Elastic-plastic Contact Model Research Articles

A revised elastic-plastic contact model of cycloidal pinwheel based on length scale

This study explores the relationship between surface roughness and characteristic scale through theoretical analyses and experimental data. Considering the concavity and convexity of cycloidal gear tooth profile curvatures, a curved surface contact coefficient model suitable for both inner and outer contacts, with either equal or unequal curvatures, has been developed. Moreover, a fractal contact model is constructed for cycloidal pinwheels. This model considers scale correlation and analyzes the influence of microscopic parameters on the elastic-plastic critical grade and the behavior of the contact area. Additionally, the influence of the micro-convex body frequency index on surface contact performance is explored to provide theoretical insights for improving the elastic contact ratio and reducing wear on contact surfaces.

Modeling the elastic–plastic contact forces and deformations of nonrotationally symmetric lunar dust particles

The sharp morphological features of lunar dust particles generate significant elastic–plastic contact forces and deformations upon contact with material surfaces, which considerably affect the mechanical properties of lunar dust particles, including their contact, collision, adhesion, transport, and wear characteristics. Despite these severe effects, valid models considering the contact characteristics of typical sharp-featured lunar dust particles are currently lacking. This study proposes an elastic–plastic contact model for nonrotationally symmetric lunar dust particles showing typical sharp features. Detailed derivations of the expressions for various physical responses observed when lunar dust particles establish normal contacts with elastic and elastic–plastic half-spaces under adhesive conditions are also provided. These include derivations for elastic forces, elastic–plastic forces, contact areas, pull-off forces, residual displacements, and plastic deformation areas. Furthermore, the tangential pull-off force during the tangential loading of lunar dust particles is derived, and the tangential contact characteristics are explored. Comparisons of the results of the proposed model with those of previous experiments reveal that the proposed model shows errors of only 6.06 % and 1.03 % in the maximum indentation depth and residual displacement, respectively. These errors are substantially lower than those of conventional spherical models (60.30 % and 60.13 %, respectively), confirming the superior accuracy of the proposed model. Furthermore, the discrete element method is employed to analyze the effects of normal and tangential contacts, dynamic characteristics, and plastic deformations on the considered lunar dust particles. The results are then compared with those of existing contact models. They reveal that maximum elastic–plastic forces under normal contact conditions are positively correlated with the initial velocity but negatively correlated with the lateral angle. Furthermore, the tangential pull-off force is positively correlated with the normal force and surface energy. In addition, the contact duration of lunar dust particles is positively correlated with their initial velocities, while the residual displacement is negatively correlation. For instance, as the initial velocity increases from 10 to 50 m/s, the maximum elastic–plastic force increases from 37.64 to 321.72 mN. Comparisons of the proposed model with other contact models reveal that the maximum elastic–plastic force of the elastic–plastic triangular pyramid model is only 14.93 % that of the cylindrical model, 34.23 % that of the spherical model, and 76.27 % that of the conical model, indicating significant reductions in the maximum elastic–plastic force owing to the plastic deformations of particles with typical sharp features. Overall, the results of this study offer crucial insights into the mechanical characteristics of nonspherical lunar dust particles under various contact conditions, such as elastic–plastic and adhesive contacts, and can guide in situ resource utilization on the lunar surface and for craft landings.

New deterministic model for calculating mesh stiffness and damping of rough-surface gears considering elastic–plastic contact and energy-dissipation mechanism

For a long time, meshing parameter calculations and dynamic modeling of gear systems have assumed smooth tooth surfaces, disregarding the impact of actual three-dimensional (3D) microscopic topography. Based on elastic–plastic contact and energy-dissipation mechanisms, this work developed a comprehensive deterministic model that integrates 3D rough surface modeling, reconstruction, and contact analysis, for calculating the time-varying mesh stiffness (TVMS) and mesh damping (TVMD) of deterministic rough-surface gears. Distinct from fractal and statistical models, the deterministic model analyzes deterministic, real 3D rough surfaces rather than simple surfaces defined by a few parameters. Utilizing stochastic process theory, different-topography surfaces are obtained using height and spatial features and reconstructed employing watershed algorithm and ellipsoidal asperity fitting. Subsequently, a deterministic elastic–plastic contact model based on equivalent rough curved-surface contact is constructed, emphasizing local contact states and energy dissipation for calculating contact stiffness (CS) and damping (CD) of gears. Accordingly, a meshing characteristics analysis model is established for calculating TVMS, TVMD, and load sharing ratio (LSR). Experimental validation and comparisons with several statistical and gear contact models demonstrate the effectiveness, reliability, and superiority of the proposed deterministic model. Multi-parameter impact analysis reveals small Sq (meaning low roughness Sa) and Ssk and high load correlate with increased CS and TVMS, while CD and TVMD depend on their interaction and hardness. Overall, by bridging the micro-surface topography and macro-meshing parameters, our model provides essential insights for the design and manufacturing of high-performance gear to reduce vibration and noise.

Calibration and Testing of Parameters for the Discrete Element Simulation of Soil Particles in Paddy Fields

The parameters of the discrete element simulation model for rice field soils serve as valuable data references for investigating the dynamic characteristics of the walking wheel of high-speed precision seeding machinery in paddy fields. The research specifically targets clay loam soil from a paddy field in South China. Calibration of essential soil parameters was achieved using EDEM_2022 software (and subsequent versions) discrete element simulation software, employing the Edinburgh Elasto-Plastic Adhesion (EEPA) nonlinear elastic-plastic contact model. The tillage layer and plough sub-base layer underwent calibration through slump and uniaxial compression tests, respectively. Influential contact parameters affecting slump and axial pressure were identified through a Plackett–Burman test. The optimal contact parameter combinations for the discrete element model of the tillage layer and plough sub-base layer were determined via a quadratic rotational orthogonal test. The accuracy of the discrete element simulation model’s parameters for paddy field soils was further validated through a comparative analysis of the simulation test’s cone penetration and the field soil trench test. Results indicate that the Coefficient of Restitution, surface energy, Contact Plasticity Ratio, and Tensile Exp significantly influence slump (p < 0.05). Additionally, the Coefficient of Restitution, Contact Plasticity Ratio, coefficient of rolling friction, and Tangential Stiff Multiplier significantly impact axial pressure (p < 0.05). Optimal contact parameters for the plough layer were achieved with a particle recovery coefficient of 0.49, a surface energy of 18.52 J/m2, a plastic deformation ratio of 0.45, and a tensile strength of 3.74. For the plough subsoil layer, optimal contact parameters were a particle recovery coefficient of 0.47, a coefficient of interparticle kinetic friction of 0.32, a plastic deformation ratio of 0.49, and a tangential stiffness factor of 0.31. Results from the cone penetration test reveal no significant disparity in compactness between the actual experiment and the simulation test. The calibrated discrete element model’s contact parameters have been verified as accurate and reliable. The findings of this study offer valuable data references for understanding the dynamic characteristics of the walking wheel of the entire machinery in high-speed precision seeding in paddy fields.

A single asperity elastic-plastic contact model with the effect of kinematic strain hardening

A single asperity elastic-plastic contact model with the effect of kinematic strain hardening

An improved elastic–plastic contact model with asperity interactions based on Greenwood–Williamson theory

An improved elastic–plastic contact model with asperity interactions based on Greenwood–Williamson theory

CFD-DEM analysis of internal packing structure and pressure characteristics in compressible filter cakes using a novel elastic–plastic contact model

Cake-forming filtration is a proven method for separating particles from suspensions. Most filtration models are based on the simplification of incompressible and homogeneous cake structures. However, most filter cakes are in fact unevenly compressed by e.g. the high transmembrane pressures, leading to dense structures with high flow resistance at the filtration membrane. Experimental investigations of these inhomogeneous cakes are challenging due to mostly invasive procedures after filtration has already taken place. In contrast, numerical methods can provide extensive information about fluid flow, particle separation and cake formation during filtration. However, this requires that both elastic and plastic particle deformation and forces are modeled correctly. To achieve this, the present study implemented a novel elastic–plastic DEM model that only requires measurable material parameters and therefore does not need any fitting. Subsequently, previously measured material parameters for elastic–plastic cellulose-lactose pellets (MCC) were used to investigate the packing density, fluid pressure levels and contact forces inside compressible filter cakes using CFD-DEM coupling. A comparison with incompressible and elastically compressible filter cakes showed a significant difference in the filtration behavior. Due to plastic deformation, a strong increase of the packing density when nearing the filtration membrane was found, leading to higher flow resistance for the filtration process. For cyclic filtration events, only the plastically deformed cake showed reduced height recovery in a relaxed state.

Numerical Analysis of the Mixed-Lubrication Performance of Staved Stern Tube Bearings Lubricated with Water

The present study aims to establish a mixed lubrication model for staved stern tube bearings lubricated with water, in which the average Reynolds equation and a KE elastic–plastic contact model are introduced to calculate the hydrodynamic pressure and contact pressure, respectively. The difference in the mixed lubrication behaviors between circular- and flat-staved bearings is compared; moreover, the effects of the number of staves on the mixed-lubrication performance of these two kinds of staved bearing are investigated. The mechanism of action of the number of staves in staved bearings on the mixed-lubrication performance is revealed. The numerical results show that the number of staves has a significant effect on the mixed-lubrication performance in circular- and flat-staved bearings. Furthermore, there is an optimal value for the number of staves, shown to be 30 in the current simulation, for improving the mixed-lubrication performance of flat-staved stern tube bearings lubricated with water.

Friction of Coated and Uncoated Rough Surfaces in Additive-Free and Fully Formulated Engine Oils Under Boundary and Mixed Lubrication Conditions

Abstract Downsizing in spark-ignited engines becomes one of the most effective concepts to achieve fuel economy and emissions requirements and drives operating conditions of major moving engine components into more mixed and boundary lubrication regimes. Piston ring design faces considerable challenge to reduce friction losses, oil consumption, blow-by, and wear. Surface coatings have received great attention in applications of automotive engine components due to their unique friction properties. In this study, an elastic–plastic contact model of rough surfaces with hard coatings is used to provide proper design of the ring coating thickness concerning the plasticity-yielding resistance of stiff coating. A diamond-like carbon (DLC) coating with surface hardness higher than current production ring coatings has been evaluated in additive-free base oil and fully formulated engine oil under boundary and mixed lubrication conditions. The friction behavior of the coated material relative to uncoated materials is compared in boundary and mixed lubrication regimes. A traction-merging rolling speed in the mixed lubrication regime is observed, at which friction coefficient is independent of applied loads. By using a mixed lubrication model previously published, calculations indicate that the lower the traction-merging rolling speed, the earlier the contact approaches elastohydrodynamic lubrication (EHL), therefore reducing the risk of asperity-interacting fatigue in boundary and mixed lubrication regimes. Effects of tribofilm on friction behavior for DLC coating and uncoated steel in fully formulated oil are investigated by using measured Stribeck curves in conjunction with the model. The results from this study analytically support one of the possible mechanisms of tribofilm-dependent friction enhancement in mixed lubrication conditions proposed in the earlier publication.

Polishing Performance and Removal Mechanism of Core-Shell Structured Diamond/SiO2 Abrasives on Sapphire Wafer.

Corrosive and toxic solutions are normally employed to polish sapphire wafers, which easily cause environmental pollution. Applying green polishing techniques to obtain an ultrasmooth sapphire surface that is scratch-free and has low damage at high polishing efficiency is a great challenge. In this paper, novel diamond/SiO2 composite abrasives were successfully synthesized by a simplified sol-gel strategy. The prepared composite abrasives were used in the semi-fixed polishing technology of sapphire wafers, where the polishing slurry contains only deionized water and no other chemicals during the whole polishing process, effectively avoiding environmental pollution. The experimental results showed that diamond/SiO2 composite abrasives exhibited excellent polishing performance, along with a 27.2% decrease in surface roughness, and the material removal rate was increased by more than 8.8% compared with pure diamond. Furthermore, through characterizations of polished sapphire surfaces and wear debris, the chemical action mechanism of composite abrasives was investigated, which confirmed the solid-state reaction between the SiO2 shell and the sapphire surface. Finally, applying the elastic-plastic contact model revealed that the reduction of indentation depth and the synergistic effect of chemical corrosion and mechanical removal are the keys to improving polishing performance.

Effects of wall slip on the dynamic characteristics of water-lubricated bearing considering rough contact

PurposeThis paper aims to identify the role of the wall slip on the dynamic characteristics of the multi-groove water-lubricated bearing considering rough contact, including stiffness and damping coefficients of the water film and contact stiffness coefficient of the asperity contact.Design/methodology/approachThe modified perturbed average Reynolds equations with the wall slip are derived, and the calculated perturbed hydrodynamic pressures are integrated to obtain the stiffness and damping coefficients of the water film. The elastic-plastic contact model of Kogut and Etsion is used to determine the contact stiffness coefficient.FindingsNumerical results reveal that the wall slip has the more significant impact on the water film stiffness coefficients compared with the damping and contact stiffness coefficients. When the slip angle lies in a reasonable range, the lubrication performance can be effectively improved, especially in the mixed lubrication condition. In addition, it is worth emphasizing that the abrupt change of the water film stiffness coefficients occurs at the region II (pressure zone) in this study.Originality/valueThe influence mechanism of the wall slip on the dynamic characteristics of the water-lubricated bearing considering rough contact is first revealed.

Fretting fatigue performance and life prediction of 1120 aluminum alloy wires of overhead conductors

Aluminum alloy (AA) 1120 wires have increasingly been used in overhead conductors due to their high tensile and creep resistance and electrical conductivity compared to other aluminum alloys. However, few studies have been conducted to characterize the fatigue strength of this material, specially under fretting conditions. In this work, fretting fatigue tests are performed on AA1120 wires of an AAAC 823 MCM conductor. A tension test, and fatigue tests on smooth and circumferentially V-notched wires were also carried out. The experimental results are compared to test data from AA1350 and AA6201 wires. Under tension, the AA1120 displayed an intermediate ultimate tensile strength between the ones from the AA1350 and AA6201. For the same stress amplitudes, the AA1120 wires used in the axial fatigue tests had longer lives than the AA1350 wires but considerably shorter lives than the AA6201 wires. However, under fretting fatigue, both AA1120 and AA6201 wires had similar fatigue strengths. A nonlocal life prediction criterion was evaluated using the fretting fatigue data. Most of the life estimates were within a factor of 3 of the observed lives when the input stress field was obtained from an elastic-plastic contact model.

Elevated temperature contact creep and friction of nickel-based superalloys using machine learning assisted finite element analysis

Nickel-based superalloys with superior thermochemical, mechanical, and tribological properties are highly utilized for critical components in several high temperature applications such as gas turbines and nuclear reactors. Inconel 617, in particular, is considered as one of the main candidate superalloys for tribo-components in very-high-temperature gas-cooled nuclear reactors. Recent findings indicate that this alloy grows unique surface oxide especially in a high-temperature helium environment with distinctive wear, friction, and contact properties. This study investigates the high temperature contact area evolution and frictional behavior of Inconel 617 using finite element simulation and provides predictive models for the contact and friction performance at different normal loads, dwell times, and temperatures. High temperature helium-aged Inconel 617 top surface properties (up to 600 °C) are utilized along with a single asperity-based deformable elastic-plastic contact model under combined normal and tangential loading. Machine learning is used to assist the finite element results and to predict friction coefficient as well as contact area evolution. While a small difference is observed in the instantaneous friction coefficient (no dwell time) for all temperatures, friction coefficient increases considerably with dwell time. This shows that the effect of contact creep for longer dwell times significantly dominants the effect of high temperature variation in basic mechanical parameters such as modulus and yield strength. It is found that increasing temperature and dwell times lead to the friction coefficient increase, yet the dominance of dwell time effects decreases at higher temperatures and loads. While the analysis is presented for Inconel 617, the methodology is easy to be generalized and can be applied to other HT alloys.

Numerical and Experimental Study on Rod-Fastened Rotor Dynamics Using Semi-Analytical Elastic-Plastic Model

Abstract Rod-fastened rotor is the core rotating section of the heavy-duty gas turbine. To accurately analyze its dynamic characteristics, the contact model for the disk contact interface needs to be defined and established. Traditional statistical contact models, including the elastic model and elastoplastic model, cannot describe microscopic atomic behavior during the contact process of asperities, while the microscopic contact behavior of the asperities is one of the main factors in affecting the contact stiffness of the rough surface. In this work, the molecular dynamics simulation of the microscopic contact behavior of the rough surface is carried out and the semi-analytical model is built upon that. The semi-analytical model is later combined with the Timoshenko beam element in modeling the rotor system. The influence of plasticity index and surface roughness on the contact model and dynamic characteristics of the rotor is analyzed. Moreover, the experimental tests of natural frequencies and mode shapes are carried out. The results show that the proposed semi-analytical contact model is effective and more accurate compared to other elastic and elastic-plastic contact models.

Розрахунок контактного тиску та зони контакту в парах ковзання судових дизелів

Annotation – The durability of marine diesels significantly depends on the operation of friction pairs, such as: piston rings - cylinder liner; crankshaft - bearing shell, plunger - sleeve, and others. This is primarily due to the constant contact interaction of the elements of the friction pairs at different temperatures and load. Therefore, the research of normal pressure and the definition of contact areas in the friction pairs, the studying of the influence of the quality of lubricants on these characteristics are important tasks for predicting the longevity of marine diesels. The solution of these problems is based on the application of mathematical models of processes (numerical simulations) that occur in friction pairs. This considers two main processes that occur during the operation of the friction pairs: the research of contact and tangential stresses that occur in friction pairs in the framework of elastic or elastic-plastic contact models; study of hydrodynamic processes in a thin layer of oil between the elements of the friction pairs. The combination of these processes allows to sufficiently assess the influence of the elastic-mechanical properties of the sliding vapor elements and the viscosity and hydrodynamic characteristics of the oils on the durability of the marine diesel unit. The first process is researched in this work. In particular, for the analysis of contact stresses and contact zones in friction pairs, the method of numerical modeling is used, which is based on the differential equations of the theory of elasticity. With the help of fundamental solutions (influence functions), the problem is reduced to an integra-differential equation with the Gilbert’s kernel. The solution of which is constructed using the method of orthogonal polynomials as well as easy-to-use approximation formulas. Numerical simulations were performed, as a result, the maximum pressure and contact zone parameters for some combinations of friction pairs materials of marine diesel engines were determined. In particular, the influence of the radial gap on the pressure distribution and the size of the contact zone between the elements of the friction pairs of marine diesels is established.

Study of a parabolic cylinder elastic-plastic contact model

Based on Hertz contact theory, two parabolic cylinder normal contact models are established. The effect of contact angle on normal approach, actual contact area, and normal contact stiffness are investigated, and the effect of the distance from the focus to the directrix (focus distance) on the mechanical characteristics of the models is further analyzed. The parabolic cylinder contact model was verified by simulation analysis and comparison with cylinder contact model. The results demonstrated that the contact angle, focal distance, and load have significant effects on the mechanical properties of the model. The simulation data are basically consistent with the contact model data, and the parabolic cylinder contact model and cylinder contact model have the same change trend. The results verify the correctness of the parabolic cylinder contact model and reveal the variation of the mechanical properties of the contact model.

Analytical Model for Studying the Influence of Thickness on the Protective Effect

This paper presents an analytical model to study the influence of the thickness of the built-up layer (BUL) / built-up edge (BUE) on its protective effect during cutting. A new elastic-plastic contact model at the tool-chip interface is proposed to analyze the sliding contact problem with a layer of adhesion (including the BUL and BUE). The equivalent inclusion method (EIM) is utilized to analyze the stress disturbance caused by the adhesion and to evaluate the protective effect of the adhesion. In this method, the adhesion is considered as an equivalent elliptical inclusion at the tool-chip interface. The protective effect of the adhesion and the influence of the adhesion thickness on its protective effect can be evaluated. The proposed analytical model was verified based on experimental data obtained from dry cutting of SUS304 stainless steel. From the results, it can be confirmed that BUL/BUE can protect the cutting tool by affecting the stress distributions in the tool, the positions of yield initiation, and the tangential force acting on the tool. It can also be concluded that a greater thickness improves the protective effect of the BUL/BUE. Furthermore, the proposed model can also provide a clear understanding of the BUL/BUE formation phenomenon.

Rock fragmentation induced by a TBM disc-cutter considering the effects of joints: A numerical simulation by DEM

The study of rock fragmentation mechanism significantly contributes to the advancing speed of tunnel boring machines (TBMs). In this sense, numerous factors are shaping the rock fragmentation mechanism of their disc-cutters. Among them, rock structural parameters, such as joint inclination, orientation, spacing, etc., considerably impact cutting force as well as rock-cutting process. However, detailed relationships between rock-cutting parameters and rock mass ones have not been to date proven, and rock fragmentation mechanism still needs to be investigated in depth. In this paper, a three-dimensional (3D) discrete element model of rock-cutting using a disc-cutter was established via the high-performance MatDEM software. To simulate the fragmentation performance of the rock undergoing the impact load, an elastic–plastic contact model was firstly proposed based on the linear elastic contact model, verified by several mechanical experiments. Then, the influence of different joint parameters (e.g., joint inclination, orientation, spacing, etc.) on cutting force and rock fragmentation volume was examined. At the same time, the effect of joint parameters on specific energy (SE) was calculated to explore the joint influence on rock-cutting efficiency. The simulation results show that the elastic–plastic contact model can better simulate the plastic deformation characteristics of the brittle rock, and the improved model can imitate the generation of the rock fragment structure. As well, the influence of the joint orientation and spacing on the mean value of the cutting force and the rock fragmentation volume is obvious, and the propagation mode of the internal cracks in the rock varies with reference to the joint orientation. The existence of the joints also decreases the rock-cutting SE, and consequently the rock-cutting efficiency can reach the highest level when the joint spacing is equal to 50 mm and the joint orientation is about 30°. The opposite inclination of the joint correspondingly leads to the opposite change in the rock-cutting parameters, which can be eliminated through rotating cutting in practice. This study explores the influence of joint parameters on rock-cutting ones and reveals crack distribution mechanism in jointed rock mass.

Numerical study on the dynamic characteristics of water-lubricated rubber bearing under asperity contact

PurposeIn this study, the dynamic characteristics of the water-lubricated rubber bearing considering asperity contact are numerically studied, including water-film stiffness and damping coefficients and plastic-elastic contact stiffness coefficient.Design/methodology/approachThe Kogut-Etsion elastic-plastic contact model is applied to calculate the contact stiffness coefficient at the bearing-bush interface and the perturbed method is used to calculate the stiffness and damping coefficients of water-film. In addition, the rubber deformation is determined by the finite element method (FEM) during the simulation. Parametric studies are conducted to assess the effects of the radial clearance, rubber thickness and elastic modulus on the dynamic characteristic of water-lubricated rubber bearing.FindingsNumerical results indicate that stiffness and damping coefficients of water film and the contact stiffness of asperity are increased with the decreasing of the radial clearance and the dynamic coefficients are less sensitive to the rubber thickness compared with the elastic modulus of rubber. Furthermore, due to the existed groove, a sudden change of the water film direct stiffness and damping coefficients is observed when the eccentricity ratio ranges from 0.6 to 1.0.Originality/valueIt is expected this study can provide more information to establish a dynamic equation of water-lubricated rubber bearings exposed to mixed lubrication conditions.

Fretting fatigue of 6201 aluminum alloy wires of overhead conductors

Fretting fatigue tests were conducted on 6201-T81 aluminum alloy wires of an AAAC 900 MCM conductor. A finite element-based contact model combined with a nonlocal Smith–Watson–Topper criterion was used to estimate fatigue life. To account for the stress gradients beneath the contact, an average stress over a fatigue damage zone was adopted. A procedure for determining the size of the damage zone from V-notched wire test data is presented. Fatigue lives estimated using stresses from a linear elastic contact model were overly conservative, while the use of an elastic-plastic contact model significantly improved the estimates.