytical thermal model considering the wheel-work contact geometry and its effect on the grinding heat flux distribution has been established and experimentally validated. The heat flux distribution in cup wheel grinding varies with the contact geometry and also the grinding parameters, which has never been mentioned in previous works. It has been found that the variation of the contact geometry significantly changes the local material removal pattern, and thus affects the grinding temperature distribution. Validation experiment results have demonstrated that the developed model could, to a great extent, describe the realistic grinding temperature. The relative errors of the maximum temperature are less than 6.6%, and the relative errors of the position of the maximum temperature are less than 8.5%. This research not only provides a new method to predict grinding temperature, but also enhances the understanding of cup wheel grinding processes.

Plint (IMechE 182 (1):300–306,1967) reported a reduced coefficient of friction with increasing roller sizes in EHL traction measurements. In this study, a similar scale effect has been observed when comparing measured traction curves at the same operating conditions between a ball-on-disc rig and a twin-disc machine of different geometrical sizes. This scale effect has been studied numerically for point contacts of different radii of curvature Rx based on thermal EHL simulations. Results show that the reduced friction for large Rx is caused by an increase in film thickness and the enhanced thermal effects. The mechanisms are: (1) heat is hard to conduct across a thicker EHL film due to bad thermal conductivity; (2) shear is mainly localized in the middle film.

A continuum mechanics approach is applied to model fretting wear in gross-slip regime with accounting for the third-body layer, which is formed by wear debris trapped within contact interface. The developed modeling framework employs the known concept of a third-body conversion factor and utilizes it in a self-similar form. A two-dimensional Hertzian type contact geometry (cylinder on a plate of relatively large thickness) is assumed, though a major part of the presented analysis is curried out for an arbitrary initial gap function. A Winkler foundation model is used to describe the contact deformation of the third-body layer. The effect of elasticity is neglected in describing the self-similar evolution of the contact pressure profile in the advanced stage of fretting wear. A comparison with the FEM-based simulations available in the literature is given. The fact that the elasticity effect plays a minor role has been verified a posteriori in the considered example. Simple formulas are derived to estimate the continuous variation of the third body layer profile, thickness, and volume.

In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case., Comment: 40 pages, final version accepted in Annals of Physics

The analytical modelling of coupled slip and sliding contact response of two elastic spheres is presented for the kinematically imposed sphere centre relative motion trajectories. One sphere is assumed as a fixed, the other translating along a specified trajectory and remaining in contact condition. Two cases are considered, the first is corresponding to a linear trajectory with the contact engagement in the combined slip-sliding mode, the other is related to the contact initiation by normal loading and subsequent motion along an inclined linear trajectory. The formulae and diagrams of the evolution of driving force along the sliding path in terms of main contact geometry parameters were analytically specified. Further extensions and applications of the analysis can be envisaged in the creation of the translation controlled apparatus for the measurements of friction and restitution coefficients for the pair of spherical grains.

Here we compare the wear performance of silica and polyurethane in a vacuum gripper. The problem is modeled numerically by evaluating the energy dissipated at the interface, and experimentally by examining surface damage in contact subjected to cyclic normal loading. In the numerical model, the energy dissipated during unloading is found to be negligible with respect to that of loading. Changing the contact geometry has a good effect in terms of frictional work reduction, but this is not as significant as the effect obtained by changing the material. Replacing silica with polyurethane reduces the frictional work by a factor of at least 20. The latter finding is qualitatively validated in experiments.

This work presents a complete and systematic method for the analysis and simulation of geometric characteristics of mating surfaces of globoidal cam mechanisms. Based on the fundamental forms of globoidal cam surface, the asymptotic curves, the principal directions and curvatures, and the Dupin's indicatrix are obtained and simulated. The curvatures of asymptotic curves are calculated to verify whether the cam surface is a ruled surface or not, which is an important issue to determine the machining process of the globoidal cam. In addition, the relationship between the local shapes of the cam surface and the motion periods is presented. The characteristic curves of relative normal curvature at different contact points are depicted and compared as well. Based on the Dupin's indicatrix, the indicatrix of conformity (Dr. Radzevich, 1980s) is first applied to analyze the contact geometry of mating surfaces of globoidal cam mechanism. The indicatrix of conformity in the case of contact of saddle-like surface with convex parabolic-like surface is first discussed here. A globoidal cam mechanism used in automatic tool changer of CNC machines is presented to clarify the outlined methods. The proposed methodology is important for design, manufacture, and contact analysis of globoidal cam mechanisms.

A transient three-dimensional thermal elastohydrodynamic calculation model is introduced to simulate the contact of tooth flanks of helical gear pairs with involute gearing. At any time, contact geometry is derived from the real involute curves of gears. In addition to the consideration of mass conserving cavitation and the non-Newtonian fluid behavior, models to capture conditions of mixed friction and microhydrodynamic effects are included. To consider the non-Newtonian fluid behavior, a shear thinning fluid model with limiting shear stress is applied. A selected helical gear pair is used as example to examine the influence DLC coated tooth flanks have on tribological behavior. It shows that friction and temperature behavior of the gearing can be significantly influenced with DLC coating.

In this paper a new framework for FE simulation of reeling operations that utilizes a Lagrangian–Eulerian description of the beam kinematics is proposed. In contrast to the conventional Lagrangian approach, the material is enabled to flow with an axial velocity through a nearly space-fixed beam mesh. This gives far more effective and robust simulations since the length of the beam model reduces significantly and because the contact geometry undergoes less changes. The main ingredients of the Lagrangian–Eulerian framework and a flexible pipe beam model are presented. An idealized spoolbase-vessel load-out operation is considered in order to gain insight into the torsional failures experienced by subsea contractors in recent years. Here, three different mechanisms were found to provoke torsional failure of the pipe. Strategies to avoid the torsional failures and FE modeling remarks are provided.

The first paper of this series establishes a unified theoretical framework that lays a solid foundation for developing energy-conserving normal contact models for arbitrarily shaped bodies in the discrete element method. It is derived based solely on the requirement that the potential energy must be conserved for an elastic impact of two shapes under any condition. The resulting general energy-conserving contact model states that the normal force as a vector must be the gradient of a contact potential field. When such a contact potential or energy function is specified, a complete normal contact model for a pair of arbitrarily shaped particles, including the contact normal direction, contact point/line and force magnitude, will be automatically followed without introducing any additional assumptions. In this framework, the contact geometry and contact force are indispensably related and are evaluated in a consistent manner. Due to the paramount role that the energy function plays in the current theory, its fundamental properties are discussed, which serve as general guidance for choosing a valid energy function. In addition, both single and multiple contacts and their evolution can be handled in a seamless way. Some symmetric properties of particle shapes can also be utilised to simplify the contact models. Within the proposed theoretical framework, different choices or combinations of geometric features as variables for the contact energy function can give rise to unique types of energy-conserving contact models with distinct characteristics and features. Two such functions using only one primary feature, which lead to two specialised energy-conserving contact models, will be presented in the subsequent papers of this series.

We have used atomic force microscopy (AFM) to measure the snap-off forces between a micron sized flat silicon AFM tip and a rough Si(0 0 1) surface. The current paper is a natural continuation of our previous paper (Çolak et al., 2014), dealing with snap-off forces between an identical flat tip and flat Si(0 0 1). Within the applied experimental parameter windows we observed no dependence of the snap-off forces on the applied normal loads (3-18 μN) and residence times (0.5-35 s) for the current flat-on-rough geometry as was the case for the former flat-on-flat geometry. The snap-off forces were found to increase with relative humidity in both geometries. As in the case of the flat-on-flat contact geometry, a strong dependence of the snap-off forces on the retraction speed of the tip was observed. Here, we find a strong decrease of the snap-off forces with increasing tip speed, especially at low velocities in the range 40-1000 nm/s for the flat-on-rough geometry. This is in contrast with the flat-on-flat geometry, where we found a strong increase of the snap-off force with increasing tip speed. These observations are explained in terms of a cross-over of the importance of capillary forces and viscous forces. We suggest that the relative importance of both forces can be checked via variation of the tip speed.

It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher's Information Matrix. In this work we analyze several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production., Comment: 33 pages, 2 figures, substantial improvement of http://arxiv.org/abs/1308.6740

In this paper, we present a solution to the contact problem for two elastic bodies with friction loaded by an arbitrarily varying force in 2D. The general statement of the problem concerns the following two important challenges. On one hand, the consideration of an arbitrary contact geometry implies that a multitude of individual arbitrarily-shaped contact zones appears, which can split and merge as a result of changes in the normal loading. On the other hand, the existence of friction invokes the presence of a tangential force and, consequently of a complicated traction distribution inside each of the contact zones. The complexity of these traction distributions results from the fact that, generally, each contact spot contains stick and slip zones with various boundary conditions defined by the previous tangential contact interaction forces. The presence of two classes of boundary conditions makes the problem memory-dependent and hysteretic. In spite of this, by using both conventional and original methods of contact mechanics, it is possible to drastically simplify the problem. First of all, the geometric difficulty residing in the description of arbitrary multiple contacts can be successfully dealt with by applying the reduced friction principle that expresses the tangential solution through the normal loading curve, for both normal and tangential forces kept constant. The principle is valid for a broad range of geometries and makes it possible to replace an arbitrary contact geometry by an equivalent system of two axisymmetric bodies. Secondly, the hysteretic character of the equivalent axisymmetric problem can be addressed through the method of memory diagrams which replaces the complex traction distribution in the contact zone by a simple internal functional dependency comprising the same memory information. Following any change of loading, the internal “memory function” evolves in accordance to a definite procedure that is based on the force balance equation written for small increments of the normal and tangential forces. In this paper, we formulate the method, prove its validity, and illustrate its numerical implementation with some simulated examples of hysteretic load–displacement curves. These obtained results might be of use for applications related to solids with cracks and contacts showing acoustical nonlinearity, and for any modeling requiring physics-based boundary conditions to describe and predict the effect of mechanical contacts with friction.

Sub-surface cracks can be initiated due to surface fatigue, which eventually reach the surface, leading to pitting, spalling and removal of material. In this investigation, a new approach based on shear stress reversal at the crack tips is implemented to propagate a subsurface initiated crack under fretting load. Hertzian line contact geometry is used to investigate the effects of different factors such as Hertzian pressure, coefficient of friction, displacement amplitude, and depth of the initial crack. Crack propagation paths and propagation life of the cracks under the surface are investigated in detail. Once the crack reaches the surface, it is assumed that the material enclosed is spalled and thus removed. Wear volumes and wear rates are calculated and effect of each variable on wear is analyzed. Wear rates increase with increase in maximum Hertzian pressure, displacement amplitude, coefficient of friction and depth of initial crack. The wear rates are also correlated to crack propagation rates and are in agreement with the dissipated energy wear coefficients obtained from literature.

In this investigation an approach to fretting fatigue life prediction is developed with consideration of damage-coupled elastic–plastic constitutive model and wear. Nonlinear kinematic hardening is employed in the analysis of elastic–plastic damage, and the total damage is divided into two parts, elastic damage and plastic damage, which are related to the cyclic stress and accumulated plastic strain, respectively. Wear is modeled by the energy wear law to simulate the evolution of contact geometry. A two dimensional plane strain finite element implementation is presented for fretting, including the case of partial slip and gross sliding. The progressive fatigue damage and wear is simulated and the results are compared with experimental data from the literature.

This paper studies geometric properties of a class of irreversible dynamical systems, referred to in the literature as metriplectic systems. This class of systems, related to generalized (or dissipative) Hamiltonian systems, are generated by a conserved component and a dissipative component and appear, for example, in non-equilibrium thermodynamics. In non-equilibrium thermodynamics, the two potentials generating the dynamics are interpreted as generalized energy and generalized entropy, respectively. Stability and stabilization results for metriplectic systems have been presented in the literature, however, some aspects are still poorly understood, in particular the existence of dynamical invariants such as periodic orbits. In this note, we study the properties of metriplectic systems by considering a lift from the n-dimensional state space to a (2n+1)-dimensional contact space, following an approach introduced in recent years to study irreversible control systems. This lift leads to a deeper geometric characterization of metriplectic systems in the extended space. An example is provided to illustrate the approach proposed in this paper.

A model describing the influence of self-assembled monolayers on the contact resistance of bottom-contact organic thin-film transistors is presented. The model takes the contact geometry, the energy level alignment and the structural order of the organic films into consideration when describing the contact effects of organic transistors. The treatment of the metal source/drain electrodes of the transistors by self-assembled monolayers allows for tuning the work function of the metal contact and an improved ordering of the organic molecules on top of the source/drain contacts. The results reveal that the contact resistance is mainly determined by the molecular ordering, rather than the tuning of the work function. The model is compared to experimentally measured contact resistances for different self-assembled monolayers.

A new silicon-based thermogenerator with a reduced parasitic contact resistivity and a large temperature working range from 250 K up to 1000 K is presented. Three-dimensional contact geometry and additional doping reduces the contact resistivity from 12.7 MΩ μm 2 to 57.6 kΩ μm 2 . In this way, for all temperatures above 250 K the contact resistivity is negligible with respect to the inner resistivity of the thermoelectric materials. At room temperature it is only 1% of the total resistivity. The thermogenerator was embedded in metal using the method of metal-spray-deposition, which ensures high yield of the successfully embedded thermogenerators (30 functional of the total of 32) due to relatively low mechanical forces applied during the embedding process and reduced thermo-mechanical stress during the following cool-down phase. Our results demonstrate that it is possible to embed silicon microsystems in metals during high-temperature metallurgic primary forming processes.

Stress distribution at the contact edge plays a dominant role in fretting fatigue strength. In the previous studies, based on the stress distribution at the contact edge, a generalized tangential stress range–compressive stress range (TSR–CSR) diagram has been proposed as a fretting fatigue fracture criterion. It has been also confirmed that the proposed diagram would be very useful to predict the fretting fatigue strength regardless of contact geometry, loading condition, material strength, environment, etc. for laboratory-type specimens. In the present study, fretting fatigue strengths of actual components, such as a dovetail joint and a bolted joint, have been predicted based on the generalized TSR–CSR diagram. To verify the effectiveness of the prediction based on the generalized TSR–CSR diagram, the fretting fatigue tests of dovetail joints and bolted joints were carried out. The fretting fatigue strengths of dovetail joints and bolted joints predicted based on the generalized TSR–CSR diagram were in good agreement with the experimental results.