Velocity-dependent Friction Research Articles

Velocity Dependence of Moiré Friction.

Friction force microscopy experiments on moiré superstructures of graphene-coated platinum surfaces demonstrate that in addition to atomic stick-slip dynamics, a new dominant energy dissipation route emerges. The underlying mechanism, revealed by atomistic molecular dynamics simulations, is related to moiré ridge elastic deformations and subsequent relaxation due to the action of the pushing tip. The measured frictional velocity dependence displays two distinct regimes: (i) at low velocities, the friction force is small and nearly constant; and (ii) above some threshold, friction increases logarithmically with velocity. The threshold velocity, separating the two frictional regimes, decreases with increasing normal load and moiré superstructure period. Based on the measurements and simulation results, a phenomenological model is derived, allowing us to calculate friction under a wide range of room temperature experimental conditions (sliding velocities of 1-104 nm/s and a broad range of normal loads) and providing excellent agreement with experimental observations.

Memory can induce oscillations of microparticles in nonlinear viscoelastic media and cause a giant enhancement of driven diffusion

We investigate analytically and numerically a basic model of driven Brownian motion with a velocity-dependent friction coefficient in nonlinear viscoelastic media featured by a stress plateau at intermediate shear velocities and profound memory effects. For constant force driving, we show that nonlinear oscillations of a microparticle velocity and position emerge by a Hopf bifurcation at a small critical force (first dynamical phase transition), where the friction's nonlinearity seems to be wholly negligible. They also disappear by a second Hopf bifurcation at a much larger force value (second dynamical phase transition). The bifurcation diagram is found in an analytical form confirmed by numerics. Surprisingly, the particles' inertial and the medium's nonlinear properties remain crucial even in a parameter regime where they were earlier considered entirely negligible. Depending on the force and other parameters, the amplitude of oscillations can significantly exceed the size of the particles, and their period can span several time decades, primarily determined by the memory time of the medium. Such oscillations can also be thermally excited near the edges of dynamical phase transitions. The second dynamical phase transition combined with thermally induced stochastic limit cycle oscillations leads to a giant enhancement of diffusion over the limit of vast driving forces, where an effective linearization of stochastic dynamics occurs.

An original experimental method for measuring friction coefficient during tribofilm formation by accumulating free sliding oscillating responses

A new experimental approach is proposed to investigate the friction behaviour and highlight the relationship with the tribofilm formation. It is based on the accumulation of several free dynamic responses of a single-degree-of-freedom damped oscillating system on the same sliding surfaces. By analysing the decreasing amplitude of the damped free dynamic responses and their associated energy decays, it is not only possible to describe the evolution of the tribological behaviour, but also to accurately identify velocity-dependent and velocity-independent friction contributions as the gradually formation of tribofilm. To demonstrate the relevance of this original technique, two tribosystems were studied, each lubricated with either base oil or formulated one, and by comparing the results with those obtained by a conventional linear tribometer.

Weakening behavior of the shallow megasplay fault in the Nankai subduction zone

The Nankai Trough megasplay fault hosts diverse modes of fault slip, ranging from slow slip events to megathrust earthquakes, and is responsible for related phenomena such as tsunamis and submarine landslides. All types of slip events require some kind of frictional weakening process in order to nucleate and propagate. We tested fluid-saturated, powdered megasplay fault samples in a direct shear apparatus under effective normal stresses of 2–18 MPa to investigate their friction velocity- and slip-dependence. The experiments show that for short distances (1 mm) after a velocity step, there is an evolution from velocity weakening at low effective normal stress to velocity strengthening at high effective normal stresses. Over a longer distance (5 mm), large velocity weakening is observed over all tested effective normal stresses. In all experiments, slip weakening behavior occurred with relatively large weakening rates at low effective normal stresses and smaller weakening rates at higher effective normal stresses. Critical stiffnesses for slip instability were calculated for both the velocity and slip dependence of friction to determine their relative importance. At shallow depths, velocity weakening would be the main cause of frictional instability for both small and large slip perturbations, whereas at greater depth instability requires either slip weakening over small slip distances, or velocity weakening induced by larger slip. Regardless of the underlying mechanism, the observed slip instability at lower effective stresses increases the likelihood for fault slip events to travel to the seafloor which may cause submarine landslides and tsunamis.Graphical

Application of enhanced coulomb models and virtual tribology in a practical study

Abstract For the final quality of the part, metal forming trends are depending on improvements of friction and tribology. As a consequence, there is a trend in which tribology and friction are becoming increasingly important for correctly replicating the forming simulation of those parts. The objective of this work was to improve the forming simulation of an automotive shell part on AutoForm. The part was provided by a vehicle industry supplier. Enhanced Coulomb models consider a change on friction coefficient due to different factors, better approximating the description of friction to reality. For the current study, pressure and velocity dependent friction models were chosen as long as the combination of both. The virtual tribology was simulated using the software TriboForm. Velocity dependent friction model and the virtual tribology have shown similar results with expected lower coefficients of friction.

A modified multibond model for nanoscale static friction.

Several key features of nanoscale friction phenomena observed in experiments, including the stick-slip to smooth sliding transition and the velocity and temperature dependence of friction, are often described by reduced-order models. The most notable of these are the thermal Prandtl-Tomlinson model and the multibond model. Here we present a modified multibond (mMB) model whereby a physically-based criterion-a critical bond stretch length-is used to describe interfacial bond breaking. The model explicitly incorporates damping in both the cantilever and the contacting materials. Comparison to the Fokker-Planck formalism supports the results of this new model, confirming its ability to capture the relevant physics. Furthermore, the mMB model replicates the near-logarithmic trend of increasing friction with lateral scanning speed seen in many experiments. The model can also be used to probe both correlated and uncorrelated stick slip. Through greater understanding of the effects of damping and noise in the system and the ability to more accurately simulate a system with multiple interaction sites, this model extends the range of frictional systems and phenomena that can be investigated. This article is part of the theme issue 'Nanocracks in nature and industry'.

Depth profile of frictional properties in the inner Nankai accretionary prism using cuttings from IODP Site C0002

We conduct frictional experiments using cuttings collected at Nankai Trough IODP Site C0002 over 980.5–3262.5 mbsf (meters below seafloor) depth interval to better understand the frictional properties through the accretionary prism. The experiments are conducted at the in situ effective normal stresses (9–37 MPa) under brine-saturated conditions, and the slip velocity is abruptly changed in a stepwise manner to either of 0.3, 3, or 33 µm/s after the steady-state friction is reached. The friction coefficient (μ) of the cuttings samples ranges from 0.45 to 0.60, with a slight increase in μ with increasing depth, related to decreasing smectite content. The velocity dependence of friction (a − b) is positive at all depths and ranges from 0.001 to 0.006, which indicates a velocity-strengthening behavior; these values are consistent with relatively homogeneous deformation microstructures. The critical slip distance (Dc) ranges from 0.5 to 123 μm, with relatively large values obtained for the smectite-rich samples. The changes in both the friction coefficient and rate- and state-friction parameters are likely associated with mineralogical change and consolidation with increasing depth. Although all of the cuttings samples collected from Site C0002 exhibit a velocity-strengthening behavior, a slight decreasing trend in a − b with increasing depth indicates either a nearly neutral velocity dependence or a possible transition to velocity-weakening behavior at greater depths, which may be attributed to the occurrence of slow earthquakes in the Nankai accretionary prism.

Velocity-weakening and -strengthening friction at single and multiasperity contacts with calcite single crystals

SignificanceThe empirical nature of rate-and-state friction (RSF) equations remains a drawback to their application to predict earthquakes. From nanoscale friction measurements on smooth and rough calcite crystals, a set of parameters is analyzed to elucidate microscopic processes dictating RSF. We infer the influence of roughness on the velocity dependence of friction in dry environment and that atomic attrition leads to stick-slip instabilities at slow velocities. In fault dynamics, stick-slip is associated with seismic slips. The aqueous environment eliminates atomic attrition and stick-slip and dissolves calcite under pressure. This yields remarkable lubrication, even more so in rough contacts, and suggests an alternative pathway for seismic slips. This work has implications for understanding mechanisms dictating fault strength and seismicity.

Identification of a Practical Digital Twin for Simulation of Machine Tools

A practical digital twin for machine tools is proposed in this study. The proposed digital twin is capable of time-domain simulation of machine tools and consists of a controller model, machining process model, and machine dynamic model. To predict the quality of the machined surface after the finishing processes, a precise dynamic model is required. The developed dynamic model consists of an interaction force model, vibration model, and friction force model. A linear auto regressive with exogenous inputs (ARX) model is adopted for the interaction and vibration models. Based on a systematic analysis of the disturbance forces of the machine tool, the friction characteristics are extracted to a displacement-dependent friction model and velocity-dependent friction model. A nonlinear Hammerstein model is adopted to identify the friction. Online identification systems based on the recursive least-squares (RLS) method are developed and tested for each model.

Friction Dynamics of Foams under Nonlinear Motion

Foams are viscoelastic soft materials with complex mechanical properties. Here, we evaluated the friction dynamics of foams between acrylic plates using a sinusoidal motion friction evaluation system and we found some interesting characteristics under accelerated conditions. On a typical solid surface, a symmetrical friction profile, in which static and kinetic frictions are observed, is obtained under reciprocating nonlinear motion. Meanwhile, significant lubricant effects and velocity-dependent friction profiles without static friction were observed in foams. The friction force in foams increased in proportion to the power of velocity, with a power index of <1. These characteristic and dynamic phenomena in foams were observed in this study. They had been caused by the formation of a thick lubricant film and various dissipative modes including surfactant diffusion, viscous dissipation, and wall slip of bubbles. Moreover, the addition of a thickener increased the friction force and the delay time of friction response and improved the foam durability against normal force and shear. These findings are useful for understanding dynamic phenomena in soft materials.

Impact factors on friction induced vibration of shaft-bearing system considering stick-slip behavior

An appropriate assessment of dynamical response of the marine propeller shaft is essential to enable optional power delivery to propeller and to minimize the dispensable mechanical friction of supporting bearings. The interaction behavior of the shaft-bearing system affects the stability of propulsion system seriously. An applicable numerical model regarding the friction induced vibration with velocity-dependent and stick-slip friction is proposed. The effect of smoothing factor, control factor, stick factor and slip factor which obtained with experimental data on the friction coefficient is analyzed separately. A cooperative Newton-Raphson & Newmark-β solving method is validated by experimental tests to be suitable to solve the proposed nonlinear model. To capture the nature of shaft-bearing interaction, the response of dynamic friction coefficient, relative velocity and reaction force with various model parameters are obtained. The residual of iteration which defined in the proposed solving method is also analyzed for each case to certificate the reliability of the numerical calculation. The stability analysis regarding various impact factor of the proposed shaft-bearing system is discussed with multiple scales method. An optimized design for propeller shaft and supporting bearing caused by friction induced by friction properties is thus realized based on proposed numerical model.

Molecular Origin of Driving-Dependent Friction in Fluids.

The friction coefficient of fluids may become a function of the velocity at increased external driving. This non-Newtonian behavior is of general theoretical interest and of great practical importance, for example, for the design of lubricants. Although the effect has been observed in large-scale atomistic simulations of bulk liquids, its theoretical formulation and microscopic origin are not well understood. Here, we use dissipation-corrected targeted molecular dynamics, which pulls apart two tagged liquid molecules in the presence of surrounding molecules, and analyze this nonequilibrium process via a generalized Langevin equation. The approach is based on a second-order cumulant expansion of Jarzynski's identity, which is shown to be valid for fluids and therefore allows for an exact computation of the friction profile as well of the underlying memory kernel. We show that velocity-dependent friction in fluids results from an intricate interplay of near-order structural effects and the non-Markovian behavior of the friction memory kernel. For complex fluids such as the model lubricant C40H82, the memory kernel exhibits a stretched-exponential long-time decay, which reflects the multitude of timescales of the system.

Role of contact plateaus on velocity-dependent friction of brake friction composite with steel fibres

The velocity-dependent friction of brake friction composites is investigated, focusing on the contact area on the sliding surface. Friction tests were performed using a reduced scale brake dynamometer. Results showed a considerable velocity dependence for the friction composites with steel fibres owing to the size reduction of wear debris compacts at a low velocity and accompanied high metallic adhesion by stress concentration on the steel fibres. The velocity weakening coefficient, which is included in the empirical equation for the velocity weakening friction, is suggested for predicting friction instability of the friction composite using six commercial products.

Frictional and Lithological Controls on Shallow Slow Slip at the Northern Hikurangi Margin

AbstractSlow slip events (SSEs) have been identified at subduction zones globally as an important link in the continuum between elastodynamic ruptures and stable creep. The northern Hikurangi margin is home to shallow SSEs which propagate to within 2 km of the seafloor and possibly to the trench, providing insights into the physical conditions conducive to SSE behavior. We report on a suite of friction experiments performed on protolith material entering the SSE source region at the Hikurangi margin, collected during the International Ocean Discovery Program Expedition 375. We performed velocity stepping and slide‐hold‐slide experiments over a range of fault slip rates, from plate rate (5 cm/yr or 1.6 × 10−9 m/s) to ∼1 mm/s (10−3 m/s) and quantified the frictional velocity dependence and healing rates for a range of lithologies atdifferent stresses. The frictional velocity dependence (a‐b) and critical slip distance DC increase with fault slip rate in our experiments. We observe atransition from velocity weakening to strengthening at slip rates of ∼0.3 µm/s. This velocity dependence of DC could be due to a combination of dilatant strengthening and a widening of the active shear zone at higher slip rates. We document low healing rates in the clay‐rich volcaniclastic conglomerates, which lie above the incoming plate basement at least locally, and relatively higher healing rates in the chalk lithology. Finally, our experimental constraints on healing rates in different input lithologies extrapolated to timescales of 1–10 years are consistent with the geodetically inferred low stress drops and healing rates characteristic of the Hikurangi SSEs.

A Numerical-Experimental Study on Orthogonal Cutting of AISI 1045 Steel and Ti6Al4V Alloy: SPH and FEM Modeling with Newly Identified Friction Coefficients

Numerical simulation of metal cutting with rigorous experimental validation is a profitable approach that facilitates process optimization and better productivity. In this work, we apply the Smoothed Particle Hydrodynamics (SPH) and Finite Element Method (FEM) to simulate the chip formation process within a thermo-mechanically coupled framework. A series of cutting experiments on two widely-used workpiece materials, i.e., AISI 1045 steel and Ti6Al4V titanium alloy, is conducted for validation purposes. Furthermore, we present a novel technique to measure the rake face temperature without manipulating the chip flow within the experimental framework, which offers a new quality of the experimental validation of thermal loads in orthogonal metal cutting. All material parameters and friction coefficients are identified in-situ, proposing new values for temperature-dependent and velocity-dependent friction coefficients of AISI 1045 and Ti6Al4V under the cutting conditions. Simulation results show that the choice of friction coefficient has a higher impact on SPH forces than FEM. Average errors of force prediction for SPH and FEM were in the range of 33% and 23%, respectively. Except for the rake face temperature of Ti6Al4V, both SPH and FEM provide accurate predictions of thermal loads with 5–20% error.

Numerical simulation of the frictional heat problem of subway brake discs considering variable friction coefficient and slope track

Friction heating during braking may causes premature wear, thermal cracks and other damages which could weak the braking performance of subway vehicles. It is therefore important to determine the temperature field of the brake disc. The purpose of this paper is to propose a one-dimensional brake disc model and apply a new solution algorithm to obtain the temperature field of the brake disc, which is validated by the Renk Dynamometer test bench. The advantage of this numerical model is that the variable friction coefficient and slope are taken into account. The experimental dependency of the coefficient of friction on the velocity is approximated by interpolation and applied to the numerical model. The calculation is based on two cases of constant and velocity-dependent friction coefficient (COF) by using the method of lines (MOL), which has the advantage of shorter computation time and improved accuracy. The numerical results agree well with the experimental data. It was proved that disregarding the velocity dependence of the coefficient of friction, the maximum temperature during the entire braking process was underestimated by 15%. In addition, the subway vehicle braking on slope should decrease the speed limit appropriately to reduce the maximum temperature of the brake disc. This study can provide a theoretical basis for further fatigue study of brake discs.

Dynamics of nonlinear waves in a Burridge and Knopoff model for earthquake with long-range interactions, velocity-dependent and hydrodynamics friction forces

We investigate the dynamics of nonlinear waves in a long-range extension of the Burridge and Knopoff model for earthquake. We consider the dissipative hydrodynamics forces. The spatio-temporal dynamics of the system is found by introducing in the coupling spring and hydrodynamics forces a linear term that decays as a power-law, with an exponent s such that 1<s≤3. The theoretical framework for the analysis is presented in the rotative wave approximation. Due to the non analytic properties of the dispersion relation, we use the discrete derivative operator technique. The dynamics of the system is governed by the complex Ginzburg-Landau equation, allowing breather-like soliton solutions. We use the relevant case s=2, and results show that the magnitude, the velocity, and area of propagation of nonlinear waves strongly depend on the frictions forces. Our analytical results are in good agreement with numerical experiments and confirm the correctness of the method.

Dynamics of modulated waves and localized energy in a Burridge and Knopoff model of earthquake with velocity-dependant and hydrodynamics friction forces

We investigate both analytically and numerically the dynamics of modulated waves in a modified Burridge and Knopoff mechanical model of earthquake. We take into account the velocity-dependent and hydrodynamics friction forces between the rock blocks of the system. The theoretical framework for the analysis is presented using the multiple scale expansion method. We show that the system can be governed by the complex Ginzburg–Landau equation, which admits soliton solutions. The modulational instability of the system is performed, showing that the bandwidth of instability increases with the friction forces parameter. The planar wave solution used as the initial condition leads to more unstable waves in the system with chaotic-like behaviour, allowing energy localization. It is also found that the wave parameters, namely, the frequency, magnitude and velocity (as well as the energy of the system) strongly depend on η. In the non-friction limit, the obtained waves propagate with a coherent behaviour for a very short time, before disappearing. Our results suggest that the damages caused by an earthquake can be important as the friction forces increase and may excite the possibility of relative predictions for the dynamics of waves propagating in the earth in the field of nonlinear science.

Effects of Stick-Slip in Behavior of Structures with Friction Damper under Near-Field Earthquakes

The present study is an attempt to investigate structures equipped with friction dampers under the influence of near-field earthquakes based on Stribeck friction behavior of velocity function. At present, the cyclic behavior of friction dampers in structural design engineering software is simple and based on the Coulomb friction force that is independent of velocity, which should be estimated and considered in terms of Stribeck velocity-dependent friction. Their sliding and vibration methods, including displacement, velocity, and acceleration, are calculated using numerical analysis and differential equation. For this purpose, the representative of the near-field records affects the structure with Stribeck frictional behavior of velocity function as a pulse of Ricker wavelet stimulation. The response of the structure is evaluated in the transition phase from impending motion with a friction coefficient of μs to kinetic motion with μk and vice versa, which makes the poor results of previous simplifications more accurate. Due to the nonlinear behavior of the damping force, programming has been used to perform nonlinear analytical dynamics. Also, behavioral models in OpenSees software are used to investigate the behavior of Stribeck friction for friction damper and to compare its results with the results obtained from accurate analysis.

An improved [formula omitted] turbulence model for FENE-P fluids without friction velocity dependence

An improved k-ω turbulence model for viscoelastic fluids is developed to predict turbulent flows, with polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin constitutive model. The k-ω model is tested against a wide range of direct numerical simulation data in fully-developed channel flow, with different rheological parameter combinations, and can predict all regimes of drag reduction (low, intermediate and high) with good performance. Closures are improved for the NLTij term, which captures the polymer extension due to turbulent fluctuations; a modified damping function, fμ, which accounts for the turbulent kinetic energy redistribution process; and the viscoelastic destruction term, Eτp. The main advantage of the current model is its ability to predict all flow features with model simplicity and without the need for friction velocity dependence, important for flows with reattachment due to their singularity caused by the stagnation points.