Friction Law Research Articles

Modeling multi-legged robot locomotion with slipping and its experimental validation

Multi-legged robots with six or more legs are not in common use, despite designs with superior stability, maneuverability, and a low number of actuators being available for over 20 years. This may be in part due to the difficulty in modeling multi-legged motion with slipping and producing reliable predictions of body velocity. Here, we present a detailed measurement of the foot contact forces in a hexapedal robot with multiple sliding contacts, and provide an algorithm for predicting these contact forces and the body velocity. The algorithm relies on the recently published observation that even while slipping, multi-legged robots are principally kinematic, and employ a friction law ansatz that allows us to compute the shape-change to body-velocity connection and the foot contact forces. This results in the ability to simulate motion plans for a large number of contacts, each potentially with slipping. Furthermore, in homogeneous environments, this kind of simulation can run in (parallel) logarithmic time of the planning horizon.

Transient Friction Analysis of Pressure Waves Propagating in Power-Law Non-Newtonian Fluids

Modulated pressure waves propagating in the drilling fluids inside the drill string are a reliable real-time communication technology that transmit data from downhole to the surface during oil and gas drilling. In the analysis of pressure waves’ propagation characteristics, the modeling of transient friction in non-Newtonian fluids remains a great challenge. This paper establishes a numerical model for transient pipe flow of power-law non-Newtonian fluids by using the weighted residual collocation method. Then, the Newton–Raphson method is applied to solve the nonlinear equations. The numerical method is validated by using the theoretical solution of Newtonian fluids and is proven to converge reliably with larger time steps. Finally, the influencing factors of the wall shear stress are analyzed using this numerical method. For shear-thinning fluids, the friction loss of periodic flow decreases with the increase in flow rate, which is opposite to the variation law of friction with the flow rate for stable pipe flow. Keeping the amplitude of pressure pulsation unchanged, an increase in frequency leads to a decrease in velocity fluctuations; therefore, the friction loss decreases with the increase in frequency.

Dissipative solutions to the model of a general compressible viscous fluid with the Coulomb friction law boundary condition

We study a model of a general compressible viscous fluid subject to the Coulomb friction law boundary condition. For this model, we introduce a dissipative formulation and prove the existence of dissipative solutions. The proof of this result consists of a three level approximation method: A Galerkin approximation, the classical parabolic regularization of the continuity equation as well as convex regularizations of the potential generating the viscouss stress and the boundary terms incorporating the Coulomb friction law into the dissipative formulation. This approach combines the techniques already known from the proof of the existence of dissipative solutions to a model of general compressible viscous fluids under inflow-outflow boundary conditions as well as the proof of the existence of weak solution to the incompressible Navier-Stokes equations under the Coulomb friction law boundary condition. It is the first time that this type of boundary condition is considered in the case of compressible flow.

Observing and Modeling Short‐Term Changes in Basal Friction During Rain‐Induced Speed‐Ups on an Alpine Glacier

AbstractBasal shear stress on hard‐bedded glaciers results from normal stress against bed roughness, which depends on basal water pressure and cavity size. These quantities are related in a steady state but are expected to behave differently under rapid changes in water input, which may lead to a transient frictional response not captured by existing friction laws. Here, we investigate transient friction using Global Positioning System vertical displacement and horizontal velocity observations, basal water pressure measurements, and cavitation model predictions during rain‐induced speed‐up events at Glacier d'Argentière, French Alps. We observe up to a threefold increase in horizontal surface velocity, spatially migrating at rates consistent with subglacial flow drainage, and associated with surface uplift and increased water pressure. We show that frictional changes are mainly driven by changes in water pressure at nearly constant cavity size. We propose a generalized friction law capable of capturing observations in both the transient and steady‐state regimes.

Simulation of impacts between spherical rigid bodies with frictional effects

AbstractThis work studies the impact between spherical rigid bodies in the frame of nonsmooth contact dynamics considering friction effects. A new impact element formulation based on the classical instantaneous local Newton impact law is presented. The kinematics properties of the spheres are described by a rigid body formulation with translational and rotational degrees of freedom referred to an inertial frame. In addition, an extension of the nonsmooth generalized‐ time integration scheme applied to collisions with multiple impacts including Coulomb's friction law is given. Six numerical examples are presented to evaluate the robustness and the performance of the proposed methodology.

Computational framework for predicting friction law under mixed-boundary lubrication, and its application to sheet metal forming process

The role of friction in the forming of automotive parts composed of ultra-high-strength lightweight metals has become increasingly important as industry attempts to overcome inferior formability and springback against enhanced strength. At the tool-design stage, finite-element simulations should use more accurate and efficient friction models that account for complex friction behavior between the metal and tool surfaces. Complex friction behavior is commonly dependent on contact pressure, sliding velocity, microscale surface effects (or roughness), and lubrication, among other factors. This study presents a microscale, asperity-based friction model of mixed-boundary lubrication. The developed hydrodynamic friction model is based on the load-sharing concept, which considers the lubrication area and metal-to-metal contact separately. Lubricant film thickness is calculated to couple the existing boundary lubrication model, and film lubrication behavior is formulated using finite-element programming of the Reynolds equation to obtain the hydrodynamic pressure. The proposed computational framework is validated by simulating an in-line incremental die-forming process. The result shows that the predicted friction law with multi-scale, mixed-boundary lubrication can be efficiently applied to realistic sheet-metal-forming simulations with reasonable accuracy by accounting for complex frictional behavior.

Asymptotic behavior of a viscoelastic problem with long-term memory and Tresca friction law

Asymptotic behavior of a viscoelastic problem with long-term memory and Tresca friction law

Variation in Granular Frictional Resistance Across Nine Orders of Magnitude in Shear Velocity

AbstractDetermining the shear‐velocity dependence of dry granular friction can provide insight into the controlling variables in a dry granular friction law. Some laboratories believe that the quality of this study is at the forefront of the discipline for the following reasons. Results suggest that granular friction is greatly affected by shear‐velocity (v), but shear experiments over the large range of naturally occurring shear‐velocities are lacking. Herein we examined the shear velocity dependence of dry friction for three granular materials, quartz sand, glass beads and fluorspar, across nine orders of magnitude of shear velocity (10−8–2 m/s). Within this range, granular friction exhibited four regimes, following a broad approximate “m” shape including two velocity‐strengthening and two velocity‐weakening regimes. We discuss the possible physical mechanisms of each regime. This shear velocity dependence appeared to be universal for all particle types, shapes, sizes, and for all normal stresses over the tested range. We also found that ultra‐high frequency vibration as grain surfaces were scoured by micro‐chips were formed by spalling at high shear velocities, creating ∼20 μm diameter impact pits on particle surfaces. This study provides laboratory laws of a friction‐velocity (μ‐v) model for granular materials.

Competition between rate strengthening and gravitational acceleration induces stick-slips of inclined granular flow

This study conducted experiments on dry granular mass released on an inclined flume. The periodic acceleration and deceleration of the flow, that is, the stick-slip phenomenon, was observed during the experiments. To investigate the stick-slip motion mechanism, numerical simulations were conducted with the inclusion of the shear-strengthening μ(I)-rheology into the elasto-plastic models of granular flow. The stick-slip phenomenon was captured naturally without the modification of the empirical friction law. The results revealed that the competition between the rate strengthening implemented by the μ(I)-rheology and the gravitational acceleration along the inclined plane induces stick-slips. By considering the experimental results in combination with the simulation results, the effects of the particle size, gate size opening, surface roughness, and frictional parameters of μ(I)-rheology on the stick-slip phenomenon were elucidated.

The dynamic behaviour of flexible oscillators rocking and sliding on concentrated springs

AbstractThis study presents the Flexible Rocking Model on Concentrated Springs (FRMCS), developed to investigate 2D laterally flexible oscillators rocking and sliding on deformable support media during ground excitations. In this model, concentrated vertical springs and viscous dampers simulate the contact forces from support medium at the corners of the body; the tensionless vertical contact element is linear in compression. Horizontal concentrated springs and linear viscous dampers simulate the frictional behaviour at the corners; the constitutive law for the springs models elastic deformations and sliding (according to Coulomb's friction law). With these elements, FRMCS can model the response of a rocking body which can experience sliding and free‐flight phases of motion. The consideration of the flexibility of the support medium enables the evaluation of the forces exerted by the support medium on the structure during an impact. In this study, the FRMCS response is first compared to a previous model where the support medium deformability and the effects of sliding and free‐flight are ignored. Then, the responses of four configurations, which feature either stiff or soft lateral springs and stiff or soft high‐grip support media, are examined under the influence of pulse excitations. Finally, to understand the potential influence of sliding, a configuration with a low‐grip support medium is explored. The comparative influence of lateral flexibility and support medium deformability and sliding is quantified with stability diagrams and various response spectra, describing structural force and moment demands.

Controlling the Friction Coefficient and Adhesive Properties of a Contact by Varying the Indenter Geometry

In the present paper, we describe a series of laboratory experiments on the friction between rigid indenters with different geometrical forms and an elastic sheet of elastomer as a function of the normal load. We show that the law of friction can be controlled by the shape of the surface profile. Since the formulation of the adhesive theory of friction by Bowden and Tabor, it is widely accepted and confirmed by experimental evidence that the friction force is roughly proportional to the real contact area. This means that producing surfaces with a desired dependence of the real contact area on the normal force will allow to “design the law of friction”. However, the real contact area in question is that during sliding and differs from that at the pure normal contact. Our experimental studies show that for indenters having a power law profile f(r) = cnrn with an index n < 1, the system exhibits a constant friction coefficient, which, however, is different for different values of n. This opens possibilities for creating surfaces with a predefined coefficient of friction.

An effective nonlinear dynamic formulation to analyze grasping capability of soft pneumatic robotic gripper

ABSTRACT Soft pneumatic robotic grippers have found extensive applications across various engineering domains, which prompts active research due to their splendid compliance, high flexibility, and safe human-robot interaction over conventional stiff counterparts. Previously simplified rod-based models principally focused on clarifying overall large deformation and bending postures of soft grippers from static or quasi-static perspectives, whereas it is challenging to elaborate grasping characteristics of soft grippers without considering contact interaction and nonlinear large deformation behaviors. To address this, based on absolute nodal coordinate formulation (ANCF), comprehensively allowing for structural complexity, geometric, material and boundary nonlinearities, and incorporating Coulomb’ friction law with a multiple-point contact method, we put forward an effective nonlinear dynamic modeling approach for exploring grasping capability of soft gripper. Moreover, we solved the established dynamic equations using Generalized-α scheme, and conducted thorough numerical simulation analysis on a three-jaw soft pneumatic gripper (SPG) in terms of grasping configurations, displacements and contact forces. The proposed dynamic approach can accurately both describe complicated deformed configurations along with stress distribution and provide a feasible solution to simulate grasping targets, whose effectiveness and precision were analyzed theoretically and verified experimentally, which may shed new light on devising and optimizing other multifunctional SPGs.

Tribology in arthroplasty : Friction and wear, akey to along lifetime

This article is intended to highlight one of the key roles in endoprosthetic treatment with artificial implants and the extension of service life. Like every joint, artificial joints are subject to the physical laws of friction and wear-in short, tribology. Material pairings, surfaces and mechanisms of action in particular play adecisive role here. The special features and current findings relating to the three largest synovial joints (hip, knee and shoulder) will be discussed in detail and suggestions will be made for future developments. Continuous developments in the field of the tribology of artificial joints can massively improve care for patients. The revision figures and reasons already show the success of individual improvements in recent years.

Velocity and Temperature Dependence of Steady‐State Friction of Natural Gouge Controlled by Competing Healing Mechanisms

AbstractThe empirical rate‐ and state‐dependent friction law is widely used to explain the frictional resistance of rocks. However, the constitutive parameters vary with temperature and sliding velocity, preventing extrapolation of laboratory results to natural conditions. Here, we explain the frictional properties of natural gouge from the San Andreas Fault, Alpine Fault, and the Nankai Trough from room temperature to ∼300°C for a wide range of slip‐rates with constant constitutive parameters by invoking the competition between two healing mechanisms with different thermodynamic properties. A transition from velocity‐strengthening to velocity‐weakening at steady‐state can be attained either by decreasing the slip‐rate or by increasing temperature. Our study provides a framework to understand the physics underlying the slip‐rate and state dependence of friction and the dependence of frictional properties on ambient physical conditions.

A novel physics-based modeling approach for tangential fretting contact behavior of jointed interface considering multi-scale effects

A novel physics-based constitutive model has been developed to map the tangential fretting behavior of joint surfaces. The model integrates the fractal normal contact model, which considers multi-scale effects, and the Iwan model through the Coulomb friction law. In this model, a new distribution of yield force is proposed for Jenkins elements, which is determined by fractal topography and material parameters and related to the scale of asperity. The effects of fractal topography, material parameters, and the normal load applied to the joint surface on the tangential responses such as tangential force, tangential stiffness, energy dissipation, and the distribution of yield force have been discussed. It has been found that the fractal parameters D and G have opposite effects on the tangential responses and yield force distribution.

Responses of the Pine Island and Thwaites glaciers to melt and sliding parameterizations

Abstract. The Pine Island and Thwaites glaciers are the two largest contributors to sea level rise from Antarctica. Here we examine the influence of basal friction and ice shelf basal melt in determining projected losses. We examine both Weertman and Coulomb friction laws with explicit weakening as the ice thins to flotation, which many friction laws include implicitly via the effective pressure. We find relatively small differences with the choice of friction law (Weertman or Coulomb) but find losses to be highly sensitive to the rate at which the basal traction is reduced as the area upstream of the grounding line thins. Consistent with earlier work on Pine Island Glacier, we find sea level contributions from both glaciers to vary linearly with the melt volume averaged over time and space, with little influence from the spatial or temporal distribution of melt. Based on recent estimates of melt from other studies, our simulations suggest that the combined melt-driven and sea level rise contribution from both glaciers may not exceed 10 cm by 2200, although the uncertainty in model parameters allows for larger increases. We do not include other factors, such as ice shelf breakup, that might increase loss, or factors such as increased accumulation and isostatic uplift that may mitigate loss.

A doubly history‐dependent quasivariational inequality arising in viscoelastic frictional contact problems with wear

AbstractWe aim here to investigate a new mathematical model that describes the contact between a viscoelastic body, accounting for long memory and wear effects, and an obstacle referred to as the foundation. The contact model is governed by a normal compliance condition, coupled with Coulomb's law of dry friction for sliding, and wear effects. We derive the variational formulation of the model, which involves coupling of a quasi‐variational inequality with a nonlinear equation. By pursuing the abstract history‐dependent quasi‐variational inequalities and leveraging the fixed point theorem, we establish results concerning both existence and uniqueness.

Phase-field model for 2D cohesive-frictional shear fracture: An energetic formulation

This paper presents a phase-field model for cohesive-frictional shear fracture. The model is derived based on two energetic principles: the energy conservation law and a variational inequality of virtual work that serves as a stability condition. We show that all the governing equations for frictional fracture can be obtained from the above two principles, including the equilibrium condition, the phase-field evolution law and, most importantly, the yield function and flow rule for the plasticity-like frictional slip. The information of crack direction is naturally included in the flow rule. Theoretical and numerical results show that the proposed model is faithfully consistent with the Mohr–Coulomb theory of frictional failure in terms of the crack nucleation stress and direction. In addition, the presented phase-field model has an explicit frictional cohesive law.

Sliding frictional and adhesive coupling contact analysis of FGPM layered half-space under an insulating indenter

This paper proposes an analysis model for the sliding frictional and adhesive coupling contact problem in the plane strain state between the FGPM layered half-space and an insulating indenter. The electro-mechanical properties of FGPM layer vary exponentially along the thickness direction. By applying the Fourier integral transformation and superposition principle to the governing boundary value problem, the general solution for the sliding frictional and adhesive coupling contact problem can be derived by using the Maugis type of adhesion theory and extended Amonton’s law of friction. A Cauchy singular integral equation is further derived for present problem which is then numerically solved. The primary aim of this paper is to provide insight into the likely behavior for the effect of the gradient index, friction coefficient and adhesion parameters on the surface electro-mechanical response of FGPM layered half-space. For given values of parameters R, w, βh and μ, when value of σ0 decreases from infinity to zero there is a continuous transition from the JKR approximation to the DMT approximation. The research not only helps to further understand the frictional and adhesive damage mechanisms of MEMS devices composed of FGPM, but also provides reference basis for FGPM layer experimental analysis and intelligent structure design.

Effect of Protein (Bovine Serum Albumin) Content on the Frictional Behaviour of Soft Contact Lenses Using a Dynamic Oscillating Tribometer

Proteins can adsorb on the surface of materials, such as soft contact lenses (SCLs), and can affect the hydrophobicity, roughness, and surface properties of the contact lenses (CLs), which, in turn, can influence the friction between the lenses and the ocular surface. Excessive friction between contact lenses and the ocular surface can lead to discomfort for the wearer and may cause irritation or inflammation of the cornea, better known as corneal ulcers (keratitis). Bovine Serum Albumin (BSA) is often used as a standard protein in biocompatibility testing of materials, including contact lenses. One standard commercial contact lens was tested under lubricated conditions to access the coefficient of friction (CoF). The contact was lubricated with a tear-like fluid (TLF) solution containing six different concentrations of BSA. In all cases, good linearity of the results of the friction force was verified, suggesting that the first friction law can be applied to determine the value of the coefficient of friction. It was found that friction increases with the increase in protein concentration.