Normal Contact Force Research Articles

A numerical study of particle friction and initial state effects on the liquefaction of granular assemblies

Liquefaction of sandy soil due to cyclic loading can result in catastrophic damage to the built environment. Liquefaction has been previously studied through field testing, laboratory experiments, and numerical simulations. However, the particle-scale behavior of granular materials during the initiation of liquefaction has not been comprehensively quantified. In the current work, the discrete element method is employed to study the effect of global void ratio, initial confining stress, overconsolidation ratio, and particle friction on liquefaction resistance. Mechanical coordination number, local void ratio distribution (LVRD) entropy, fabric anisotropy and average rotational velocity are quantified in each assembly to provide insight into the particle-scale physics governing liquefaction resistance. Results show that lower global void ratio, increased confining stress, higher OCR values, and higher particle friction all increase liquefaction resistance. Immediately prior to the onset of liquefaction, the mechanical coordination number in each assembly sharply decreased to approximately 2.5, with the remaining contacts attributed primarily to particle collision after liquefaction initiation and fabric collapse. Anisotropy induced in the cyclic loading process was due to normal contact force anisotropy, which was more prominent in the specimens with higher initial confining pressures. Liquefaction resistance for overconsolidated specimens was found to be lower than that of normally consolidated specimens at the same void ratio. We observe liquefaction resistance to be sensitive to the coefficient of interparticle sliding friction, especially for lower friction coefficients. Average particle rotational velocities are shown to increase with increasing interparticle friction. The quantity of energy dissipated through frictional sliding was controlled by both the rate of dissipation and the number of loading cycles to liquefaction. In sum, the simulations elucidate significant connections between micromechanical properties and liquefaction response at different initial states and with different particle frictions.

DEM investigation of angle of repose for super-ellipsoidal particles

We explore the effect of particle shape on the angle of repose (AoR) in granular packing using a three-dimensional discrete element method. Non-spherical particles were modeled using super-ellipsoids characterized by aspect ratio and blockiness. The relationship between AoR and particle shape was examined, followed by a series of analyses on the origin of AoR from a microscopic perspective. Results show that, with blockiness deviating from unity, AoR has an approximate “M” shape that exhibits a strong to weak trend with aspect ratio, matching results of previous reports. Another finding suggests a parabolic relationship between normalized AoR and normalized coordination number. AoR increases with anisotropy related more with the anisotropy of particle orientation than with the anisotropy of contact normal. Particle shape is more likely to affect AoR by affecting the tangential force than the normal contact force. An analysis based on traction indicates that dips in stress associated with the tangential force (compared with the normal force) and non-spherical particles (compared with spheres) are more significant. For various particle shapes, AoR is positively correlated with friction mobilization but is negatively correlated with friction mobilization for various coefficient of friction.

Implementation of a non-Hertzian contact model for railway dynamic application

The development of wheel–rail contact models is an active topic of railway research with the dual objective of improving the accuracy of multibody simulations and reducing its computational effort. This paper extends the online Hertzian contact model, proposed by Pombo et al. (Veh. Syst. Dyn. 45: 165–189, 2007) to propose a non-Hertzian contact model. The new methodology presented here includes the following steps: (i) search of the points of contact; (ii) identification of the undeformed distance function; (iii) evaluation of the contact patch; (iv) calculation of the normal and tangential contact forces; (v) application of the contact forces in the multibody vehicle model. Among several contact models available in the literature, this non-Hertzian contact approach uses the Kik–Piotrowski model for the normal contact force, while the tangential forces are obtained from the interpolation of the available Kalker Book of Tables for non-Hertzian (KBTNH) contact. With the purpose to demonstrate the proper implementation and selection of parameters that define this new model, several contact analysis and dynamic simulations are performed in which the wheel S1002 and the rail UIC50 are considered. First, the contact analyses that determine the contact condition of different wheel–rail interactions serve to assess the accuracy of the Hertzian and non-Hertzian models with respect to the software of reference CONTACT. Second, the Hertzian and non-Hertzian models are utilised to perform dynamic simulations of a wheelset, a bogie and a vehicle running in tangent and curved tracks. In short, this work provides, not only a complete description of the implementation of a non-Hertzian contact model in a multibody code, but also suggests for the proper selection of the parameters that promote better accuracy and optimal computational efficiency.

Multi-particle FEM modelling on hot pressing of TiC-316L composite powders

316L stainless steel (abbreviated by 316L) has been applied in many key industrial areas due to its outstanding properties like corrosion resistance, ductility and biocompatibility etc. However, the relatively low strength and wear resistance of this material restrict its further application. This problem can be solved by the introduction of TiC particulate reinforcement into 316L matrix, which can effectively improve the strength, stiffness, wear resistance and high temperature strength. In the present work, three-dimensional hot pressing (HPing) of TiC-316L composite powders in a closed die is numerically reproduced by multi-particle finite element method from particulate scale. The evolution of macro- and microscopic properties during HPing is systematically characterized and analyzed, and the densification dynamics and mechanisms are identified. The results show that HPing can not only significantly decrease the pressing pressure, but also alleviate the stress concentration in the final compacts. With the increase of pressing temperature, the equivalent von Mises stresses in the compacts get smaller and the equivalent strains of TiC-316L composite powders get larger. During HPing, the voids are mainly filled by particle rearrangement and plastic deformation of 316L particles. Meanwhile, the equivalent von Mises stresses concentrated within the 316L particles firstly increase and then decrease, and the equivalent von Mises stresses concentrated within the TiC particles increase monotonically. Large stresses are mainly concentrated within the TiC particles, which are decreasing from the surface to the center of each particle. Also, larger contact normal forces are mainly distributed within and around the TiC particles.

Trajectories of magnetically-actuated helical swimmers in cylindrical channels at low Reynolds numbers

Artificial microswimmers have a huge potential in various microfluidic and medical applications. Most of the swimming scenarios involve some kind of confinement such as arteries or microchannels for both natural and artificial swimmers. It is shown both experimentally and numerically that confinement influences the swimmer trajectories significantly at low Reynolds numbers. Magnetically-actuated helical microswimmers follow helical or straight trajectories depending on whether the tail is pushing or pulling the swimmer. To improve the understanding of this behavior, we use a direct numerical approach that couples a simple kinematic model with a computational fluid dynamics (CFD) model to solve steady Stokes equations for low Reynolds number swimming. The kinematic model updates the position and the orientation of the swimmer by using the linear and angular velocities from the CFD model at each instant. In addition to the viscous force, the external magnetic torque, the gravity force and the normal contact force on the swimmer are also considered in the CFD model. Simulations are used to study the effects of the Mason number, which is the ratio of viscous and magnetic torques, the diameter ratio of the swimmer and the channel, the tail length and the channel flow. In addition to improving the fundamental understanding, these results bear strong relevance to the development of control systems for microswimming robots.

Painlevé paradox and dynamic self-locking during passive walking of bipedal robot

When analyzing the passive walking of bipedal robot using the traditional methods, it usually assumes the contact foot and the slope maintain stick state. However, in the actual stable walking, the sliding contact caused by structural vibration is inevitable. Some special configuration of bipedal robot can result in dynamic self-locking or “jam” at the sliding contact if the coefficient of friction (COF) is sufficiently large; this has been termed, Painlevé paradox in rigid body dynamics. The objective of this paper is to propose a rigid body dynamic combined with Linear Complementary Problem to calculate the occurrence conditions of Painlevé paradox, and develop a completely flexible body model (CFBM) to analyze its bouncing motion induced by dynamic self-locking during passive walking of bipedal robots. The structural deformation field and inertial field of CFBM are discretized by finite element method. The contact forces and transient waves propagating in the CFBM are calculated. In the range of configurations and COF where Painlevé paradox occurs, analysis based on rigid body dynamics gives results indicating that either there are multiple solutions or the solution doesn't exist; analysis using CFBM finds that the bouncing motion will cause walking unstable and the normal contact force increases abruptly. In addition, increasing structural compliance will decrease the critical COF of dynamic self-locking roughly by 46%.

Dynamic computation of 2D segment-to-segment frictionless contact for a flexible multibody system subject to large deformation

A new formulation of segment-to-segment frictionless contact dynamics is proposed for the planar multibody systems subject to large deformations, based on the absolute nodal coordinate formulation, which is not only able to describe both large deformations and overall motions, but also to offer the C1-continuous surface representation for contact problems. The mortar method is used to discretize the contact constraints, established in an integral form on the nonconforming contact surfaces. A rescale and reconstruction strategy is proposed to recover the gap function as following. The gap function is revised via a scale factor first, and then the slope of the gap function is reconstructed via weighted average method. To satisfy the frictionless contact condition, the magnitude of the normal contact force is discretized via the third-order Hermite interpolation, while the direction of the force is along the normal vector of the contact surface. The penalty method is used to enforce the contact constraints. The generalized forms and Jacobians of the contact forces are derived. The generalized-alpha method is adapted to solve the dynamic equations. Finally, four numerical examples are given to verify the accuracy, convergence, and robustness of the proposed algorithm.

Analysis and prediction of high‐speed train wheel wear based on SIMPACK and backpropagation neural networks

AbstractAs train running speeds increase, the wheel–rail interactions of high‐speed trains are becoming more complicated, and predicting and monitoring wheel wear are becoming increasingly important for the safe operation of high‐speed trains. Therefore, identifying the critical factors that affect the wear of wheel–rail interactions and developing novel methods to predict wheel wear are of great importance. In this work, SIMPACK is used to establish a dynamic model of a high‐speed train and to investigate the normal and lateral contact forces of the wheel–rail interfaces and the wear of the wheels for a train passing through a specially designed route that consists of straight‐line, smooth‐curved, and circular tracks. The wheel wear is predicted by means of the Archard wear model based on the SIMPACK analysis, and the wear is validated by a backpropagation neural network (BPNN) classification based on daily measured data provided by the Beijing Railway Administration. The results from the SIMPACK dynamic simulation and the BPNN classification show that the position of a wheel in a bogie has a significant effect on the wheel wear, but the position of a carriage in a train does not have a significant effect on the wheel wear. The findings from this study are very useful for the maintenance and safe operation of high‐speed trains.

New insights into the effect of interparticle friction on the critical state friction angle of granular materials

This letter examines the effect of interparticle friction (μ) on the critical state friction angle (φcs) of granular materials via the discrete element method. A series of drained triaxial tests are conducted on multisphere ellipsoids. The results indicate that φcs first increases with μ and then reaches a plateau when μ ≥ 0.3. Anisotropic analysis provides new insights into the underlying mechanisms of the φcs evolution from two perspectives. First, the initial increase of φcs results from the increases of contact normal anisotropy ac, normal contact force anisotropy an and tangential contact force anisotropy at; subsequently, the saturation of φcs is a consequence of the decrease of an being compensated by the increase of at. Second, the relationship between the stress ratio q/p and the contact normal anisotropy within the strong and nonsliding contacts acsn is nearly linear for ellipsoids (i.e., q/p = kacsn). Accordingly, the initial increase of φcs is related to the increase of k and acsn at low μ. The plateau of φcs at high μ can be attributed to the decrease of acsn being compensated by the increase of k.

3D DEM investigation on the morphology and structure of landslide dams formed by dry granular flows

Large-scale landslide dams triggered by earthquakes or rainfall can cause disasters due to inundation upstream and outburst floods downstream after dam failure. Landslide dams formed by rock/debris avalanches are loose in structure and have a lack of stability; thus they are more susceptible to breaking. The morphological and structural features of landslide dams directly depend on the formation process, and greatly affect the dam stability as well as the dam failure modes. This study presents the transportation and deposition characteristics of dry granular flows with grains of mixed sizes during the formation of landslide dams via 3D discrete element method (DEM) simulations, mainly taking into consideration of the influence of the sliding area length, angle and roughness. The results show reverse segregation during grain transportation and deposition processes. The position of the particles forming the initial deposited layers was also reversed. It was found that when the sliding area angle was larger, the crest surface frontal angle and deposit width increased with the increment of the sliding area length. For lower sliding area angles, the deposit width and crest surface frontal angle showed little change. The increase of sliding length and base friction coefficient as well as the decrease of the sliding area angle will enhance the size segregation. As the slope angle increases, the dominant direction of the force chains shifts significantly and the sliding length mainly influences the magnitude of the normal contact force in the other directions. These considerations can contribute to a better understanding of the landslide dam morphology and structure after their formation.

Shear behaviors of granular mixtures of gravel-shaped coarse and spherical fine particles investigated via discrete element method

The shear behaviors of granular mixtures are studied using the discrete element method. These granular materials contain real gravel-shaped coarse particles and spherical fine particles. Dense samples have been created by the isotropic compression method. The samples are then sheared under drained triaxial compression to a large strain to determine the peak and residual shear strengths. The emphasis of this study is placed on assessing the evolutions of contributions of the coarse-coarse (CC) contacts, coarse-fine (CF) contacts and fine-fine (FF) contacts to the peak and critical deviator stresses. The results are used to classify the structure of granular mixtures. Specifically, the granular mixtures are fine-dominated or coarse-dominated materials when the coarse particle content is <30%–40% or >65%–70%, respectively. A comparison with previous findings suggests that the spherical binary mixtures will become coarse-dominated materials at a relatively larger coarse particle content (i.e., 75%–80%) than this study (i.e., 65%–70%), which is attributed to the particle shape effect of coarse particles. A microscopic analysis of CC, CF and FF contacts at the peak and critical states, including normal contact forces and proportions of strong and weak contacts of each contact type to total contacts, reveals why the contributions of CC, CF and FF contacts to the peak and residual shear strengths are varied. Finally, a detailed analysis of the anisotropies indicates that the increases of peak and residual shear strengths are primarily related to the gradual increases in geometrical anisotropy ac and tangential contact force anisotropy at to compensate for the continuous decrease in normal contact force anisotropy an. Furthermore, it is interesting to note that the branch vector frame provides a better linear relationship between the stress ratio and the geometric anisotropy of the strong and nonsliding subnetwork than the contact frame for the coarse-dominated materials.

A procedure to estimate normal and friction contact parameters in the stance phase of the human gait

A new approach to estimate normal and tangential contact parameters in the foot-ground contact during human gait was proposed. A correct estimation of the contact parameters would be very important in the resolution of predictive forward dynamic problems. The normal contact forces have been well estimated in the literature. But accurate estimation of tangential forces has not been reached yet. This work proposed a new procedure to accurately estimate friction forces. The approach has been based on the consideration of the modulus of the tangential force instead of its components. This modulus was introduced together with the modulus of the normal contact force and its two associated moments in an optimization algorithm to fit the contact forces provided by the model to the experimental data obtained with a force plate. An inverse dynamics problem was solved as a step previous to the optimization algorithm. The results showed that both the normal and tangential forces and the moments in the horizontal plane were in agreement with the experimental measurements. This work also analyzed the influence on the results of the friction law. The results obtained with the general friction law, which considered dry (static and dynamic) and viscous friction, were compared with results provided by simpler laws. The analysis of the components of the friction forces pointed out the importance of the Stribeck component in the resultant force instead of the viscous friction which played a minimal role. But for modelling the stick-slip transition, the implementation of a general friction law is necessary.

Experimental Studies on Torsional Stiffness of Cycloid Gear Based on Machining Parameters of Tooth Surfaces

Estimating the torsional stiffness has always been the primary issue in analyzing the dynamic characteristics of cycloid gears. The traditional method of obtaining torsional rigidity involves calculating the ratio of the input torque and rotation angle, treating the deformation of cycloid gear as a black box. In order to thoroughly understand the rotation angle caused by the local contact deformation of each cycloid pin gear, a Majumdar–Bhushan contact model and the finite element method are combined to express the normal contact stiffness. By multiplying the normal contact stiffness of each pin gear and the arm of normal contact force, the torsional stiffness of the cycloidal pin wheel system can be calculated. Experiments are conducted to establish the relationship between the torsional stiffness and roughness parameters of the machined tooth surface. The effect of input torque on the torsional stiffness has also been analyzed. This study formulates a relationship between the torsional stiffness and surface characteristics of cycloid gears, which can help improve their design and manufacture in the future.

Research of non-linear frictional contact model in vehicle-pedestrian accidents based on computer simulation

In numerical simulation of vehicle–pedestrian accidents, pedestrian rest positions are greatly influenced by the friction coefficient between pedestrian and ground. Current researches on vehicle–pedestrian accident reconstruction often regard pedestrian–ground friction coefficient as a constant value. However, clothing fabric belongs to viscoelastic material. Some researches show that friction coefficient of viscoelastic material can be influenced by normal contact force. In this paper, a contact model between clothing fabric and asphalt road is built by computer simulations. The calculation based on this contact model indicates that the pedestrian–ground friction coefficient in accidents is not constant. Relationship between friction force and contact pressure is non-linear. Meanwhile, according to the simulation results of a real-world vehicle–pedestrian accident, influence of vehicle– pedestrian contact stiffness on pedestrian projection has been discussed, and simulation errors under different pedestrian–ground friction coefficients are calculated. Simulation results show that compared with traditional pedestrian–ground contact model, the non-linear pedestrian–ground contact model can obtain smaller simulation error with higher stability, which has validated the rationality of this contact model.AbbreviationsShear stress at surface contact pointsAReal contact areaRMS roughness of the surfaceConstant related to the average height of the surfaceCorrelation length of the surface in X-directionCorrelation length of the surface in Y-directionZ1Height matrix of surface 1Z2Height matrix of surface 2Average height of peaks on surface 1Average height of peaks on surface 2Distance between two rough surfacesCharacterised distance between rough surfacesDistance matrix between rough surfacesRatio of real contact area to nominal contact areaGaussian contact radiusReal contact area of a single rough peakAccuracy of contact area calculationContact matrix between rough surfacesLocal contact force of a single rough peakElastic modulus of surface 1Elastic modulus of surface 2Poisson ratio of surface 1Poisson ratio of surface 2Friction forceFriction coefficientFeature friction coefficientConstant related to material property parameters

An Electronic Force Sensor for Medical Jet Injection

In medical jet injection, a narrow fluid drug stream is propelled at high velocity into skin without a needle. Previous studies have shown that the volume delivered is highly dependent on a number of factors. This paper details the development of an electronic force sensor for medical jet injection and shows that the normal contact force exerted on the tissue by the nozzle is an additional factor affecting volume delivered. Using this sensor, we measure the forces at the nozzle tip in the normal direction with a sensitivity of 18 μN, calibrated over a range from 1 N to 8 N with a mean absolute error of 8 mN, and a maximum overload of 300 N. We further measure forces at the nozzle tip in the lateral direction with a sensitivity of 8 μN, calibrated over a range from 0.1 N to 7 N, with a mean absolute error of 101 mN for lateral contact force magnitude and 1.60 deg for lateral contact force direction. Experimental validation confirms that the force sensor does not adversely affect the accuracy and precision of ejected volume from the jet injector. We use this setup to examine the effect of normal contact force on volume delivered into postmortem porcine tissue. Experimental results demonstrate that volume delivered with normal contact force between 4 N and 8 N is significantly more accurate and precise compared to volume delivered with normal contact force between 0 N and 3.9 N.

Wear damage of out-of-round wheels in rail wagons under braking

Periodic deviation of the diameter of wheel across its circumference is referred to as the out-of-round (OOR) defect that can cause significant damages to wheel – rail interface, affect the service life of various components of the vehicle/track system and the safety of trains. Under braking, OOR defect may exacerbate these damages; to uncover such exacerbation, a multi-body dynamic simulation model in a fixed coordinate system for wagons containing new/ defect free or OOR wheels subject to braking torques has been formulated and validated using a dataset in the literature. Using the validated model, the effects of the repetition order (single or multiple deviations of diameter) of OOR defect and the severity of application of braking torques to wheel wear has been examined. It has been found that under constant speed, the normal contact force increased with the repetition order. The OOR defect dominated the normal contact force with a dynamic impact force factor of 1.48, whilst the new/ defect free wheels exhibited negligible impact force. It is shown that the effect of OOR defect is significant for wear of wheels under normal braking whist under wheel skid, braking torque dominates wear. Wheel unloading ratio is shown to be a better indicator for the determination of risk to derailment, than the commonly used Nadal's derailment quotient where the wheel contains OOR defect.

Effect of fine-grained dipping interlayers on mechanical behavior of tailings using discrete element method

Due to the presence of fine-grained interlayers (frequently called lenticles), the stability of tailings dams can deteriorate. In this study, a two-dimensional numerical model with flexible boundary was constructed, and biaxial tests were carried out for samples with interlayers at different dip angles. The influence of the interlayer inclination on the mechanical properties of tailings was analyzed. The simulation results revealed that the shear strength of tailings with interlayers decreases with the increase in the interlayer dip angle. Obvious anisotropy of shear strengths was observed due to the presence of interlayers. All the deformations of the samples with interlayers were well captured in the DEM simulations. Bulging deformations were found in the samples with interlayers at dip angles of 0°, 15° and 30°. Shear slip along the fine interlayer plane was generated in the samples with interlayers with dip angles of 45° and 60°. The principal orientation of the contact unit normal and the normal contact force aligns with the loading direction for the samples with interlayer at small dip angle (i.e., 0°). However, for the sample with interlayer at large dip angle (i.e., 60°), the principal orientation trends to the direction normal to the interlayer.

A Multibody Dynamics Approach to Limit Cycle Walking

SummaryThough significant efforts are made to develop mathematical models of the limit cycle walking (LCW), there is still a lack of a general and efficient framework to study the periodic solution and robustness of a complex model like human with knees, ankles and flat feet. In this study, a numerical framework of the LCW based on general multibody system dynamics is proposed, especially the impacts between the feet and the ground are modeled by Hunt–Crossley normal contact force and Coulomb friction force, and the modeling of the knee locking is presented as well. Moreover, event-based operating strategies are presented to deal with controls for the ground clearance and the knee locking. Importantly, a fast and efficient two-step algorithm is proposed to search for stable periodic gaits. Finally, maximum allowable disturbance is adopted as the index for stability analysis. All these features could be readily implemented in the framework. The presented solution is verified on a compass-like passive dynamic walking (PDW) walker with results in the literature. Based on this framework, a fairly complicated level-walking walkers with ankles and knees under control are analyzed and their periodic gaits are obtained, and surprisingly, double stable periodic gaits with, respectively, low speed and high speed are found.

Normal force and displacement amplitude influences on silver-plated electrical contacts subjected to fretting wear: A basic friction energy – contact compliance formulation

During the last decades, the use of connectors in electrical devices for automotive has significantly increased. This raise in the number of electrical and electronic devices on board has led to a growing number of breakdowns. Indeed, this connectors need to keep a low and stable electrical contact resistance (ECR) but due to engine vibrations, fretting wear damage occur. Characterized by small oscillatory motions, fretting induces wear and oxide debris layer (third body) decaying the electrical contact resistance. The aim of this work is to study the effects of two main factors, which are the normal contact force and the displacement amplitude. In this study, a silver-plated contact (2 µm of thickness) was investigated applying various loading parameters: 2 N < P < 6 N and ±3 µm < δ* < ±20 µm. Results show that the ECR endurance decreases when the displacement amplitude increases regardless of the normal force. However, a non-monotonic evolution is found regarding normal force effect. Indeed, for a given displacement amplitude, a rise of the normal force tends to increase the contact pressure but at the same time induces a reduction of the effective sliding amplitude due a larger tangential accommodation. Hence, by coupling a friction energy density approach with a basic compliance description, the synergic effect of the normal force and the displacement amplitude is described and the ECR endurance predicted.

A normal contact force approach for viscoelastic spheres of the same material

This paper presents a normal contact force approach for viscoelastic spheres of the same material based on the theory of viscoelasticity. The approach treats the normal contact force as an elastic component superposed with a dissipative component based on which to derive a reduced expression, and is numerically analyzed for the viscoelastic spheres modelled by the standard linear solid with the sinusoidal displacement history. The influences of relaxation time and viscosity upon the approach are discussed. An application of the approach with the collinear impact of viscoelastic balls is carried out and its adequacy to reality is validated by the comparison of the numerical solution against the impact experiment of Golf and Superball, to conclude that the suggested approach is applicable to build the kinematic equation describing the normal contact of viscoelastic bodies.