Simple Contact Model Research Articles

Experimental Evaluation of a Simple Contact Model Containing Two Elastic Particles Bonded by a Thin Layer of Viscoelastic Binder

AbstractThis paper presents an experimental study on the aggregate contact behavior in asphalt mixture. As a three-phase material composed of aggregates, asphalt binder, and air voids, asphalt mixture is considered as a viscoelastic material at a low stress level. The behavior of the mixture depends largely on the interaction among different components. A contact model between two aggregates is very important for understanding the deformation mechanism of the mixture. In this study, a contact model between two aggregates was reviewed in details. A closed-form time-dependent relationship between the contact forces and the relative particle/binder movements was derived. An experimental test was designed to evaluate the model which contains two elastic particles bonded by a thin layer of asphalt binder. The displacement and resistant force of the aggregate-binder system under uniaxial compression loading were documented using a cabinet X-ray tomography system. The effectiveness of the model was evaluated by ...

The effect of the contact model on the impact-vibration response of continuous and discrete systems

Impact is a phenomenon that is ubiquitous in mechanical design; however, the modeling of impacts in complex systems is often a simplified, imprecise process. In many high fidelity finite element simulations, an impractically large number of elements are required to model the constitutive properties of an impact event accurately. As a result, rigid body dynamics with approximate representations of the impact dynamics are commonly used. These approximations can include a constant coefficient of restitution, an artificially large penalty stiffness, or a single degree of freedom constitutive model for the impact dynamics that is specific to the type of materials involved (elastic, plastic, viscoelastic, etc.). In this paper, the effect of the contact model on the prediction of a system's dynamics is analyzed. In order to understand the effect of the impact model on the system's dynamics, simulations are conducted to investigate a single degree of freedom system, a two degrees of freedom system, and a continuous system, each with rigid stops limiting the amplitude of vibration. Five different contact models are considered: a coefficient of restitution method, a penalty stiffness method, two similar elastic–plastic constitutive models, and a dissimilar elastic–plastic constitutive model. Frequency sweeps and parametric studies show that simplified contact models can lead to incorrect assessments of the system's dynamics. In the worst case, periodic behavior can be predicted in a chaotic regime. Additionally, the choice of contact model can significantly affect the prediction of wear and damage in the system, as is evidenced by the prominence of chatter and high amplitude responses.

Introduction of the linear contact model in the dynamic model of laminated structure dynamics: An experimental and numerical identification

A numerical model of a laminated stack's dynamics applicable to general laminated structures was developed. A simple linear contact model facilitated the computational efficiency and in this way enabled the modelling of the stack's dynamics using a large number of laminas. The numerical model employs contact elements characterized by stiffness and damping parameters in a tangential contact direction and nonlinear contact stiffness in a normal contact direction. In order to identify the contact element parameters and to validate the developed numerical model of the laminated stack, several stack configurations were investigated using experimental modal analysis. The identified modal parameters were used in the optimization process to extract the contact element parameters. This made it possible to analyse the effects of the steel type, producer type, additional silicon layers and other treatments on the laminated stack's dynamics.

A simple distinct element modeling of the mechanical behavior of methane hydrate-bearing sediments in deep seabed

The study on the mechanical behavior of methane hydrate-bearing sediments (HBS) in deep seabed is of great significance for the safe exploitation of methane hydrate in the future. Recent studies have shown that the mechanical behavior of HBS is significantly influenced by methane hydrate since it leads to cementation among soil grains. For better understanding its microscopic mechanical mechanism, this paper presents a simple numerical model of HBS using the distinct element method (DEM). First, a set of tests on two bonded aluminum rods were performed under different loading paths with a specially designed apparatus. Then, a simple bond contact model was proposed based on the experimental data and implemented into our two-dimensional DEM code, NS2D. Finally, a series of drained biaxial compression tests under different confining stresses on HBS samples with different bond strengths, which are used to represent different methane hydrate saturations \((S_{\mathrm{MH}})\), were carried out with this code. By comparing the results of numerical simulations with the experimental data obtained from triaxial compression tests, the study shows that the DEM incorporating the new bond contact model is capable of capturing the main mechanical characteristics of HBS such as the strain softening and dilation. And it can also capture that (a) the peak shear strength increases as \(S_{\mathrm{MH}}\) or the confining stress increases, while the dilation increases as \(S_{\mathrm{MH}}\) increases or the confining stress decreases; (b) both the cohesion and friction angle increase with the increasing of \(S_{\mathrm{MH}}\), but the influence of \(S_{\mathrm{MH}}\) on the cohesion is much more significant than on the friction angle.

A simplified elastohydrodynamic contact model capturing the nonlinear vibration behaviour

A simplified model of elastohydrodynamic line contacts is presented. It consists of a series connection of a hydrodynamic and a Hertzian force element and is particularly suitable for nonlinear analysis of oscillatory systems.Since the model is based on physical reflections rather than on numerical curve fits it reveals the physical parameters. Due to its simplicity and compactness it allows for fast calculations and thus lends itself to investigations of large and complex mechanical systems with numerous elastohydrodynamic contacts.To demonstrate the usefulness of this model, the nonlinear vibration behaviour of a 1-DoF oscillator incorporating an elastohydrodynamic contact is investigated.

Comparative Contact Analysis Study of Finite Element Method Based Deterministic, Simplified Multi-Asperity and Modified Statistical Contact Models

The study of the contact stresses generated when two surfaces are in contact plays a significant role in understanding the tribology of contact pairs. Most of the present contact models are based on the statistical treatment of the single asperity contact model. For a clear understanding about the elastic-plastic behavior of two rough surfaces in contact, comparative study involving the deterministic contact model, simplified multi-asperity contact model, and modified statistical model are undertaken. In deterministic contact model analysis, a three dimensional deformable rough surface pressed against a rigid flat surface is carried out using the finite element method in steps. A simplified multi-asperity contact model is developed using actual summit radii deduced from the rough surface, applying single asperity contact model results. The resultant contact parameters like contact load, contact area, and contact pressure are compared. The asperity interaction noticed in the deterministic contact model analysis leads to wide disparity in the results. Observing the elastic-plastic transition of the summits and the sharing of contact load and contact area among the summits, modifications are employed in single asperity statistical contact model approaches in the form of a correction factor arising from asperity interaction to reduce the variations. Consequently, the modified statistical contact model and simplified multi-asperity contact model based on actual summit radius results show improved agreement with the deterministic contact model results.

Fault-Tolerant Control Strategy for Steering Failures in Wheeled Planetary Rovers

Fault-tolerant control design of wheeled planetary rovers is described. This paper covers all steps of the design process, from modeling/simulation to experimentation. A simplified contact model is used with a multibody simulation model and tuned to fit the experimental data. The nominal mode controller is designed to be stable and has its parameters optimized to improve tracking performance and cope with physical boundaries and actuator saturations. This controller was implemented in the real rover and validated experimentally. An impact analysis defines the repertory of faults to be handled. Failures in steering joints are chosen as fault modes; they combined six fault modes and a total of 63 possible configurations of these faults. The fault-tolerant controller is designed as a two-step procedure to provide alternative steering and reuse the nominal controller in a way that resembles a crab-like driving mode. Three fault modes are injected (one, two, and three failed steering joints) in the real rover to evaluate the response of the nonreconfigured and reconfigured control systems in face of these faults. The experimental results justify our proposed fault-tolerant controller very satisfactorily. Additional concluding comments and an outlook summarize the lessons learned during the whole design process and foresee the next steps of the research.

Finite Element Contact Analysis for Sprocket of an Armoured Face Conveyor

Sprocket has an important role in improving the transport performance and life of the armoured face conveyor, which is the key component in the transmission system of armoured face conveyor (AFC). In this paper, true stress-true strain curves of materials of the sprocket and the ring chain are obtained by computing the data of static tensile test. A simplified symmetric finite element contact model is established based on the nonlinear finite element software ABAQUS. Stress field and torsional stiffness coefficient of the sprocket are calculated according to loads and boundary conditions. Simulation results are in good accordance with the test results. The finite element model and the simulation results provide useful guidance for design and test of the sprocket. Meanwhile, accurate torsional stiffness coefficient of the sprocket is obtained for simulation of the transmission system of AFC.

Stick-slip algorithm in a tangential contact force model for multi-body system dynamics

Contact force of Multi-body dynamics (MBD) system can be classified two parts. First is a normal force and the other is a tangential force called friction force. And the friction force can be represented by two states such as stick and slip. The stick-slip phenomenon is simply described as a simple contact model which is a rigid body contacted on a sloped surface. If the calculated friction coefficient between the body and sloped surface is less than the static friction coefficient, the body should be stuck. If the calculated friction coefficient is greater than the static friction coefficient, the body will be sliding along the surface. The phenomenon is called as stick and slip state of friction, respectively. Usually many researchers and commercial MBD software used a coulomb friction force model which is defined with an only function of relative velocity. This kind of friction force model will be called a conventional friction force model in this paper. A big problem of the conventional model can not describe a stick state of friction phenomenon. In the case of conventional friction force model, the body will be sliding even though friction state is stick. Because, the relative velocity must have a non-zero value in order to generate the friction force. To solve this kind of problem, we propose a stick-slip friction force model including a spring like force. In the case of stick-slip friction force model, the body can be stuck on the sloped surface because the friction force will be a non-zero value, even though the relative velocity approaches zero. We defined a relative displacement variable called stiction deformation. In this paper, the stick-slip friction model is proposed and applied in the contact algorithm of MBD system. And then two friction models are compared with numerical examples. With the proposed stick-slip friction model, more realistic results are achieved.

Contact Mechanics Analysis of Two Rough Surfaces in Contact

In this paper, the calculation formulas of the asperity’s deformation related with the surface contact pressure are deduced by using the simplified contact model. Firstly, we assume that the rough surface is composed of a set of cones as asperities, and the cones are arranged in different ways along two directions. Secondly, according to the mechanical analysis of a rigid conical punch on a half-space, the theoretical relationship between the average pressure of the micro contact area and the property parameters of a conical punch is obtained. Meanwhile, the calculation formula of the average pressure is given under the reasonable assumptions, which is related with the asperity’s deformation and the contact pressure. Finally, combining two theoretical relationships above, the quantitative analysis method for micro asperity’s deformation of two rough surfaces in contact is provided by using the average pressure as a connection bridge.

Load Transfer and Recovery Length in Parallel Wires of Suspension Bridge Cables

A new simplified contact model aimed at capturing the load transfer and recovery length in parallel steel wires, commonly used in main cables of suspension bridges, is presented. The approach is based on placing elastic–perfectly plastic spring elements at the contact region between the objects. These springs have varying stiffness (Model I) or yielding (Model II) depending on their proximity to the clamping loads. Their stiffness or yielding is highest when they are closer to this force, and it decays when they are farther away from the clamp. This decayed behavior is assigned according to Boussinesq’s well-known solution to a point load (applied on a half space). Both models converge quickly compared with a full contact model and recover Coulomb friction law on a two-dimensional (2D) benchmark problem. Moreover, when the same properties are chosen for all springs (disregarding Boussinesq solutions), the models reduce to the classical shear-lag model, which for high clamping (point) loads gives inaccurat...

Analysis on the fundamental deformation effect of a robot soft finger and its contact width during power grasping

This paper attempts to develop a simple contact model of a robot soft finger which is applied for power grasping. The geometrical relationship between contact parameters such as the deformation, contact width, and touch angle are derived for the developed cylindrical finger of soft material. The proposed nonlinear model of the soft finger deforms on the application of load and contact surface grows correspondingly with an angle. The deformation and contact width are related with contact touch angle, which changes as load varies. The force relationship between contact parameters and geometrical data is then derived. The developed analytical model enables to determine the total contact force at the contact surface during the manipulation. An experiment is conducted with three different hyper elastic materials and the deformations and contact width for various loads are determined. The material properties of finger materials are computed using measured deformation. The suitable soft material for developing robot soft fingers is then selected based on the deformation of the finger and frictional coefficients between finger material and the selected target materials. The numerical simulation is also done for the developed model, and it well matches with the experimental results. The developed soft finger model and its force function can be usefully applied to soft-fingered object manipulations in future.

Effect of thermal treatments on the wear behaviour of duplex stainless steels

Duplex stainless steel (DSS) is a family of steels characterized by two-phase microstructure with similar percentages of ferrite (α) and austenite (γ).Their attractive combination of mechanical properties and corrosion resistance has increased its use in last decades in the marine and petrochemical industries. Nevertheless, an inappropriate heat treatment can induce the precipitation of secondary phases which affect directly their mechanical properties and corrosion resistance. There are few works dealing with the influence of heat treatments on wear behaviour of these steels in the literature. For instances, this paper aims to determine wear kinetic and sliding wear volume developed as a function of heat treatment conditions. Therefore, the samples were heat treated from 850 °C to 975 °C before sliding wear tests. These wear tests were carried out using ball on disk technique at constant sliding velocity and different sliding distances. Two methodologies were used to calculate the wear volume: weight loss and area measurement using a simplified contact model. Microstructural observations showed the presence of sigma phase for all studied conditions. The formation kinetics of this phase is faster at 875 °C and decrease at higher temperatures. Results related to wear showed that the hardness introduced due to the presence of sigma phase plays an important role on wear behaviour for this steel. It was observed also that wear rates decreased when increasing the percentage of sigma phase on the microstructure.

Flow–obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment

This paper investigates the interaction between rapid granular flow and an obstacle. The distinct element method (DEM) is used to simulate the flow regimes observed in laboratory experiments. The relationship between the particle properties and the overall flow behaviour is obtained by using the DEM with a simple linear contact model. The flow regime is primarily controlled by the particle friction, viscous normal damping and particle rotation rather than the contact stiffness. Rolling constriction is introduced to account for dispersive flow. The velocity depth-profiles around the obstacles are not uniform but varying over the depth. The numerical results are compared with laboratory experiments of chute flow with dry granular material. Some important model parameters are obtained, which can be used to optimize defense structures in alpine regions.

Friction from nano to macroforce scales analyzed by single and multiple-asperity contact approaches

Understanding friction and wear at different force and length scales is an interesting aspect in tribology. The variety of processes that make friction such a complex phenomenon includes mechanical, chemical and atomic interactions, each operating at their own time, length, and force scale. Extending local tribological information obtained from a single-asperity contact study (e.g. by lateral force microscopy LFM experiments) to contacts with multiple-asperity interactions is a challenging task. In this work, we analyze the localized friction recorded during a single-asperity LFM experiment, and compare it with that of multiple-asperity sliding contacts. Such a detailed study is relevant for miniature contacts which prevail in microelectromechanical systems of devices. In this work, the friction loops (i.e., tangential force versus displacement curves) obtained from nano to macroforce and different length scales were used to understand the scale effects of friction. Experiments were performed in reciprocating sliding conditions with a ball-on-flat configuration on diamond-like carbon and titanium nitride coatings. With decreasing contact size and stiffness of the measuring equipment, the effect of roughness is strikingly evident. The effect of surface roughness is clearly visible on the recorded friction loops as fluctuations, which were later attributed to geometrical and adhesive components. Based on our observations, a simple contact model was proposed to describe the nature of localized friction in single and multiple-asperity configurations during a sliding pass. The existing friction model for smooth and chemically interacting surfaces was extended to rough surfaces and it was found that most of the existing experimental claims could be explained as special cases of the proposed model.

Simulation of wear on a rough rail using a time-domain wheel–track interaction model

This paper presents results from simulations of railhead wear due to initial sinusoidal and broad-band roughness using a time-domain wheel–track vertical interaction model integrated with a three-dimensional wheel–rail contact model. As typical roughness wavelengths are short and frequencies are high compared with vehicle body motions, the vehicle is simplified to an unsprung wheel mass. The rail is modelled as a Timoshenko beam discretely supported by pads, sleepers and ballast. The wheel–rail contact in the interaction model is modelled with a non-linear Hertzian contact spring. The obtained wheel–rail forces are then incorporated into the three-dimensional contact model to calculate wear over the railhead. The wheel–rail contact is modelled as non-Hertzian and non-steady based on the Variational Method [G. Xie, S.D. Iwnicki, Calculation of wear on a corrugated rail using a three-dimensional contact model, in: Proceedings of the Seventh International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Brisbane, Australia, Materials Australia, 2006] and the wear is assumed to be proportional to the friction work. Cases of both a free and a driven wheel with a constant torque are considered. The phase angles between dynamic wheel–rail force and roughness are examined and wear is found to be almost in-phase with roughness and therefore, no roughness growth is predicted by the model as presented in its current form. Although clearly in contradiction to reality where roughness grows under certain conditions this work leads to interesting question about why roughness growth is predicted by a simple contact model but not when complexity is increased to include non-Hertzian and non-steady contact conditions.

Validation of a simplified numerical contact model

Surface roughness tends to have a significant effect on how loads are transmitted at the contact interface between solid bodies. Most numerical contact models for analyzing rough surface contacts are computational demanding and more computationally efficient contact models are required. Depending on the purpose of the simulation, simplified and less accurate models can be preferable to more accurate, but also more complex, models. This paper discusses a simplified contact model called the elastic foundation model and its applicability to rough surfaces. The advantage of the model is that it is fast to evaluate, but its disadvantage is that it only gives an approximate solution to the contact problem. It is studied how surface roughness influences the errors in the elastic foundation solution in terms of predicted pressure distribution, real contact area, and normal and tangential contact stiffness. The results can be used to estimate the extent of error in the elastic foundation model, depending on the degree of surface roughness. The conclusion is that the elastic foundation model is not accurate enough to give a correct prediction of the actual contact stresses and contact areas, but it might be good enough for simulations where contact stiffness are of interest.

A Model of Adhesion Excited Micro-vibrations

Understanding the mechanism of “rubbing” noise and low-amplitude friction exited vibration generation in steady sliding can be helped by models describing the contact interactions. In the current article, we consider a simple microscopic contact model for surfaces in sliding, which is based on the adhesion theory of friction. In the proposed model, we consider that the formation and shearing of a junction contributes to a small change in the real contact area. The model incorporates random size and random spacing between junctions. We investigate the dependence of the instantaneous real contact area on the average size and number of junctions. We find that from the viewpoint of vibration reduction, it is advantageous if the real contact area needed to support the given load is obtained as a sum of many small-sized micro-contacts, instead of few large-sized micro-contacts. The above result is in agreement with experimentally observed reduction of vibrations of a hard-disk slider after texturing.

Modelling of vibrations excited by formation and shearing of adhesive micro-junctions during sliding

Understanding of the mechanism of “rubbing” noise and low amplitude friction exited vibration generation in steady sliding can be helped by models describing the contact interactions. In the current paper, we consider a simple microscopic contact model for surfaces in sliding, which is based on the adhesion theory of friction. In the proposed model, we consider that the formation and shearing of a junction contributes to a small change in the real contact area. The model incorporates random size and random spacing between junctions. We investigate the dependence of the instantaneous real contact area on the average size and number of junctions. We find that, from the viewpoint of vibration reduction, it is advantageous if the real contact area needed to support a given load is obtained as a sum of many small-sized micro-contacts, instead of few large-sized micro-contacts. The above result is in agreement with experimentally observed reduction of vibrations of a hard-disc slider after texturing.

Surface roughness effect in instrumented indentation: A simple contact depth model and its verification

Since in instrumented indentation the contact area is indirectly measured from the contact depth, the natural and unavoidable roughness of real surfaces can induce some errors in determining the contact area and thus in calculating hardness and Young's modulus. To alleviate these possible errors and evaluate mechanical properties more precisely, here a simple contact model that takes into account the surface roughness is proposed. A series of instrumented indentations were made on W and Ni samples whose surface roughness is intentionally controlled, and the results are discussed in terms of the proposed model.