Coulomb Friction Model Research Articles

Sliding friction of a pillar array interface: part II, contact mechanics of single pillar pairs.

Insects and small animals often utilize structured surfaces to create friction during their movements. These surfaces typically consist of pillar-like fibrils that interact with a counter surface. Understanding the mechanical interaction between such surfaces is crucial for designing structured surfaces for engineering applications. In the first part of our study, we examined friction between poly(dimethylsiloxane) (PDMS) samples with surfaces patterned with pillar-arrays. We observed that sliding between these surfaces occurs through the interfacial glide of dislocation structures. The frictional force that resists this dislocation glide is a result of periodic single pillar-pillar contact and sliding. Hence, comprehending the intricate interaction between individual pillar contacts is a fundamental prerequisite for accurately modeling the friction behavior of the pillar array. In this second part of the study, we thoroughly investigated the contact interaction between two pillars located on opposite sides of an interface, with different lateral and vertical offsets. We conducted experiments using PDMS pillars to measure both the reaction shear and normal forces. Contact interaction between pillars was then studied using finite element (FE) simulations with the Coulomb friction model, which yielded results that aligned well with the experimental data. Our result offers a fundamental solution for comprehending how fibrillar surfaces contact and interact during sliding, which has broad applications in both natural and artificial surfaces.

Research of influencing factors on tripping speed of double plungers turbine overspeed protector

The over-speed protection mechanism is very important for the safe operation of the steam turbine, but in actual production, the tripping speed often fluctuates and deviates from the set value, resulting in a decrease in the reliability of the unit operation. In this paper, the factors that affect the tripping speed of double plungers turbine overspeed protection mechanism are analysed, the mechanism of mechanical vibration and friction that cause the tripping speed to fluctuate is explored through theoretical calculation and simulation analysis, and the change of spring dynamic stiffness by using the dynamic stiffness matrix method and finite element simulation is analysed. The change of friction force under different contact modes is calculated by using the L-N contact force model and the modified Coulomb friction model, and the change of tripping speed under non-ideal friction conditions is explored through dynamic simulation.

Frictional behavior of pure titanium thin sheet in stamping process: Experiments and modeling

Friction behavior is crucial for metal deformation and failure analysis. Tests on contact between specimens and rigid mold (S-S) and rubber (S-R) were conducted. Results show that S-S friction coefficient decreases with normal pressure, while S-R static friction coefficient increases and kinetic remains low. Friction coefficient is influenced by real contact area changes due to softer surface deformation. S-S friction depends on specimen strength, and S-R friction on rubber properties. A proposed friction model based on contact area variation accurately predicts friction changes with normal pressure and workpiece properties. Integrated with finite element simulation, the model improves efficiency and accuracy compared to classical Coulomb friction model.

Pipe-soil interaction behaviors of deepwater J-lay pipeline on sloping seabed

The pipe-soil interaction behaviors are crucial factors for the J-lay pipeline design, which are mainly investigated on the horizontal seabed in previous studies. This paper develops an innovative method for the static and dynamic analyses of pipe-soil interactions considering the J-lay pipeline on a sloping seabed. This approach simulates the motion processes of the pipeline particles and solves the internal forces of the pipeline elements by the vector mechanics and finite element principle. The position coordinates formulations of pipeline particles are derived to calculate the pipeline locations on the sloping seabed. The non-linear hysteretic soil model and the modified Coulomb friction model are employed to simulate pipe-soil interactions in the vertical seabed plane as well as the axial and lateral directions. Moreover, a large-scale pipe-laying experimental test system is established to carry out the model experiments of a J-lay pipeline on different seabed conditions. The static and dynamic pipe-soil interaction responses are then analyzed by the VFIFE method for a 6-inch gas pipeline J-laying on the negative sloping seabed. The influence of seabed slope type and angle and soil characteristics is further explored on the pipe-soil interaction behaviors, which provide significant evidence for the design of pipe-lay on the sloping seabed.

Effect of different friction coefficient models on numerical simulation of inertia friction welding of 2219 Al alloy to 304 stainless steel

In inertia friction welding (IFW) of Al alloy to steel, the friction coefficient of interface influences the friction heat production and determines the accuracy of the numerical simulation of welding process. A fully coupled three-dimensional model was established to simulate the IFW process of 2219 Al alloy to 304 stainless steel. By taking different simplifications in the influencing factors (i.e., temperature, sliding velocity, and pressure) of friction coefficient, three types of friction coefficient models were established and utilized in the simulation of IFW process. The strain compensated Arrhenius and Johnson-Cook models were employed to describe the deformation behavior of Al alloy and steel, respectively. Both Al alloy and steel were assumed to be the elastic-plastic body, and the friction stress was calculated by the Coulomb friction model. The friction interface temperature, angular velocity attenuation, axial shortening distance, and joint appearance were measured to verify and compare the accuracy of the established models. The temperature and stress evolutions during the IFW process were also analyzed. With the smallest error in validation, the friction coefficient model, which was a function of temperature, sliding rate, and pressure, showed the best accuracy in describing the friction behavior. By considering the effect of pressure, a more accurate shear stress at the center region of the interface was calculated with a lower value. It means that the friction resistance at the region was lower, promoting the flow of internal Al alloy and the formation of curly-shape flash.

Numerical analysis of whirl for drill string with aluminium alloy drill pipes in deep vertical well

In this study, a new finite element (FE) model using beam-shell composite elements is established. The model combines the advantage of computational speed for beam elements with the contact details of shell elements. The thermal instability of aluminium alloy materials and geothermal gradient are considered. Besides, kinematic contact model, Coulomb friction model, and initial imperfection are considered in this model. The drill string with aluminium alloy drill pipes of Songke-2 (SK-2) well is selected to simulation. The calculation results are consistent with the failure mode of the aluminium alloy drill pipes at engineering site. The effects of aluminium alloy drill pipes position, geothermal gradient, and rotational speed on the whirl characteristics of drill string with aluminium alloy drill pipes are analyzed. The results show that the closer the aluminium alloy drill pipes are to the drill bit, the more obvious the whirl phenomenon of the drill strings is. For deep wells with a maximum temperature of 170 °C, the temperature gradient has limited effect on the whirl state. The rotational speed has a significant impact on the whirl. When the rotational speed reaches 80 rpm, backward whirl occurs at the bottom of the borehole. Moreover, when the distance from the drill bit is different, the drill string will exhibit different whirl states. This work provides a new approach for modeling the dynamics of drill strings, selecting different element types based on the importance of different parts. Geothermal gradient is also considered in this model, which can help to calculate drill string dynamics for ultra deep drilling and geothermal drilling.

Research on dynamic characteristic of compressor RIP under thermal oxygen aging and variable preload conditions

The dynamic characteristics of rubber isolation pad (abbreviated as RIP) after service under the high temperature thermal oxygen aging and the variable preloads have preload dependence and thermal oxygen aging dependence, which is a crucial problem for matching the vibration isolation system of air conditioner compressor to reveal the dynamic characteristic mechanism of the RIP with different preloads and thermal oxygen aging conditions. The Peck model is first introduced to characterize the thermal oxygen aging factor, the fractional derivative Kelvin-Voigt thermal oxygen aging-perturbation model (FDKVTPM) and the Coulomb frictional thermal oxygen aging-perturbation model (CFTPM) are established to describe the frequency dependence and the amplitude dependence, respectively. The thermal oxygen aging-dynamic characteristic model of the RIP is built by considering the influence of variable preloads, the model parameters under different preloads are further identified, the validity of the model was examined by the experimental data. The concepts of the stiffness transition point (STP) and the stiffness transition frequency (STF) are innovatively proposed to better describe softening effect of the RIP under variable preload and variable amplitude working conditions. The results show that the static stiffness of RIP increases by 20.7%, the dynamic stiffness increases by 9.3%, and the loss factor decreases by 35% after thermal oxygen aging under different preload conditions, which can lay a theoretical foundation for in-depth study of the stiffness matching and optimization of air conditioner compressor with the RIP.

Numerical prediction of railhead rolling contact fatigue crack growth

The influence of crack face friction on predicted crack growth in a 2D rail model is investigated numerically. An isolated surface-breaking inclined rolling contact fatigue crack is propagated into a rail under (i) a moving contact load, (ii) a combined thermal and contact load, and (iii) a combination of (rail) bending and contact load. Crack face friction is modelled by the Coulomb friction model. The crack growth direction is predicted using an accumulated vector crack tip displacement criterion and two Paris-type equations are employed to estimate crack growth rates. The model is validated towards a twin-disc experiment in the literature. The influence of the crack face friction coefficient and parameters in the crack growth direction criterion are assessed. Frictional cracks tend to go deeper into the rail although the influence under combined thermal and contact loading is minor. In all investigated load scenarios, crack face friction is shown to reduce crack growth rates.

Simulation of deep drawing of dual phase steel sheets incorporating tribological behaviour predicted by advanced friction modelling

In a deep drawing process, friction at the sheet metal-die contact interface affects the material flow in the flange as well as at the die entry affecting product quality significantly. The accuracy of predicted drawing force and thinning in deep drawing simulation strongly depends on friction modelling. The Coulomb friction model with a constant coefficient of friction is generally assumed in simulations. In reality, the actual friction coefficient depends on process variables such as local contact pressure, relative sliding velocity, and strain in the sheet material. In this work, an approach is presented for deep drawing simulation of dual phase (DP600) steel sheets incorporating the effect of these variables on the friction coefficient. Strip drawing tests under conditions similar to that exist in the flange area during deep drawing have been carried out. Deep drawing simulations have been performed using two friction models taking into consideration the variation of friction coefficient with respect to pressure and velocity. The predicted punch force and thickness variation are validated using deep drawing experiments. A considerable improvement in the accuracy of predicted results has been observed when compared to a constant coefficient of friction.

Dynamics and fatigue life investigation of push-the-bit rotary steerable bottom hole assembly with whirling finite element model

In this paper, a new whirling finite element model of the bottom hole assembly with static push-the-bit rotary steerable system (RSBHA) is established. Initial imperfection, kinematic contact with clearance, Coulomb friction model, and coupling with the drilling fluid are considered within the model. The effects of rotational speed, friction coefficient, and steering displacement on the whirling behavior are investigated, while the whirling effect on fatigue life is explored by employing the numerical model. With an increase in the rotational speed and friction coefficient, the whirl gradually changes from the forward whirl to the random whirl and then to the backward whirl, while the fatigue life decreases significantly. Compared with the forward whirl, the influence of backward whirl on fatigue life is particularly obvious, the reduction rate of fatigue life can reach 80%–84.5%. Relevant research results can provide theoretical foundation for reducing failure of the RSBHA in field drilling.

Performance Comparison Analysis of a Bridge Installed with Anti-seismic Devices using PVDF/MgO Friction Material According to Friction Analysis Models

In this study, structural analyses were conducted to analyze the performance of a bridge to which friction pendulum systems (FPSs) were applied using different friction models. A Coulomb friction model and a rate dependent friction model were constructed using the friction coefficient of a PVDF/MgO friction material to analyze the effect of different friction analysis models. The Coulomb friction model uses a single friction coefficient regardless of friction velocity, while the rate dependent friction model can reflect the change in the friction coefficient with friction velocity. Nonlinear time history and seismic fragility analyses were conducted to confirm responses of the bridge. The seismic responses of a deck and a column were used to evaluate the performance of the base isolated bridge, and a friction model that can effectively evaluate the performance of isolated bridges was analyzed.

Dynamic Analysis of Bidirectional Solar Arrays with Flexible Panels and Clearance Joints

The dynamic characteristics of a two-step deployable bidirectional solar array system with flexible panels and clearance joints are studied in this paper. Driving mechanisms, closed cable loop configurations, and latch mechanisms are considered in this system where normal contact force is established using a nonlinear spring damping model and the friction effect is determined by a modified Coulomb friction model. With the simulation strategy of activating different constraint states and applying latch torques, the multiple deployment and locking processes of the system are implemented. The results indicate that the second locking causes obvious vibration on the dynamic responses of the yoke and main panels and leads to a complex bidirectional vibration of the main panel connected to the side clearance joints. The equivalent suspension damping property produced by the coupling of the flexibility and clearances can reduce the vibration of the deployable components. Moreover, the attitude and orbital motion results reveal the effect of different deployment methods of the system on the spacecraft attitude. Finally, the trajectories of journal centers and contact forces are analyzed to indicate the foundation of the dynamic behavior of the system.

Research on Multi-Body Collision Dynamics of Ball Cage Flexible Drill Pipe Considering Borehole Curvature

A ball cage flexible drill pipe is a new type of ultra-short-radius drilling tool, which consists of multiple flexible joints hinged together. During the drilling process, the flexible members will come into contact and wear, which reduces the efficiency of load transfer. The multi-body collision contact dynamics model was proposed to study the performance of the ball cage flexible drill pipe. The method considered the influence of the borehole curvature. The kinematic equations of the ball cage flexible drill pipe were established. The Lankarani–Nikravesh collisional contact model was used to characterize the normal contact force, and the Coulomb friction model was used to describe the tangential contact force. The multi-body motion state of the flexible drill pipe was simulated, the contact force distribution of the flexible drill pipe during the motion cycle was analyzed, and the influence of the borehole curvature radius on the size of the flexible joints and the contact force was studied. The results show that the running form of the ball cage flexible drill pipe shows a “folded” shape compared with the initial form; the contact force of different flexible joints is in a state of fluctuation; the normal contact force is much larger than the tangential contact force; the matching relationship between the borehole curvature and the length and radius of the flexible joints is derived, which provides criteria for the design of the flexible joints to ensure the reliability of the flexible drill pipe in large curvature borehole; the borehole curvature has an important influence on the collision contact force and load transfer efficiency of flexible drill pipe.

Experimental and Numerical Study on the Influence of Lubrication Conditions on AA6068 Aluminum Alloy Cold Deformation Behavior

The aim of this manuscript is the experimental and numerical study regarding the influence of friction conditions on plastic deformation behavior by upsetting the A6082 aluminum alloy. The upsetting operation is characteristic of a significant number of metal forming processes: close die forging, open die forging, extrusion, and rolling. The purpose of the experimental tests was to determine: by the ring compression method, the friction coefficient for 3 surface lubrication conditions (dry, mineral oil, graphite in oil) by using the Coulomb friction model; the influence of strains on the friction coefficient; the influence of friction conditions on the formability of the A6082 aluminum alloy upsetted on hammer; study of non-uniformity of strains in upsetting by measuring hardness; change of the tool-sample contact surface and non-uniformity of strains distribution in a material by numerical simulation. Regarding the tribological studies involving numerical simulations on the deformation of metals, they mainly focused on the development of friction models that characterize the friction at the tool-sample interface. The software used for the numerical analysis was Forge@ from Transvalor.

Nonlinear Dynamic Characteristics of Deep Groove Ball Bearings with an Improved Contact Model

In this paper, the nonlinear dynamic response of deep groove ball bearings with clearance was studied numerically. The imperfect connections with the clearance of raceways and rolling balls were established by the contact elements. In order to describe the contact characteristics accurately, a hysteresis damping coefficient was introduced into the Hertz contact model, which represented the dissipative term during the contact–impact process. The tangential force of the contact bodies was obtained based on a modified Coulomb friction model. Then, the dynamic analysis model of the deep groove ball bearings with clearance was built. Meanwhile, the experimental test platform of the deep groove ball bearings with various operation conditions was built and the dynamic simulation was utilized as the demonstrative case to conduct the investigation. The numerical results revealed that the existence of clearance would change the motion trajectory of a rolling ball and the appearance of the different movement states (free, contact, and penetration). In addition, the contact characteristics and sliding features would be changed with the variations in the operation conditions and structural characteristics.

Study on the Prediction of Debris Flow Risk Using LS-RAPID

In this study, the LS-RAPID program was applied to evaluate the debris flow deposition area using the field surveyed topographical data in the areas of debris flow occurrence. In 2020, aerial photogrammetry was performed using an unmanned aerial vehicle in Seonseri, Osan-myeon, and Gokseong-gun. The erosion and deposition areas owing to debris flow were estimated using the orthographic images generated from photogrammetry and high-resolution Digital Surface Mode (DSM), and the extent of debris flow was accurately estimated. For debris flow simulation, the LS-RAPID program, with the apparent friction angle of the Coulomb's friction model as an important factor, was applied. The simulation results were significantly affected by the quality of the topographical data. It is essential to apply DSM data for obtaining a highly accurate simulation of the deposition area where damage generally occurs. To evaluate the performance of the simulation, the LSSI index with the deposition area as a factor was applied; it was found to be 65%, showing a superior predictive performance. In conclusion, it is possible to predict the debris-flow damage using LS-RAPID simulation, and the DSM data on deposition areas are required to generate a reliable disaster map.

Finite Element Modeling of the Soil-Nailing Process in Nailed-Soil Slopes

The finite element technique has been accepted as a tool for modeling geotechnical complex processes. In this study, finite element (FE) modeling of various stages of the soil-nailing process, i.e., construction stages and overburden pressure stages, is carried out considering different soil parameters, simulating with in-house developed laboratory models. The soil-nailing process built in laboratory models is idealized as a plain strain problem and modeled in PLAXIS software. The laboratory models of the soil-nailing process consist of a Perspex sheet box containing a sandy soil slope, a Perspex sheet facing, steel bars as reinforcement and a steel plate as foundation. The stress–strain relationship of the sand is represented by a Hardening-Soil model. The interface at the soil and nail is described by the Coulomb friction model. The behavior of the soil-nailing process, during the construction stage and under varying overburden pressure and varying soil density, are investigated in terms of displacements of slope and stress conditions in slope soil mass. The slope displacements and stress conditions in slope soil mass are all well presented by the FE modeling and compared with laboratory model test data. The sensitivity analysis of the laboratory models’ dimensions is carried out by three-dimensional modeling of the nailed-soil slope. It can be concluded that the developed finite element model has the potential to simulate the performance of a field nailed-soil slope during construction and working stages and could provide guidance for the construction/maintenance of soil-nailed cut slopes in granular soils/weathered rocks.

Nonlinear Dynamics and Vibration Localization of Shrouded Blisk with Contact and Friction Effects

Shrouds have been widely used to reduce the level of excessive vibration of blisks. However, complicated nonlinear motion can be induced by the contact and friction between shrouds. Even worse, harmful localization of vibration can be encountered due to nonsmooth behaviour at the shroud contact interfaces in the tuned disk. In this paper, the nonlinear dynamics and localization of vibration of a shrouded blisk are studied considering the spin softening. The continuous parametric model of a shrouded blisk is established, and the transition boundaries between different status (i.e., stick, slip and separation) of shrouds are determined based on the Coulomb friction model. The steady-state responses of the blisk are analysed using variable rotation speed, and the primary resonance, beat and quasi-periodic vibration are presented in connection with the non-smooth behaviour of contact. A particular type of vibration localization initiated by the contact and friction effect of the shrouds in the form of asymmetric vibration in the tuned blisk is discovered. It is found that the blades-disk coupling has strong influences on the level of the localization. The effects of the contact stiffness and localization on the blade vibration are demonstrated through the change in the powers of the blade motions.

Dynamic Research on Nonlinear Locomotion of Inchworm-Inspired Soft Crawling Robot.

Inchworm-inspired bionic soft crawling robot (SCR) composed of soft materials possesses preeminent active compliant deformation ability and has obvious advantages over traditional hard robots when moving in a confined space, which is up-and-coming candidate in robotic community. Nevertheless, there are rare investigations on dynamic modeling problems of the SCR allowing for its nonlinear deformation properties and frictional contact that affects its crawling performance. In view of this, within the theoretical framework of absolute nodal coordinate formulation, in consideration of material, geometry, and boundary nonlinearities, combining a multiple-point contact model with the Coulomb friction model, an effective and accurate nonlinear dynamic model for a bioinspired SCR with one single limb is proposed to elucidate its motion law. We implement an in-depth dynamic research and analysis on the SCR in terms of average velocity, stick-slip characteristic, gaits and successfully simulate its successive forward crawling locomotion meanwhile gaining dynamic response. The proposed theoretical dynamic model correctly captures the SCR' complex geometry configurations and nonlinear deformations, discloses its stick-slip dynamic behaviors and crawling locomotion mechanism, whose effectiveness and superiority are validated experimentally, which inspires a deep insight to motion analysis of other types of soft robots, and enlightens new ideas of their diversified architecture designs.

Numerical analysis of frictional contact between crack lips in the framework of Linear Elastic Fracture Mechanics by a mesh-free approach

In this paper, a mesh-free approach is presented for the numerical analysis of frictional contact in the framework of Linear Elastic Fracture Mechanics (LEFM). This approach (WLS-HOCM) is obtained by combining a Weighted Least Square approximation (WLS) under a strong formulation with a High Order Continuation Method (HOCM), the Coulomb friction model and the visibility criterion to investigate the contact that occurs between the crack lips under compression loads. The contact between the crack lips is regarded as boundary conditions, and a regularization technique is used to replace these no-smoothed conditions with smoothed ones. We were able to avoid the numerical integration encountered in the weak formulation by using the strong formulation. The stick and slip phenomena of closed cracks are studied using numerical examples. The numerical results obtained demonstrate the effectiveness and precision of the suggested method for computing frictional self contact problems.