Coulomb Friction Coefficient Research Articles

Compressibility regularizes the 𝜇(I)-rheology for dense granular flows

The $\unicode[STIX]{x1D707}(I)$-rheology was recently proposed as a potential candidate to model the incompressible flow of frictional grains in the dense inertial regime. However, this rheology was shown to be ill-posed in the mathematical sense for a large range of parameters, notably in the low and large inertial number limits (Barker et al., J. Fluid Mech., vol. 779, 2015, pp. 794–818). In this rapid communication, we extend the stability analysis of Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818) to compressible flows. We show that compressibility regularizes the equations, making the problem well-posed for all parameters, with the condition that sufficient dissipation be associated with volume changes. In addition to the usual Coulomb shear friction coefficient $\unicode[STIX]{x1D707}$, we introduce a bulk friction coefficient $\unicode[STIX]{x1D707}_{b}$, associated with volume changes and show that the problem is well-posed if $\unicode[STIX]{x1D707}_{b}>1-7\unicode[STIX]{x1D707}/6$. Moreover, we show that the ill-posed domain defined by Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818) transforms into a domain where the flow is unstable but remains well-posed when compressibility is taken into account. These results suggest the importance of taking into account dynamic compressibility for the modelling of dense granular flows and open new perspectives to investigate the emission and propagation of acoustic waves inside these flows.

A novel LLSDPso method for nonlinear dynamic parameter identification

PurposeThis paper aims to propose a novel method to identify the parameters of robotic manipulators using the torque exerted by the robot joint motors (measured by current sensors).Design/methodology/approachPrevious studies used additional sensors like force sensor and inertia measurement unit, or additional payload mounted on the end-effector to perform parameter identification. The settings of these previous works were complicated. They could only identify part of the parameters. This paper uses the torque exerted by each joint while performing Fourier periodic excited trajectories. It divides the parameters into a linear part and a non-linear part, and uses linear least square (LLS) parameter estimation and dual-swarm-based particle swarm optimization (DPso) to compute the linear and non-linear parts, respectively.FindingsThe settings are simpler and can identify the dynamic parameters, the viscous friction coefficients and the Coulomb friction coefficients of two joints at the same time. A SIASUN 7-Axis Flexible Robot is used to experimentally validate the proposal. Comparison between the predicted torque values and ground-truth values of the joints confirms the effectiveness of the method.Originality/valueThe proposed method identifies two joints at the same time with satisfying precision and high efficiency. The identification errors of joints do not accumulate.

Calculation method and experimental study of coulomb friction coefficient in sheet metal forming

Friction is one of the important factors influencing the formability of sheet metal and improving the forming quality. According to the relationship between the drawing force and the stroke, the linear fitting algorithm of the friction coefficient is given based on the least squares method. Based on the drawing die of the cylindrical parts, a friction coefficient measuring apparatus is developed, which has fixed calculation program. Through a series of deep drawing tests, the friction coefficients and force-stroke curves are measured for different combinations of sheet metal and lubricant. What’s more,the drawing process of the cylindrical part with different specifications is carried out to examine the application of the measured friction coefficient. The results show that the friction coefficient calculated by the linear fitting algorithm can accurately reflect the friction state of the whole drawing process; the measurement of the friction coefficient is not limited by the size of the mould; the established test system, can be used for the measurement of friction coefficient in sheet metal forming.

Determination of friction conditions in cold-rolling process of shaft part by using incremental ring compression test

The incremental ring compression test (IRCT) was developed to investigate the friction condition in cold-rolling process of spline or thread shaft. During IRCT process, the upper die is loaded intermittently and new oil film between ring and dies will appear, which can reflect the lubrication characteristic in the spline or thread rolling process. The Coulomb friction coefficient and Tresca friction factor were determined by the IRCT, respectively. The magnitude of friction obtained by IRCT presents a notable difference from that obtained by traditional ring compression test. The results provide an accurate friction parameter for studying the cold-rolling process of shaft part.

Friction Calculation and Simulation of Column Electric Power Steering System

This study presents a procedure for friction calculation of column electric power steering (C-EPS) system which affects handling and comfort in driving. The friction losses estimation is obtained from experimental tests and mathematical calculation. Parts in C-EPS mainly involved in friction losses are bearings and worm gear. In the theoretical approach, the gear geometry and Hertz law were employed to measure the normal load and the sliding velocity and contact areas from the worm gears driving conditions. The viscous friction generated in the worm gear was obtained with a theoretical approach and the result was applied to model the friction in the steering system. Finally, by viscous friction coefficient and Coulomb friction coefficient, values of friction in worm gear were calculated. According to the Bearing Company and the characteristics of each bearing, the friction torques due to load and due to speed were calculated. A MATLAB Simulink model for calculating the friction in bearings and worm gear in C-EPS were done and the total friction value was estimated

Incremental versus continuous load-lubrication procedure in the determination of friction conditions by the ring compression test

This work presents the differences found when using two types of methodology (continuous and incremental) in the application of load-lubricant during ring compression tests. Friction calibration maps have been obtained by conducting ring compression tests to flat rings of aluminium alloy UNS A97075-T6 with molybdenum disulphide (MoS2) as lubricant. Accordingly, in order to determine the particular values of the Coulomb friction coefficient, the problem was simulated using an elasto-plastic model with the finite element code Abaqus/Standard. A friction coefficients map from experiments and finite element simulation is drawn to compare the friction coefficient values derived from the continuous and incremental procedure. A comparison with experiments done with graphite powder as lubricant is also presented. Results of this investigation show that friction curves are affected by the methodology of load-lubricant application, and some guidelines about the use of these maps depending on the actual process conditions are provided.

Self-Loosening Failure Analysis of Bolt Joints under Vibration considering the Tightening Process

By considering the tightening process, a three-dimensional elastic finite element analysis is conducted to explore the mechanism of bolt self-loosening under transverse cyclic loading. According to the geometrical features of the thread, a hexahedral meshing is implemented by modifying the node coordinates based on cylinder meshes and an ABAQUS plug-in is made for parametric modeling. The accuracy of the finite element model is verified and validated by comparison with the analytical and experimental results on torque-tension relationship. And, then, the fastening states acquired by different means are compared. The results show that the tightening process cannot be replaced by a simplified method because its fastening state is different from the real process. With combining the tightening and self-loosening processes, this paper utilizes the relative rotation angles and velocities to investigate the slip states on contact surfaces instead of the Coulomb friction coefficient method, which is used in most previous researches. By contrast, this method can describe the slip states in greater detail. In addition, the simulation result reveals that there exists a creep slip phenomenon at contact surface, which causes the bolt self-loosening to occur even when some contact facets are stuck.

Incremental versus continuous load-lubrication procedure in the determination of friction conditions by the ring compression test

This work presents the differences found when using two types of methodology (continuous and incremental) in the application of load-lubricant during ring compression tests. Friction calibration maps have been obtained by conducting ring compression tests to flat rings of aluminium alloy UNS A97075-T6 with molybdenum disulphide (MoS2) as lubricant. Accordingly, in order to determine the particular values of the Coulomb friction coefficient, the problem was simulated using an elasto-plastic model with the finite element code Abaqus/Standard. A friction coefficients map from experiments and finite element simulation is drawn to compare the friction coefficient values derived from the continuous and incremental procedure. A comparison with experiments done with graphite powder as lubricant is also presented. Results of this investigation show that friction curves are affected by the methodology of load-lubricant application, and some guidelines about the use of these maps depending on the actual process conditions are provided.

Controlling the Quality of Two-Way Euler/Lagrange Numerical Modeling of Bubbling and Spouted Fluidized Beds Dynamics

We numerically simulate three-dimensional fluidized beds of monodisperse spheres using a two-way Euler/Lagrange method. Particles trajectories are tracked in a Lagrangian way, and particles collisions are computed by a soft sphere model. The fluid conservation equations are written in a classical Eulerian fashion and are locally averaged on cells 1 order of magnitude larger than particles. We detail the equations of the model and their numerical implementation. We study the influence of numerical parameters and simulation domain size on computed results in a biperiodic fluidized bed. We then validate the model against theoretical results for a bubbling fluidized bed and against experimental data for a single- and multi-nozzle spouted bed. Finally, we investigate the influence of the Coulomb friction coefficient magnitude on a single-nozzle spouted bed dynamics in order to emphasize the importance of tangential friction in such processes.

Impact of the Heat Treatment Condition of Steel AISI 4140 on Its Frictional Contact Behavior in Dry Metal Cutting

In this work, the impact of the heat treatment condition of steel AISI 4140 on its frictional contact behavior with coated cemented carbide and cubic boron nitride (CBN) in dry metal cutting is experimentally investigated. Two different kinds of tests were performed. The frictional behavior was investigated under conditions very similar to metal cutting on a frictional test bench, which was installed on a broaching machine. Additionally, orthogonal cutting processes with linear workpiece geometries were conducted on the same machine. The cutting experiments included observations of cutting forces, high-speed filming of chip formation, chip thickness ratio analysis as well as a comprehensive metallographic characterization of the chips and workpiece surfaces. The impacts of the undeformed chip thickness and cutting speed were investigated individually for coated cemented carbide and CBN as cutting materials. The frictional examinations delivered the Coulomb friction coefficients for all four combinations of work and cutting materials as a function of the relative velocity. The identified frictional behaviors explain the dependencies of forces, chip thicknesses, and surface microstructures on the tool and process conditions during the cutting tests.

Shakedown limit theorems for frictional contact on a linear elastic body

Abstract The paper considers the problem of a body composed of a linear elastic material in contact with a planar rigid surface with an inter-surface coefficient of Coulomb friction μ. The body is subjected to a cyclic history of loading, λPi(xi,t) where λ denotes a scalar multiplier. The objective is to assess the conditions when movement occurs between the elastic body and the surface. The problem has a close analogy with classical plasticity, where shakedown and limit load bounds exist. However, existing plasticity theory is not generally applicable to frictional slip as it obeys a non-associated flow rule. In this paper upper and lower bound shakedown theorems are derived in terms of the Coulomb coefficient of friction μ. It is shown that optimal kinematic and static bounds do not coincide. This implies that for a prescribed λPi(xi,t) there are ranges of μ for which shakedown definitely occurs and for which shakedown definitely does not occur, independent of the state of slip at the beginning and end of the cycle. However there exists an intermediate range of μ for which it is not possible to say whether shakedown or ratchetting occurs without detailed knowledge of the slip displacements at the beginning and end of the cycle of loading. This observation accords with simulations reported by Flecek R.C., Hills D.A., Barber J.B. and Dini D., (2015). A programming method for the shakedown limit is developed, based on the Linear Matching Method. The method is illustrated by a simple example. The theory derived in this paper paves the way for a new theory of limit and shakedown analysis for structures and materials with a non-associated flow rule.

Evaluation of the Coulomb Friction Coefficient in DC05 Sheet Metal Forming

This paper describes the identification of the Coulomb friction coefficient for sheet metal forming using a comparison between numerical and experimental results. Using finite element method, the work examines some aspects of the Erichsen test in order to measure the interfacial friction. Preliminary results on the evaluation of a typical tool-workpiece interface are shown for a stainless steel punch vs. a DC05 sheet metal.

Relationship between friction parameters in a Coulomb–Tresca friction model for bulk metal forming

The ring compression test was employed to investigate the relationship between Coulomb friction coefficient and Tresca friction factor in a Coulomb–Tresca friction model. The results indicated that the ratio (k) of Coulomb friction coefficient to Tresca friction factor varies under lubricated and dry conditions. The ratio k can be described by a parabolic function under lubricated conditions and by an exponential function under dry condition. There is a transitional region between lubricated and dry conditions.

Algebraic Equations for the Pile-Up Geometry in Debris Particle Indentation of Rolling Elastohydrodynamic Contacts

Metallic microparticles of 5–100 μm in size often contaminate elastohydrodynamic (EHD) contacts and indent surfaces. The geometrical characteristics of dents by such solid particles are linked to the way surface damage may evolve and how it may affect the life of the damaged contacts. In many cases, debris dents appear with shoulders raised above the original surface. Material piling-up this way causes high-pressure spikes when dents are over-rolled by an element such as a ball in a rolling bearing. This study introduces an approximate analytical method based on the so-called expanding cavity model (ECM) to calculate pile-up geometry with simple algebraic equations in thermoviscoplastic indentation of rolling EHD contacts by ductile spherical microparticles. Based on an experimentally validated debris indentation model published by the author, the pile-up model is shown to give realistic predictions in a wide range of operating parameters. Upon experimental validation, the new model is used to study the effects of particle size and hardness, Coulomb friction coefficient (CFC), strain hardening, and rolling velocity of EHD contacts on pile-up geometrical parameters including length, height, volume, and curvature.

Inverse Analysis Procedure to Determine Flow Stress and Friction Data for Metal Cutting Finite Element Modeling

This paper describes an automated procedure developed for the identification of Johnson-Cook (JC) law material parameters and Coulomb friction coefficient at the tool-chip interface, in the specific case of metal cutting FE analysis. The procedure has been developed in iSight environment, through the integration between AdvantEdge metal cutting FE code and an appropriately selected optimization algorithm. The identification of JC and friction parameters, in fact, has been performed considering it as an optimization problem, in which the objective function is the numerical/experimental error function minimization (in the specific case, it is related to the forces and temperatures responses). The calibration and validation phases have been performed using forces and temperatures experimental data, collected in orthogonal cutting test on SAF2507 superduplex steel.

Modeling Dark and White Layer Formation on Elastohydrodynamically Lubricated Steel Surfaces by Thermomechanical Indentation or Abrasion by Metallic Particles

In a series of publications, the author has shown that the passage of ductile microparticles through elastohydrodynamic (EHD) contacts results in frictional heating that can greatly affect surface damage. The thermoviscoplastic numerical model built for those studies is extended in the present article. A more rigorous analysis of dynamic (strain-rate) effects is performed and a new element of heating is introduced, namely, that owed to plastic work of the surfaces being indented. The model is then quantitatively validated against experimental data on soft and hard particles extruded in rolling and rolling–sliding contacts. It is also compared to past numerical predictions of the author. Following its validation, the model is further expanded to predict the formation of dark and white tribochemical layers of overtempered and untempered martensite, respectively, on steel surfaces, caused by the particle-induced frictional heating. Such layers are well-known in machining processes of hardened steels as being the result of phase transformations and play a critical role in contact fatigue. The debris model in this article is used to predict the layer thickness and relative hardness for a variety of operating conditions. Layers of micrometric thickness are typically found and graphic examples are presented, linking their location to that of debris dents. A parametric study examines the role of particle size and hardness, Coulomb friction coefficient, and contact rolling velocity on dark and white layer thickness and relative hardness. The layers are zones of great inhomogeneity and thermomechanical anisotropy, increasing the risk of spalling by delamination as they are potential sources of crack initiation, particularly in sliding contacts. However, white layers in particular may actually be beneficial to contact fatigue in rolling contacts because of their substantially increased hardness. The conclusion of the study is that debris-driven surface indentation and abrasion should no longer be viewed from a purely mechanistic or geometrical perspective but has to consider the tribochemical or microstructural-modification factor for the correct evaluation of the remaining useful life of a dented or abraded contact.

Tribology behavior during indentation and scratch of thin films on substrates: effects of plastic friction

When friction stress on a contact surface reaches material yield strength in shear, contact slippage can occur even if the slipping condition for Coulomb friction is not satisfied. In this paper, a three-dimensional (3-D) scratch model is proposed, which considers combined Coulomb and plastic friction. Influences of plastic friction are discussed for two continuous displacement loading steps: indentation and scratch. For indentation, initially the sliding on the contact surface can not take place and the complete cohesion condition should be employed; then as the indenter is further compressed down to the coating surface, plastic friction instead of Coulomb friction prevails in most of the contact region. For scratch, the previous complete cohesion at the initial indentation is substituted by plastic or Coulomb slipping, and the slippage becomes plastic-sliding governed for a slightly large indentation depth. The effects of the indentation depth and the Coulomb friction coefficient on the scratch friction coefficient are discussed in detail. Several experimental phenomena are interpreted, which include that with an increase of the normal loading, the scratch friction coefficient reduces for the soft coating but grows for the hard coating; and with the growth of hardness after heat treatment, the scratch friction coefficient increases due to weak plastic slippage. Obtained results help to elucidate tribological behaviors during scratch and are helpful for the interpretation of experimental phenomena and the improvement of numerical simulations for the scratch process.

Comprehensive parameter identification of feed servo systems with friction based on responses of the worktable

A comprehensive identification method for structure and friction parameters of feed servo systems is put forward. A motor direct-connected feed system with Stribeck friction law is investigated. The relation between the critical stick-slip velocity of the worktable and the structure parameters as well as the difference between the static and Coulomb friction coefficient is derived first. Then, according to the data of critical stick-slip velocities at different feed positions, the structural parameters (such as diameter, lead and bearing length of the ball screw) are estimated using the nonlinear least square method. Furthermore, based on the stick-slip displacement response of the worktable, the Stribeck friction parameters are obtained using the direct graphical registration method. The feasibility and validity of the presented identification method is verified by numerical simulation. All the work can provide a theoretical reference for the comprehensive parameters identification of feed systems.

Finite element continuum modeling of vibrationally-fluidized granular flows

Discrete element modeling of granular flows is effective, but requires large numerical models. In an effort to reduce computational effort, this paper presents a finite element (FE) continuum model of the vibrationally fluidized granular flow produced by a tub vibratory finisher. The constitutive equations governing the continuum model were calibrated using the discrete element method (DEM). A constant stiffness was used for the normal contact of the polyurethane tub wall and the spherical steel media, and an effective coefficient of Coulomb friction was obtained by studying the variation of the shear and normal forces at different points along the tub wall using DEM simulations. The DEM predictions of the ratio of the tangential to normal contact forces showed that rolling of the media on the tub wall was much more common than sliding, and the average effective coefficient of friction was relatively uniform over the wall. Average values of the equivalent elastic and plastic properties of the media were used in the continuum model, neglecting the small local variations that existed within the vibrationally-fluidized bed. The bulk flow behavior of the equivalent continuum media was then studied using both Lagrangian and Eulerian FE formulations. The bulk flow velocities predicted by the Lagrangian approach were in good agreement with those obtained using DEM simulations over a wide range of tub wall amplitudes. The qualitative trend of the local impact velocity distribution at various locations in the tub predicted by the DEM agreed with the trend predicted by the continuum model using the shear rate as a measure of the granular temperature and hence local velocity. The FE simulations required approximately 8 times less computing time than the equivalent DEM.

Characterisation of friction behaviour of flake, spheroidal, and compacted vermicular graphite cast irons

This paper investigates friction behaviour of flake, spheroidal, and compacted vermicular graphite cast irons used for piston rings of automobile engines. Pin–on–disc friction tests are conducted under dry and room temperature conditions. Pins are made of graphite cast irons, and discs are chromium molybdenum steels. During a test, Coulomb friction coefficient and sliding distance are recorded. Graphite size fraction on the initial surface of the cast iron is determined and its influence on friction coefficient is investigated. Results show that friction coefficient growth rate during the 'running–in' period can be expressed as a power–law function of sliding distance. Two parameters in the power–law form, the damage rate constant and the damage exponent, can describe a friction coefficient evolution during the period. It is identified that graphite size fraction has an influence on a friction coefficient evolution. The influence of graphite size in cast iron is described with the damage rate constant.