Coulomb Friction Coefficient Research Articles

Effects of restitution, friction, and attitude on 2D low-velocity rigid-body impacts

The impact of nonspherical bodies is complex, even at low velocities where contacting bodies are assumed to be rigid. Models of varying complexity (e.g. finite element methods) can be used to evaluate such impacts, but it is advantageous to use impulsive models such as that by Stronge, which are computationally inexpensive and governed by (fixed) material interaction coefficients. Stronge’s model parameterizes nonspherical rigid-body impacts with energetic restitution and Coulomb friction coefficients. This model was successfully used in large-scale simulations of ballistic lander deployment to asteroids and comets, whose trajectories involve dozens of chaotic bounces. To better understand the complex dynamics of these bouncing trajectories, this paper performs a dedicated study of idealized bouncing in two dimensions and on a flat plane, in order to limit the involved degrees of freedom. Using a numerical implementation of Stronge’s model, the motion of a bouncing square is simulated with different impact conditions: the square’s impact attitude, velocity, and mass distribution as well as the surface restitution and friction coefficients. The simulation results are used to investigate how these conditions affect the bouncing motion of the square, with a distinction between first impacts with zero angular velocity and successive impacts in which the square is spinning. This reveals how a single “macroscopic” bounce that separates two ballistic arcs may often consist of multiple micro-impacts that occur in quick succession. For the different impact conditions, we show how the number of micro-impacts per macro-bounce varies, as well as the normal, tangential, and total kinematic restitution coefficients. These are different from the energetic material restitution coefficient that parameterizes the impact. Finally, we examine how the settling time and distance of the bouncing trajectories change. These trends provide insight into the bouncing motion of ballistic lander spacecraft in small-body microgravity.

Numerical simulation on post-earthquake debris flows: A case study of the Chutou gully in Wenchuan, China

Since the 2008 Wenchuan earthquake, post-earthquake debris flows have severely threatened people’s lives and the safety of public transit facilities, making particularly crucial to understand their formation mechanism. We focused on the Chutou gully debris flow and analyzed its formation mechanism based on field investigations and satellite images. The main inducing factor of this debris flow was a continuous heavy rainfall that exceeded the threshold of the study area: this, combined with the large amount of loose material created by the earthquake, dramatically promoted the volume and hazard degree of the debris flow. The three-dimensional debris flow simulation software RAMMS, based on an improved Voellmy–Salm fluid model, was used to simulate the movement process of the Chutou gully debris flow. The calibrated Coulomb friction (μ) and viscous turbulent friction (ξ) coefficients in the study area were 0.225 and 180 m/s2, respectively. The simulation results revealed the post-earthquake debris flow mechanism in terms of flow height, velocity, flow rate, and deposition area. The results of the numerical simulation were in good agreement with those of the field investigations. In particular, it was found that the peak flow of debris flow upstream of the Chutou gully was shorter in duration than the one upstream; however, due to the convergence of the branch gully, the downstream peak flow of debris flow increased significantly, while a large amount of solid material stranded downstream of the channel. Notably, this process is prone to occur again. This study proposes a new post-earthquake debris flow evaluation method, and its results are of reference value for the design of debris flow prevention engineering in meizoseismal areas.

The Influence of Hydrothermal Aging on the Dynamic Friction Model of Rubber Seals.

Cylinder has become an indispensable and important pneumatic actuator in the development of green production technology. The sealing performance of the cylinder directly affects its safety and reliability. Under the service environment of the cylinder, hydrothermal aging of the rubber sealing ring directly affects the dynamic friction performance of the cylinder. So, the dynamic friction model of the cylinder has been developed based on the LuGre friction model, which considers the influence of hydrothermal aging. Here, the influences of the static friction coefficient and Coulomb friction coefficient on the friction model are analyzed. Then, the aging characteristic equation of rubber is embedded in the model for revealing the influence of aging on the friction coefficient of the model. Results show that the aging temperature, aging time, and compressive stress affects the friction coefficient; the variation of the static friction coefficient is larger than that of the Coulomb friction coefficient. The improved cylinder friction model can describe the influence of the aging process on the cylinder friction characteristics, which is of great significance in the design of the cylinder’s dynamic performance.

Analytical and numerical analysis on the collapse modes of least-thickness circular masonry arches at decreasing friction

Departing from pioneering Heyman modern rational investigations on the purely-rotational collapse mode of least-thickness circular masonry arches, the hypothesis that joint friction shall be high enough to prevent inter-block sliding is here released. The influence of a reducing Coulomb friction coefficient on the collapse modes of the arch is explicitly inspected, both analytically and numerically, by tracing the appearance of purely-rotational, mixed sliding-rotational and purely-sliding modes. A classical doubly built-in, symmetric, complete semi-circular arch, with radial joints, under self-weight is specifically considered, for a main illustration. The characteristic values of the friction coefficient limiting the ranges associated to each collapse mode arc first analytically derived and then numerically identified, by an independent self-implementation, with consistent outcomes. Explicit analytical representations are provided to estimate the geometric parameters defining the limit equilibrium states of the arch, specifically the minimum thickness to radius ratio, at reducing friction. These formulas, starting from the analysis of classical Heymanian instance of purely-rotational collapse, make new explicit reference to the mixed sliding-rotational collapse mode, arising within a narrow range of limited friction coefficients (or friction angles). The obtained results are consistently compared to existing numerical ones from the competent literature.

The critical effect of rail vertical phase response in railway curve squeal generation

Squeal of rail-bound vehicles emitted in tight curves is characterized by high sound pressure levels at pure medium and high frequencies. Many models have been proposed in the literature to explain the occurrence of this noise with different instability mechanisms: negative damping due to falling friction or instability with a constant friction coefficient. The aim of the paper is to contribute to the understanding of the instability mechanisms in the case of a constant friction coefficient. A stability analysis of the wheel/rail contact dynamics in curve is performed by using an equivalent point contact model combined with wheel and rail modal bases. Results show that even with an assumption of a constant Coulomb friction coefficient, two types of instabilities may occur in the wheel/rail system: classical mode coupling and instabilities due to negative damping added to a single wheel mode when the track dynamical behavior, especially in the vertical direction, is included. For this second type of instabilities, an 1-degree of freedom model can be formulated. By using this model, it is found that the equivalent damper behavior of the infinite track is the origin of these instabilities.

Sensitivity Analysis of Johnson-Cook Material Constants and Friction Coefficient Influence on Finite Element Simulation of Turning Inconel 718.

The Johnson-Cook (J-C) constitutive model, including five material constants (A, B, n, C, m), and the Coulomb friction coefficient (μ) are critical preprocessed data in machining simulations. Before they become reliable preprocessed data, investigating these parameters’ effect on simulation results benefits parameter-selecting. This paper aims to investigate the different influence of five settings of the J-C constitutive equation and Coulomb friction coefficient on the turning simulation results of Inconel 718 under low-high cutting conditions, including residual stress, chip morphology, cutting force and temperature. A three-dimensional (3-D) finite element model was built, meanwhile, the reliability of the model was verified by comparing the experiment with the simulation. Sensitivity analysis of J-C parameters and friction coefficient on simulation results at low-high cutting conditions was carried out by the hybrid orthogonal test. The results demonstrate that the simulation accuracy of Inconel 718 is more susceptible to strain hardening and thermal softening in the J-C constitutive model. The friction coefficient only has significant effects on axial and radial forces in the high cutting condition. The influences of the coefficient A, n, and m on the residual stress, chip thickness, cutting force and temperature are especially significant. As the cutting parameters increase, the effect of the three coefficients will change visibly. This paper provides direction for controlling simulation results through the adjustment of the J-C constitutive model of Inconel 718 and the friction coefficient.

Motion of a Puck on a Rotating Horizontal Plane

The motion of a puck on a horizontal plane rotating about a vertical axis with dry friction is considered. It is assumed that the Coulomb law of dry friction is locally valid at each point belonging to the lower surface of the puck. The resultant force and friction torque are determined according to the dynamically consistent model of contact stresses. This problem generalizes the problem of motion of a puck on a fixed plane and the motion of a disk (a puck of zero height) on a rotating plane. The invariant sets of the problem are found and their properties are studied. In the case of a sufficiently small Coulomb friction coefficient, the general solution to the equations of motion of the puck is constructed as a power series expansion with respect to this coefficient.

On critical surface strain during hot forging of lubricated aluminum alloy

Abstract We present a new concept of critical surface strain to evaluate the lubrication-effective limit for process design in metal forming. Finite-element predictions obtained at various fixed Coulomb friction coefficients were compared in hot-forging experiments of a passenger car piston fabricated from short cylindrical aluminum alloy specimens well-lubricated with a solid film of water-dispersed lubricant. The Coulomb friction coefficient was formulated as a function of temperature, pressure, and material strain, and optimized by minimizing the difference between the predicted and experimental results. We established that the effect of surface strain dominated the metal-forming process, and that the optimized Coulomb friction coefficient changed abruptly at the critical surface strain at which the solid lubricating film used in the process is suddenly disrupted.

Lateral resistance of “rigid” pipelines and cables on rocky seabeds

Accurate assessment of lateral resistance is critical to ensure the on-bottom stability and integrity of subsea pipelines and cables in the oil–gas and marine renewable energy industries. However, on rocky seabeds recommended practices provide limited recommendations on pipe–seabed interaction, suggesting only a single value for the friction coefficient of 0.6. This paper reports on a programme of physical experiments and theoretical modelling investigating the lateral resistance of pipes on rocky seabeds. It is shown that the peak and mean effective friction can significantly exceed the interface (or Coulomb) friction coefficient when the pipe diameter (D) is similar to the median rock diameter (dn50). Only when the pipe diameter becomes large compared to the rock size does the mean effective friction approach the interface friction. The effective friction coefficient was found to vary with variability in rock size and shape, as well as the length of pipe relative to median rock diameter. Each of these findings is reproduced well using the theoretical model. Collectively, the results demonstrate that the effective lateral friction coefficient may be higher than 0.6 for mean friction, and significantly higher for peak friction. This implies that inaccuracy may exist in current design, which may be rectified using the theoretical model.

Variation of the friction conditions in cold ring compression tests of medium carbon steel

Lubrication and friction conditions vary with deformation during metal forming processes. Significant macro-variations can be observed when a threshold of deformation is reached. This study shows that during the cold compression processing of #45 (AISI 1045) steel rings, the magnitude of friction and surface roughness (Ra) changes significantly upon reaching a 45% reduction in ring height. For example, the Ra of compressed ring specimens increased by approximately 55% immediately before and after reaching this threshold, compared to an 18% or 25%variation over a 35%-45% or a 45%-55% reduction in height, respectively. The ring compression test conducted by this study indicates that the Coulomb friction coefficient μ and Tresca friction factor m are 0.105 and 0.22, respectively, when the reduction in height is less than 45%; and 0.11 and 0.24, respectively, when the reduction in height is greater than 45%.

КОМПЛЕКСНОЕ КОНЕЧНО-ЭЛЕМЕНТНОЕ ИССЛЕДОВАНИЕ ПРОЦЕССОВ ПРОИЗВОДСТВА ТИТАНОВЫХ ПОЛОС НЕСИММЕТРИЧНОЙ ХОЛОДНОЙ ПРОКАТКОЙ ПОРОШКА С ПОСЛЕДУЮЩИМ СПЕКАНИЕМ

Finite-element numerical modeling was implemented and a study of the production processes of thin titanium strips was carried out on the basis of two key sequential processes: asymmetric powder rolling and sintering of the rolled product using the Brand-Nielson model. The results of studying the processes of compaction and sintering of titanium powder using a single mathematical model proposed by Jan Brandt are presented. For the calculations we used experimentally determined shear stresses and volumetric compression modulus under hydrostatic compression and uniaxial compression. The friction conditions between the surfaces of the rolls and the powder were determined as a function of the change in the Coulomb coefficient of friction on the relative sliding speed of the surfaces of the roll and the workpiece. An analysis of the results allows a quantitative assessment of the influence of the technology parameters of the compaction and sintering processes on the change in the stress state and relative density in the volume of products at the stages of production processes. It is shown that the application of the von Mises density and stress diagrams for the correction of the sintering regime allows avoiding the appearance of defects (insufficiently uniform density of the sintered material and the presence of microcracks) during intense heating of the metal in the furnace. The development of sintering modes based on the Brand-Nielson model simplifies the improvement of technology in the sintering of bulk bodies, which is a more time-consuming process than sintering of thin plates. This model can be used in the development of sintering regimes for various materials since it takes into account the influence of basic phenomena in this process. By varying the technology parameters it is possible to achieve targeted effects on product quality indicators and prevent the formation of microcracks in them.

Energy dissipation in sheared wet granular assemblies

Energy dissipation in sheared dry and wet granulates is considered in the presence of an externally applied confining pressure. Discrete element simulations reveal that for sufficiently small confining pressures, the energy dissipation is dominated by the effects related to the presence of cohesive forces between the particles. The residual resistance against shear can be quantitatively explained by a combination of two effects arising in a wet granulate: i) enhanced friction at particle contacts in the presence of attractive capillary forces, and ii) energy dissipation due to the rupture and reformation of liquid bridges. Coulomb friction at grain contacts gives rise to an energy dissipation which grows linearly with increasing confining pressure, for both dry and wet granulates. Because of a lower Coulomb friction coefficient in the case of wet grains, as the confining pressure increases the energy dissipation for dry systems is faster than for wet ones.

Experimental Estimation of Friction and Friction Coefficient of a Lightweight Hydraulic Cylinder Intended for Robotics Applications

Recently, hydraulic actuator has been used in several engineering applications such as: aeronautics, construction and robotics. This is due to the need of high torque and power density in such engineering applications. Despite these advantages, hydraulic actuators are fabricated from metallic materials, which provoke their heavy weight, which necessitate the development of a lightweight hydraulic actuator, fabricated of composite materials. Using composite materials in hydraulic cylinders, it is important to study the friction force characteristics and to estimate the friction coefficient between composites and O-rings, which is presented in this paper. This paper deals with the estimation of Coulomb friction and friction coefficient in the lightweight hydraulic cylinder fabricated mainly of composite materials. The actuator is presented by its dynamic equation of motion, where each term is discussed including the stiffness coefficient, the viscous damping coefficient, the kinematics and the pressure parameters. Meanwhile, these coefficients and parameters are obtained according to data recorded from conducted experiments. As a result, the new methodology which uses the experimental measurements combined the dynamic model has succeeded to evaluate the friction inside the hydraulic cylinder which has been estimated and found to be around 166[Formula: see text]N, while the corresponding coefficient of friction is computed (about 0.61 as average value). These results will be important for further optimization of the material choice and actuator design, which will help in the amelioration of the hydraulic cylinder.

Energy-based friction analysis

This paper describes a new approach for parameterizing friction models. Velocity measurements of a spring-mass-damper oscillator with a friction contact are used to determine the Coulomb friction coefficient for the friction-based energy dissipation. The energy-based friction force is then calculated and compared to the friction force determined from the product of the friction coefficient and normal force. The friction measuring machine, or FMM, is used to enable transient, linear sliding motion between friction contact pairs under constant normal force loading and a laser vibrometer is used to measure the corresponding time dependent velocity. Tests results are presented for a pin on oscillating flat contact with three different initial displacements. The measured velocity is used together with the FMM structural dynamics to determine the Coulomb friction coefficient and estimate the corresponding friction force during motion.

Frictional forces for disc-type pigging of pipelines

We investigate the frictional force which is acting on a pipeline pig. Two complementary experimental setups have been designed and used to study the sealing disc of a pig, which is responsible for the frictional force between the pig and the pipe wall. Six 12'' off the shelf sealing discs from two different vendors have been used. The first setup is a static setup in which the sealing disc is subjected to a normal wall force and a tangential friction force. A unique feature of the setup is that the ratio between the friction force and the wall force can be readily adjusted. This allows to experimentally determine the force ratio which is directly related to the Coulomb friction coefficient, which is often a difficult parameter to predict. Furthermore, the static setup is used to systematically study the effect of oversize, thickness, and Young's modulus of the sealing disc on the frictional force. A direct comparison with Finite Element (FE) calculations is made. The second experimental facility consist of a dynamic setup in which a sealing disc is pulled through a vertical 1.7 m long pipe. The effect of possible lubrication on the frictional force is studied by applying water to the sliding contact and comparing the results with dry pull tests for different sliding velocities. The corresponding difference in the Coulomb friction coefficient was quantified using FE calculations which were successfully verified with the static setup. The sensitivity of possible wear of the sealing disc on the frictional force is discussed.

초고강도강 성형공정에서 소재산포에 의한 스프링백 경향

In this paper, the reliability-based parameter study is carried out for the stamping process of a front rail roof member with the ultra high strength steel, considering the scatters of the material properties and the process parameters. With the reliability-based design optimization (RBDO) scheme, the springback tendency is investigated from the perturbation of the process parameters such as the sheet thickness, ultimate tensile strength, yield strength, Coulomb friction coefficient, and applied padding force. The amount of the elastic recovery along the height direction is quantified to describe the springback tendency from the analysis. The analysis shows the springback-amount scattering is not ignorable when the yield stress scatters within the similar range of the ultimate tensile strength. The analysis results fully explain the importance of controlling the scatters as well as the average yield-strength amount in the mass production of the stamped products.

Numerical study on flow behavior of multi-component particles in a fluidized bed using a TFM-DEM hybrid model

Flow behaviors of multi-type particles are investigated by TFM-DEM hybrid model coupled with kinetic theory of granular flow in a gas-solids bubbling fluidized bed. The flow behaviors of different discrete particles and continuum solids phase are analyzed. The effects of drag models, coefficient of restitution and friction coefficient on the flow behavior are predicted. Simulated results reveal that the higher restitution coefficient and friction coefficient give rise to higher velocities and lower solids volume fractions. The Huilin-Gidaspow drag model provides a better correspondence with the experiments. The influence of Coulomb friction coefficient on hydrodynamics is considered to simulate the flow of discrete particles, and the simulated results with Coulomb friction coefficient are in better agreement with experiments, comparing to results without Coulomb friction coefficient.

Effect of Workpiece Surface Topography on Friction in Cold Forging Using Environmentally-Friendly Lubricant

An optimal surface topography for the use of an environmentally friendly lubricant was elucidated, by making a wide combination of surface roughnesses Ra and RSm representing height and frequency of surface asperity, using the wet blast treatment. A forward conical can - backward straight can extruded friction test method proposed by the present authors was used. Coulomb friction coefficient was evaluated using a calibration curve representing the relationship between the surface friction coefficient of the conical punch and the front/back extrusion height of the workpiece. It was found that the surface topography of workpiece largely affects the lubricating property when the friction coefficient is large. Especially, the surface treatment with larger Ra and smaller RSm is effective for improving the friction. Furthermore, the correlation between the friction coefficient and the proposed parameter for the surface topography Ra/RSm was shown to be better than the Ra.

Automatic detection of abnormal torque while reaming

A lumped element model is implemented to describe the torsional vibrations of the drillstring while reaming, i.e. rotating off-bottom. The rotary motions and the torques anywhere in the drillstring are simply convolutions of the surface rotary motion with analytical expressions that are derived in this paper. The Coulomb friction forces are divided into steady-state forces and time-dependent forces. The drillstring vibrates around a stable position that is determined by the steady-state friction torques. The vibrations are damped by viscous friction forces and in particular the Basset forces dominate the damping. The time-dependent part of the Coulomb friction forces are related to when something is not normal in the well. For instance, when the drill bit is hindered by a cuttings bed or the bottom part of the drillstring is hung up in a sharp curvature.The model is further used in an algorithm for detecting the time-dependent Coulomb friction coefficients. A sensitivity study is added and the detection algorithm seems to be mathematically robust. This motivates experimental verifications of both the model and the detection algorithm in the future.

Guidelines for Selecting Plugs Used in Thin-Walled Tube Drawing Processes of Metallic Alloys

In this paper, some practical guidelines to select the plug or set of plugs more adequate to carry out drawing processes of thin-walled tubes carried out with fixed conical inner plug are presented. For this purpose, the most relevant input parameters have been considered in this study: the tube material, the most important geometrical parameters of the process (die semiangle, α , and cross-sectional area reduction, r ) and the friction conditions (Coulomb friction coefficients, μ 1 , between the die and the tube outer surface, and μ 2 , between the plug and the tube inner surface). Three work-hardening materials are analyzed: the annealed copper UNS C11000, the aluminum UNS A91100, and the stainless steel UNS S34000. The analysis is realized by means of the upper bound method (UBM), modelling the plastic deformation zone by triangular rigid zones (TRZ), under the validated assumption that the process occurs under plane strain conditions. The obtained results allow establishing, for each material, a group of geometrical parameters, friction conditions, a set of plugs that make possible to carry out the process under good conditions, and the optimum plug to carry out the process using the minimum amount of energy. The proposed model is validated by means of an own finite element analysis (FEA) carried out under different conditions and, in addition, by other finite element method (FEM) simulations and real experiments taken from other researchers found in the literature (called literature simulations and literature experimental results, respectively). As a main conclusion, it is possible to affirm that the plug that allows carrying out the process with minimum quantity of energy is cylindrical in most cases.