Critical Friction Coefficient Research Articles

A novel fracture criterion for elastic‐brittle cracked body under compression and shear conditions

AbstractWhen the elastic‐brittle cracked body is subjected to compressive‐shear loading, not only does the phenomenon of wing crack initiation and propagation occur, but there is also a notable incidence of secondary crack initiation and propagation due to shear stress. Moreover, the shear fracture toughness (KIIc) predicted by the fracture criterion in the framework of classical fracture mechanics is usually smaller than the tensile fracture toughness (KIc), which is inconsistent with the actual observations. Therefore, this research firstly establishes a mechanical model of an elastic‐brittle cracked body under biaxial compression considering three kinds of crack parameters and materials' mechanical properties. Then, the stress field characteristics at the crack tip are analyzed. Next, a compression‐shear mixed fracture criterion is proposed. Finally, the effects of the lateral pressure coefficient (λ), critical plastic zone size (rc), friction coefficient (f), and deformation parameters of the crack surface on the failure modes at the crack tip are investigated.

Slip at the edge of complete contacts

We describe an asymptotic method for calculating the size of a zone of partial slip at the edge of a complete contact of arbitrary edge angle and coefficient of friction. Above a critical coefficient of friction the contact remains stuck, and this critical value is explored. A distributed dislocation method is used and the use of different types of numerical quadrature is explored. The size of the slip zone, and its dependence on the contact edge angle and coefficient of friction, are explored.

Investigation of the singularity under non-proportional damping in an analytical solution of brake squeal

This research investigates a singularity in a published analytical solution of brake squeal due to mode coupling. Brake squeal is an annoying tonal noise that results from the slowing of a vehicle with friction brakes. Recent research has identified an efficient analytical prediction for occurrence, growth, limit cycle amplitude and mitigation of brake squeal noise. The analytical solution predicts squeal accurately, except at a singularity associated with large non-proportional damping and repeated roots. Physically this occurs at the exact transition to stiffness mode coupling, ie. complex roots (Δ = 0). By taking the limit of the eigenvalue expressions at Δ = 0, it is found that the analytical eigenvalues approach infinity. The singularity occurs because modal mass matrix goes to zero at Δ = 0. The eigenvalues at Δ = 0 can be approximated by averaging the eigenvalues that are located on both sides of the critical friction coefficient (the average of eigenvalues at μcrit-Δμ and μcrit+Δμ). The approximations are closest to the numerical solution when Δμ is at the critical points of the Im(λavg) vs Δμ plot. In summary, the analytical solution under non-proportional damping is undefined at Δ = 0 because of the zero modal mass matrix. Moreover, the eigenvalues at the point where singularity occurs can be approximated by taking the average of the eigenvalues located on both sides of the critical friction coefficient. It is shown that reasonable approximations can be obtained at the critical points of the Im(λavg) vs Δμ plot.

Theoretical Study of the Friction Coefficient in the M-B Model

In order to study the influencing factors of friction coefficient in an M-B model, based on the basic model of fractal theory, the distribution function and probability distribution density of the micro-convex body truncation area are derived by using mathematical and statistical means, and a new model of critical truncation area and friction coefficient in fractal surface contact process are proposed. Considering the differences between the actual contact area and the truncated area during plastic deformation of the micro-convex body, a correction factor is introduced. Focusing on the mechanism of the elastic-plastic transition phase, and finally a friction coefficient model based on the fractal dimension, the normal force and correction factor is derived. Finally, the friction coefficient of fractal surface is simulated and verified by taking nickel as an example, and it is proved that the new model is correct in predicting the change trend of friction coefficient in the M-B model.

Plane strain wedge indentation revisited

For a plane strain wedge indentation problem, detailed comparisons between slip-line field theory (SLFT) solutions, experimental observations and finite-element analysis results are carried out. Several past remaining questions on this problem are explored. The finite-element computations appear to account for the nature of a modified slip-line field solution (Petryk H. 1980 Journal de Mécanique Appliquée 4 , 255–282) that assumes the existence of an additional fan-shaped slip-line field just above the boundary between yielding and unyielding regions. For obtuse-angled wedges, finite-element computations show that the indentation load could be smaller for a rough wedge than for a smooth wedge. The question that was raised in the literature with respect to the reversed order of required loads for smooth and rough wedges is not necessarily a paradox. It is revealed that with increasing friction coefficient, a distinct deformation mode resembling the dead metal cap solution in the SLFT is established immediately after passing the critical friction coefficient value at which the contact mode theoretically changes from frictional sliding to perfect sticking. The profiles of the bulged-out lip material remain straight in all the finite-element computations for non-hardening materials. Nonlinearity of the lip profiles frequently observed in experiments appears in the presence of strain hardening or strain-rate sensitivity.

A coupled CFD-DEM simulation of fracture sealing: Effect of lost circulation material, drilling fluid and fracture conditions

Lost circulation could be one of the most troublesome and expensive situations during drilling, especially in naturally fractured formations. Sealing fractures by granular lost circulation materials (LCMs) is one of the common methods for lost circulation control. However, this type of LCM has a limited effectiveness partly due to the poor understanding of how granular LCMs work. To fill this gap, a coupled CFD-DEM model is utilized for simulating the sealing process of a typical granular LCM (calcium carbonate) in a wedge-shaped fracture. In this paper, we first defined a set of comprehensive evaluation criteria for the sealing performance of LCMs, which include sealing probability, sealing time, location and stability of the seal, total loss volume and pressure gradient within the sealing zone. Effects of LCM, base fluid and fracture geometry on the sealing performance were investigated using the above-mentioned criteria based on differential pressure buildup, cumulative loss volume, and LCM loss rate, and differential pressure along depth. Our results show that LCM bridging and sealing in the fractures are initialed and controlled under interactive fluid-particle forces (drag force, viscous force and pressure gradient force), contact forces (normal and tangential) and friction forces (static and sliding). Essentially, it is the fluid-particle interactions, ratio of particle size to fracture width, volume concentration and friction effect that determine the fracture sealing performance. For the 1 mm–0.34 mm wedge-shaped fractures, sealing by LCM suspension with particle volume concentration of 9%, the critical bridging and sealing particle size are 200 μm and 330 μm, respectively. For the base simulation case considered in this paper, the critical bridging concentration and the sealing initiation concentration are both between 5% and 7%, and the critical sealing concentration is ranging between 7% and 9%. The critical coefficient of friction between particles for a stable fracture sealing varies between 0.2 and 0.4, and the critical coefficient of friction between particles and fracture surface for stable fracture sealing is ranging between 0 and 0.2. The critical Young’s modulus of particles for dual-particle bridging is between 0.1 and 1 GPa. The critical fluid injection rate is ranging between 1.25 and 3 m/s beyond which the LCM cannot seal the fracture. The rest of factors affect LCM bridging and sealing by changing these four factors to some extents. Particle size, volume concentration, Young’s modulus and the coefficient of friction of bridging granular LCM, and density, viscosity and injection rate of base fluid should be optimized synergistically to achieve an efficient fracture sealing. This research provides a better insight into the working principle of LCMs, which gives a solid scientific basis for LCM selection and design in practical problems.

Prediction of Dynamic Stick-Slip Events in Belt-Drives Using a High-Fidelity Finite Element Model

AbstractA high-fidelity dynamic finite element model of a one-pulley belt-drive system is used to study how Coulomb friction coefficient and adhesion stress affect belt stick-slip events over driver and driven pulleys. The model shows that at Coulomb friction coefficient below a certain critical value, the belt undergoes pure sliding in the slip arc on driver and driven pulleys with no stick-slip dynamic events. Above that critical friction coefficient value dynamic stick-slip events start to occur in both driver and driven pulleys resulting in torque pulses, which for practical belt-drives may cause nonsmooth operation, excessive belt noise and/or excessive belt wear. For driver pulleys the dynamic stick-slip events are in the form of Schallamach waves, while for driven pulleys the dynamic stick-slip events are in the form of expansion pulses. The model results are validated using recently generated experimental results.

Sensitivity Analysis of Holdback Bar Release Load during Catapult-Assisted Takeoff of Carrier-Based Aircraft

The release load of holdback bar will affect the safety of catapult-assisted takeoff of carrier-based aircraft, and the accurate control of releasing the load will ensure success. The magnitude and the control accuracy of release load are important parameters which impact the takeoff performance, therefore unstable release load and insufficient release precision are the main factors affecting the takeoff safety. In this paper, mechanical models of the carrier-based aircraft in the catapult-assisted takeoff tensioning state and gliding state after release are established based on multi-body dynamics, contact mechanics and tribological theory, and the influence of the release load of the holdback bar on the catapult-assisted takeoff performance is analyzed. Furthermore, a kinetic model of the holdback bar device is established, and the kinetic characteristics of the release process of the holdback bar are studied. Based on the kinetic model and friction model of the holdback bar, the influencing factors of the sensitivity of the holdback bar release load are analyzed and the structural parameters are optimized. The results show that the released load decreases slowly with the increase of the contact surface angle of the holdback bar structure and increases rapidly when that angle reaches the critical value; besides, the release load increases slowly with the increase of the friction coefficient of the contact surface and increases faster when the critical friction coefficient is reached.

On Ziegler Effect with Arbitrary Large Viscous Friction

We study a mechanical system with two degrees of freedom simulating the motion of rotor blades on an elastic bushing of a medium-sized helicopter. For small values of some problem parameters, the destabilizing effect due to small linear viscous friction forces has been studied earlier. Here we study the problem with arbitrary large friction forces for arbitrary values of the problem parameters. In the plane of parameters, the regions of asymptotic stability and instability are calculated. As a result, necessary and sufficient conditions for the existence of a destabilizing effect under the action of potential, follower forces and arbitrary friction forces have been obtained. It is shown that, if some critical friction coefficient $k_{*}$ tends to infinity, then there exists a Ziegler area with arbitrarily large dissipative forces.

Rheology of mobile sediment beds in laminar shear flow: effects of creep and polydispersity

Classical scaling relationships for rheological quantities such as the $\mu (J)$ -rheology have become increasingly popular for closures of two-phase flow modelling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modelling by using a more realistic sediment composition. We investigate the rheological behaviour of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to 10, which corresponds to grains ranging from fine to coarse sand. The data was generated using fully coupled, grain resolved direct numerical simulations using a combined lattice Boltzmann–discrete element method. These highly resolved data yield detailed depth-resolved profiles of the relevant physical quantities that determine the rheology, i.e. the local shear rate of the fluid, particle volume fraction, total shear and granular pressure. A comparison against experimental data shows excellent agreement for the monodisperse case. We improve upon the parameterization of the $\mu (J)$ -rheology by expressing its empirically derived parameters as a function of the maximum particle volume fraction. Furthermore, we extend these considerations by exploring the creeping regime for viscous numbers much lower than used by previous studies to calibrate these correlations. Considering the low viscous numbers of our data, we found that the friction coefficient governing the quasi-static state in the creeping regime tends to a finite value for vanishing shear, which decreases the critical friction coefficient by a factor of three for all cases investigated.

Failure analysis of extractor slipping in the cartridge case extraction process under different working conditions

A cartridge case extractor is a component which is used to extract cartridge cases out of a gun barrel. The extractor slipping from the cartridge case is a kind of motion failure caused by the coupled effects of friction and deformation. Certain working conditions have significant effects on this failure mode. In this study, a method for analyzing the failure behavior and condition of the extractor slipping is presented. The failure mode and theoretical model of the extractor slipping are firstly discussed. A finite element model is then established to simulate the cartridge case extraction process of a machine-gun. The effects of different working conditions, including ambient temperature, number of consecutive shots, and friction coefficient, on the cartridge case extraction process, are also analyzed. A concept of critical friction coefficient under a specific working condition is introduced in the extractor slipping condition analysis. The experimental results are also illustrated to verify the simulation results. Finally, the sensitive parameters of the extraction mechanism are analyzed and redesigned based on the established simulation model in order to reduce the failure rate of the cartridge extraction process.

Investigation of Piezoelectric Energy Harvesting via Nonlinear Friction-Induced Vibration

In this work, piezoelectric energy harvesting (PEH) performance via friction-induced vibration (FIV) is studied numerically. A nonlinear two-degree-of-freedom friction system (mass-on-belt) with piezoelectric elements, which simultaneously considers the stick-slip motion, model coupling instability, separation, and reattachment between the mass and belt, is proposed. Both complex eigenvalue analyses and transient dynamic analysis of this nonlinear system are carried out. Results show that it is feasible to convert FIV energy to electrical energy when the friction system is operating in the unstable vibration region. There exists a critical friction coefficient (μc) for the system to generate FIV and output visible voltage. The friction coefficient plays a significant role in affecting the dynamics and PEH performance of the friction system. The friction system is able to generate stronger vibration and higher voltage in the case that both the kinetic friction coefficient and static friction coefficient are larger thanμc. Moreover, it is seen that the separation behavior between contact pair can result in overestimating or underestimating the vibration magnitude and output voltage amplitude, and the overestimate or underestimate phenomenon is determined by the located range of friction coefficient. Furthermore, it is confirmed that an appropriate value of external resistance is beneficial for the friction system to achieve the highest output voltage. The obtained results will be beneficial for the design of PEH device by means of FIV.

Sequential Track–Bridge Interaction Analysis of Quick-Hardening Track on Bridge Considering Interlayer Friction

A quick-hardening track (QHT) was developed by injecting quick-hardening mortar into an existing ballast track to rapidly substitute the ballast track with a slab track, thereby improving maintainability and running safety. QHT tracks on a bridge undergo track–bridge interactions similar to other track systems. This paper presents a model to analyze the interaction between the QHT and the bridge. This model considers the longitudinal resistances of rail fasteners and anchors, as well as the interlayer friction between the track and the bridge. A sequential analysis method was applied to systematically consider such effects, revealing that rail additional stress will be high if the track slips over the bridge for a very low frictional coefficient of 0.1. Furthermore, a track segment without an anchor can slip under train traction load when the frictional coefficient is 0.3 or lower. For low friction cases, low-speed operation is advised to prevent the accumulation of the resulting longitudinal slip displacements of the track. An anchor should be installed immediately after the quick-hardening mortar provides sufficient bearing strength to the anchors. The proposed sequential analysis is useful for determining the critical friction coefficient and appropriate longitudinal resistance of a rail fastener, as well as for verifying track safety.

Existence and multiplicity of solutions in frictional contact mechanics. Part II: Analytical and numerical case study

In the first Part (Part I) of this series, the plane quasi-static incremental problem was formulated as a mixed complementarity-inclusion problem and as a linear complementarity problem. The current paper (Part II of the series) presents a numerical examination for the existence or the occurrence of multiple solutions to the quasi-static incremental problem of a two degree of freedom elastic system in the presence of a frictional rectilinear obstacle. The onset of multiplicity of solutions is studied and numerical examples are presented. All the solutions for two dimensional finite element examples are computed and their dependence on some parameters is discussed. The conditions for the occurrence of multiple solutions were discussed for finite element models. A particular attention was devoted to finite element models of rectangular blocks and finite element versions of the one particle model of Klarbring. For finite element blocks, it was found that the critical friction coefficient for solution uniqueness depends on the Poisson's ratio (μI decreases with ν). It was also noticed that slender structures with respect to the obstacle lead to smaller coefficients of friction. The same behavior was detected for the finite element version of Klarbring's example except that Poisson's ratio had a weak influence on the critical value of the friction coefficient. An algorithm is used for the computation of all the solutions of the incremental problem and to verify the sharpness of the frictional coefficient estimates corresponding to the several criteria. Comparison of different criteria for the uniqueness of the solution (for any loading) of the quasi-static incremental problem in finite element models is presented.

Coordinated Particle Relocation Using Finite Static Friction With Boundary Walls

We present theoretical and practical methods for achieving arbitrary reconfiguration of a set of objects, based on the use of external forces, such as a magnetic field or gravity: Upon actuation, each object is pushed in the same direction until it collides with an obstruction. This concept can be used for a wide range of applications in which particles do not have their own energy supply. A crucial challenge for achieving any desired target configuration is breaking global symmetry in a controlled fashion. Previous work made use of specifically placed barriers; however, introducing precisely located obstacles into the workspace is impractical for many scenarios. In this letter, we present a different, less intrusive method: making use of the interplay between static friction with a boundary and the external force to achieve arbitrary reconfiguration . Our key contributions are a precise theoretical characterization of the critical coefficient of friction that is sufficient for rearranging two particles in triangles, convex polygons, and regular polygons; a method for reconfiguring multiple particles in rectangular workspaces, and deriving practical algorithms for these rearrangements. Hardware experiments show the efficacy of these procedures, demonstrating the usefulness of this novel approach.

Determination of critical wedging coefficient for full-contact frictional systems using positive spanning

Wedging is a contact phenomenon in which slip displacement persists after the complete removal of the external loading on the system. As no positive spanning sets exist in non-wedged systems, a suitable algorithm is proposed for determining the critical coefficient of friction for wedging. The objective of the algorithm is to determine successive positive bases as the friction coefficient gradually increases, until all the bases are exhausted; therefore, the algorithm determines the critical coefficient of friction for unilateral contact wedging. The algorithm is validated using several examples in the framework of the method of finite elements, which yields the critical wedging coefficient and the corresponding wedge state.

Evaluation of nanosecond laser ablation and scratch resistance of tantalum carbide coated graphite substrates

The present work aimed at investigating the effect of nanosecond laser parameters on ablation characteristics such as ablation depth and surface roughness of plasma sprayed tantalum carbide coated graphite substrates. The micro scratch tests were performed on the laser ablated and as-sprayed coatings to evaluate the critical loads and coefficient of friction. The laser ablated surface with minimum ablation depth and surface roughness was found to exhibit 18% higher critical loads when compared to that of as-sprayed surface. However, laser ablated surfaces exhibited slightly higher friction coefficient than as-sprayed surfaces due to formation of metastable oxide layer (Ta6O) on the top surface of TaC coatings as indicated by XRD. The maximum ablation and scratch resistance could be found at maximum pulse energy of 250 μJ, maximum scanning speed of 1000 mm/s and moderate hatch spacing of 20 μm. While, the failure of as-sprayed TaC coatings was attributed to local collapsing of material due to degradation of mechanical properties such as elastic modulus, surface porosity and surface roughness, laser ablated surfaces exhibited wedge spallation at the end of scratch zone only.

Corner stress fields in sliding at high friction coefficients

If an elastic body with a sharp corner slides over an elastic half-plane, the stress and displacement fields near the corner can be characterized by the leading term in an asymptotic [eigenfunction] series. However, there exists a critical friction coefficient f=fd at which an infinitesimal increase in f appears to imply a discontinuous change from singular to bounded local fields at the leading edge. Here, we show that this conclusion is incorrect. Instead, the contact region shrinks to zero at f=fd implying the existence of a concentrated contact force, but the singular field associated with point contact is retained for f>fd. We also show that a non-linear solution using a Generalized Neo-Hookean constitutive law gives the same conclusion, and that the concentrated force generated is well predicted by the linear analysis. However, in contrast to the linear solution, the total strain energy in the non-linear solution is bounded.

Strength Analysis of Bolts Connection of Composite Plywood of Low-Noise Brake Beam

As the key subsystem of the locomotive, the braking performance of the brake system has a crucial impact on the safety of the vehicle, as the most critical connecting component in the braking system, the connecting bolts have a direct impact on the braking performance of the braking system. Therefore, the strength of the bolt must be checked and analyzed before the braking system is installed. Aiming at the braking system of a freight train, this paper adopts the method of combining theory with finite element numerical analysis to check and analyze the strength of the bolts during the braking process. Firstly, the bolt is subjected to force analysis and the reasonable preload range of the bolt and the critical friction coefficient between the friction plate and the brake caliper are deduced theoretically. Then by using finite element numerical analysis method, the influence of preload on the bolt and friction coefficient between friction plate and brake caliper on force loaded bolts during braking is analyzed by simulating the actual braking process. The results show that the bolt pretension is uneven and the friction coefficient between the friction plate and the brake caliper has a great influence on the bolt strength.

Complete contacts in almost conforming sockets

The behaviour of a contact formed when a flat-faced contact sits in an almost conforming socket is studied. Conditions for the avoidance of all slip are found, and the critical coefficient of friction needed is found. The results derived are of a general nature and apply to many problems of this class, for example, when a dovetail is pulled into a socket having the same angle.