Coulomb Friction Coefficient Research Articles

Transient behavior and steady-state rheology of dense frictional suspensions in pressure-driven channel flow

AbstractResults from particle-resolved Direct numerical simulations are presented for dense suspensions of frictional non-colloidal spheres in viscous pressure-driven channel flow. The bulk solid volume fraction varies between $$\phi _b=0.2$$ ϕ b = 0.2 and 0.6, and the Coulomb friction coefficient is either $$\mu _c = 0$$ μ c = 0 or 0.5. The main objectives are to unravel the influence of (1) $$\phi _b$$ ϕ b and $$\mu _c$$ μ c on the flow development time and of (2) heterogeneous shear on the steady-state suspension rheology. Starting from an initially homogeneous distribution, the particles show shear-induced migration toward the core until equilibrium is reached. The flow development time decays exponentially with increasing $$\phi _b/\Phi _R$$ ϕ b / Φ R , where $$\Phi _R$$ Φ R is a friction-dependent reference bulk concentration beyond which particle contacts cause a rapid increase in the particle stress. The steady-state rheology is studied by means of the ‘viscous’ and ‘frictional’ rheology frameworks. Excluding the central core and wall regions, the data for the local relative suspension viscosity collapse onto a single curve as function of the normalized local concentration $${\bar{\phi }}/\phi _m$$ ϕ ¯ / ϕ m , where $$\phi _m$$ ϕ m is the friction-dependent maximum flowable packing fraction. The frictional rheology shows ‘subyielding’ at low viscous number $$I_v$$ I v in the core region, where the macroscopic friction coefficient $$\mu $$ μ drops below the minimal value found for homogeneous shear flows. A modified frictional rheology model is presented that captures subyielding. Finally, a model is presented for $${\bar{\phi }}/\phi _{mp}$$ ϕ ¯ / ϕ mp as function of $$I_v$$ I v , where $$\phi _{mp}$$ ϕ mp is a modified maximum flowable packing fraction. It captures both ‘overcompaction’ in the core beyond $$\phi _{m}$$ ϕ m at high $$\phi _b$$ ϕ b and maximum core concentrations below $$\phi _m$$ ϕ m at lower $$\phi _b$$ ϕ b .

Interparticle friction in sheared dense suspensions: Comparison of the viscous and frictional rheology descriptions

In the literature, two different frameworks exist for describing the rheology of solid/liquid suspensions: (1) the “viscous” framework in terms of the relative suspension viscosity, ηr, as a function of the reduced solid volume fraction, ϕ/ϕm, with ϕm the maximum flowable packing fraction, and (2) the “frictional” framework in terms of a macroscopic friction coefficient, μ, as a function of the viscous number, Iv, defined as the ratio of the viscous shear to the wall-normal particle stress. Our goal is to compare the two different frameworks, focusing on the effect of friction between particles. We have conducted a particle-resolved direct numerical simulation study of a dense non-Brownian suspension of neutrally buoyant spheres in slow plane Couette flow. We varied the bulk solid volume fraction from ϕb=0.1 to 0.6 and considered three different Coulomb friction coefficients: μc=0, 0.2, and 0.39. We find that ηr scales well with ϕ/ϕm, with ϕm obtained from fitting the Maron–Pierce correlation. We also find that μ scales well with Iv. Furthermore, we find a monotonic relation between ϕ/ϕm and Iv, which depends only weakly on μc. Since ηr=μ/Iv, we thus find that the two frameworks are largely equivalent and that both account implicitly for Coulomb friction. However, we find that the normal particle stress differences, N1 and N2, when normalized with the total shear stress and plotted against either ϕ/ϕm or Iv, remain explicitly dependent on μc in a manner that is not yet fully understood.

The influence of coefficient of friction in thermal prediction of refill friction stir spot welding process of AA7075‐T6

AbstractNumerical modelling of refill friction stir spot welding helps in the deep investigation of physics involved in the joining process. The current study investigates four variants of contact models and their influence on thermal prediction in the process. The contact models with constant shear and coulomb friction coefficients and temperature‐dependent shear and coulomb friction coefficients were used in the numerical models to investigate the influence of friction coefficients in the prediction of thermal cycles in refill friction stir spot welding. The results from the numerical model are compared and validated with the experimental results from a previous study. The contact model with temperature‐dependent coulomb friction coefficient was concluded to be more reliable when compared to the other three contact models. The temperature for this contact model at the centre of the weld is 505 °C, which differs from the temperature recorded in the experiment by 2 %. The peak temperatures of numerical models with constant coulomb and shear friction coefficients differ from the experimental temperature at the weld centre by 5.17 % and 16.8 % respectively.

Hydrodynamic clogging of micro-particles in planar channels under electrostatic forces

Hydrodynamic clogging in planar channels is studied via direct numerical simulation for the first time, utilising a novel numerical test cell and stochastic methodology with special focus on the influence of electrostatic forces. Electrostatic physics is incorporated into an existing coupled lattice Boltzmann-discrete element method framework, which is verified rigorously. First, the dynamics of the problem is governed by the Stokes number, $St$ . At low $St$ , the clogging probability, $P$ , increases with $St$ due to increasing collision frequency. At high $St$ , however, $P$ decreases with $St$ due to quadratic scaling of hydrodynamic force acting on arches. Under electrostatic forces, clogging is well represented by the wall adhesion number, $Ad_w$ . For $Ad_w \lesssim 4$ , the mechanical dependence on $St$ is exhibited, while for $4 < Ad_w < 20$ , there is a transition to high $P$ as sliding along, and attachment to, the channel surface occurs increasingly. For $Ad_w \gtrsim 20$ , clogging occurs with $P > 0.95$ . Particle agglomeration, however, can also decrease $P$ due to diminished interaction with channel walls. Distinct parametric regions of clogging are also observed in relation to the channel width, while a critical width $w/d^*=2.6$ is reported, which increases to $w/d^*=4$ with strong electrostatic surface attachment. The number of particles that form stable arches across a planar channel is determined to be $n=\left \lceil {w/d}\right \rceil + 1$ . Finally, sensitivity to the Coulomb friction coefficient is determined in favour of calibrating numerical parameters to bulk system behaviour. The greatest sensitivities occur in situations where the arch stability is lowest, while clogging becomes independent of friction for strong wall adhesion.

Speed-Controller-Independent Mechanical Parameter Identification in SPMSM Drive Achieved via Signal Injection

The mechanical parameters, including the Coulomb and viscous friction coefficients together with the moment of inertia, are of great interest for the performance optimization and condition evaluation of surface-mounted permanent magnet synchronous motor (SPMSM) drives. This article contributes a speed-controller-independent mechanical parameter identification scheme using open-loop speed response due to signal injection, which has not been reported in existing works. It is designed based on the premise that the viscous friction torque is disproportional to the rotor speed, which is a new progress toward estimating the mechanical parameters with high precision. Moreover, as a practical full-participation-type solution, this scheme involves a new electrical parameter estimation technique based on differential algebra to assist in identifying the mechanical parameters. This auxiliary technique attains the current-controller-free estimation of the electrical parameters with the inverter nonlinearity eliminated, thereby addressing the current controller self-commissioning and serving to acquire the accurate electromagnetic torque. The experimental evaluations on two prototype SPMSM drive systems validate the feasibility of this suggested scheme.

A thorough comparison between measurements and predictions of the amplitude dependent natural frequencies and damping of a bolted structure

Bolted joints are a significant source of damping and nonlinearity in built up structures. In the micro-slip regime (i.e. when the bolts do not slip completely) the log of the damping tends to increase linearly with the log of the vibration amplitude, the so-called power-law behavior. The natural frequency also tends to decrease slightly with vibration amplitude. While many works have successfully tuned phenomenological models to capture these behaviors, far fewer have sought to predict the nonlinearity in a bolted joint and validated the predictions with measurements over a range of bolt preloads and vibration amplitudes. This work presents a step towards such a prediction, using a detailed finite element model of a structure, including the preload forces in the bolts and Coulomb friction in the contact, to seek to predict the nonlinear damping and stiffness of the structure and how they vary with preload. The structure studied consists of two beams bolted together at their free ends, the so-called S4 Beam. While the contact interfaces were machined to be nominally flat, the micron-scale curvature in the contact interface is included in the model, approximated in two different ways, to seek to understand what fidelity is needed at the contact interface to successfully capture its dynamic behavior. The recently presented Quasi-Static Modal Analysis (QSMA) method is employed, where the amplitude dependent damping and natural frequency can be predicted from a single quasi-static simulation, avoiding the expense of numerical integration. The predicted damping and natural frequency are compared with measurements at various preloads, showing reasonable agreement if a Coulomb friction coefficient of 0.2 is used for all simulations. The simulations also revealed that, while the micron-scale curvature of the interfaces was important, the results were not very sensitive to how it was approximated.

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.

Derivation of the Coefficients in the Coulomb Constant Shear Friction Law from Experimental Data on the Extrusion of a Material into V-Shaped Channels with Different Convergence Angles: New Method and Algorithm

The combined Coulomb constant shear friction law is widely used in commercial and research software for the finite-element analysis (FEA) of metalworking and is naturally more flexible and hence, more relevant to real-life manufacturing than the individual Coulomb and constant shear friction laws. In this work, a new mathematical model of coefficients in the Coulomb constant shear friction law for extruding a metal through narrow V-shaped channels with small convergence angles has been developed and evaluated and compared with laboratory measurements. The extrusion of the model material (lead) through narrow V-shaped channels with small convergence angles varying from 0 to 3.5 degrees has been studied. The Coulomb friction coefficient µ and the constant friction factor m appear to be independent of the dimension ratio and are influenced mostly by roughness and range from µ = 0.363 (with lubricant) to µ = 0.488 (without lubricant) and from m = 0.726 (with lubricant) to 0.99 (without lubricant). The relative length dominated by the Coulomb friction law is less than 1%, and the Coulomb’s coefficient of friction can be approximated as ½ the constant shear friction factor for all tested cases. The developed method and algorithm can be used in both FEA of manufacturing processes and efficiency tests for lubricants used in metalworking.

On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution

The paper considers a heavy homogeneous ball rolling without slipping on the outside of a real rough fixed surface of revolution, which is generated by rotating a plane curve around a vertical axis. By applying the Coulomb sliding friction law, the position is established at which slipping occurs during rolling down the surface, and thereafter this mechanical system ceases to be holonomic. Dynamic differential equations of motion are obtained using general theorems of mechanics. The paper presents the procedure of determining the tangential and normal component of the reaction of constraint depending on the height of the contact point between the ball and the surface. On the basis of the initial total mechanical energy of the system and the value of Coulomb friction coefficient, the condition is determined to prevent the ball from slipping, as well as the height interval in which the considered system behaves as a nonholonomic system. The procedure is illustrated by examples of surfaces generated by rotating segments of the circular arc, line and parabola. In the last example there is not a closed-form solution, so that numerical integration of a corresponding Cauchy problem is performed.

Estudio de simuladores dinámicos con ADAMS y Matlab/Simulink para sistemas de control

ADAMS-MATLAB co-simulation is widely used in complex system development to control models of closed-loop mechanisms. An advantage of ADAMS is to facilitate the configuration of parameters such as friction. However, its mathematical friction model is unknown. There are alternatives such as Simscape Multibody that facilitate the configuration of any friction model. This paper presents a case study of dynamic simulation using the mathematical model of a mechanism in order to compare it with ADAMS and Simscape Multibody. The state-space model uses the parameters b and fc – viscous and Coulomb friction coefficients. However, ADAMS uses only one dynamic friction parameter µ. Since both friction parameters do not appear in ADAMS, a parametric identification procedure was used to determine the equivalency between the friction coefficients b and fc compared to µ. To identify the friction model of ADAMS, open-loop and closed-loop simulations were proposed. To compare the simulation results numerically, the L2 norm was used. The reference was the model solved with the ODE45 function.

Numerical analysis of undercut anchor effect on rock

The paper presents the results of a numerical analysis using the Finite Element Method (FEM) of the friction issue in the contact between the undercut anchor head and rock during anchor pull-out. Formation of failure zone of rock medium was analysed assuming different Coulomb friction coefficients in the contact zone of conical anchor head with a rock. The problem is interesting as regards practical aspects of rock mass loosening during anchor pull-out. The analysis revealed a significant effect of the friction coefficient on the propagation and extent of the failure zone. Increasing the friction factor significantly decreases the extent of the failure zone measured on a free rock surface.

Position Tracking Performance with Fine Tune Ziegler-Nichols PID Controller for Electro-Hydraulic Actuator in Aerospace Vehicle Model

Electro-Hydraulic Actuator (EHA) system is a third order non-linear system which is highly suffer from system uncertainties such as Coulomb friction, viscous friction and pump leakage coefficient which makes this system more complicated for the designing of the controller. The Proportional-Integral-Derivative (PID) controller has proposed in this paper to control EHA system and main problem in its application is to tune the parameter to its optimum value. Two different methods are used to tune the PID controller which are trial and error and Ziegler-Nichols method. MATLAB Simulink is used to simulate the system. In order to determine the performance of EHA system for the position tracking. 3 different of external disturbance such as 0N, 5000N and 10000N has been injected into the system. Simulation results show that the Ziegler-Nichols fine tuning method provides the better tracking performance when compared to the trial and error method for every specific disturbance setting. The Ziegler Nichols method provides better disturbance rejection as the performances indexes such as percentage overshoot, settling time and steady state error are not affected by the varying of disturbance.

Online Parallel Estimation of Mechanical Parameters for PMSM Drives via a Network of Interconnected Extended Sliding-Mode Observers

The accurate estimation of mechanical parameters is essential for the control optimization and condition monitoring of permanent-magnet synchronous motor (PMSM) drives. In this article, an online parallel estimation scheme is proposed based on a network of three interconnected extended sliding-mode observers. With a two-step mechanism derived from the developed network, this scheme can simultaneously achieve the accurate real-time observation of three mechanical parameters, including the viscous friction coefficient, the moment of inertia, and the load torque. The first step utilizes the presented network to precisely acquire the Coulomb friction coefficient by offering only one speed. With aiding from this estimated coefficient, the second step attains the high-precision online identification of the three concerned parameters by compensating the Coulomb friction torque to counteract its adverse effect. These two steps are implemented utilizing the identical network, thus, furthest avoiding increasing the estimation complexity. Besides, any additional knowledge other than the rotor speed and electromagnetic torque is no longer required for guaranteeing the asymptotic convergence of the estimation errors. Sufficient evaluations from simulations and experiments confirm the validity of the proposed scheme.

Multiscale friction model for hot sheet metal forming

The accurate description of friction is critical in the finite element (FE) simulation of the sheet metal forming process. Usually, friction is oversimplified through the use of a constant Coulomb friction coefficient. In this study, the application of an existing multiscale friction model is extended to the hot stamping process. The model accounts for the effects of tool and sheet metal surface topography as well as the evolution of contact pressure, temperature, and bulk strain during hot stamping. Normal load flattening and strip drawing experiments are performed to calibrate the model. The results show that the model can relatively well predict friction in strip draw experiments when the tool surface evolution due to wear is incorporated. Finally, the application of the formulated multiscale friction model was demonstrated in the FE simulation of a hot-stamped part.

Application of an Advanced Friction Model in Hot Stamping Simulations: A Numerical and Experimental Investigation of an A-Pillar Reinforcement Panel from Volvo Cars

Although hot stamping is now an established method, numerical analysis of the process is still a challenge. In industrial applications, process engineers use sophisticated models which consider complex physical effects including phase transformation, phase dependent flow curves, temperature dependent r-values and temperature dependent FLC’s. However, in most of the industrial applications the tribological system is still oversimplified by using a constant Coulomb friction coefficient. Currently, there is enough experimental evidence in literature showing that friction coefficients evolve during the process, depending on contact pressure, temperature and sliding velocity. This work focuses on accurate modelling of friction in hot stamping processes. The advanced modelling technique presented in this paper tracks each material point and calculates the corresponding coefficient of friction depending on the current process conditions. This technique was used on simple part geometries in order to generate fundamental knowledge. In this analysis, part geometry, process conditions and tool kinematics are varied. In the next step, an A-Pillar reinforcement panel from Volvo Cars was analyzed experimentally and numerically. It was seen that accurate friction modelling enhances the quality of the simulation results and evolving friction conditions have a direct effect on the feasibility analysis of industrial parts.

Influence of the contact with friction on the deformation behavior of advanced high strength steels in the Nakajima test

This work presents a new understanding on the deformation mechanics involved in the Nakajima test, which is commonly used to determine the forming limit curve of sheet metals, and is focused on the interaction between the friction conditions and the deformation behaviour of a dual phase steel. The methodology is based on the finite element analysis of the Nakajima test, considering different values of the classic Coulomb friction coefficient, including a pressure-dependent model. The validity of the finite element model is examined through a comparison with experimental data. The results show that friction affects the location and strain path of the necking point by changing the strain rate distribution in the specimen. The strain localization alters the contact status from slip to stick at a portion of the contact area from the pole to the necking zone. This leads to the sharp increase of the strain rate at the necking point, as the punch rises further. The influence of the pressure-dependent friction coefficient on the deformation behaviour is very small, due to the uniform distribution of the contact pressure in the Nakajima test. Moreover, the low contact pressure range attained cannot properly replicate real contact condition in sheet metal forming processes of advanced high strength steels.

Role of the Rheological Parameters in Debris Flow Modelling

Nowadays, the debris flow model has become an essential part of risk analysis and impact engineering. Coupled with field observations and historical records, these models have proven powerful tools to understand the behaviour of debris flow in complex terrain. However, their application poses several new challenges to scholars and engineers. A detailed understanding of the debris flow phenomena requires a sound knowledge of the shallow water equation and rheological model used to simulate the debris flow hazard. In this study, important rheological models used to analyse the debris flow process and their limitations have been highlighted. Furthermore, the suitability of the Voellmy-Salm rheological model has been studied for 2D pyroclastic flow taking different combinations of the coefficient of friction namely coulomb friction coefficient \\i,and turbulent coefficient of friction £ using IMEX SFLOW 2D dynamic continuum model. It was found that velocity and runout distances are significantly influenced by the variation of the coefficient of the turbulent friction © at a large scale. It is then concluded that the identification of a suitable rheological model is necessary to simulate the precise behaviour of complex and heterogeneous debris flow

Dry friction under pressure variation of PACVD TiN surfaces on selected automotive sheet metals for the application in unlubricated metal forming

Forming without lubricants opens up ecologic and economic benefits for producing industries. In addition, dry friction allows better transmission of the process loads to the required forming force. Without any surface treatment, however, unlubricated contact leads to highly increased wear during forming. One way to describe friction in a way relevant for metal forming processes is the determination of Coulomb's friction coefficients over varying process parameters, which is usually measured on highly dedicated test facilities. Within the present study, kinetic and static friction coefficients have been examined by strip drawing on universal tensile testing machines. Contact pressure was varied from 1 to 100 MPa by deploying two different friction tools. Amongst the material specific coefficients and the resulting trends of friction vs. pressure, their comprehensive connectibility overarching the test assemblies was of key research interest. Plasma assisted chemical vapor deposition (PACVD) of titanium nitride (TiN) has been deployed to the friction jaws of the testing tools, after conventional surface treatments for sheet metal forming tools (i.e. Tenifer nitro-carburation, plasma nitration and PVD-AlTiN) have failed in preliminary dry friction experiments. With this coating technology, dry friction of different automotive-typical sheet metal materials was tested successfully even at elevated pressure. Proportionally increasing trends of kinetic and static friction over pressure were obtained, which are linked overarching the experimental setups by linear regression.

Contact pressure-dependent friction characterization by using a single sheet metal compression test

Tribology has a major impact on process stability, product quality and tool life in metal forming processes. Today, the complex system of friction is simplified by the Coulomb friction coefficient or friction factor model for analytical and numerical process analysis. These friction values are determined in laboratory tests and assumed to be constant. Due to smoothing of the surface, displacement of lubricant from the active joint and locally different relative velocities, the friction state changes while forming. To achieve a high accuracy of finite element analysis, it is essential to consider these changing boundary conditions. Identifying strain-dependent friction coefficient or friction factor models by conventional characterization tests, such as the pin extrusion test or ring compression test, require a high number of experiments. Besides that, these tests are not suitable for low plastic strains due to their poor sensitivity. The sheet metal compression test, analyzed in this contribution, enables the description of the strain and contact pressure dependent progression of the friction values in one simple experimental setup. To determine the friction coefficients, the experimentally measured force-displacement curves will be assigned to friction coefficients in a numerically determined nomogram. The calibration of the nomogram is done analytically for the friction-free condition by using the flow curve determined in the uniaxial tensile test. The sheet metal compression test reacts sensitive to changes of the tribological system due to the high ratio of surface to specimen volume and the direct measuring of the press force as an evaluation quantity. The characterization of friction value progression is done for the materials DP600, DC06, Cu-OFE and CuZn30 with different tribological conditions. The results confirm that the friction values and thus the friction condition is changing during the forming process. Additionally, the validity limit of the friction coefficient model can be easily identified by analysing the friction coefficient progression.

Dependence of earthquake faulting type on fault strike across the Korean Peninsula: Evidence for weak faults and comparison with the Japanese Archipelago

We re-evaluate the stress state across the Korean Peninsula by analyzing the stress tensor inversion results, strike–rake relationships, and faulting-type indicator–magnitude relationships of published earthquake focal mechanism data. Previous studies have shown that the stress state is characterized by a strike-slip faulting stress regime with ENE–WSW maximum compression, NNW–SSE minimum compression, and vertical intermediate stress. The differential stress magnitudes are estimated to be on the order of 100 MPa under the assumption of the strong-fault earthquake with a high Coulomb friction coefficient of 0.85. Conversely, other studies have shown that the weak-fault model is applicable across the Japanese Archipelago, where the differential stress level is only a few tens of MPa. We, therefore, review previous studies, evaluate the focal mechanism data across the Korean Peninsula, and infer the absolute stress level. Our comparison of the geological and tectonic histories of the Korean Peninsula and Japanese Archipelago suggests that the NNW–SSE tensional stresses in the Korean Peninsula are caused by slab rollback of the Philippine Sea Plate at around 5 Ma, west of Kyushu Island, southwestern Japan. We also find that the earthquake faulting types across the Korean Peninsula are closely related to their fault strikes, confirming a spatially uniform distribution of the strike-slip stress regime with nearly equal tensional and compressional tectonic stresses. However, this situation leads to the apparent paradox of strike-dependent fault strength. We eliminate this paradox by proposing a model whereby reverse- and normal-faulting events are caused by local stress heterogeneities around the edges of strike-slip faults under a uniform low-strength strike-slip stress state for all faulting types. We also highlight the usefulness of strike–rake and faulting-type indicator–magnitude diagrams in considering stress states.