Elastoplastic Contact Research Articles

Transient response and rub-impact phenomenon of liquid lubricated non-contacting mechanical seals during external pressure fluctuation

The purpose of this paper is to investigate the dynamic contact behavior and transient response of liquid lubricated non-contacting mechanical seals during external pressure fluctuation. The presented model of spiral groove mechanical seals includes the Reynolds equation considering surface roughness and mass-conserving cavitation boundary, elastoplastic asperity contact model expressing rub-impact phenomenon, as well as the dynamic equation describing the vibrations of stator which were solved simultaneously with a numerical method. Results indicate that the vibration amplitude and frequency of sealing performances are affected significantly by the external pressure. The increment of rotational speed avoids face rub-contact and reduces the instantaneous variation of leakage. The results presented in the study are expected to provide a theoretical guidance to improve stability and safety of sealing system.

A complete elastic-plastic spherical asperity contact model with the effect of isotropic strain hardening

Understanding the deformation behavior of rough surface contacts is essential to minimise the tribological consequences of contacts. Mostly, statistical, deterministic and fractal approaches are adopted to explore the contact of rough surfaces. In statistical approach, a single asperity contact model is developed and extended to the whole surface. In the present work, a deformable spherical asperity contact with a rigid flat is modeled and analysed by accounting the combined effect of Young’s modulus, Poisson’s ratio, yield strength and isotropic strain hardening rate using finite element method. The results reveal that the elastic, elastoplastic and plastic contact states are highly influenced by E/Y ratio and strain hardening rate followed by Poisson’s ratio. The dimensionless contact radius is an inadequate parameter to explore the combined effect of material properties. For all E/Y ratio and Poisson’s ratio, as the strain hardening rate increases, the dimensionless contact area decreases for the same dimensionless contact load at elastoplastic and fully plastic contact states. As the strain hardening rate increases, the fully plastic contact state is reached at low dimensionless interference compared to elastic perfectly plastic materials for all E/Y ratio and Poisson’s ratio. For a common elastic-plastic material, empirical relations are developed to calculate the contact load and contact area appropriately with E/Y ratio, Poisson’s ratio and interference ratio as input variables. It can be utilised to study the interaction of rough surface contacts for most of the practical materials.

Strain-rate-dependent model for the elastoplastic dynamic contact of sphere and plate

A force-indentation contact model is presented for the dynamic contact loading of elastoplastic particle and plate to incorporate the material’s strain-rate-dependent plasticity, built theoretically from the well-known Hertz contact law and Hill’s solution for elastic and elastoplastic quasi-static contacts. A theoretical relation of the relative impact velocity and plastic strain rate is introduced to solve the model’s parameters. A Johnson–Cook strain rate dependence is included into the model to consider dynamic effects. We validate the model using finite element analysis and show that the model can accurately simulate the force-indentation relation. The impact responses of plate simulated by applying the model combined with a substructure technique are validated using finite element analysis and laboratory test. With the aid of the model, a significant decrease in contact pressure during fully plastic indentation and the independence of dynamic contact-loading path upon loading rate are observed.

A nominal radial stiffness prediction model for HSK tool holder-spindle flange interface

The connection characteristics of HSK tool holder-spindle system have great influences on machining precision and security of computer numerical control machine tools. In order to predict dynamic behaviors and avoid connection failure of HSK tool holder-spindle system, a nominal radial stiffness prediction model for HSK tool holder-spindle flange interface is constructed. Contact stress of spindle and HSK tool holder can be obtained by considering actual interference and actual clamping force. Considering elastic contact deformation, the plastic contact deformation, and two different regimes of elastoplastic contact deformation, a fractal model of nominal contact stiffness of HSK tool holder-spindle flange interface is proposed. In order to prove the rationality of the model, the tests are validated by a self-designed equipment. The effects of different parameters to the maximal permissible rotational speed, critical bending moment, and nominal radial stiffness of HSK tool holder-spindle connection system are researched. The results can be used as an instruction for the application of HSK tool holder and optimization of geometry parameters.

A hybrid particle-geometric scaling approach for elasto-plastic adhesive DEM contact models

The computation time of Discrete Element Method (DEM) simulations increases exponentially when particle size is reduced or the number of particles increased. This critical challenge limits the use of DEM simulation for industrial applications, such as powder flow in silos. Scaling techniques can offer a solution to reduce computation time. In this paper, we have developed a hybrid particle-geometric scaling approach with a focus on Elasto-Plastic Adhesive contact models. It established relationships between particle scaling factors and DEM contact input parameters. The isolated effects of varying particle size and geometric dimensions on bulk properties were also evaluated using uniaxial consolidation, static angle of repose, and ring shear tests. This paper shows how the particle scaling can be applied together with geometric scaling to incorporate two important aspects of bulk materials, their Elasto-Plastic behaviour and their cohesive forces.

An Elasto-plastic Contact Solving Method for Two Spheres

The traditional Hertz contact theory has been widely used in solving contact problems. However, it is only applicable to the elastic contact, and cannot truly reflect the contact stress distribution and contact radius in the elasto-plastic contact. In this work, based on the Hertz contact theory, a fast solving method is proposed to calculate the contact stress distribution and contact radius in the elasto-plastic contact between two spheres. It is assumed that the elastic contact only occurs at the outer edge of contact patch and its contact stress distribution satisfies the Hertz contact theory, and the contact stress distribution at the inner edge of contact patch can be superimposed by a constant contact stress and several small ellipsoidal contact stress distributions. Moreover, based on the equivalent relation between the resultant force of contact stress and the normal external load, the contact radius in the elasto-plastic contact can be solved. Finally, an elasto-plastic contact example of two spheres is given based on the power-law hardening material model, and the influences of material parameters, contact radii and normal external loads on the accuracy of the proposed method are discussed by comparing the differences between the numerical results by finite element method and the predicted ones by the proposed method. It is shown that the proposed method can accurately calculate the maximum contact stress and contact radius in the elasto-plastic contact, and the relative errors of both maximum contact stress and contact radius are within $$\pm \,5{\%}$$. To sum up, the proposed fast solving method can be applied to perform the elasto-plastic contact analysis in engineering practice.

Валидация модели упругопластического контакта спироидных передач

The paper considers the problem of analyzing the elastoplastic contact of teeth in a heavy-loaded low-speed multi-pair spiroid gear. This problem is an integral part of the strength analysis that enables forecasting the load-carrying capacity of the product at the initial stage of its development. The relevance of the considered method and algorithm of calculating the load distribution and plastic strain of teeth is emphasized by its increased productive efficiency as compared to the widely used finite element method. The paper considers a common issue of validation of the developed algorithm, i.e. the correspondence of the obtained solution to the results of a real loading process. The main steps of the algorithm are given with account of the multi-pair contact and macro-roughnesses on the contact flanks that are represented as the set of areas (cells). The coordinates of the cell centers are calculated taking account of the factors influencing the load distribution in the spiroid gearing, such as manufacturing and/or assembly errors, surface micro- and macro-roughnesses, and deformations of the gearbox parts. To validate the algorithm, only one dominating factor — the gearwheel surface undulation — is chosen, since all the other factors are negligibly small. The object of the study is a gear in one of the mass-produced multi-turn spiroid gearboxes for pipeline valves. The criteria for the algorithm validation are formulated, namely, the plastic strain value, the area, shape and arrangement of the pattern of the plastic strain. By analyzing the results of numerical and experimental modeling it is possible to draw a conclusion on the validity of the results obtained by means of the studied numerical method of analysis. The divergence of the plastic strain value obtained experimentally and through calculation was under 10%, and the area of the plastic strain pattern was under 10%.

Elastic and Elasto-Plastic Contact Behavior on Ball Bearing

https://doi.org/Contact%20pressure%20has%20a%20great%20influence%20on%20the%20realiability%20and%20the%20life%20of%20ball%20bearings.%20However,%20most%20of%20the%20previous%20contact%20and%20wear%20model%20mainly%20focussed%20on%20the%20elastic%20model.%20In%20this%20paper,%20considering%20the%20contact%20between%20ball%20bearing%20and%20inner%20ring,%20both%20elastic%20and%20elasto-plastic%20contact%20model%20are%20established%20to%20investigate%20the%20contact%20behaviour%20on%20ball%20bearing.%20Three%20types%20of%20materials%20have%20been%20used%20to%20compare%20the%20contact%20behaviour%20which%20are%20bearing%20steel,%20silicon%20nitride%20and%20aluminium%20oxide.%20Aluminium%20oxide%20experienced%20highest%20maximum%20contact%20pressure%20for%20elastic%20model%20while%20silicon%20nitride%20experienced%20highest%20maximum%20contact%20pressure%20for%20elasto-plastic%20model.%20The%20stress%20contour%20of%20elastic%20model%20was%20elliptical%20shape%20while%20elasto-plastic%20model%20was%20elliptical%20shape%20before%20the%20material%20yields.

An Elasto-Plastic Ball Bearing Contact with Bilinear Hardening

This study is an analytical evaluation of contact and wear on ball bearings using the finite element method. Ball bearings are used in various sectors, such as in the automobile, turbine and aircraft engine industries, to reduce rotational friction and support radial loads. Nevertheless, ball bearings often experience failure due to wear as a consequence of contact pressure. The contact between the ball bearing components will affect the surface of the balls, and the inner and outer rings. Therefore, the main objective of this study was to examine the stress distribution and elasto-plastic deformation in order to analyse the contact between the ball bearing components. Most of the existing contact and wear models for ball bearings only take into account the elastic model. However, an analytical evaluation of contact and wear using an elastic model, while ignoring plastic deformation, is inaccurate. In this study, a contact analysis was performed using elasto-plastic models of a ball bearing, and the results were validated using data from a previous research. Boundary loads of between 100 N to 800 N were applied and plasticity values of 550 MPa, 1050 MPa, 1550 MPa and 2050 MPa were used to analyse the contact behaviour. As the boundary load increased, the maximum contact pressure and displacement of the ball bearing increased. As the plasticity, E2 rose higher, the maximum plastic strain was lowered proportionally.

DEM calibration of cohesive material in the ring shear test by applying a genetic algorithm framework

This research demonstrates capturing different stress states and history dependency in a cohesive bulk material by DEM simulations. An automated calibration procedure, based on the Non-dominated Sorting Genetic Algorithm, is applied. It searches for the appropriate simulation parameters of an Elasto-Plastic Adhesive contact model such that its response is best fitted to the shear stress measured in experiments. Using this calibration procedure, the optimal set of DEM input parameters are successfully found to reproduce the measured shear stresses of the cohesive coal sample in two different pre-consolidation levels. The calibrated simulation resembles the stress history dependent values of shear stress, bulk density and wall friction. Through the case study of the ring shear tester, this research demonstrates the robustness and accuracy of the calibration framework using multi-objective optimization on multi-variable calibration problems irrespective of the chosen contact model.

Analytical investigation of the friction reduction performance of longitudinal vibration based on the modified elastoplastic contact model

An analytical friction model considering material properties and surface topography is established to predict the friction reduction performance of longitudinal vibration, and a set of closed-form solutions are derived and verified. A parameter study is conducted based on the model. Results show that the vibration parameters, normal load, surface morphology, and material properties have significant influences on the friction reduction effect. The friction reduction mechanism is mainly attributed to the changes in the magnitude and direction of asperities tangential deformation. The analytical model can efficiently and accurately calculate the contact parameters and instantaneous friction force of rough contact surfaces, and provide theoretical guidance for the rational utilization of longitudinal vibration to achieve better friction reduction performance in mechanical systems.

A survey on dynamic modeling of manipulation of nanoparticles based on atomic force microscope and investigation of involved factors

In this article, the collection of studies with regard to the modeling of nanomanipulation based on atomic force microscope (AFM) is discussed. To model the manipulation process, two-dimensional and three-dimensional models in the classical environment and molecular dynamics can be presented. The decisive factor in determining the solution’s type depends on the dimensions and application of manipulation. In general, however, benefiting from multiscale methods offers more realistic results from the inherent characteristics of AFM point of view. In addition, the manipulation process is examined empirically. Different parameters affect the process. Overall, these include the geometric properties of AFM, geometric properties and material of nanoparticles, process execution environment, initial impact of nanoparticles, contact mechanics, and roughness. The geometric parameters of AFM have less importance compared with other factors. The material and geometry of nanoparticles and environmental reaction play their most dominant role in contact and roughness equations as well as intermolecular forces. For instance, for softer nanoparticles, elastoplastic and viscoelastic contact theories are more suited. In contrast, in environments except vacuum and air, roughness models with more developed adhesion terms are better choices. Employing complex contact theories can provide us with permanent deformations, roughness, reduction in force, and critical indentation depth. In addition to the involved parameters in modeling the nanomanipulation process, path planning techniques for obtaining the optimal path and control of the AFM set for its exact execution are other influential notions.

An elasto-plastic contact model for conformal contacts between cylinders

In this paper, we present a new model for the elasto-plastic conformal contact between cylinders. By using finite element simulation, it is observed that the transition of elasto-plastic contact in conformal case is different from the transition in Hertz contact. The plastic contact of conformal case can be physically represented by the plastic-Winkler model. The new model provides an explicit solution for the normal force–displacement relation of elasto-plastic conformal contact. Compared to other elastic contact models of conformal contact, the advantages of our model are: (1) it can be used for high load contact and (2) plasticity is taken into account by using the plastic-Winkler model. Our model, therefore, is capable of dealing with realistic engineering problem with high load and plasticity.

Nonlinear analysis of compact and thin-walled metallic structures including localized plasticity under contact conditions

This work presents the numerical analysis of elastoplastic contact problems of compact and thin-walled metallic structures. The emphasis is on the use of higher-order 1D elements with pure displacement variables and based on the Carrera Unified Formulation (CUF) to capture localized effects and cross-sectional distortions. Contact interactions are normal and frictionless via a node-to-node contact algorithm with the penalty approach for contact enforcement. The analysis considers the material nonlinearity via the von Mises constitutive law. Numerical assessments compare the CUF solutions with 3D finite element analysis concerning the solution quality, computational size, and analysis time. The results show the ability of 1D CUF models of accurately evaluating localized deformations and plasticity. The CUF results are in good agreement with reference 3D finite element solutions, and require an order of magnitude fewer degrees of freedom and analysis time, making them computationally efficient.

Permeability model of fractured rock with consideration of elastic‐plastic deformation

AbstractThe evolution of rock permeability has been studied exhaustively, and a broad array of permeability models has been proposed. These models are normally derived under the assumption of elastic deformation when subjected to external stress. Under this assumption, these models define fracture permeability as a function of either gas pressure or effective stress. However, experimental observations indicate that rock fracture may experience unrecoverable deformation during the loading process. The goal of this study is to resolve this contradiction. In this study, derivation of fracture permeability correlation for elastoplastic contact of rough surfaces is presented. The proposed method for describing permeability evolution not only considers the topography of fracture surfaces but also and, more importantly, integrates the plastic deformation of rock fracture. Subsequently, the deformation and permeability change of shale sample containing a single rough‐walled fracture is experimentally investigated. The results show that the permeabilities obtained during the loading process are larger than the permeabilities obtained during the unloading process under the same stress conditions and that the fracture deformation cannot be fully recovered during the unloading process. At last, the proposed permeability model is applied to the experimental results and it is shown that the proposed model can predict the laboratory permeability data.

Research on Mixed Lubrication Problems of the Non-Gaussian Rough Textured Surface With the Influence of Stochastic Roughness in Consideration

Abstract In order to find the effects of surface topography on the tribological properties of the rough textured surfaces, an improved mixed lubrication model allowing specifying the standard deviation, the skewness, and the kurtosis was developed. In this model, by considering the non-Gaussian properties of rough surfaces, an improved average flow model was combined with a modified statistical elastoplastic asperity contact model. The performances of the slider bearings with two arrays of anisotropic textures were studied in terms of Stribeck curves. It appears that the tribological properties of the anisotropic textures are sensitive to the sliding direction. Meanwhile, the surfaces with more negative skewness or the lower kurtosis can obtain better tribological performances related to friction and wear.

Modeling the Fatigue Wear of the Cylinder Liner in Internal Combustion Engines during the Break-In Period and Its Impact on Piston Ring Lubrication

In internal combustion engines, a significant portion of the total fuel energy is consumed to overcome the mechanical friction between the cylinder liner and the piston rings. The engine work loss through friction gradually reduces during the engine break-in period, as the result of liner surface topography changes caused by wear. This work is the first step toward the development of a physics-based liner wear model to predict the evolution of liner roughness and ring pack lubrication during the break-in period. Two major mechanisms are involved in the wear model: plastic deformation and asperity fatigue. The two mechanisms are simulated through a set of submodels, including elastoplastic asperity contact, crack initiation, and crack propagation within the contact stress field. Compared to experimental measurements, the calculated friction evolution of different liner surface finishes during break-in exhibits the same trend and a comparable magnitude. Moreover, the simulation results indicate that the liner wear rate or duration of break-in depends greatly on the roughness, which may provide guidance for surface roughness design and manufacturing processes.

Multiple Impacts and Multiple-Compression Process in the Dynamics of Granular Chains

Abstract In this paper, we study the dynamics of one-dimensional chains composed of elastoplastic beads. Three uniform chains, which were experimentally studied in the existing literature, are taken as benchmark examples for manifesting wave propagation induced by multiple impacts between particles and by multiple-compression process in a single contact point. We perform simulations using an elastoplastic contact model developed recently for the binary contact of a sphere. Numerical results show good agreement with the experimental observations, including the profile and amplitude of the incident and reflected solitary waves, the travel time of the wave propagation, and the high-frequency oscillations residing in the high-amplitude stress wave. Our simulations also show that the multiple-compression process of the contact between particles is responsible for the oscillations residing in the pulse profile.

Tensorial stress\u2212strain fields and large elastoplasticity as well as friction in diamond anvil cell up to 400\u2009GPa

Various phenomena (fracture, phase transformations, and chemical reactions) studied under extreme pressures in diamond anvil cell are strongly affected by fields of all components of stress and plastic strain tensors. However, they could not be measured. Here, we suggest a coupled experimental−theoretical−computational approach that allowed us (using published experimental data) to refine, calibrate, and verify models for elastoplastic behavior and contact friction for tungsten (W) and diamond up to 400 GPa and reconstruct fields of all components of stress and large plastic strain tensors in W and diamond. Despite the generally accepted strain-induced anisotropy, strain hardening, and path-dependent plasticity, here we showed that W after large plastic strains behaves as isotropic and perfectly plastic with path-independent surface of perfect plasticity. Moreover, scale-independence of elastoplastic properties is found even for such large field gradients. Obtained results open opportunities for quantitative extreme stress science and reaching record high pressures.

Stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities

PurposeThe purpose of this paper is to establish a stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities.Design/methodology/approachThe proposed model considers that asperities of different scales are interrelated rather than independent. For elastoplastic contact, a spring-damper model and an elastic deformation ratio function were proposed to calculate the contact stiffness of asperities.FindingsA revised fractal asperity model was proposed to calculate the contact stiffness of fixed joint, the impacts of the fractal dimension, the fractal roughness parameter and the Meyer index on the contact stiffness were discussed, and the present experimental results and the Jiang’s experimental results showed that the stiffness can be well predicted by proposed model.Originality/valueThe contradiction between the Majumdar and Bhushan model and the Morag and Etsion model can be well explained by considering the interaction among asperities of different scales. For elastoplastic contact, elastic deformation ratio should be considered, and the stiffness of asperities increases first and then decreases with the increasing of interference.