Friction Boundary Conditions Research Articles

Understanding tool–workpiece interfacial friction in friction stir welding/processing and its effect on weld formation

ABSTRACT Friction Stir Welding and Processing (FSW/P) is a solid-state joining and/or processing technique largely used for aluminium and its alloys. Although the process matured over a period, there is ambiguity over quantification of frictional values at tool–workpiece interface. Such data are crucial in Finite Element (FE) modelling of the process and understanding the frictional boundary condition plays a crucial role in its development. The paper discusses quantification of frictional boundary condition and its impact on weld formation. The evaluation suggested the necessity of stick conditions for weld consolidation and its mandatory occurrence during the process. Simulations performed with m = 1 yielded temperature results closer to experiments and facilitated in closure of void.

Unsteady non-Newtonian fluid flow with heat transfer and Tresca\u2019s friction boundary conditions

We consider an unsteady non-isothermal flow problem for a general class of non-Newtonian fluids. More precisely the stress tensor follows a power law of parameter p, namely sigma = 2 mu ( theta , upsilon , | D(upsilon ) |) |D( upsilon ) |^{p-2} D(upsilon ) - pi mathrm{Id} where θ is the temperature, π is the pressure, υ is the velocity, and D(upsilon ) is the strain rate tensor of the fluid. The problem is then described by a non-stationary p-Laplacian Stokes system coupled to an L^{1}-parabolic equation describing thermal effects in the fluid. We also assume that the velocity field satisfies non-standard threshold slip-adhesion boundary conditions reminiscent of Tresca’s friction law for solids. First, we consider an approximate problem (P_{delta }), where the L^{1} coupling term in the heat equation is replaced by a bounded one depending on a small parameter 0 < delta ll 1, and we establish the existence of a solution to (P_{delta }) by using a fixed point technique. Then we prove the convergence of the approximate solutions to a solution to our original fluid flow/heat transfer problem as δ tends to zero.

Testing of logarithmic-law for the slip with friction boundary condition

Abstract Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ $\bar{u}$ of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary layer theories to improve numerical boundary conditions for flow averages.

An improved multi-phase weakly-compressible SPH model for modeling various landslides

A novel weakly compressible multi-phase SPH method is developed for modeling various landslides. In this model, the multi-phase system of fluid and granular materials is regarded as a continuum with multi-viscosity and multi-density. The mechanical behavior of the granular materials is described by the μ(I) rheological model and the dynamic effective pressure. An incremental diffusive term is developed to eliminate the non-physical fluctuation in the pressure field of multi-phase flow. A dynamic calculation method of effective pressure is introduced to overcome the additional calculation and error caused by the traditional method in searching for the phase interface. A friction boundary condition called the momentum method is introduced to consider the influence of basal friction on the evolution of granular landslides. The Particle Shifting Technique (PST) of the single-phase WCSPH is introduced into the multi-phase WCSPH by the two-step shifting procedure to ensure the uniform distribution of particles in each phase and phase interface during the simulation process. The effectiveness of the incremental diffusive term is first validated using a benchmark case of the two phases hydrostatic stratified column. Then the model is applied to the numerical simulation of dry granular landslide, sub-aerial granular landslide, submerged granular landslide, and rigid landslide. The calculated results are compared with experimental results and previous numerical models to verify and evaluate the performance of the current model. Proven that this model is well consistent with experimental results and has higher accuracy than previous numerical models.

Seismic response investigation of 1/20 scale container crane through shake table test and finite element analysis

This paper summarizes all detailed results obtained from a series of shake table testings of a 1/20 scale container crane with friction and pin boundary conditions at the Seismic Research and Test Center in South Korea and compared them with those from its finite element analysis (FEA). The tested 1/20 scale container crane was initially designed based on the similitude laws with scaling factors proportional to the sectional properties and dynamic characteristics of a commonly used full-scale crane. To determine experimental natural frequencies of the tested crane, a white noise test was conducted on the shake table. Then, three different ground motions, including Manjil Iran Abbar, Nahanni Canada, and Mineral Virginia, were individually applied in a trolley-boom direction to the crane placed on the shake table to secure its seismic responses, especially for derailment, uplift and drift. A finite element model of the tested crane was also created using multi-frame elements available in commercially used FEA software and simulated to replicate the testing results. Key findings revealed that the effect of the boundary conditions did not significantly affect the mode shapes and frequencies of the tested crane, but the drifts of the crane with the friction boundary condition resulting from each of the ground motions changed substantially as compared to those from the crane with the pin boundary condition. The derailment displacement at the landside legs of the tested crane was also found to be 12.5 mm for the Manjil Iran and Nahanni Canada earthquakes and 11.5 mm for the Mineral Virginia earthquake. The results from the testing were, largely, in good agreement with those from the FEA.

Tribotechnical Properties of a Copper-Based Powdered Friction Material with Addition of Titanium Powder

The paper presents the results of a study on how the addition of titanium powder affects the tribotechnical properties of a copper-based powdered friction material when operating under friction boundary conditions. It is shown that the introduction of 5–25 vol % titanium powder increases the friction coefficient from 0.054 to 0.096. This is due to the formation of a layer of carbide, carbon nitride, and titanium nitride on the surface of a titanium particle during sintering of the friction material, as well as an intermetallic compound of the titanium-copper system up to 6 μm thick with a microhardness of 4000–3000 MPa. The data obtained made it possible to develop a friction material that increases the service life of oil-cooled brakes.

Numerical simulation of pile installations in a hypoplastic framework using an SPH based method

This paper presents a tool to estimate the stresses, and thus the expected forces, at a retaining wall by the installation of piles. The solution method is based on Smoothed Particle Hydrodynamics (SPH) and the soil is modeled using a simplified hypoplastic material law. In order to correctly compute the forces on the soil due to the contact between the pile and the soil, a formulation for imposing frictional boundary conditions using SPH is developed. Modeling the soil with the chosen hypoplastic approach also allows for tensile forces in the soil. However, these are not physical. Therefore, an alternative formulation is presented which directly eliminates unphysical tensile stresses in the cohesionless soil without any additional numerical parameters. The numerical code is firstly validated against benchmark problems. Then several test cases are simulated including monotonic and cyclic penetration of piles into the soil. A good agreement with the experimental observation is found. Additionally, the impact of pile driving in the presence of sheetpiles (retainers) is investigated to see how the pile driving can alter the applied forces on the sheet piles. The simulation of such complex geotechnical problems that involve large deformation, material nonlinearity, and moving boundary conditions demonstrates the applicability and versatility of the proposed numerical tool in this field.

Modelling of Stoneley wave transference at the frictional interface between ice and rock medium

The present article attempts to study the propagation of surface seismic waves (Stoneley waves) in the layered structure composed of rock and ice medium. The interface between the two media (ice and rock) is considered to be frictional. Mathematical model of the present problem is formulated by adapting the Coulomb frictional boundary conditions. The frequency relation is obtained in the determinant form. The non-dispersive nature of the Stoneley wave is observed through the frequency relation. The non-dimensional phase velocity and damping parameter curves have been plotted against the non-dimensional angular frequency. Effect of different parameters (viscoelastic coefficient of the rock medium, frictional interface parameter, anisotropy parameter and initial stress of both the media) on the phase velocity and damping has been distinctly marked and shown graphically.

Exploring the impact of atmospheric forcing and basal drag on the Antarctic Ice Sheet under Last Glacial Maximum conditions

Abstract. Little is known about the distribution of ice in the Antarctic Ice Sheet (AIS) during the Last Glacial Maximum (LGM). Whereas marine and terrestrial geological data indicate that the grounded ice advanced to a position close to the continental-shelf break, the total ice volume is unclear. Glacial boundary conditions are potentially important sources of uncertainty, in particular basal friction and climatic boundary conditions. Basal friction exerts a strong control on the large-scale dynamics of the ice sheet and thus affects its size and is not well constrained. Glacial climatic boundary conditions determine the net accumulation and ice temperature and are also poorly known. Here we explore the effect of the uncertainty in both features on the total simulated ice storage of the AIS at the LGM. For this purpose we use a hybrid ice sheet shelf model that is forced with different basal drag choices and glacial background climatic conditions obtained from the LGM ensemble climate simulations of the third phase of the Paleoclimate Modelling Intercomparison Project (PMIP3). Overall, we find that the spread in the simulated ice volume for the tested basal drag parameterizations is about the same range as for the different general circulation model (GCM) forcings (4 to 6 m sea level equivalent). For a wide range of plausible basal friction configurations, the simulated ice dynamics vary widely but all simulations produce fully extended ice sheets towards the continental-shelf break. More dynamically active ice sheets correspond to lower ice volumes, while they remain consistent with the available constraints on ice extent. Thus, this work points to the possibility of an AIS with very active ice streams during the LGM. In addition, we find that the surface boundary temperature field plays a crucial role in determining the ice extent through its effect on viscosity. For ice sheets of a similar extent and comparable dynamics, we find that the precipitation field determines the total AIS volume. However, precipitation is highly uncertain. Climatic fields simulated by climate models show more precipitation in coastal regions than a spatially uniform anomaly, which can lead to larger ice volumes. Our results strongly support using these paleoclimatic fields to simulate and study the LGM and potentially other time periods like the last interglacial. However, their accuracy must be assessed as well, as differences between climate model forcing lead to a large spread in the simulated ice volume and extension.

Collisional SPH: A method to model frictional collisions with SPH

Accurate modeling of rebound kinematics in particle-substrate collisions is essential in a wide range of applications like milling and mixing. To accurately model these real-world collisions the forces arising due to elastoplastic deformation and friction need to be modelled accurately. In this study the use of frictional boundary conditions in modeling elastic collisions with Smooth Particle Hydrodynamics (SPH) is explored. The collision dynamics for an oblique impact of a 3D spherical granule on an elastic substrate is assessed for SPH (a) without any special treatment for friction and (b) using Coulomb's friction model, and it is identified that these approaches are inaccurate in some instances. To resolve this, spring-based contact models are incorporated in SPH to develop a new method for improved contact modeling. We call this method Collisional SPH. This Collisional SPH method predicts both rebound kinematics and surface deformation accurately. This method opens new avenues for further development in modeling collisional deformations and collision dynamics in granular systems using SPH.

A study of shear friction factor in friction stir welding for developing a finite element model and its importance in the context of formation of defect free and defective weld

Friction Stir Welding (FSW) and Friction Stir Processing (FSP) are novel technologies where FSW is used to join materials in solid state and FSP is used to eliminate defects and refine the micro-structure of a cast material. Though it has been successfully demonstrated for few commercial alloys, technique lacks an efficient and effective method to track optimized process parameters required to obtain good weld. Finite element (FE) modeling seems to be a promising approach for the same. The paper emphasizes on quantification of friction boundary condition and its impact on formation of welds. It is found that stick condition between tool and work-piece is essential to obtain consolidated welds. Further, FE simulations for temperature predictions were validated with experimental results with shear friction factor of one. The importance of interfacial stick was corroborated with plasticine experiments.

Micropolar fluid flow in a thick domain with multiscale oscillating roughness and friction boundary conditions

We consider an unsteady micropolar fluid flow in a two-dimensional domain Ωε. The velocity field is assumed to satisfy a fluid-solid friction interface condition on a part of the boundary while the micro-rotation field satisfies non-homogeneous Dirichlet boundary conditions. The problem is thus described by a non-linear coupled variational parabolic system for the fluid velocity vϵ, the pressure pϵ and the angular micro-rotation field Zϵ. The thickness and the roughness of the fluid domain are described by multiple separated scales of periodic oscillations, i.e. Ωε={(z1,z2):0<z1<L,0<z2<εmhε(z1)} with hε(z1)=h(z1,z1ε,z1ε2,⋯,z1εm), 0<ε<<1, and m≥2. Existence, uniqueness and uniform estimates of the solution (vϵ,pϵ,Zϵ) are stated. Then we study the asymptotic behaviour of the flow as ε tends to zero by using the multiple scale convergence method for reiterated homogenization. The assumption m≥2 raises several technical difficulties in the limit process and leads to non-standard divergence free conditions for the limit velocity. We derive the limit problem which is totally decoupled for the limit velocity and pressure (v0,p0) on the one hand and the limit micro-rotation field Z0 on the other hand. More precisely (v0,p0) is solution of a variational elliptic inequality and Z0 solves an elliptic partial differential equation, where the time variable appears as a parameter. Moreover we prove that v0,p0 and Z0 are uniquely determined by auxiliary well-posed problems.

Simulation system for collisions and two-way coupling of non-Newtonian fluids and solids

To solve the problem of unreasonable boundary conditions of the existing smoothed particle hydrodynamics (SPH) non-Newtonian fluid simulation, a simulation system for collisions and two-way coupling of non-Newtonian fluids and solids is proposed to alleviate the loss of physical properties of simulated non-Newtonian fluid. In this paper, solids are sampled as single-layer boundary particles, and the corresponding density calculation formula is given. Fluid particles are interacting directly with the boundary particles under our interaction force calculation formula. The velocity of fluid particles near the boundary is iteratively updated using Coulomb friction boundary conditions. This method can be integrated into the existing SPH non-Newtonian fluid simulation system. Experiments show that the friction coefficient of the fluid–solid boundary can be adjusted according to the user’s experimental needs. Compared to simulation under free-slip boundary conditions, in our method non-Newtonian fluids can exhibit more diverse physical characteristics and have a good sense of reality effect.

STUDY OF THE EFFECT OF FRICTION ON THE POWER PARAMETERS OF ROLLING WITH ONE DRIVE ROLL

The influence of friction conditions in the deformation cell is studied, taking into account the differences of the distribution of contact stresses on the drive and non-drive rolls, on the normal pressure and rolling force. The research methodology involved the development of a mathematical model of the process and conducting a numerical experiment. The rolling process model is based on the numerical solution of the Karman`s equation using the Coulomb friction law and boundary conditions appropriate of the rolling process with a single drive roll. When conducting a numerical experiment, the coefficient of friction in the deformation cell was changed at four levels in the range from 0.15 to 0.30. The coefficient of friction in the journal bearings non-drive rolls was varied at three levels. From the analysis of the obtained distributions of contact stresses along the length of the deformation cell by the drive and non-drive rolls, it was found that with decreasing the coefficient of friction in the deformation cell, the normal pressure decreases proportionally, as well as the difference between the pressure on the drive and non-drive rolls. The occurrence of longitudinal tensile stresses with a coefficient of friction in the deformation cell of 0.25 and more is noted. The coefficient of friction in the non-drive roller bearings, for the entire range of values taken, does not have a significant effect on the contact stresses, pressure and rolling power. The presence of tensile stresses when rolling with one drive roll leads to a decrease in the average pressure and rolling power within 8-10%. Therefore, rolling with one drive roller can be used to reduce energy costs. In addition, the presence of tensile stresses, at certain values of the coefficient of friction in the deformation cell, accordingly affects the mechanical and technological properties of the rolled products, but this feature of the process requires additional study.

Topology optimization of tribological composites for multifunctional performance at sliding interfaces

This paper presents the first application of topology optimization to designing multifunctional tribological composites. In particular, composites are designed to minimize temperature rise caused by frictional heating associated with wear at sliding interfaces. Wear and frictional heating both have significant influence on the performance of tribological composite systems. A steady-state heat transfer model is used to obtain the thermal field within the sliding body, including a frictional heat flux boundary condition determined by the steady-state wear response of the bi-material composite sliding interface. The material thermal conductivity and frictional heat generated within each material are interpolated using the Solid Isotropic Material with Penalization optimization method. The optimization problem is solved using a gradient-based optimizer, the Method of Moving Asymptotes, with sensitivities obtained by the adjoint method. Two case studies are presented to demonstrate the effectiveness and utility of the established optimization framework. It is found that the average and maximum temperature rises are reduced by 40–60% compared to reference structures with the same material volume fractions.

New approach to the generation of orthogonal body-fitted meshes and its application to non-steady plane-strain ideal plastic flow

For rigid-perfect plastic solids, ideal plastic flow happens when all material elements follow minimum work paths and the two principal stretch lines are materially embedded. To describe its kinematics effectively, Lagrange convective orthogonal curvilinear system has to be constructed. Therefore, a numerical procedure for generating orthogonal body-fitted meshes has been developed and applied to non-steady plane-strain ideal plastic flow. The mapping between the Cartesian system and the orthogonal system is based on Laplace equations and Cauchy–Riemann condition. The numerical procedure takes into consideration of all the prescribed boundary curves instead of one as the boundary conditions, which has been adopted in earlier studies when using conventional characteristic line method. After each iteration step, the obtained boundary points are adjusted towards the orthogonality conditions until error tolerance requirement is met. For demonstration purpose, the numerical procedure is applied to the optimization of a bulk part under forging. The obtained orthogonal body-fitted meshes are in good agreement with previous methods. Then the optimal initial scale factor is also calculated based on this method and compared with earlier studies. Finally, the evolution of the intermediate shapes and frictional external boundary conditions is also calculated when there are no elastic dead zones.

Zero-Viscosity Limit of the Navier--Stokes Equations with the Navier Friction Boundary Condition

In this paper, we consider the zero-viscosity limit of the Navier-Stokes equations in a half space with the Navier friction boundary condition $$ (\beta u^{\varepsilon}-\varepsilon^{\gamma}\partial_y u^{\varepsilon})|_{y=0}=0, $$ where $\beta$ is a constant and $\gamma\in (0,1]$. In the case of $\gamma=1$, the convergence to the Euler equations and the Prandtl equation with the Robin boundary condition is justified for the analytic data. In the case of $\gamma\in (0,1)$, the convergence to the Euler equations and the linearized Prandtl equation is justified for the data in the Gevrey class $\frac 1 {\gamma}$.

Effect of frictional boundary conditions and percentage area reduction on the extrusion pressure of Aluminum AA6063 alloy using FE analysis modelling

© 2020 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

A new class of variational‐hemivariational inequalities for steady Oseen flow with unilateral and frictional type boundary conditions

AbstractWe study a new class of elliptic variational‐hemivariational inequalities in a reflexive Banach space. Based on a surjectivity result for an operator inclusion of Clarke's subdifferential type, we prove existence of solution. Then, we apply this result to a mathematical analysis of the steady Oseen model for a generalized Newtonian incompressible fluid. A variational‐hemivariational inequality for the flow problem is derived and sufficient conditions for existence of weak solutions are obtained. The mixed boundary conditions involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier‐Fujita slip condition, and the threshold slip and leak condition of frictional type.

A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids

In this paper we are concerned with a non-steady system for motion of incompressible viscous Newtonian heat-conducting fluids under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions based on total stress, velocity, total pressure, rotation, total stress together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity and shape of boundary surface, we get variational formulation. The formulation consists of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. We first study existence, estimation and relative compactness of solutions to an approximate equation. By passing to limits as the parameter for approximation goes to zero, we get existence of a solution with “defect measure” for temperature.