Numerical Contact Model Research Articles

Numerical Point Contact Model of Mixed Elastohydrodynamic Lubrication for Transversely Isotropic Coating

Abstract Transverse isotropy, a typical property of coating providing protection or lubrication for transmission parts, is different from isotropy focused in most of previous research, catching increasing attention in recent years. This study aims to make the lubricating contact behavior of transversely isotropic coating under different working conditions better understood, with the assistance of a proposed mixed elastohydrodynamic lubrication (EHL) model for a rigid ball in contact with transversely isotropic coating. Explicit analytical expressions of frequency response functions (FRFs) of the elastic field for transversely isotropic coating were derived, which could be used to work out surface/subsurface displacement and stress if surface pressure is known. The proposed EHL model for transversely isotropic coating was verified by comparing the film thickness and pressure distribution with those from literature by an uncoated model. Furthermore, the effects of coating elastic property, coating thickness, velocity, and load on lubrication performance and mechanical responses are investigated. In addition, the results under different coating parameters are also compared and discussed with those obtained by the Hamrock–Dowson equations to demonstrate the effectiveness of the latter. This investigation may provide a potential application for coating optimal design considering lubrication.

A test rig for the full characterization of the dynamics of shrouded turbine blades

Highly stressed forced vibrations experienced by Low Pressure Turbine (LPT) blades during their operation can result in high cycle fatigue (HCF) which can ultimately lead to failure. To avoid this occurrence, the vibration amplitudes must be anticipated and reduced. This is generally done by employing friction damping devices like under-platform dampers, shrouds and snubbers. In case of blades with shrouds at their tips, the adjacent shrouded blades are coupled to each other and three-dimensional periodic shroud contact forces acting on shrouds significantly influence the vibration amplitudes as energy is dissipated due to friction. Hence, for the experimental validation of the numerical contact models that are used for the prediction of nonlinear forced response of shrouded blades, it is equally necessary to measure the contact forces acting at the shrouds. Moreover, present-day requirement of more accurate and detailed models requires thorough and comprehensive experimental validation calling for the measurement of three-dimensional shroud contact forces from purposely designed test rigs.This study presents the design, development and operation of an experimental test rig that allows full characterization of the dynamics of shrouded turbine blade, i.e., simultaneous measurement of three-dimensional shroud contact forces and shrouded blade forced response. The starting point was the design of the test rig components based on the design requirements. This is followed by the description of the major components of the proposed test rig i.e., the three-dimensional contact force measurement system and the torque screw mechanism. In the subsequent section, the details of the experimental setup to measure the forced response and three-dimensional shroud contact forces simultaneously are highlighted as the test campaign is performed for different normal preloads and excitation force levels. Consequently, the effects of the variation in the normal preload and excitation force on the measured response and shroud contact forces are discussed. Finally, it is shown how the results establish the efficacy of the proposed test rig in providing a comprehensive depiction of the dynamic response of the shrouded blade and 3D shroud contact forces that will result in more accurate and reliable experimental validation of numerical tools.

Viscoelastic adhesive contact between a sphere and a two-dimensional nano-wavy surface

For contact involving viscoelastic materials with nanoscale roughness surfaces, both the viscoelasticity and the adhesive interaction play significant roles, and an in-depth understanding of this viscoelastic adhesive contact behavior is essential. This paper establishes a numerical viscoelastic adhesive contact model between a smooth sphere and a two-dimensional nano-wavy surface based on the Derjaguin approximation and elastic–viscoelastic correspondence principle, and the wavy surface is considered by introducing the height distribution into the surface gap equation. Influences of approach speed, contact position and wavy surface parameters on the viscoelastic adhesive contact behavior are quantitatively analyzed. It is shown that the viscoelasticity can be ignored at large approach speed, while when the speed is small, viscoelasticity significantly increases the maximum contact area and pull-off force. Variations of maximum contact area and pull-off force with contact position or wavy surface parameters are not completely consistent, where the contact positions with relatively large maximum contact area may exhibit small pull-off force. The pull-off force changes monotonically with increasing wavy parameter, while the maximum contact area changes nonmonotonically. This study can offer guidance for the application of wavy surface in viscoelastic adhesion regulation, and provide basis for the surface design and parameter determination of viscoelastic materials.

On the controlled adhesive contact and electrical performance of vertical contact-separation mode triboelectric nanogenerators with micro-grooved surfaces

The triboelectric nanogenerator (TENG) is a new energy technology to convert mechanical energy into electricity based on contact electrification and electrostatic induction. Altering the alignment state of TENG with two micro-grooved surfaces is a simple way to achieve controlled electrical output. To guide the output regulation of TENG with micro-grooved surfaces and avoid causing interface separation failure, comprehensive analysis based on adhesive contact mechanics is essential. In this paper, the relation between charge density and contact stress is measured. Numerical adhesive contact and electrical models of TENG with grooved surfaces considering the charge density-contact stress relation and material properties are established to quantitatively analyze the effects of alignment angle, applied pressure and loading time on adhesive contact and electrical performance. It is shown that there exists an exponential relation between charge density and contact stress. Alignment angle of grooved surfaces in TENG significantly affects the adhesive contact and electrical performance. Under low and high applied pressures, the variations of output voltage with alignment angle are 630.5% and 301.1%, respectively, while same pull-off force variation of 532.6% is exhibited. Large pull-off force usually comes along with high voltage output, except for alignment angle of 10°, at which relative high voltage and low pull-off force are exhibited. Strategies for the output regulation of TENG with grooved surfaces without causing interface separation difficulty are presented.

Nonlinear frictional contact behavior of porous polymer hydrogels for soft robot

Focusing on the oblique frictional contact problem of hydrogel for soft robot, a numerical contact model is developed to analyze the nonlinear behaviors including local contact large deformation and friction effect of hydrogel soft material during oblique contact. Based on the constitutive relation of hyperelastic material, the updated free energy function of hydrogel is derived. The contact algorithm is given to compute the contact responses of both collinear contact example and oblique contact example. The applicability of classical Hertz contact theory is discussed. The influence of coefficient of friction on the stress distribution of contact zone and the contact states of contact surface are also investigated. The numerical results show that the material nonlinearity and the geometric nonlinearity (i.e. large deformation) of hydrogel lead to the invalidation of classical Hertz contact theory. For the oblique contact, the internal stress grads of hydrogel will be redistributed as the coefficient of friction increases. Meanwhile, the maximum stress position moves from underside to the contact surface. Two high stress zones occur inside and on the contact surface at the same time, respectively. Besides, when the coefficient of friction is smaller (i.e. <i>μ</i> < 0.05), for the collinear contact all contact points on the contact surface are in critical state from static friction to dynamic friction. But for the oblique contact, some contact points are always in stable static friction state.

A numerical model to investigate contact status for rail grinding by abrasive belt with an axial deflection

In order to calculate analytically the contact status for rail grinding by abrasive belt with an axis deflection, as well as considering limitations of using Hertz contact theory for that, a numerical contact model (NCM) based on the local geometrical relationship between contact wheel and rail surface was developed. The effectiveness and accuracy of the proposed model have been validated by the corresponding finite element model (FEM) by comparing the contact boundary and contact stress distribution. Comparative cases at two typical grinding positions with different attitudes were involved, and the effects of applying axis deflection on contact behavior were investigated in detail. The results from NCM and FEM both agreed belt grinding with an axis deflection was able to enlarge the contact width of the belt and the total grinding force under the premise of ensuring required width of grinding trace on the rail. The model provides insights into understanding contact behavior under actual working conditions and gives a theoretical basis for future researches based on contact analysis.

An Empirical Approach for the Determination of Skin Elasticity: Finger pad Friction against Textured Surfaces

Surface topography significantly influences tactile friction and perception. While friction forces can be reduced by surface texturing, selection of pattern dimensions is challenging due to the highly variable elastic modulus of the skin. This work proposes an empirical approach for the evaluation of the skin elasticity through surface transition from asperity to full contact state. To highlight the contact transition, two textures with evenly distributed identical micro asperities, but varying density, were moulded with several grades of silicone rubber. Dynamic friction coefficient measurements were performed during finger pad sliding against the textured samples with a range of normal loads up to 5 N. A combination of analytical and numerical contact models is used to explain the observed friction behaviour, estimate the development of contact area and calculate the effective elastic modulus of the skin at the micro-scale. Low density textures clearly indicate the transition to the full contact state, which is reflected in friction coefficient development, while high density textures remain in an asperity contact state, with significantly lower friction values. The effective Young's modulus is hereby estimated in the range of 0.2–0.5 MPa. Observed frictional behaviour is explained by the change in the apparent and real contact areas. The presented approach allows to study the influence of individual surface parameters on effective skin elastic modulus, which is essential for the development of functional surfaces with improved tactile perception.

A closed-form contact model for gas face seals during the opened operation

PurposeFace contact has a strong impact on the service life of non-contacting gas face seals; the current research which mainly focuses on the face contact had appeared during the startup or shutdown operation. This paper aims to present a closed-form contact model of a gas face seal during the opened operation.Design/methodology/approachReferring to the axial rub-impact model of rotor dynamics, a closed-form contact model is developed under a nonparallel plane contact condition that corresponds to the local face contact of sealing rings arising from some disturbances during the opened operation. The closed-form contact model and a direct numerical contact model are performed on Gaussian surfaces to compare the contact behavior.FindingsThe closed-form contact model is in a good agreement with the direct numerical contact model. However, the closed-form contact model cannot involve the influence of grooves on the sealing ends. The error is eliminated in some other types of gas face seals such as coned gas face seals. Besides non-contacting face seals, the closed-form model can be applied to the axial rub impact of rotor dynamics.Originality valueA closed-form contact model of a gas face seal is established during the opened operation. The closed-form contact model is validated by a direct numerical contact model. The closed-form contact model also suits for axial rub-impact of rotor dynamics.

A test-validated prediction model of thermal contact resistance for Ti-6Al-4V alloy

The precise prediction or test of thermal contact resistance is a key issue on increasing or decreasing thermal energy transmission efficiency between two solids. This paper raises a thermal contact resistance prediction model based on measuring actual surface topography under different loading pressures and different heating temperatures. The actual topography of contact surfaces is measured by a 3-D optical microscope named Bruker Contour GT-K. The contact surfaces are reconstructed with language Python according to the data of surface topography from the microscope and the numerical contact model is generated. Then the thermal contact resistance simulation is implemented with software ABAQUS. Based on the elastic-plastic constitutive equations and steady state heat conduction theory, finite element analysis of mechanical and heat transfer performance of the contact model is performed with ABAQUS in the light of sequential coupling method. The studied material pairs are Ti-6Al-4V—Ti-6Al-4V with three kinds of different interstitial material e.g., vacuum, air and conductive silicone grease. The effect of radiation on thermal contact resistance under air and vacuum atmosphere is further studied and analyzed. Besides, the solid thermal conductivity on thermal contact resistance is investigated. To verify the accuracy of the method, the simulated results from ABAQUS are compared with the experimental results of air gap with the same boundary conditions. The maximum deviation between simulation results and experimental results is 9.57% while 75% of the deviations are within 5%. A correlation of thermal contact conductance with the average contact surface temperature and loading pressure is proposed. The results show that this method has high precision to predict thermal contact resistance in the engineering application.

Comprehensive contact analysis for vertical-contact-mode triboelectric nanogenerators with micro-/nano-textured surfaces

The triboelectric nanogenerator (TENG) is a new energy technology to convert mechanical energy into electricity based on contact charging and electrostatic induction. To increase the effective power generation in a limited device size, micro-/nano-textures are often designed at the contact surfaces. As the contact region decreases to micro/nano scale, adhesive forces such as van der Waals and electrostatic forces become dominant. However, there is currently no comprehensive model including micro-/nano-textures and the above adhesive forces, and thus the selection and design of textures are still lack of theoretical guidance. In this paper, the numerical contact and electrical models considering van der Waals and electrostatic forces are established, and the computational methods such as inexact Newton method, bi-conjugate stabilized (Bi-CGSTAB) method and fast Fourier transform (FFT) technique are employed to quantitatively analyze the effects of charge densities, applied loads, texture shapes and sizes on both contact and electrical performance. It is shown that the electrostatic force can be ignored when the charge density is small, while with large charge density, the electrical performance is significantly overestimated if the electrostatic forces are neglected. Among the four selected types of textures (pyramid, cone, cylinder and cube), the pyramid and cube textures are found to provide the larger output voltage under different applied loads, and also the optimal sizes for high voltage are presented, respectively. This study can provide the guideline for the texture design of high power generation TENGs.

Evaluation of Contact Fatigue Life of a Wind Turbine Gear Pair Considering Residual Stress

Contact fatigue is a main fatigue mode of gears such as those used in wind turbines, due to heavy duties occurring in engineering practice. The understanding of the gear contact fatigue should be based on the interaction between the local material strength and the stress state. Under the rolling–sliding motion, the multi-axial stress state makes the gear contact fatigue problem more complicated. A numerical contact model is proposed to evaluate the contact fatigue life of an intermediate parallel gear stage of a megawatt level wind turbine gearbox. The gear meshing theory is applied to calculate the geometry kinematics parameters of the gear pair. The gear contact is assumed as a plane strain contact problem without the consideration of the influence of the helical angle. The quasi-static tooth surface load distribution is assumed along the line of action. The elastic mechanics theory is used to calculate the elastic stress field generated by surface tractions. The discrete convolute, fast Fourier transformation method is applied to estimate the subsurface stresses distributions. In order to describe the time-varying multi-axial stress states during contact, the Matake, Findley, and Dang Van multi-axial fatigue criteria are used to calculate the critical planes and equivalent stresses. Both the statistic and the deterministic fatigue life models are applied by choosing the Lundberg–Palmgren (LP), Zaretsky models, respectively. The effect of the residual stress distribution on the contact fatigue initiation lives is discussed. In addition, the crack propagation lives are estimated by using the Paris theory.

Wear model for describing the time dependence of the material degradation mechanisms of the AISI 316L in a NaCl solution

The tribo-electrochemical behavior of AISI 316L has been investigated under tribocorrosion conditions in a 3% NaCl solution and the material damage evolution with time has been analyzed. A numerical contact model based on a Boundary Element Method (BEM) has been developed in order to determine the contact pressure distribution and to quantify the worn material as a function of time. The time dependence of the tribological behavior of the material has been described. At the initial state, the high contact pressures generate a material flow causing an increase in the worn area. After around 300 cycles, the Archard wear model linearly describes the wear evolution with time. The proposed model describes the evolution with time of the wear profiles of the tested material and takes into account the plastic behavior of the material during the first cycles.

Effects of hierarchical structures and insulating liquid media on adhesion

Effects of hierarchical structures and insulating liquid media on adhesion are investigated through a numerical adhesive contact model established in this paper, in which hierarchical structures are considered by introducing the height distribution into the surface gap equation, and media are taken into account through the Hamaker constant in Lifshitz-Hamaker approach. Computational methods such as inexact Newton method, bi-conjugate stabilized (Bi-CGSTAB) method and fast Fourier transform (FFT) technique are employed to obtain the adhesive force. It is shown that hierarchical structured surface exhibits excellent anti-adhesive properties compared with flat, micro or nano structured surfaces. Adhesion force is more dependent on the sizes of nanostructures than those of microstructures, and the optimal ranges of nanostructure pitch and maximum height for small adhesion force are presented. Insulating liquid media effectively decrease the adhesive interaction and 1-bromonaphthalene exhibits the smallest adhesion force among the five selected media. In addition, effects of hierarchical structures with optimal sizes on reducing adhesion are more obvious than those of the selected insulating liquid media.

Detailed contact pressure between wire rope and friction lining

The authors have studied the contact pressure between a wire rope and a friction lining block. The current study is crucial for the subsequent work on frictional heating under sliding conditions. The contact equations are solved on a fine grid, using multigrid techniques. Results from the numerical contact model show that the local maximum contact pressure is about 45 times higher than the average one obtained from the “plane method” formula. Two approximate analytical calculations are proposed that give a maximum contact pressure with a relative error of the order of 10% with only a small computational effort.

A complete strategy for efficient and accurate multibody dynamics of flexible structures with large lap joints considering contact and friction

This paper deals with the dynamics of jointed flexible structures in multibody simulations. Joints are areas where the surfaces of substructures come into contact, for example, screwed or bolted joints. Depending on the spatial distribution of the joint, the overall dynamic behavior can be influenced significantly. Therefore, it is essential to consider the nonlinear contact and friction phenomena over the entire joint. In multibody dynamics, flexible bodies are often treated by the use of reduction methods, such as component mode synthesis (CMS). For jointed flexible structures, it is important to accurately compute the local deformations inside the joint in order to get a realistic representation of the nonlinear contact and friction forces. CMS alone is not suitable for the capture of these local nonlinearities and therefore is extended in this paper with problem-oriented trial vectors. The computation of these trial vectors is based on trial vector derivatives of the CMS reduction base. This paper describes the application of this extended reduction method to general multibody systems, under consideration of the contact and friction forces in the vector of generalized forces and the Jacobian. To ensure accuracy and numerical efficiency, different contact and friction models are investigated and evaluated. The complete strategy is applied to a multibody system containing a multilayered flexible structure. The numerical results confirm that the method leads to accurate results with low computational effort.

An 2-D SGBEM formulation of contact models coupling the interface damage and Coulomb friction in fibre–matrix composites

A new numerical contact model able to predict the interface debonding and damage considering Coulomb friction contact between debonded surfaces has been developed. A comparison of two variants of this model is presented from the mathematical point of view, the Linear Elastic–Brittle Interface Model (LEBIM) and the Cohesive Interface Model (CIM), both combined with frictional contact. The paper discusses the process of the interface debonding in the two subsequent fracture steps: (i) the crack initiation and (ii) the crack propagation in the fibre–matrix interface. The concept of the solution is approximated by a time-stepping procedure and a boundary element approach.

Contact force model including the liquid-bridge force for wet-particle simulation using the discrete element method

The handling of wet particles in chemical engineering is often difficult because cohesive forces acting on wet particles cause particulate aggregation and the adherence of devices, unlike what occurs under a dry condition. The liquid-bridge force is introduced to the discrete element method in the investigation of the behavior of wet particles. However, existing numerical modeling has problems from the viewpoint of the effect of cohesion in contact states. Specifically, the cohesive force is treated as a constant value for contact states. This means the effect of the cohesive force is not only dependent on the spring constant in the discrete element simulation but is also frequently overestimated. To solve this problem, the present study developed a numerical contact model considering quantitatively the effect of the cohesive force in contact states and validated the model for a pan pelletizer. The behaviors and cascading angles of wet particles in simulation and experiments were in good agreement and the validity of the contact model was thus demonstrated. The present numerical contact model is thus a promising model for the numerical simulation of wet particles.

Indentation of PU at different scales and computational modeling: identification of viscoelasticity and quantification of adhesion effects

In the present study, nanoindentation and macroindentation tests are performed on a soft polymer: polyurethane (PU). Strong viscoelasticity is represented by the force-displacement data on both scales. A finite element method based on an inverse procedure is employed to identify the nonlinear viscoelasticity of PU. An appropriate viscoelastic model is chosen, and the corresponding parameters are identified by matching the experimental responses with the predictions of the computational model. At the very beginning, the uniaxial tensile test, which has a homogeneous deformation, is used to prove the isotropic properties and incompressibility of PU and to identify the viscoelasticity as a reference and verification source. The comparison between the identified results from nanoindentation and macroindentation allows to quantifying the adhesion effects in nanoindentation. The quantification is treated with a traction–separation relationship incorporated into the numerical adhesive contact model. Comparable strain rates in the macro-, nanoindentation and uniaxial tensile tests are considered to identify the viscoelasticity.

Importance of tread inertia and damping on the tyre/road contact stiffness

Predicting tyre/road interaction processes like roughness excitation, stick-slip, stick-snap, wear and traction requires detailed information about the road surface, the tyre dynamics and the local deformation of the tread at the interface. Aspects of inertia and damping when the tread is locally deformed are often neglected in many existing tyre/road interaction models. The objective of this paper is to study how the dynamic features of the tread affect contact forces and contact stiffness during local deformation. This is done by simulating the detailed contact between an elastic layer and a rough road surface using a previously developed numerical time domain contact model. Road roughness on length scales smaller than the discretisation scale is included by the addition of nonlinear contact springs between each pair of contact elements. The dynamic case, with an elastic layer impulse response extending in time, is compared with the case where the corresponding quasi-static response is used. Results highlight the difficulty of estimating a constant contact stiffness as it increases during the indentation process between the elastic layer and the rough road surface. The stiffness–indentation relation additionally depends on how rapidly the contact develops; a faster process gives a stiffer contact. Material properties like loss factor and density also alter the contact development. This work implies that dynamic properties of the local tread deformation may be of importance when simulating contact details during normal tyre/road interaction conditions. There are however indications that the significant effect of damping could approximately be included as an increased stiffness in a quasi-static tread model.

Thermo-mechanical modelling of the contact between rough surfaces using homogenisation technique

In this study, thermo-mechanical behaviour of contacting rough surfaces has been modelled. Firstly, a numerical microscopic contact model that considers the properties of engineering surfaces has been developed. Geometrical characteristics of rough surfaces are deduced using the standard procedure for roughness and waviness parameter determination according to the so-called “motif” procedure. Secondly, an equivalent macroscopic contact model using a homogenisation technique has been presented. The interfacial behaviour of this model has been governed by the curves deduced from the microscopic model. The transition from microscopic to macroscopic scale was also validated.