Normal Contact Force Research Articles

Non-Hertzian contact analysis of heavy-haul locomotive wheel/rail dynamic interactions under changeable friction conditions

Wheel/rail dynamic interactions of heavy-haul locomotives are highly nonlinear and complicated due to large traction/braking loads, frequent anti-slip control and complex wheel/rail interface environment. The wheel/rail dynamic interactions, as well as the interface wear, have been broadly studied by means of Hertzian contact analysis, but the wheel/rail contact is essentially a non-Hertzian contact matter. This paper presents an investigation of wheel/rail dynamic interaction characteristics of a heavy-haul locomotive subjected to traction loads and dry/wet/greasy contact conditions by using a non-Hertzian contact method. For this purpose, a comprehensive dynamics model for heavy-haul train-track coupled system is established. A non-Hertzian normal contact algorithm and the corresponding creep algorithm are employed to solve wheel/rail normal and tangential contact forces, respectively. The locomotive wheel/rail dynamic interactions under different contact conditions and traction efforts are discussed. The simulation results indicate that traction effort and friction conditions have a significant influence on the contact forces, distributions of contact stress, and adhesion-slip region in the wheel/rail contact patch. The adhesion-slip distributions were found to reach full-slip under the lowest-adhesion conditions, and the wear index was found to be much greater than that under dry condition.

Micro-modelling of shear localization during quasi-static confined granular flow in silos using DEM

The paper deals with the quasi-static confined flow of cohesionless sand in a plane strain model silo with parallel walls and a slowly movable bottom. Numerical modelling was carried out by the discrete element method (DEM) using spheres with contact moments to approximately capture a non-uniform shape of sand particles. Different initial void ratios of sand and silo wall roughness grades were employed. Regular triangular grooves (asperities) with the same inclination and a different height were used to describe the varying wall surface topography. The emphasis was on the formation and evolution of both wall and internal shear zones during sand flow. DEM simulation outcomes were compared with corresponding model experiments and theoretical solutions. In addition, the particle displacements, particle rotations, normal contact forces, void ratios and wall stresses were evaluated. The numerical findings enhance the understanding of shear localization at the grain level during confined flow in silos and its strong impact on the magnitude, distribution and oscillation of wall stresses.

Discussion on Failure Mechanism and Strength Criterion of Sandstone Based on Particle Discrete Element Method

In order to study the mechanism of loading failure process of deep rock mass, particle flow numerical simulation (PFC2D) was used to carry out rock mechanical unit tests under different loading strain rates for sandstone in Haitangshan Tunnel, Fuxin. The applicability of several classical strength criteria was compared according to the test. The results show that, except Poisson’s ratio, the other mechanical parameters are positively correlated with the loading strain rate, including peak strength, elastic modulus, cohesion, internal friction angle and tensile strength. And the Poisson’s ratio is negatively correlated with the loading strain rate. And the crack initiation stress σci and dilatation stress σcd increased gradually, but the effects on σci/σpk, σcd/σpk and σci/σcd were not obvious; and at the same volume strain, the corresponding axial strain decreased gradually. The anisotropy of normal and tangential contact forces between particles increases with the increase of loading strain rate. The normal contact force was approximately symmetrical distributed up and down, while the tangential contact force was approximately symmetrical distributed in the center. The cumulative number of cracks and the number of cracks every 10 steps gradually increased with the loading strain rate, and the crack development and failure degree gradually increased, and the crack hot spot map at the shear fracture zone gradually tended to be irregular. By comparing different strength criteria, it was found that the error of ROCKER strength criterion was relatively small, and the calculation was simple. It was considered that ROCKER strength criterion was more suitable for sandstone strength prediction under different loading strain rates.

Analysis of contact force characteristics of vibratory finishing within pipe-cavity

Vibratory finishing realizes the finishing of the workpiece surface by vibrationally-fluidized granular media. Due to the granular media’s fluidized nature, vibratory finishing can be applied to surface finishing in restricted space, such as the cavity of integral casting casing. In this work, taking the typical elongated pipe-cavity inside the casings as the analysis object, based on the discrete element method (DEM), a series of simulations were carried out on the length and diameter of pipe-cavity, the load of media, vibration amplitude, and frequency. The frequency multiplication of the normal contact force between the granular media and the surface in restricted space was discovered. A method of processing contact force data based on the Fourier transform was proposed. And then, the normal contact force, its average, and coefficient of variation at different positions of the slender pipe-cavity were analyzed. It is found that the normal force fluctuates along the axial direction and is symmetric on the circumferential positions. Furthermore, the effects of various variables, including length, diameter, load, amplitude, and frequency on the normal force, have been obtained. The method and results can reference studying the dynamic behavior of granular media in restricted space.

Numerical investigation on the evolution of landslide-induced river blocking using coupled DEM-CFD

This paper presents a two-way coupled discrete element method (DEM) and computational fluid dynamics (CFD) scheme to quantitatively investigate the evolution of landslide-induced river blocking. The particle–fluid interaction is considered by exchanging interaction forces, such as drag force, buoyancy force, and lift force, which are essential for describing the evolution of river blocking. The coupled DEM-CFD scheme is first benchmarked by comparing the settling velocities of particles with different diameters with corresponding experiments. The scheme is then employed to investigate the effects of river flow velocity, river water depth, landslide velocity, and landslide volume on the evolution of river blocking. Based on the understanding of the river blocking mechanism, we propose a river blockage coefficient (Ic) to predict the river blocking. The results indicate that river water reduces the mean normal contact force of landslide particles, leading to river water quickly washing them away. The deposit velocity along the direction of the river valley is positively correlated with river water depth and river flow velocity but negatively correlated with the initial landslide velocity and landslide mass volume. The study indicates that when Ic > 1, a river is completely blocked. Otherwise, a river is unblocked or partially blocked.

Innovative squeak noise prediction: An approach using the harmonic balance method and a variable normal contact force

A flawless interior acoustics is a customer requirement in automotive industry. Any disturbing noise e.g. squeak or rattle must be avoided to meet the customer’s expectations regarding quality. This work presents an improved approach to predict squeak noise. For this purpose, a test rig generating the underlying stick-slip phenomenon by harmonic excitation is used and a corresponding finite element model is built describing the system’s dynamic behavior. The Harmonic Balance Method is applied for solving the nonlinear equations of motion. The major difference to previous approaches consists in the implementation of a contact algorithm allowing variable normal forces in the contact domain. The calculated nonlinear system response is compared to existing methods using a constant normal force. The proposed method is capable of predicting odd harmonics, which is a significant improvement in assessing squeak noise. Furthermore, good agreement between simulation and experiment is observed which validates the approach.

DEM simulation of the thermo-geomechanical effect of recycled concrete aggregate assemblies in geothermal pavement bases

This paper studies the discrete element modeling (DEM) of the thermal-geomechanical effect of recycled concrete aggregate (RCA) assemblies when harnessing renewable geothermal energy from pavement bases. This research study aims to simulate the behavior of RCA under repeated load triaxial test (RLT) at temperatures varying from 20 °C to 80 °C, to simulate temperature effects when harnessing geothermal energy from pavements. The DEM approach was used to simulate unsaturated soil considering interparticle water meniscus and the variation in its force due to the temperature fluctuation. In this research study, RCA samples with different particle size distributions were simulated under RLT test condition for various temperature conditions. According to the macro-geomechanical results, the resilient modulus (MR), porosity, and accumulated strain of samples showed different trends under varying temperatures. Comparing the micro-geomechanical behavior of the samples indicated that matric suction decreased with increasing temperature. Furthermore, the particle scale matric suction was found to be affected by the size ratio of the contacted particles. It was observed that varying the size ratio between 1 and 4 led to a higher average matric suction. The evolution of coordination number (CN), contact normal and contact normal force indicated that samples with higher sand content experienced decrease in CN and magnitude of contact normal by increasing temperature. Meanwhile, samples with lower sand content tended to have an increased CN and magnitude of contact normal in the direction of anisotropy at increased temperatures. An equation was also proposed to predict MR based on matric suction and the ratio of fine over coarse content, based on the RCA particle sizes.

Friction Properties at the Contact Interfaces of Overhead Line Aluminium Conductors

Overhead conductors may undergo fretting fatigue failures at contact interfaces located at or near the suspension clamps. Some recent experimental studies were carried out on individual wires to understand the fretting fatigue phenomenon. However, the majority of the available results are for the wire-to-wire contact configuration, while little interest has been brought to the wire-to-clamp contact configuration, which is typically a critical interface for conductor fatigue. A new experimental test bench intended to perform fretting fatigue tests on individual strands of overhead conductors is used to study the wire-to-clamp and the wire-to-wire contact configurations. Variable displacement amplitude (VDA) tests under different normal contact forces were carried out on 1350-H19 aluminium wires for both contact types. The experimental results showed a slight difference between the studied contact configurations in terms of the friction coefficient values and the transition sliding amplitude. To complete this analysis, constant displacement amplitude (CDA) tests were carried out sweeping the displacement range and replacing the tested specimen for each test. The resulting contact marks are observed using an optical microscope and a good correlation is found between both types of tests in terms of friction coefficient and transition sliding amplitude. This study allowed characterizing the sliding conditions of wire-to-clamp contact in the context of fretting fatigue of aluminium conductors and is an important step in the development of a method to evaluate the fatigue life of conductors using fretting fatigue tests of individual wire-to-clamp contacts.

Analysis of fretting cracking condition for nub of steam turbine blade

Nub-and-sleeve of last-stage blade for steam turbine is a part-span damper. The nub is susceptible to fretting cracking since the nub is in contact with the sleeve under centrifugal force and vibration of blade causes a small-amplitude oscillatory movement at the nub-sleeve contact interface. Previous study of the authors achieved the experimental result that the minimum tangential contact force amplitude for cracking increases almost proportionally to the normal contact force when the nub-sleeve contact interface is in partial slip state. Present study aims at establishing the fretting cracking condition for nub that can be applicable to design of nub-and-sleeve. For this purpose, the experimental result was analyzed with fatigue damage parameters: Smith-Watson-Topper, Fatemi-Socie and Crossland. Finite element analyses were carried out to obtain stress and strain data for estimation of fatigue damage. It is demonstrated that the fretting cracking of nub can be predicted with a single fatigue damage parameter value in a range of the normal contact force if plasticity is considered. However, if plasticity is ignored, the minimum fatigue damage parameter value for cracking increases with the normal contact force.

Micromechanical investigation of particle breakage behavior in confined compression tests

This paper aims to give a micromechanical investigation into the progressive size reduction mechanism and its effects on macro responses of granular assemblies during confined compression tests. A series of numerical studies based on the cohesive zone model are presented, incorporating internal deformation and fragmentation behaviors, and the variations of feed profiles are considered. Simulation results reasonably reproduce experimental observations in terms of macro compression responses and typical particle breakage modes. A scaling method is proposed for considering the contributions of fine products. With this method, the fragment size distribution is refined and compare favorably with physical results. The breakage degree is found to be dependent on input energy, regardless of variations of feed profiles including material heterogeneity, gradations, or friction conditions. Furthermore, a quantitative micro-analysis of normalized and cumulative normal contact force distribution, as well as contact orientation distribution is presented in this study, demonstrating the different roles of fragmentation in micro-mechanical response of particle assemblies owing to different materials or boundary friction effects.

Experimental and numerical investigation on the fretting fatigue behavior of cold expanded Al-alloy 2024-T3 plates

In this paper, fretting fatigue behavior of the cold expanded plates have been studied both numerically and experimentally. For this purpose, fretting fatigue testing fixture has been designed and fabricated for simulating fretting condition on the holed plates. The test specimens were cut from aluminum alloy 2024-T3 plate and have been cold expanded at two sizes of 1.5% and 4.7% before fretting fatigue tests. Two values of cyclic longitudinal load and normal contact force were applied to the specimens. The results of the experiments revealed that applying high level of cold expansion affects the frictional force on the contact interface. Moreover, cold expansion makes the fretting fatigue phenomenon to be likely to occur at locations away from the hole. The obtained numerical results indicated that tensile residual stress would be generated at areas away from the hole edge by cold expanding the holes. During fatigue loading, the tensile residual stress is superimposed to the tensile fatigue load which intensifies the stress severity and reduces the fretting fatigue life. The intensity of the tensile residual stress increases by increasing the level of cold expansion. As a result, lower fretting fatigue life is expected on higher size cold expanded plates.

Biomechanical Model of Human Index Finger During Examination

We have developed a mathematical model based on the Hunt-Crossley’s viscoelastic contact formulation for predicting the contact forces in the upper-body. The simulations were carried out in OpenSim software package and the simulations results were compared to experimentally recorded contact forces measured using a pressure algometer for assessing pressure pain sensitivity in the pelvic region 1.
 We observed a very good agreement between the model prediction and algometer data. Our simulation revealed that by pressing down on the tissue both normal and frictional contact forces increase up to a point- ceiling effect. Moreover, viscoelastic properties of the examinee’s tissue were associated with force; specifically, as the stiffness of the tissue declined both normal and frictional contact forces similarly declined albeit in a different way.
 Once the contact force reaches a peak point (irrespective of the baseline stiffness of the tissue) additional pressure application by the examiner was associated with incremental decrease in both normal and frictional (wasted) contact force.

Scanning control based on real-time contact force feedback for ultrasonic thickness measurement

An effective contact force control strategy is of great significance for accurate and stable ultrasonic thickness on-machine measurement. However, it is difficult to adjust the contact force dynamically due to the uncertainty of the geometric characteristics of the measured workpiece. In this paper, a contact force control method based on the combination of adaptive impedance controller and sliding mode variable structure position controller is proposed. First, the control process with the force tracking impedance control and a normal contact force calculation model is established. Then, a force-position conversion model and a sliding mode variable structure controller are proposed. Further, a simulation with a typical S-shaped measured surface is given to show that the algorithm for controlling contact force can achieve good real-time tracking performance and has stronger robustness than traditional methods. Finally, an arc-shaped aluminum alloy thin-wall part thickness is sampled along the scan trajectory to verify the effectiveness of the algorithm. The experimental results show that the proposed algorithm for controlling contact force can quickly adjust the measuring device to the target position and maintain the stability of the normal contact force to ensure the accuracy of ultrasonic thickness on-machine measurement.

Micro-characteristics and meso-shear mechanism of the soils of a slip zone in a landslide

The microstructure characteristics of slip zone soils and the variation law of microstructural parameters during shearing are the focus of the study of landslide mechanism, which is of great importance for the study of landslide prevention and control technology. Providing satisfactory explanations at the macro view is impossible because many phenomena occur after the soil is stressed in a slip zone. At present, the microscopic and meso analyses of slip zone soils are single and emphasize the macroscopic strength and deformation characteristics of slip zone soils during shearing. This study takes the landslide on the south slope of west open-pit mine in Fushun as the research object. The mineral composition and micro-characteristics of slip zone soils were studied with an X-ray diffractometer and a scanning electron microscope. Discrete element method was used to simulate the direct shear test. The meso parameters of slip zone soils were obtained by matching the direct shear test curve. The comparative analysis of meso parameters, such as the meso displacement vector field, distribution of maximum and minimum principal stresses, contact force chain, and evolution of normal and tangential contact forces, with four groups of particle gradations under different weathering conditions was conducted. Results show that the main mineral compositions of slip zone soils are original mineral-quartz and secondary mineral-clay minerals. The content of montmorillonite in clay minerals is relatively high, reaching 43.8%. The particles of slip zone soils are mainly flakes, with compact structure, and have obvious characteristics of oriented arrangement. Slip zone soils with a low degree of weathering contain coarse particles (quartz). The shear stress-displacement curves of slip zone soils with four groups of particle gradations show a strain hardening trend. Particle gradation affects the macroscopic and microscopic geotechnical and mechanical properties of slip zone soils. The displacement zone of the displacement field after shearing under poor gradation is characterized with large particles as the boundary, and its dilatancy is pronounced under the same normal stress. When the gradation is good, the particles have contact force chain, normal direction, and shear. The distribution of directional contact force before shearing is relatively uniform, the grading of large particles is mostly poor, and the stress concentration is considerable. In the case of poor grading, the distribution range of normal and tangential contact forces after shearing is smaller than that of good grading. The distribution of contact force in the same direction angle shorter than that in the case of good grading.

A data-driven normal contact force model based on artificial neural network for complex contacting surfaces

Proper modelling of contact/impact phenomenon is critical to ensure reliable description of the overall dynamic behaviors of mechanical systems. The past few decades witnessed substantial developments on contact/impact dynamics modelling, especially for the smooth contacting surfaces, like spheres or cylinders. Contrastingly, less attention has been paid to the urgent modelling demand for complex contacting bodies. By utilizing the data-driven modelling framework based on artificial neural network, this paper aims to provide a new and feasible scheme for the research of contact/impact process between complex contacting surfaces. Taking the contact/impact process between barrel and bourrelet as our research object, the indoor experiment rig is manufactured and displayed for the first time. Measurement results collected under different initial indentation velocities serve as the training datasets of the learning process for the data-driven normal contact force model. After that, the optimum hyper-parameters of the neural network, mainly including the performance index, activation function, structure of network, and learning algorithms, are tuned for the contact/impact process between barrel and bourrelet through trail-and-error method. Eventually, the neural-network-based normal contact force model can be established, of which the prediction performance for interaction modelling is further analyzed and verified. Simulation results confirm that the proposed data-driven normal contact force model can achieve high accuracy and also present excellent generalization ability. Great agreements with the experimental results under the chosen network structure demonstrate the effectiveness of data-driven interaction modelling methodology presented for complex contacting geometries.

3D DEM insights into the effect of particle overall regularity on macro and micro mechanical behaviours of dense sands

Particle shape affects the mechanical properties of sands, but the underlying micro-mechanisms are not yet explored, at least partially, due to difficulties in accessing the particle scale information in the laboratory. This study aims to fill this gap through DEM by proposing a general framework for DEM simulation considering realistic particle shape and grading characteristics. Within the proposed framework, the irregular sand particle is approximated by 3D clump, and numerical triaxial drained compression tests are conducted for five granular assemblies of different overall regularity. The simulated critical state friction angles of these five assemblies are consistent with those predicted by an empirical formula proposed in the literature. The simulation results demonstrate that decreasing of overall regularity enhances the interlock effect between particles, making the assembly a higher stiffness and shear strength. Moreover, among different fabric anisotropies, the anisotropies of contact normal and normal contact force fabrics contribute to about 80% of the critical shear strength regardless of the overall regularity. With the decreasing of the overall regularity, the contribution of the anisotropy of contact normal fabric increases while that of normal contact force fabric decreases. The overall regularity mainly affects the anisotropies of contact normal and shear contact force fabrics.

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

A new formulation is presented to simulate the segment-to-segment frictional contact dynamics of planar multibody systems that are subjected to large deformations and large motions. The contact bodies are meshed via planar elements of the absolute nodal coordinate formulation, which offers a C1-continuous surface representation for contact regions. To maintain the optimal convergence, the mortar method is used to discretize the contact constraints, which are established in an integral form on the nonconforming contact surface. By using Coulomb's friction law, the switch between stick and slip status can be realized. The penalty approach and return mapping algorithm are adopted to enforce contact constraints. The rescale and reconstruction strategy proposed in the previous study of authors is improved to recover the gap functions and the tangential friction force. In the mortar space, the magnitudes of the normal contact force and tangential friction force are discretized via the third-order Hermite interpolation, while their directions are along the normal vector and tangential vector of the contact surface, respectively. Several numerical examples are presented to demonstrate the effectiveness of the formulation.

Dynamic Simulation of Space Debris Cloud Capture Using the Tethered Net

Space debris, especially the space debris cloud, has threatened severely the safety of future space missions. In the framework of multibody system dynamics, a computational approach is proposed in this study to investigate the dynamics of net deployment and capture of space debris cloud using this net subject to large overall motions and large deformations. To obtain high simulation fidelity of capturing space debris cloud, the gradient deficient beam element of the absolute nodal coordinate formulation (ANCF) is employed to discretize threads which are woven into the net. The normal contact force between the net and the debris cloud and among debris particles is computed by using the penalty method. Some deployment examples are presented to investigate the influences of shooting velocity of bullets and microgravity as well as the angle between the traveling direction of the net and the microgravity direction on the deployment characteristics of the tethered net. Other capturing examples are given to clarify the effect of the deployment area of the net at the moment it starts to contact with the debris cloud on the capture rate and to demonstrate the effectiveness of the proposed approach for capturing space debris cloud using the net in microgravity conditions.

Progressive failure and friction motion characteristics of contact surface of composite rock mass

The structural planes existing in natural rock mass can control the failure process of rock mass. Based on the progressive response-stability failure process of a single fracture interface, the relationship between progressive response and material failure of composite rock mass is discussed. The method of friction contact plane analysis in PANDAS numerical analysis software is applied to explore the correlation between the movement and mechanical properties of composite rock mass under external forces. The motion index is mainly represented by the sliding speed and distance of the contact surface, while the mechanical properties are mainly explained by the normal contact force, the friction of the contact surface, the friction coefficient and the material damage. The relationship between these six variables illustrates the progressive response relationship during the movement of the composite rock mass. Based on the static and progressive characteristics of the progressive response process of deep rock mass engineering, the failure evolution law and energy dissipation law of composite rock mass loading process and the synergistic failure characteristics of composite rock mass are discussed. The scientific problems that need to be studied in the structure, deformation and failure of deep rock mass are put forward. The reference is provided for the failure law of fractured rock mass in water inrush process under the influence of mining, as well as fault plate material and the study of mechanical state of rock mass in fault fracture zone.

Contact force controlled robotic polishing for complex PMMA parts with an active end-effector

Due to the advantages in weather resistance, light transmittance and dimension stability, PMMA has been widely used in various fields such as aerospace and optical engineering. However, fully automatic robot systems are seldom used for polishing complex PMMA parts with high surface integrity. Therefore, a robotic polishing system with a new active end-effector is developed in this paper. In the system, a 6-degree-of-freedom industrial robot is utilized to polish the part profile along the preprogrammed paths, and then the system configuration is introduced in detail. For precisely controlling the normal contact force, both a linear voice coil motor and a force sensor are used in the designed end-effector. Meanwhile, a tilt sensor is also used to compensate the gravity component of the polishing tool along the force-controlled direction. Subsequently, a hybrid force controller, which consists of a PID controller and a Fuzzy controller, is designed to maintain the contact force between the polishing tool and the part within an allowable range. Finally, validation experiments are conducted with the designed robotic polishing system on a complex PMMA part. The experimental results show that the proposed robotic polishing system can strictly control the normal contact force and ensure high surface integrity of the PMMA part.