Frictional Contact Interaction Research Articles

The Geometric Configuration of Lubricant Recesses of the Polymer Sliding Layer of the Bearing

Polymers have gained a foothold in the international market and are actively utilized at a large scale in various industries. They are used as sliding layers in various types of friction units. However, there is a lack of research on their deformation behavior under different design conditions. This work is focused on studying the influence of the geometrical design of lubrication recesses in a polymer sliding layer operating under conditions of frictional contact interaction. The article investigated an element of bridge-bearing steel plate with recesses for lubrication. Two geometrical configurations of recesses are studied: the annular groove and spherical well in the engineering software package ANSYS Mechanical APDL. Polytetrafluoroethylene (PTFE) is considered an elastic-plastic sliding layer. A comparative analysis of two models with different geometrical configurations of cutouts for lubrication, with/without taking into account its volume in the recess, has been conducted. The article establishes that in the absence of lubrication in the recesses, large deformations of the polymer sliding layer occur. This effect negatively affects the structure as a whole. Changing the geometry of the recess for lubrication has the greatest effect on the intensity of plastic deformations. Its maximum level is lowered by almost ~60% when spherical notches are used for lubrication instead of grooves. The friction coefficient of the polymer has a great influence on the contact tangential stress. At the experimental coefficient of friction, it is lowered on average by ~85%. The friction coefficient of the lubricant has almost no effect on the deformation of the cell (<1%).

Discovering the causes for the change of the vibration characteristics of the core support barrel in PWR nuclear power plants: A combined investigation based on ex-core neutron noise analysis and numerical modal analysis

As a key component of pressurized water reactor (PWR) nuclear power plants, the motion of the core support barrel (CSB) has a great impact on the safety of the nuclear reactor. However, the vibration characteristics of the CSB have not yet been fully investigated and may change due to the high doses of radiation and high temperature in the reactor. In this paper, the ex-core neutron noise signals of two PWR units throughout the multiple fuel cycles were analyzed and the vibration frequency of the CSB beam mode was found, for the first time, to drop with time during the operation of PWRs. Then, the statics analysis of the CSB was conducted to preliminarily identify the potential causes. For the further clarification of such vibration frequency drop phenomenon, a numerical assembly model of PWR reactor internals, including the CSB, hold-down ring (HDR), fuel assembly hold-down spring (FAHDS), etc., was proposed with consideration of the frictional contact and fluid-structure interaction for the modal analysis of the CSB. The results showed that the decrease of the FAHDS stiffness is the main cause for the drop of the vibration frequency of the CSB beam mode in real conditions.

Fully Coupled Analysis of Flutter Induced Limit Cycles: Frequency Versus Time Domain Methods

Abstract To save resources and reduce emissions, it is crucial to reduce weight of aircraft engines and further increase aerodynamic efficiency of gas and steam turbines. For turbine blades, these goals often lead to flutter. Thus, innovative flutter-tolerant designs are explored, where flutter induces limit cycle oscillations (LCOs) of tolerable yet nonzero levels. Flutter represents a self-excitation mechanism and, in the linear case, would lead to exponential divergence. Flutter-induced LCOs are therefore an inherently nonlinear phenomenon. The saturation of flutter-induced vibrations can be caused by nonlinear frictional contact interactions, e.g., in tip shroud interfaces. To develop flutter-tolerant designs, efficient methods are required which compute LCOs based on an appropriate modeling of elastic, inertia, aerodynamic, and contact forces. We recently developed a Frequency Domain Fluid-Structure Interaction (FD-FSI) solver for flutter-induced LCOs. The solver relies on the Harmonic Balance method applied to the structure as well as the fluid domain. It was shown that especially for long and slender blades with friction in shroud interfaces and strong aerodynamic influence, a coupled analysis can significantly increase the accuracy of predicted LCOs compared to the current state-of-the-art methods. Conventional methods do not properly account for the nonlinear change of frequency and deflection shape, and the effect of these changes on the aerodynamic damping, and thus fail in predicting certain LCOs at all. In the current work, the FD-FSI solver is numerically validated against Time Domain Fluid-Structure Interaction (TD-FSI) simulations. As a test case, a shrouded low-pressure turbine with friction in the shroud interfaces is considered. The point of operation is highly loaded and transonic in order to make the test case challenging. Apart from a successful validation of the FD-FSI solver, we shed light on important advantages and disadvantages of both solvers. Due to the lack of robust phase-lag boundary conditions for time domain solvers, a full blade row must be simulated. Thus, the FD-FSI solver typically requires only a fraction of the computational costs. Moreover, the FD-FSI solver contributes to an increased physical understanding of the coupled vibrations: By analyzing the contribution of individual harmonics, we analyze why unexpected even harmonics appear in a certain LCO. On the other hand, the FD-FSI solver does not provide information on the asymptotic stability of the LCOs and is strictly limited to periodic oscillations. Indeed, quasi-periodic limit torus oscillations (LTOs) appear in our test case. Using the TD-FSI solver, we confirm the internal combination resonance, postulated recently as necessary condition for LTOs, for the first time, in a fully coupled analysis.

A mixed stress-strain driven computational homogenization of spiral strands

Spiral strands subjected to tensile force and bending loading display a nonlinear dissipative behavior due to frictional interactions between their elementary wires. This study aims to provide an efficient method, based on a computational homogenization procedure, to accurately characterize the nonlinear response of such strands. By using 1D beam elements in both micro- and macro-scale, homogenization is performed along the axial direction of a representative volume element (RVE), leading to expressing a boundary value problem on RVE, driven in a mixed manner by either strains or resulting forces or moments. The boundary value problem on the RVE is solved using an in–house implicit finite element solver for finite strain, considering all frictional contact interactions. A method is proposed to predict the bending moment’s evolution for any curvature variation from the simulation results of only one bending loading test on the RVE. The nonlinear behavior of the strand in the micro-scale identified through this offline technique can then be used in the macro-model to simulate various bending loading tests under constant tensile load. Results obtained with the multiscale model are compared to those provided by direct numerical simulation to demonstrate the validity of the proposed approach.

Study on wear and contact behaviors in discrete elliptical contact areas of a cyclically bended regular lay wire rope

Interwire wear occurs in a regular lay wire rope that is wound repeatedly around a sheave, in particular for the discrete elliptical contact areas between the helical layers. In this study, an analysis method for the wear behavior in the said elliptical contact areas of a regular lay wire rope that is subjected to a cyclic bending load is proposed based on finite element method and Archard wear theory. The contact and slip parameters between the helical layers are solved first, and then the wear depth due to the frictional contact interaction is obtained with a Fortran program. The results show that both the interwire wear depth and contact pressure between the helical layers of the regular lay wire rope change at a large rate in the early stage, and tend to be stable as the wear process goes on. The increase of wear cycles leads to enlarged and deeper wear scars but decreased contact interactions at the elliptical contact regions. The wear and contact properties depend on the phase angle position of the contact interface, and the area at the phase angle of 45° is in the most danger of failures that are caused by severe wear and contact.

An approach to describe the shear-thickening viscosity of cement paste incorporating microfines of manufactured sand

This paper investigates the mechanisms affecting the viscosity in shear thickening regimes of cement pastes. Limestone, slate, and tuff microfines (≤125 μm) with different physical properties obtained in the processing of manufactured sand were employed as additional mineral materials to cement pastes prepared with variable dosages of polycarboxylate ether superplasticizer (PCE) and water-to-cement mass ratios (W/C) of 0.40 and 0.275. Test results show that the addition of microfines reduced the shear thickening properties of cement pastes at a fixed PCE dosage, mainly due to a smaller growth of particle inertial interactions from the pseudo-Newtonian plateau to a given shear rate. But the shear thickening reduction did not always cause a lower increase of the apparent viscosity, Δηthicγ̇, for paste mixtures made with 0.275 W/C, due to a greater enhancement of particle friction contacts. Meanwhile, the shear thickening performance at a given mini-slump flow increased by using the microfines, given the stronger particle friction contacts caused by the increased flow index of Herschel-Bulkley model. This corresponded to a greater Δηthicγ̇ of the pastes. A prediction model of Δηthicγ̇ was proposed based on the mechanisms of particle inertia forces and friction contacts. The model can efficiently characterize particle frictional contact interactions in shear thickening regimes by taking into consideration the flow index, particle packing density, and solid volume fraction, regardless of the W/C and the content and type of microfines.

Extraction of microstructural parameters from sculptured thin films nanoindentation

This work deals with the indentation analysis of nanocolumnar thin films and the difficulties encountered to deduce relevant mechanical parameters by this methodology. SiO 2 thin films prepared by physical vapour oblique angle deposition with different nanocolumnar microstructures have been subjected to indentation analysis. Despite the fact that the films had been made of the same material, deposited on the same substrate and had similar thickness, their indentation responses were different and depended on their particular microstructure. It has been also reali s ed that the measured hardness and elastic modulus variation with the indentation depth were length scale dependent and that there is not a unique analytical thin-film nanoindentation model to extract the mechanical properties from the experimental nanoindentation curves. To overcome these limitations a numerical finite element model (FEM) of the nanocolumnar coatings has been built to figure out the contributions of the different physical phenomena intervening in the indentation process. This FEM simulation relies on a description of the elasto-plastic microstructural units of the coatings and the contact friction interactions between them. Based on this simulation a parametrical representation, incorporating two length scales and the contributions of densification and/or the buckling of nanocolumnar units, has been developed to account for the evolution of the apparent elastic modulus deduced from numerical indentation tests . A Hall-Petch modification of this description considering two length scales instead of the common approximation considering a single length scale has rendered the best agreement with the elastic values determined experimentally. Although, at the present stage, the particular microstructure of the films can not be deduced from the evolution of their elastic moduli with the indentation depth, the obtained results and their interpretation constitute a first though essential step for the elaboration of an inverse analysis methodology capable of correlating microstructure and elastic response of nanocolumnar coatings. • The indentation response of multi-layered PVOAD columnar coatings greatly depends on their microstructure. • Buckling but also densification drive the evolution of indentation elastic modulus and hardness with indentation depth. • FEM of a columnar structure under indentation allow s to reproduce the experimental response of multi-layered PVOAD coatings. • Size dependent model allows to extract length scale parameters from elastic response of PVOAD coatings.

Analysis of Friction-Saturated Flutter Vibrations With a Fully Coupled Frequency Domain Method

Abstract Flutter stability is a dominant design constraint of modern turbines. Thus, flutter-tolerant designs are currently explored, where the resulting vibrations remain within acceptable bounds. In particular, friction damping has the potential to yield limit cycle oscillations (LCOs) in the presence of a flutter instability. To predict such LCOs, it is the current practice to model the aerodynamic forces in terms of aerodynamic influence coefficients for a linearized structural model with fixed oscillation frequency. This approach neglects that both the nonlinear contact interactions and the aerodynamic stiffness cause a change in the deflection shape and the frequency of the LCO. This, in turn, may have a substantial effect on the aerodynamic damping. The goal of this paper is to assess the importance of these neglected interactions. To this end, a state-of-the-art aero-elastic model of a low pressure turbine blade row is considered, undergoing nonlinear frictional contact interactions in the tip shroud interfaces. The LCOs are computed with a fully coupled harmonic balance method, which iteratively computes the Fourier coefficients of structural deformation and conservative flow variables, as well as the a priori unknown frequency. The coupled algorithm was found to provide excellent computational robustness and efficiency. Moreover, a refinement of the conventional energy method is developed and assessed, which accounts for both the nonlinear contact boundary conditions and the linearized aerodynamic influence. It is found that the conventional energy method may not predict a limit cycle oscillation at all while the novel approach presented here can.

Explanation of the self-adaptive dynamics of a harmonically forced beam with a sliding mass

The self-adaptive behavior of a clamped–clamped beam with an attached slider has been experimentally demonstrated by several research groups. In a wide range of excitation frequencies, the system shows its signature move: The slider first slowly moves away from the beam’s center, at a certain point the vibrations jump to a high level, then the slider slowly moves back toward the center and stops at some point, while the system further increases its high vibration level. In our previous work, we explained the unexpected movement of the slider away from the beam’s vibration antinode at the center by the unilateral and frictional contact interactions permitted via a small clearance between slider and beam. However, this model did not predict the signature move correctly. In simulations, the vibration level did not increase significantly and the slider did not turn around. In the present work, we explain, for the first time, the complete signature move. We show that the timescales of vibration and slider movement along the beam are well separated, such that the adaptive system closely follows the periodic vibration response obtained for axially fixed slider. We demonstrate that the beam’s geometric stiffening nonlinearity, which we neglected in our previous work, is of utmost importance for the vibration levels encountered in the experiments. This stiffening nonlinearity leads to coexisting periodic vibration responses and to a turning point bifurcation with respect to the slider position. We associate the experimentally observed jump phenomenon to this turning point and explain why the slider moves back toward the center and stops at some point.

Modeling frictional dynamics of a visco-elastic pillar rubbed on a smooth surface

Abstract This study proposes an approximate analytical model on frictional dynamics of a single visco-elastic pillar used for texturing soft surfaces. The frictional dynamics and contact interaction of the pillar with the smooth flat counter surface is modeled with lumped parameters in order to estimate the friction force and the normal load. The effect of aspect ratio of the pillar, preload and sliding velocity are obtained numerically and the analytical model is validated experimentally. The relative error of the proposed model on the calculation of friction force is around 5% while preload applied is in the neighborhood of Euler buckling limit for aspect ratio of 4, and increases to 30% at lower preload values for aspect ratio of 2.

Time finite element based Moreau‐type integrators

SummaryWith the postulation of the principle of virtual action, we propose, in this paper, a variational framework for describing the dynamics of finite dimensional mechanical systems, which contain frictional contact interactions. Together with the contact and impact laws formulated as normal cone inclusions, the principle of virtual action directly leads to the measure differential inclusions commonly used in the dynamics of nonsmooth mechanical systems. The discretization of the principle of virtual action in its strong and weak variational form by local finite elements in time provides a structured way to derive various time‐stepping schemes. The constitutive laws for the impulsive and nonimpulsive contact forces, ie, the contact and impact laws, are treated on velocity‐level by using a discrete contact law for the percussion increments in the sense of Moreau. Using linear shape functions and different quadrature rules, we obtain three different stepping schemes. Besides the well‐established Moreau time‐stepping scheme, we can present two alternative integrators referred to as symmetric and variational Moreau‐type stepping schemes. A suitable benchmark example shows the superiority of the newly proposed integrators in terms of energy conservation properties, accuracy, and convergence.

Mixed mode fracture analysis of multiple cracks in flat and curved stiffened panels of aircraft fuselage structures

In real time, aircraft panels are mainly subjected to fatigue loading induced by the pressurization cycle. When two cracks approach one another, their stress fields influence each other and produce enhancing or shielding effect depending on the position of the cracks. In the present work, an attempt has been made to determine the effect of plate curvature on mixed mode stress intensity factor (SIF) of multiple cracks in a riveted joint using numerical and experimental methods. Diametrically opposite surface cracks of various crack depth ratios [(a / t); ‘a’ crack length and ‘t’ thickness of the plate] were considered for a typical longitudinal splice joint. ‘Frictional contact interaction’ was defined between rivet hole, rivet head-sheet, between sheet surfaces and stringer to sheet interfaces in order to simulate the service conditions. At lower crack depths, [\(({a}/{t}) =2\)] higher SIF was observed for biaxial loading compared to uniaxial loading. Marginal influence of loading condition was observed for deep cracks [\(({a}/{t})=5\)]. SIF values of curved panels were observed to be higher than that of flat panel irrespective of the crack depths considered the present work. This is mainly due to ‘flattening’ of curved plate when loading. It was also noticed that, the presence of stiffener reduces the in plane (mode-II) and out of plane (mode-III) shear fracture considerably for curved panel as it exerts compressive force on the joint. To validate the numerical observations, experiments were conducted on a Al 2024-T3 specimens to determine the fatigue crack growth rate and it showed a good correlation with numerical methods. The experimental results also indicated a higher crack growth rate for curved panel compared to flat panel which is mainly due to additional bending stress at the rivet hole region caused by eccentric loading.

Toward understanding the self-adaptive dynamics of a harmonically forced beam with a sliding mass

A mechanical system consisting of an elastic beam under harmonic excitation and an attached sliding body is investigated. Recent experimental observations suggest that the system passively (self-)adapts the axial location of the slider to achieve and maintain a condition of self-resonance, which could be useful in applications such as energy harvesting. The purpose of this work is to provide a theoretical explanation of this phenomenon based on an appropriate model. A key feature of the proposed model is a small clearance between the slider and the beam. This clearance gives rise to backlash and frictional contact interactions, both of which are found to be essential for the self-adaptive behavior. Contact is modeled in terms of the Coulomb and Signorini laws, together with the Newton impact law. The set-valued character of the contact laws is accounted for in a measure differential inclusion formulation. Numerical integration is carried out using Moreau's time-stepping scheme. The proposed model reproduces qualitatively most experimental observations. However, although the system showed a distinct self-adaptive character, the behavior was found to be non-resonant for the considered set of parameters. Beside estimating the relationship between resonance frequency and slider location, the model permits predicting the operating limits with regard to excitation level and frequency. Finally, some specific dynamical phenomena such as hysteresis effects and transient resonance captures underline the rich dynamical behavior of the system.

On the numerical simulation of sheet metal blanking process

The use of the blanking process has been widely spread in mass production industries. In this technique, the quality of the final product is directly related to the setting parameters of the process and the material response of the sheet. In the present work, a general framework based on the finite element method for the simulation of the sheet metal blanking process is presented. The proposed approach properly addresses all the numerical challenges related to blanking. First, an extension of elasto-viscoplastic constitutive equations for the large strain regime is used to take into account the material strain-rate sensitivity. Then, the inertial effects coming from high velocity operations are considered by means of an implicit time integration scheme. Moreover, the frictional contact interactions are simulated with the classical Coulomb law and an energetically consistent formulation of area regularization. Finally, ductile fracture is modeled thanks to the element deletion method coupled with a fracture criterion. The blanking process is then simulated for different setting parameters. The accuracy of this approach is evaluated by comparing the numerical predictions to experimental results for both quasi-static and dynamic conditions. Good agreement is found between experimental and numerical results for all cases.

3D BEM for orthotropic frictional contact of piezoelectric bodies

A numerical methodology to model the three-dimensional frictional contact interaction of piezoelectric materials in presence of electric fields is presented in this work. The boundary element method (BEM) is used in order to compute the electro-elastic influence coefficients. The proposed BEM formulation employs an explicit approach for the evaluation of the corresponding fundamental solutions, which are valid for general anisotropic behaviour meanwhile mathematical degeneracies in the context of the Stroh formalism are allowed. The contact methodology is based on an augmented Lagrangian formulation and uses an iterative Uzawa scheme of resolution. An orthotropic frictional law is implemented in this work so anisotropy is present both in the bulk and in the surface. The methodology is validated by comparison with benchmark analytical solutions. Some additional examples are presented and discussed in detail, revealing the importance of considering orthotropic frictional contact conditions in the electro-elastic analysis of this kind of problems.

Finite element simulation of the mechanical behavior of synthetic braided ropes and validation on a tensile test

A finite element approach to the mechanical behavior of braided ropes at the scale of their internal components is proposed in this paper. The ropes considered are composed of a few tens of textile yarns, twisted into strands, which are then braided together. The approach aims at determining the mechanical equilibrium of such structures, viewed as assemblies of yarns undergoing large displacements and developing contact–friction interactions. To solve this equilibrium within a quasi-static framework, and using an implicit solution scheme, each yarn of the rope is represented by a finite strain beam model, and special emphasis is put on the detection and modeling of contact–friction interactions between yarns. The approach is used first to determine the unknown initial configuration of the rope, starting from an arbitrary configuration and using contact interactions together with information from the selected braid pattern, to determine the braided structure as the solution of a mechanical equilibrium. Comparisons are made with experimental data on this initial geometry. Tensile test experiments were performed to characterize the mechanical response of both the elementary yarns and the braided rope. These tests were simulated with the model, and results are compared with experiment. Sensitivity analyses on design parameters showing the abilities of the model are reported.

On the transverse compression response of Kevlar KM2 using fiber-level finite element model

Flexible textile composites like woven Kevlar fabrics are widely used in high velocity impact (HVI) applications. Upon HVI they are subjected to both longitudinal tensile and transverse compressive loads. To understand the role of transverse properties, the single fiber and tow transverse compression response (SFTCR and TTCR) of Kevlar KM2 fibers are numerically analyzed using plane strain finite element (FE) models. A finite strain formulation with a minimum number of 84 finite elements is determined to be required for the fiber cross section to capture the finite strain SFTCR through a mesh convergence study. Comparison of converged numerical solution to the experimental results indicates the dominant role of geometric stiffening at finite strains due to growth in contact width. The TTCR is studied using a fiber length scale FE model of a single tow comprised of 400 fibers transversely loaded between rigid platens. This study along with micrographs of yarn after mechanical compaction illustrates fiber spreading and fiber–fiber contact friction interactions are important deformation mechanisms at finite strains. The TTCR is also studied using homogenized yarn level models with properties from the literature. Comparison of TTCR between fiber length scale and homogenized yarn length scale models indicate the need for a nonlinear material model for homogenized approaches to accurately predict the transverse compression response of the fabrics.

Comparative study of time and frequency domain BEM approaches in frictional contact problem for antiplane crack under harmonic loading

Abstract Two different boundary element methods (BEM) for crack analysis in two dimensional (2-D) antiplane, homogeneous, isotropic and linear elastic solids by considering frictional contact of the crack edges are presented. Hypersingular boundary integral equations (BIE) in time-domain (TD) and frequency domain (FD), with corresponding elastodynamic fundamental solutions are applied for this purpose. For evaluation of the hypersingular integrals involved in BIEs a special regularization process that converts the hypersingular integrals to regular integrals is applied. Simple regular formulas for their calculation are presented. For the problems solution while considering frictional contact of the crack edges a special iterative algorithm of Udzava's type is elaborated and used. Numerical results for crack opening, frictional contact forces and dynamic stress intensity factors (SIFs) are presented and discussed for a finite III-mode crack in an infinite domain subjected to a harmonic crack-face loading and considering crack edges frictional contact interaction using the TD and FD approaches.

The Combined Slip and Finite Sliding Models in a Frictional Contact Interaction of Two Spherical Particles

A simplified analytical modelling of tangential contact interaction of two elastic spheres was presented accounting for the kinematically induced sphere trajectory or a load controlled sliding process. The evolution of driving force in combined slip and finite sliding interaction was considered for both monotonic and reciprocal sliding motion. The analytical formulae and diagrams for the evolution of driving force along the sliding path in terms of the main contact geometry parameters were specified. The sliding trajectories and contact tractions were also determined. The analytical formulae were briefly presented for prediction of the tangential restitution coefficient and time of contact. The results presented can be applied in the experimental testing of frictional response of contacting bodies, wear studies of rough surfaces or in the contact interaction analysis of granular material during flow. The results can also be relevant for development of the discrete element method widely applied in simulation of granular material flow, where the sliding regime conditions prevail in intergranular contact interactions.

Transverse compression behavior of textile rovings: finite element simulation and experimental study

Results from finite element simulation of the transverse compression of Polyamide 6.6 rovings made of 40 filaments are compared in this paper against experimental data. The finite element simulation, using a finite strain beam model to represent each filament of the roving, focuses on the modeling of contact–friction interactions between filaments. Experimental tests, consisting in crushing rovings between two rigid planes, varying the twist and the tensile force, are reproduced by simulation. Experimental and simulation results are compared with a good agreement. The simulation studies the influence of the roving twist, the applied tensile force, and the friction coefficient on the transverse compression behavior. The occurrence of plateaus in the transverse compression curve is highlighted and discussed.