Waves Of Detachment Research Articles

Detachment waves in frictional contact: analysis and simulations of a two-mass system

Detachment waves in frictional contact: analysis and simulations of a two-mass system

Detachment waves in frictional contact: I — A two-mass system

This work studies a mathematical model for the motion of a two mass–spring–damper system with friction, and has a two-fold purpose. The first is to start a mathematical study of the way detachment or slip waves, when the system transits from stick to slip motion, propagate in discrete and continuous systems. The introduction of friction changes the problems into systems of differential set-valued inclusions, which are mathematically interesting, but rather complex. The second is to use such a ‘simple’ system as an example of a very general existence and uniqueness theorem for systems described by set-valued pseudomonotone operators, Kuttler and Shillor (1999) and Andrews et al. (2020).

Fifty years of Schallamach waves: from rubber friction to nanoscale fracture.

The question of how soft polymers slide against hard surfaces is of significant scientific interest, given its practical implications. Specifically, such systems commonly show interesting stick-slip dynamics, wherein the interface moves intermittently despite uniform remote loading. The year 2021 marked the 50th anniversary of the publication of a seminal paper by Adolf Schallamach (Wear, 1971), which first revealed an intimate link between stick-slip and moving detachment waves, now called Schallamach waves. We place Schallamach's results in a broader context and review subsequent investigations of stick-slip, before discussing recent observations of solitary Schallamach waves. This variant is not observable in standard contacts so that a special cylindrical contact must be used to quantify its properties. The latter configuration also reveals the occurrence of a dual wave-the so-called separation pulse-that propagates in a direction opposite to Schallamach waves. We show how the dual wave and other, more general, Schallamach-type waves can be described using continuum theory and provide pointers for future research. In the process, fundamental analogues of Schallamach-type waves emerge in nanoscale mechanics and interface fracture. The result is an ongoing application of lessons learnt from Schallamach-type waves to better understand these latter phenomena. This article is part of the theme issue 'Nanocracks in nature and industry'.

Propagating Schallamach-type waves resemble interface cracks.

Intermittent motion, called stick-slip, is a friction instability that commonly occurs during relative sliding of two elastic solids. In adhesive polymer contacts, where elasticity and interface adhesion are strongly coupled, stick-slip arises due to the propagation of slow detachment waves at the interface. Here we analyze two distinct detachment waves moving parallel (Schallamach wave) and antiparallel (separation wave) to applied remote sliding. Both waves cause slip in the same direction, travel at speeds much lesser than any elastic wave speed, and are therefore describable using the same perturbative elastodynamic framework with identical boundary conditions. A numerical scheme is used to obtain interface stresses and velocities for arbitrary Poisson ratio, along with closed-form solutions for incompressible solids. Our calculations reveal a close correspondence between moving detachment waves and bimaterial interface cracks, including the nature of the singularity and the functional forms of the stresses. Based on this correspondence, and coupled with a fracture analogy for dynamic friction, we develop a phase diagram showing domains of possible occurrence of stick-slip via detachment waves vis-á-vis steady interface sliding. Our results have interesting implications for sliding and stick-slip phenomena at soft interfaces.

Detachment Waves and Self-Oscillation in a Belt-Drive System Incorporating Tensile Cords

Abstract Recent experimental studies have shown that tension transition via detachment waves (rather than via sliding, as commonly accepted) occurs at the belt–pulley interface for systems using simple homogeneous or textured flat belts operating under slow speeds. This raises the question of whether or not such detachment waves are universal—e.g., will they persist in systems incorporating belts with composite cross sections, such as those used in commercial applications? Herein, we experimentally explore the behavior of a belt-drive system incorporating a composite belt with tensile cords, with and without a patterned contact surface, and document the persistence of detachment waves. This then leads to a re-evaluation of the Firbank model of belt shear. We also explore the effect of tensile cords on (i) the amplitude and frequency of the observed detachment waves, (ii) the ensuing oscillations of the pulley, (iii) the evolution of belt shear strain, and (iv) the frictional losses of the system. We find that the detachment frequency increases and the pulley rotates steadier with inclusion of tensile cords. The corded belt undergoes shear deformation starting from the entry point due to a speed differential between the pulley envelope and the tension members, which is consistent with the classical Firbank shear model. However, the Firbank model cannot predict the rapid relaxation of the shear traction via detachment waves at the exit region. Additionally, accounting for shear and detachment events, we find that frictional losses in the belt-drive system decrease with inclusion of tensile cords.

Minimizing self-oscillation in belt drives: Surface texturing

Detachment waves have recently been identified as one of the main sources for self-oscillation and accompanying energy losses in belt drive systems under low-speed and otherwise steady operation. In light of this, herein we explore mitigation of detachment wave-induced instabilities via regular and irregular texturing of the belt contact surface. The results document that surface texturing reduces the magnitude of belt drive oscillations, with the reduction being significantly more pronounced in the driver case than in the driven case. While both regular and irregular surface topographies are useful in minimizing the vibrations, regular patterns result in a stronger effect. The aspect ratio of surface projections is found to be the most important parameter, while excessive texturing of the belt surface is shown to result in belts losing their tractive capabilities.

Belt-Drive Mechanics: Friction in the Absence of Sliding

Recent studies have shown that steady and unsteady operation of a belt drive may exhibit regimes absent of sliding at the belt–pulley interface, where instead detachment waves serve to relax stress in the so-called “slip” arc. To explore this finding further, herein we present an experimental and theoretical investigation into frictional mechanics in a simple belt drive system. To estimate friction experimentally, we perform a stress analysis based on spatio-temporal measurements of the belt tension, traction, and contact area evolution. Subsequently, we develop a model taking into account both bulk and surface hysteretic losses to explain the experimental observations. Our results show that the shear strain at the belt–pulley interface differs significantly between the driver and the driven pulleys, resulting in much larger mechanical losses in the driver case. The shear strain drops at the transition from the adhesion to the slip arc, and, in contrast to accepted theories, the slip arc contributes little to nothing to the power transmission. Our model reveals that the contact area evolution correlates to the shear traction changes and that viscoelastic shear and stretching dominate in the belt rolling friction. A significant contribution of detachment waves to the energy dissipation explains the higher mechanical losses observed in the driver case.

Schallamach Wave-Induced Instabilities in a Belt-Drive System

We experimentally study the dynamic behavior of a belt-drive system to explore the effect of loading conditions, driving speed, and system inertia on both the frequency and amplitude of the observed frictional and rotational instabilities. A self-excited oscillation is reported whereby local detachment events in the belt–pulley interface serve as harmonic forcing of the pulley, leading to angular velocity oscillations that grow in time. Both the frictional instabilities and the pulley oscillations depend strongly on operating conditions and system inertia, and differ between the driver and driven pulleys. A larger net torque applied to the pulley generally intensifies Schallamach waves of detachment in the driver case but has little influence on other measured response quantities. Higher driving speeds accelerate the occurrence of frictional instabilities as well as pulley oscillations in both cases. Increasing the system's inertia does not affect the behavior of contact instabilities, but does lead to a steadier rotation of the pulley and more pronounced fluctuations in the belt tension. A simple dynamic model of the belt-drive system demonstrates good agreement with the experimental results and provides strong evidence that frictional instabilities are the primary source of the system's self-oscillation.

Schallamach waves in rolling: Belt drives

Abstract The contact mechanics in a belt drive has been experimentally studied to explore the mechanism of relative displacement at the belt/pulley interface. We have found that under the slow speed considered, no sliding takes place at the interface, and that relative displacement between the elastomeric belt and the pulley is achieved by cyclic detachment. The contact mechanics is different in the driver and driven pulleys, which results in different slip arc angles and calls into question the universal validity of the symmetric sliding-based approach to analysis of the belt drive contact. Waves of detachment are observed in the driver pulley, while in the driven pulley, the system instabilities result from the combination of the pulley rotation and the adhesion hysteresis.

How Staphylococcus aureus biofilms develop their characteristic structure

Biofilms cause significant problems in the environment and during the treatment of infections. However, the molecular mechanisms underlying biofilm formation are poorly understood. There is a particular lack of knowledge about biofilm maturation processes, such as biofilm structuring and detachment, which are deemed crucial for the maintenance of biofilm viability and the dissemination of cells from a biofilm. Here, we identify the phenol-soluble modulin (PSM) surfactant peptides as key biofilm structuring factors in the premier biofilm-forming pathogen Staphylococcus aureus. We provide evidence that all known PSM classes participate in structuring and detachment processes. Specifically, absence of PSMs in isogenic S. aureus psm deletion mutants led to strongly impaired formation of biofilm channels, abolishment of the characteristic waves of biofilm detachment and regrowth, and loss of control of biofilm expansion. In contrast, induced expression of psm loci in preformed biofilms promoted those processes. Furthermore, PSMs facilitated dissemination from an infected catheter in a mouse model of biofilm-associated infection. Moreover, formation of the biofilm structure was linked to strongly variable, quorum sensing-controlled PSM expression in biofilm microenvironments, whereas overall PSM production remained constant to ascertain biofilm homeostasis. Our study describes a mechanism of biofilm structuring in molecular detail, and the general principle (i.e., quorum-sensing controlled expression of surfactants) seems to be conserved in several bacteria, despite the divergence of the respective biofilm-structuring surfactants. These findings provide a deeper understanding of biofilm development processes, which represents an important basis for strategies to interfere with biofilm formation in the environment and human disease.

FEA MODELING OF SCHALLAMACH WAVES

AbstractThe term Schallamach wave is used to describe a wave of detachment that sometimes arises during the frictional sliding of a smooth rubber surface against a smooth rigid surface. Extensive experimental investigations have been made since Schallamach first observed the waves in 1971; however, no successful finite element analysis (FEA) modeling of the behavior has been reported yet. This work uses an explicit dynamics FEA approach to model both the initiation and progression of waves of detachment for the first time. The use of the finite element method allows for the detailed stress and strain analysis at the interface to be examined. Here, the limitations of using a purely elastic solution in plane-strain are explored. To validate the explicit dynamics approach for modeling the Schallamach waves, another biaxial compressive buckling mode has also been modeled.

How does rubber truly slide between Schallamach waves and stick–slip motion?

Abstract Schallamach waves have been investigated from a new viewpoint of their dynamic behaviour. Two new insights were introduced to elucidate the mechanism of the initiation and propagation of the wave of detachment, firstly the surface interaction force can produce a meniscus effect at the rubber surface and secondly the stick–slip motion can be seen to have a significant role during the sliding of rubber. The meniscus could perhaps be a source of the initiation of the wave of detachment at the leading edge and might have a role to play in the peeling of the rubber away from the trailing edge of the contact simultaneously. The characteristics in the propagation of the waves such as their frequency, their high progression velocity and the sliding velocity dependence all correlate with the periodic stick–slip motion. True finite sliding was observed to take place during a slip stage in the stick–slip motion whether waves of detachment appear or not on the contact area. Thus, the contribution of the waves to the frictional sliding of rubber is to decrease the contact area before true sliding and allow smoother sliding with less vibration of stick–slip motion to occur during rubber friction.

粘着性ゲルシートのすべり摩擦

In this paper, we report our studies on sliding friction of an adhesive gel-sheet. Due to the stickiness of the gel, it never slips at the contact area but can make relative motions via the propagation of detachment waves. We found that the patterns of the detachment waves transform from regular stripe-like at larger pull velocities to irregular bubble-like at smaller pull velocities. Furthermore, from photo-elasticity experiments to visualize the stress state of the contact area, we discovered that the irregular bubble-like patterns are closely related to inhomogeneity in stress fields.

Finite Element Analysis of a Polymer- Polymer Sliding Contact for Schallamach Wave and Wear

Sliding polymer-polymer surface contacts, due to their inherent elastic properties, exhibit detachment waves also termed as Schallamach waves. Such waves effect the initiation and propagation of wear along the sliding contacts. This paper presents quasi steady-state analysis of such a sliding contact using finite element. The contact is modeled and nodal solutions for pressure are obtained for small sliding steps. Analysis of orthogonal pressure components at the contact nodes reveals the formation of Schallamach wave phenomenon. Further, appropriate wear law is used for calculation of wear at nodal level.

Dynamic Behaviors of Contact Surfaces in the Sliding Friction of a Soft Material

It is known that detachment waves are generated on the surface of a soft material when it is slid on a hard surface under certain conditions. In the present study, the variation in the contact area that arises when a plate of a cross-linked polymer, poly-dimethylsiloxane (PDMS), is slid in contact with a glass hemisphere has been measured every 2 ms using a microscope and high-speed camera. The measurements elucidate that the behavior of the PDMS surface under sliding friction is divided into three modes. In mode I, a detachment wave is generated and it propagates across the contact zone. In mode II, a detachment wave is generated but does not propagate perfectly. In mode III, no detachment waves are generated. The Young modulus and load control the generation of detachment waves, but the contribution of the former is approximately 8 orders of magnitude larger than that of the latter.

Steep wave fronts on extrudates of polymer melts and solutions: lubrication layers and boundary lubrication

Steep wave fronts tend to develop in many regimes of lubricated, slipping flows in which waves appear. Problems of slip, spurt, fracture and extrudate distortion can be framed in terms of lubrication theory with paradigms arising from the lubrication of heavy oil with water for some problems and concepts from the theory of boundary lubrication for others. In water-lubricated pipelines, high pressures are produced at the front side of a wave on the oil when water is forced through the wavecrest and the wall, low pressures develop at the back of the wave where the gap opens. The steep waves which develop on cores of heavy oil lubricated by water are irregular and look like melt fracture. Direct numerical simulation of regular periodic waves give rise to sharkskin solutions in which the wave length decreases with the wave amplitude as the gap size decreases, preserving the steep wave front. Wave steepening seems always to occur in extrusion when the polymers slip, in the abrasion of rubber samples and in Schallamach's waves of detachment.

Viscoelastic Characteristics of Typical Shoe Outsole Materials and Their Effects on Walkway Friction Models

Abstract The physical laws governing the forces encountered when two materials in contact move, or tend to move, relative to another, have been developed over the last three hundred years. The assumptions used in these theories considered materials to be elastic in nature. A number of problems arise in applying these theories to footwear outsole materials. For example, the materials can be viscoelastic, which can alter their response to applied loads. Friction in elastomers has been shown to be made up of two different terms: adhesion and deformation. Waves of detachment have been observed in sliding elastomers that are the result of viscoelastic instability at the contact surface. Although this has been established in various laboratory tests, it has not been shown that typical conditions encountered during gait (forces, walking/sliding speed, temperatures, pressures) fit the adhesion/deformation model of elastomers. Available methods to measure/simulate friction during gait are controversial. Viscoelastic materials properties can vary with rate of loading, including friction and mechanical. Tensile tests at various strain rates were performed on typical commercially available shoe outsole materials-leather, and Neolite®. The results did not show any significant trend with respect to strain rate and measured mechanical properties.

Spatiotemporal dynamics due to stick-slip friction in an elastic-membrane system.

Frictional stick-slip dynamics is studied experimentally in an elastic continuum by means of a stretched latex membrane in contact with a translating glass rod. In contrast to other laboratory-scale experiments, the characteristic stiffness length here is small compared to the size of the system but large compared to the spatial resolution of the measurements. The internal displacement field u(s,t) is measured in detail with imaging techniques, which are shown to be more sensitive than total-force measurements. The magnitudes \ensuremath{\mu} of slipping events extend over a wide range and include both small localized events and large spatially extended ones. The shape of the distribution P(\ensuremath{\mu}) depends somewhat on the measurement threshold and also varies with the parameters describing the frictional interaction, which are affected by wear. The frictional force increases with velocity and an instability is due to waves of detachment. The temporal statistics of slipping events are also discussed. The experimental results are compared qualitatively to simplified models of earthquake faults.

Adherence, friction and wear of rubber-like materials

The underlying mechanisms of the adherence and of the sliding and rolling friction of rubber-like materials are studied on a microscale level, by scrutinizing phenomena occurring inside both static and rolling or sliding contact areas between a single hard transparent spherical or cylindrical asperity and the smooth and flat surface of a soft elastomer sample. Various mechanisms have been studied such as equilibrium conditions and kinetics of adherence of different rigid punches, contact geometry and rolling frictional force of a rigid cylinder, static friction, deformation and interfacial phenomena in sliding friction of a spherical asperity, influence of the radius of curvature of a blunt rigid asperity in sliding contact, stages of formation of reattachment folds, conditions for the appearance of detachment waves, friction of silica-filled compounds and the onset of wear.

Friction and wear in rubbers and tyres

A unified approach to the entire subject of friction and wear in rubbers and tyres is presented. Friction is regarded as a fundamental energy dissipative mechanism as a result of which surface degradation and wear occur. At the same time the rolling tyre is considered as a combination of rubber elements undergoing prescribed motions in the contact patch, and this elementary macroscopic modelling of tyre frictional behaviour provides a basic understanding of rubber friction and tyre mechanics simultaneously. An analogy between friction and wear mechanism is developed. Thus the adhesion and hysteresis contributions to friction on rough surfaces produce abrasive and fatigue wear respectively, whereas waves of detachment on smooth surfaces appear to produce wear by rolled fragments. The paper concludes with a description of an elaborate experimental rig designed to test elementary friction blocks of rubber or a complete tyre in various braking modes.