Global Friction Coefficient Research Articles

Explicit frictional stick–slip dynamics of elastic contact problem incorporating the LuGre model

Dynamical contact problem with friction is of continuous concern and have been investigated over the years. The effective and accurate description of the development of the friction force is the key to this problem. However, the stick–slip phenomenon, as typical dynamical behaviour, has rarely been considered when developing contact algorithms for frictional contact problems of elastic bodies. The conventionally used Coulomb’s model, with differentiating the static and kinetic coefficient of friction, can lead to inaccurate results due to errors generated when switch between the stick or slip states. In this work, a three-dimensional mortar-based frictional contact algorithm is proposed in an explicit scheme. The proposed algorithm incorporates the LuGre model to account for dynamical frictional behaviours such as stick–slip. The effectiveness and accuracy of the proposed algorithm are validated through several simplified two-dimensional cases. The sticking time ratio and the evolution of the global coefficient of friction with time of a three-dimensional contact problem with a randomly rough contact interface are investigated as an application.

Mechanical Behavior of Variable Nozzle Guide Vane Systems Based on Full-Scale Testing

Abstract A full-scale test bench for the analysis of frictional and modal behavior of nozzle guide vanes (NGV) is an advanced tool enabling high design accuracy for these components equipped with an increasing number of turbo-expanders. This subassembly is a key feature enabling operational flexibility for the expander. During the NGVs design, great attention must be paid to the natural frequencies of its kinematic chain, which are influenced by internal clearances and by friction. In this paper, the results of a testing campaign performed on an NGV assembly employing realistic blade geometry are presented together with details concerning the test bench commissioning and setup procedure. The testing campaign involves three different combinations of blade orientation and preload corresponding to typical design conditions of the expander. In addition, two bushing clearance values corresponding to different worn-out conditions were investigated. The measurements of the global friction coefficient based on actuator force detection are summarized. After that, the reconstruction of mode shapes based on experimental modal analysis is explained. The results highlight the importance of loading conditions on the actual value of friction force and their influence on blade natural frequencies. The testing campaign was used to properly validate finite element models to be used for further investigations.

An Isogeometric analysis based method for frictional elastic contact problems with randomly rough surfaces

The problem addressed in this paper concerns the frictional contact between an elastomer and a rigid body with randomly rough surfaces. The work is accomplished on the basis of two crucial elements: a framework for generating random geometries and a robust frictional contact algorithm, both of which are realised in the approach of Isogeometric analysis (IGA) for its high accuracy and robustness. For the former, a new Isogeometric framework for random geometry modelling is proposed, which combines the random field generation based on Karhunen–Loève expansion theory with Non-Uniform Rational B-Spline (NURBS) interpolation method. For the latter, a mortar-based frictional contact algorithm in 2D large deformation regime is adopted incorporating a modified closest point projection method for detection of contact. Numerical experiments are conducted with several settings such as ‘rough–smooth’, ‘smooth–rough’ and ‘rough–rough’ contact, depending on which side of the contact pair the randomly rough surface belongs to. The ratio of the global coefficient of friction to the prescribed local one and the ratio of true contact area to the nominal contact area are characterised under these settings, and factors like the root mean square roughness and correlation length of the random surface and the external traction are discovered to have a significant influence on the two ratios.

The ‘miniature silo’ test: A simple experimental setup to estimate the effective friction coefficient between the granular solid and a horizontally-corrugated cylindrical metal silo wall

Corrugated walls are widely employed in the construction of metal silos. Despite the long history of testing to establish bulk material parameters for silo design, there does not appear to be an established test procedure to directly determine the effective friction coefficient for a corrugated wall other than an adaptation of a classical direct shear test. EN 1991-4: 2006 prescribes a simple weighted average formula for this coefficient based on the internal friction angle of the granular solid and a ‘flat’ wall friction coefficient. This paper describes a set of miniature-scale silo tests performed at the University of Bologna intended to establish a simple but useful procedure to directly estimate an average global friction coefficient between the granular solid and a corrugated silo wall. These ‘miniature silo’ tests are simple enough to be performed in any civil engineering laboratory with standard equipment. • Particle-wall friction coefficient is fundamental for structural design of silos. • No tests are available to measure the effective friction for a corrugated wall. • A novel straightforward experimental test is proposed to fill this gap. • The miniature-silo test can be built using basic tools easy to be found in any lab. • The obtained results are in accordance with EN-1991-4 average formula predictions.

Stable channel flow with spanwise heterogeneous surface temperature

Recent studies have demonstrated that large secondary motions are excited by surface roughness with dominant spanwise length scales of the order of the flow's outer length scale. Inspired by this, we explore the effect of spanwise heterogeneous surface temperature in weakly to strongly stratified closed channel flow (at$Ri_\tau =120$, 960;$Re_\tau = 180$, 550) with direct numerical simulations. The configuration consists of equally sized strips of high and low temperature at the lower and upper boundaries, while an overall stable stratification is induced by imposing an average temperature difference between the top and bottom. We consider the influence of the width of the strips (${\rm \pi} /8 \leq \lambda /h \leq 4{\rm \pi} $), Reynolds number, stability and upper boundary condition on the mean flow structure, skin friction and heat transfer. Results indicate that secondary flows are excited, with alternating high- and low-momentum pathways and vortices, similar to the patterns induced by spanwise heterogeneous surface roughness. We find that the impact of the surface heterogeneity on the outer layer depends strongly on the spanwise heterogeneity length scale of the surface temperature. Comparison to stable channel flow with uniform temperature reveals that the heterogeneous surface temperature increases the global friction coefficient and reduces the global Nusselt number in most cases. However, for the high-Reynolds cases with$\lambda /h \geq {\rm \pi} /2$, we find a reduction of the friction coefficient. At stronger stability, the vertical extent of the vortices is reduced and the impact of the heterogeneous temperature on momentum and heat transfer is smaller.

A nonlinear FE model for wheel/rail curve squeal in the time-domain including acoustic predictions

Squeal noise of rail-bound vehicles frequently occurs in curves with a small radius and is a major nuisance for transport users and local residents. For the quantification of squeal intensity, a complete vibro-acoustic analysis is developed in this paper. This complete analysis requires time-domain analysis able to introduce non linearities leading to obtain dynamic saturation at the contact zone and a computation of sound radiation of the whole system. For time-domain analysis, a finite element (FE) formulation around the stationary position in an Eulerian reference frame is derived with a fine discretization of the contact surface combined with unilateral and Coulomb friction laws. Appropriate numerical techniques and reduction strategies are then used in order to solve the non linear discrete equations in dynamic self-sustained conditions. Both the transient approach and linear stability analysis are carried out. For sound radiation calculation, the contact forces calculated from wheel/rail contact model are then used for the calculation of squeal noise by using a coupled fluid-structure resolution based on boundary element method for the acoustic part and finite element method for the structural part. Results are first discussed in terms of unstable modes which are consistent between transient and stability analysis. Transient calculation shows that the apparent global friction coefficient during stick-slip cycles is slightly smaller than the constant local friction coefficient, and a dynamic saturation curve with hysteresis considerably different of the quasi-static curve. Finally the sound radiation calculation showed that the sound power radiated from the wheel is dominant with harmonics coming from the contact non linearities.

Finite Element Simulation and Experimental Analysis of Cutting Forces in Orthogonal Turning in AISI-1045 Steel

In this paper, a methodology to simulate the orthogonal metal turning and cutting forces using finite element method is presented. To validate the numerical results obtained from the model, experimental turning tests were performed on AISI-1045 steel, a dynamometer and an acquisition software were used to obtain experimental cutting forces. These forces were used to calculate the global friction coefficient, then, finite element method simulation of cutting metal process was done, using the Johnson-Cook material model and APDL code in a FEM software. Components of the cutting force were analyzed in the experiment tests and simulations for three carbide tools obtaining good correlation between them.

Trapped fluid in contact interface

We study the mechanical contact between a deformable body with a wavy surface and a rigid flat taking into account pressurized fluid trapped in the interface. A finite element model is formulated for a general problem of trapped fluid for frictionless and frictional contact. Using this model we investigate the evolution of the real contact area, maximal frictional traction and global coefficient of friction under increasing external pressure. Elastic and elasto-plastic material models, compressible and incompressible fluid models and different geometrical characteristics of the wavy surface are used. We show that in case of incompressible fluid, due to its pressurization, the real contact area and the global coefficient of friction decrease monotonically with the increasing external pressure. Eventually, the contact opens and the fluid occupies the entire interface resulting in vanishing of static friction. An asymptotic analytical result for the critical trap-opening pressure is found and shown to be independent of the surface slope if it is small. In case of compressible fluids with pressure-dependent bulk modulus we demonstrate a non-monotonous behaviour of the global coefficient of friction due to a competition between non-linear evolution of the contact area and of the fluid pressure. However, for realistic compressibility of solids and fluids, contact-opening cannot be reached at reasonable pressures. On the other hand, in case of elastic-perfectly plastic materials, we again observe fluid permeation into the contact interface. Finally, we study the distribution of frictional tractions during the depletion of the contact area under increasing external pressure. This process leads to emergence of singularity-like peaks in tangential tractions (bounded by the Coulomb’s limit) near the contact edges. We point out the similarity between the processes of trap opening and interfacial crack propagation, and estimate the complex stress intensity factor in the framework of linear elastic fracture mechanics.

A Comparison of Effective Tension Calculation for Design Belt Conveyor between CEMA and DIN Standard

In the present era, many industries are demanding material transfer equipment that works maximally and cheaply. Belt Conveyor is one of the most efficient material transfer equipment compared to heavy equipment or other transportation equipment, because it can transport the material in large capacity. When designing conveyor belts, many industries want large transport capacity at low cost. One of the cost savings can be done with low motor power consumption. Many standards describe the effective tension calculation on the conveyor belt in detail with the parameters, since the effective tension calculation results are essential for determining motor power. This paper aims to analyze the effective tension on conveyor belts using CEMA 5th, CEMA 6th and DIN 22101 standards with case studies of 1000 TPH carrying capacity and 3 m/s conveyor speed. The difference between CEMA and DIN when determining the effective tension is on the use of coefficient of friction, because DIN uses a global coefficient of friction while CEMA uses different friction coefficients on idler, belt and material. This difference in coefficient of friction results in different ways of calculating the resistance being the accumulation of the effective tension. The result is an effective tension value using DIN 22101 standard of 22,148.16 N with motor power consumption of 66.5 kW, while effective tension value using CEMA 5th standard is 32.201.66 N with motor power consumption 96.47 kW, and effective tension value using CEMA 6th standard is 29,686.48 N with 89.06 kW motor power consumption.

Dry friction aspects of Ni-based self-fluxing flame sprayed coatings

In this paper we present the results tribological obtained in the course of dry wear tests on samples coated with three types of coatings produced from self-fluxing Ni-based powders. In this purpose were used three commercial NiCrBSi powders produced by various manufacturers, which have been sprayed against a low alloyed steel substrate using the flame spray thermal deposition method followed by flame remelting, resulting three different samples, denoted as: A, M and P. The first test was conducted on an Amsler type machine, with rolling motion between tribological contacts of third class. The analysed coating was deposited on the generator of the low alloy steel disc and the shoe was realized from a grindstone. The test was conducted for two situations: (a) constant load of 10 kg and 6 kg applied for 5 hours; (b) progressive load starting from 2 to 10 kg for two different speeds of rotation of the disc. The second test was the one of sliding wear and it was conducted on the UMTR 2M-CTR tribometer. The analysed layers were deposited on the flat surface of a low alloy steel lamella, and the friction was achieved with a conical grinding stone. The working parameters were as follows: 20N constant load, constant speed of 10 mm / s, sliding linear length of 30mm, the test duration being 45 minutes. After conducting the tests and after analysing the results, the following conclusions are drawn: a) during the first test has been obtained a global friction coefficient between 0.3 and 0.4 - typical for dry friction, highlighting some lower values in the case of sample A, in which case there were recorded smaller mass losses; b) at the second test was recorded an approximately linear behaviour of the three samples, with a gradual increase of the friction coefficient and a superficial wear mark revealed both by SEM microscopy and by profilometry.

Skin Microstructure is a Key Contributor to Its Friction Behaviour

Due to its multifactorial nature, skin friction remains a multiphysics and multiscale phenomenon poorly understood despite its relevance for many biomedical and engineering applications (from superficial pressure ulcers, through shaving and cosmetics, to automotive safety and sports equipment). For example, it is unclear whether, and in which measure, the skin microscopic surface topography, internal microstructure and associated nonlinear mechanics can condition and modulate skin friction. This study addressed this question through the development of a parametric finite element contact homogenisation procedure which was used to study and quantify the effect of the skin microstructure on the macroscopic skin frictional response. An anatomically realistic two-dimensional image-based multilayer finite element model of human skin was used to simulate the sliding of rigid indenters of various sizes over the skin surface. A corresponding structurally idealised multilayer skin model was also built for comparison purposes. Microscopic friction specified at skin asperity or microrelief level was an input to the finite element computations. From the contact reaction force measured at the sliding indenter, a homogenised (or apparent) macroscopic friction was calculated. Results demonstrated that the naturally complex geometry of the skin microstructure and surface topography alone can play as significant role in modulating the deformation component of macroscopic friction and can significantly increase it. This effect is further amplified as the ground-state Young’s modulus of the stratum corneum is increased (for example, as a result of a dryer environment). In these conditions, the skin microstructure is a dominant factor in the deformation component of macroscopic friction, regardless of indenter size or specified local friction properties. When the skin is assumed to be an assembly of nominally flat layers, the resulting global coefficient of friction is reduced with respect to the local one. This seemingly counter-intuitive effect had already been demonstrated in a recent computational study found in the literature. Results also suggest that care should be taken when assigning a coefficient of friction in computer simulations, as it might not reflect the conditions of microscopic and macroscopic friction one intends to represent. The modelling methodology and simulation tools developed in this study go beyond what current analytical models of skin friction can offer: the ability to accommodate arbitrary kinematics (i.e. finite deformations), nonlinear constitutive properties and the complex geometry of the skin microstructural constituents. It was demonstrated how this approach offered a new level of mechanistic insight into plausible friction mechanisms associated with purely structural effects operating at the microscopic scale; the methodology should be viewed as complementary to physical experimental protocols characterising skin friction as it may facilitate the interpretation of observations and measurements and/or could also assist in the design of new experimental quantitative assays.

Analysis of adhered contacts and boundary conditions of the secondary shear zone

Prediction of the tribological parameters controlling the tool wear is one of the most complex research axes in the metal cutting literature. The nature of the friction on the tool–chip interface is the main process which influences the distribution of stresses and temperatures which in turn activates the thermomechanical process governing tool wear. Under extreme conditions of temperature, strain rates and pressure, occurring especially in high speed machining, the adhered contact phenomenon is highly localized especially near to the tool tip and extremely non-linear due to strong influence of the secondary shear zone (SSZ) and the nature of bonds between asperities of tool and chip. In addition, the analysis based on post-mortem examinations of chips and worn tools, especially in hard metal cutting alloy and high speed machining, show that the adhered friction with intimate contact and no relative motion of the material chip on the interface, are the principal cause of appearance of the plastic deformation layers (SSZ). This localized shear zone plays a role of intensive heat sources interacting with the tool side and, in turn, activates diffusive and abrasive wear. In this work, a hybrid model combining analytical and numerical approaches is performed in order to solve the non-linear thermomechanical problem on the chip and predicts the nature of friction contact, i.e. fully sliding, sticking/sliding or fully sticking contact, and these for a given distribution of asperities, characterizing the ratio between the real and apparent contact areas Ar/An on the interface, and a given global friction coefficient μ¯, characterizing the ratio of the experimental cutting forces. The shear stress generated in the primary shear band, the energy produced in the secondary shear zone, the local friction coefficient and the friction energy produced on the sliding part of contact, the proportion of the sticking/sliding interfaces, and geometrical parameters of the chip, are obtained by analytical means. The analysis of this model is based on experimental data and applied for a large cutting speed (1ms−1≤V≤60ms−1) and able to give some correlation about the distribution of adhesions marks on the contact with respect to the distribution of the tribological parameters at the interface. This model can be used in improving tool wear prediction and the estimation of tool-life.

Using FEM–DEM coupling method to study three-body friction behavior

Three-body friction is a system of complex dry particles whose behavior is difficult to predict during sliding contact. To account for the interaction of first-body deformation and third-body rheology in a three-body interface, a multi-scale method based on coupling the finite element method (FEM) and discrete element method (DEM) is used to model the shear process of two parallel plates with solid particles between them. The model has two subregions: the FEM region (upper plate) and the DEM region (third-body and lower plate). The upper plate compresses the third-body at a certain pressure, and the lower plate shears it at a constant velocity. A stress–strain transmission mechanism is established to achieve the interaction of both subregions. The results of the coupling method are energy dissipation, particle contact state and stress transmission between the first and third bodies. Particle velocity changes with the energy transmitted between particles under low pressure. The global friction coefficient increases because of strong collisions among particles under low pressure. During shear processes, particle contact distributions in the third-body are regular. The stress profiles in the FEM regions correspond to the force chain distributions in the DEM regions.

An Analytical Thermodynamic Approach to Friction of Rubber on Ice

ABSTRACT The presented investigation is motivated by the need for performance improvement in winter tires, based on the idea of innovative “functional” surfaces. Current tread design features focus on macroscopic length scales. The potential of microscopic surface effects for friction on wintery roads has not been considered extensively yet. We limit our considerations to length scales for which rubber is rough, in contrast to a perfectly smooth ice surface. Therefore we assume that the only source of frictional forces is the viscosity of a sheared intermediate thin liquid layer of melted ice. Rubber hysteresis and adhesion effects are considered to be negligible. The height of the liquid layer is driven by an equilibrium between the heat built up by viscous friction, energy consumption for phase transition between ice and water, and heat flow into the cold underlying ice. In addition, the microscopic “squeeze-out” phenomena of melted water resulting from rubber asperities are also taken into consideration. The size and microscopic real contact area of these asperities are derived from roughness parameters of the free rubber surface using Greenwood-Williamson contact theory and compared with the measured real contact area. The derived one-dimensional differential equation for the height of an averaged liquid layer is solved for stationary sliding by a piecewise analytical approximation. The frictional shear forces are deduced and integrated over the whole macroscopic contact area to result in a global coefficient of friction. The boundary condition at the leading edge of the contact area is prescribed by the height of a “quasi-liquid layer,” which already exists on the “free” ice surface. It turns out that this approach meets the measured coefficient of friction in the laboratory. More precisely, the calculated dependencies of the friction coefficient on ice temperature, sliding speed, and contact pressure are confirmed by measurements of a simple rubber block sample on artificial ice in the laboratory.

A slip-line plasticity analysis of sliding friction of rough surfaces exhibiting self-affine (fractal) behavior

A plasticity analysis of sliding friction of rough (fractal) surfaces sliding against smooth surfaces was developed based on a slip-line model of a rigid spherical asperity (wear particle) plowing and cutting through a soft semi-infinite medium. Solutions of the fraction of fully plastic asperity microcontacts responsible for the evolution of friction and energy dissipation were obtained in terms of the total normal load (global interference), interfacial adhesion characteristics, topography (fractal) parameters of the hard surface, and elastic–plastic material properties of the soft surface. This was accomplished by incorporating the slip-line model of a single microcontact into a friction analysis of sliding surfaces demonstrating multi-scale roughness. Numerical results provide insight into the effects of global interference (normal load), fractal parameters (surface roughness) of the hard surface, interfacial shear strength (adhesion), and material properties of the soft surface on plastic deformation at the microcontact level, global coefficient of friction, and frictional energy dissipated during sliding.

Finite Element Analysis on the Influence of Material Mechanical Properties in Local Contact Conditions

Previous results, obtained using the load-scanning technique, indicate that the amount of plastic deformation of the contact surface contributes to a change in the global friction coefficient. This technique allows describing the friction from a local analysis method, since the normal and tangential contact forces to the sliding direction can be measured simultaneously, independently and precisely. It also allows maintaining a constant contact surface geometry [1].

Numerical investigations in mixed friction systems

A numerical approach is here selected to investigate mixed friction phenomena where testing rigs cannot be used or need complex adaptations to deliver reliable measurements. The following work focuses on the numerical investigations of mixed friction systems combining fluidsolid and solid-solid interactions at the micro scale. Goal is to improve the accuracy of future macro models by applying them more precise boundary conditions derived from micro models. A three dimensional model is built in a Finite Elements (FE) software composed of one fluid lubricating two sliding rough surfaces. Both surfaces are generated according to a statistical method making use of measured technical surfaces. To model the interactions between the fluid and the solid structure, the ArbitraryLagrangian-Eulerian remeshing process is used. A model is built, based on an axial floating bearing on which the adhesion effects are the most present. Global friction coefficient between both lubricated solids is established using the FE solver and solid-solid friction can be separated from the fluid-solid friction with further post-processing operations.

Dissipated energy and friction coefficient evolution during fretting wear of solid lubricant coatings

In this study of key process parameters evolution during fretting wear of solid lubricant coatings for aerospace applications emphasis is placed on the analysis of the energies (total and dissipated) during fretting cycles. Key evolution trends are expressible in power law form, allowing compact and efficient description of the process. Slip ratio and slip index according to Varenberg et al. [3] are considered along the accumulated dissipated energy (ADE) and the global coefficient of friction (COF). Evolution observed admits interpretation in terms of a Kachanov-type damage parameter as a function of the accumulated reciprocal sliding distance (ARSD). Fretting wear tests were performed on samples of dry film lubricant coatings (diamond-like carbon (DLC) and MoS 2-containing coatings). Flat-and-rounded contact geometry was used to simulate the conditions observed in aero-engine components. Various pre-treatments (shot peening and grit blasting) were considered. Exponential and power law evolution laws provide convenient descriptions of the damage accumulation process in terms of two parameters (damage rate constant and damage exponent).

Friction Coefficient as a Macroscopic View of Local Dissipation

This paper presents an overview of a discrete element method approach to dry friction in the presence of a third body. Three dimensional computer simulations have been carried out to show the influence of the third body properties (and more specifically their adhesion) on friction coefficient and profiles of dissipated power. Simple interaction laws and a cohesive contact are set up to uncouple the key parameters governing the contact rheology. The model is validated through a global energy balance. As it is shown that dynamic friction coefficient can be explained only in terms of local energy dissipation, this work also emphasizes the fact that mechanism effects and third body rheology have important consequences on the energy generation and dissipation field. Therefore, asymmetries can arise and the surface temperature of first bodies can be significantly different even for the same global friction coefficient value. Such investigations highlight the fact that friction coefficient cannot be considered in the same way at the mechanism scale as at the contact scale where the third body plays a non-negligible role, although it has been neglected for years in thermal approaches to study of surfaces in contact.

The role and effects of the third body in the wheel–rail interaction

ABSTRACTThis paper focuses on the presence of the third body, a solid interfacial layer in the wheel–rail contact. This third body is studied from different viewpoints: its presence including composition, thickness and morphology; and its role with respect to its load‐carrying capacity, shearing behaviour, transfer of material and finally global friction coefficient. The general approach is phenomenological and is carried out as closely as possible of the real tribological behaviour of this contact. This paper presents a synthesis of different studies coming from: analysis of specimens taken out periodically from rails and wheels in service, and thus under real contact conditions; and test laboratories, allowing us to impose rolling–sliding conditions with very high precision. From all these studies and results, a better understanding of the role of the third body and its influence on friction, adhesion and damage mechanisms (wear, pits, cracks …) is reached and this is the first step for including its effect in numerical models.