Normal Contact Force Research Articles

Geometric generation and meshing characteristics analysis of a new S-shaped gear drive

A new type of S-shaped gear drive with a tooth profile combining involute and circular-arc curves is proposed in this paper. Tooth profile design includes convex involute, convex circular-arc, concave involute, and concave circular-arc curves is carried out. Geometric generation and mathematical model of tooth surfaces of the S-shaped gear are established based on imaginary rack method. Utilizing Hertz contact theory, the calculation formula of contact stress of tooth surfaces is provided. Furthermore, simulation analysis of contact stress based on finite element method under various working conditions is studied using ANSYS/Workbench software. And the comparisons of stress results with general involute gear are also provided. Dynamic characteristics analysis of the generated tooth surfaces is put forward using the established virtual prototype. Normal contact force, circumferential force, axial force and radial force of tooth surfaces both S-shaped gear and involute gear are analyzed. Research results show that the developed S-shaped gear has better transmission performance than involute gear. Further study on dynamic analysis and manufacturing method will be carried out.

Dynamic analysis of spacecraft truss deployment mechanism based on conformal contact

The spacecraft deployment mechanism has phenomena such as impact, vibration and creep during the unfolding process, which has an important influence on the successful unfolding of the structure and the dynamic stability of the load after unfolding. Aiming at the shortcomings of the traditional conformal contact force calculation model, the viscous damping factor is introduced into the model to obtain an improved conformal contact force calculation model. The modified contact force model is used to calculate the normal contact force of the mechanism joints, and the improved Coulomb friction model is used to calculate the tangential contact force of the mechanism joints. Then, a multi-body system dynamic model of the truss deployment mechanism with multi-clearances is established. This model is used to numerically study the effect of clearance on spacecraft’s multi-clearances deployable truss system. The simulation results show that the clearance parameters have regular effects on the dynamic characteristics of the truss unfolding mechanism. At the same time, there is a very obvious coupling effect between different clearances.

Quasi-conformal versus Hertz superposition: a comparison for two-dimensional contact

Hertz contact theory results in a relation between the normal contact force and the rigid indentation of the contact surfaces, the force is proportional to the indentation to the power of 3/2, and a semi-ellipsoidal traction distribution. It is a valid theory for non-conformal contact between smooth surfaces (curves in 2D) of elastic bodies. This force model can be derived by considering the Taylor polynomials of degree 2 at the contact point as approximations for the surfaces/curves. In the 2D case, it depends only on the curvature radii of the curves and is undefined when they are equal, the equality of radii violates the non-conformality.The Hertzian force is usually applied to the contact of solid particles as a model compensating for the small local deformations that occur in the contact region. We consider the 2D contact of a rigid convex particle with a rigid concavity enforcing the contact constraint with a barrier method, an approach that prevents overlapping of the bodies, resulting in a force that acts on the contact point. The geometries and the motion are specially designed to show the coalescence of two contact points into one. It illustrates two possible issues with convex-concave contact, the non-uniqueness of contact points and the conformality. We compare the results with a deformable finite element model for equivalent bodies and motion showing that there is a transition between a Hertzian and a non-Hertzian behavior. We conclude that a criterion for the conformality of curves must include the ever-present gap when a barrier method is used to enforce the constraint and the Hertzian force is not suitable for the coalescence of contact points.

On the hysteretic bending behavior of slack metallic cables

Short and slack stranded metallic cables are encountered in several technical applications to connect different structures or different parts of the same structural system. A couple of relevant examples are provided by flexible-bus conductors used in high-voltage electrical substations or passive damping devices installed on overhead electrical lines, such as Bretelle dampers. Bending behavior of metallic cables is nonlinear and non-holonomic due to the onset and propagation of relative sliding phenomena between the wires. While taut suspended cables have been widely studied in the literature under the classic assumptions of small sag and perfect flexibility, whenever dealing with short and slack cables, the aforementioned hypotheses typically cease to be valid, and the bending stiffness contribution plays a significative role in the determination of the overall structural response. In the present paper, two different modeling strategies for the description of the bending behavior of short and slack stranded cables are presented. The first (discrete bending model) describes the cable as a composite structural element made of wires, which are individually modeled as curved elastic thin rods interacting through normal and tangential contact forces. The second (phenomenological bending model), instead, relies on a description of the cable bending process based on an application of the well-known Bouc-Wen hysteresis model. Applications of the proposed models are presented both at the cross-sectional and at the structural levels. The systematic comparison between theoretical and experimental results allows to assess the performance of the two proposed bending models when used with “nominal” values of the model parameters, which are estimated only on the base of the knowledge of the material and geometric properties of the strand. Moreover, a back-analysis of the model parameters is carried out to get an insight on internal mechanical parameters of the cable and on the overall cross-sectional bending response (e.g. bending stiffness values).

Contribution of rolling resistance to the drag coefficient of spheres freely rolling on a rough inclined surface

The drag coefficient (CD) of a sphere freely rolling without slipping on a rough plane is presented in this study. Increasing panel roughness has been found to increase CD, although lubrication theory predicts that the larger gap imposed by the rougher panel should yield a smaller drag. We propose that this increase in drag is due to the effects of rolling resistance, which increases with panel roughness. The total drag on a sphere is decomposed into fluid drag and drag due to rolling resistance, where the fluid drag is predicted using a combined analytical–numerical approach. It is shown that rolling resistance can be modeled as a resistive torque opposing the sphere motion, generated by the offset contact normal force from the sphere center plane. This coefficient of rolling resistance (μr) can be predicted using the root mean square roughness (Rq) of the panel. Additionally, μr is observed to increase with sphere down-slope velocity and an empirical relationship between μr, Rq, and non-dimensional velocity (U∗) is given. A comparison of the drag predicted by the proposed model with measured data indicates good agreement for all the four panels considered. Consistent with previous literature, a non-linear relationship between μr, Rq, and U∗ is proposed. Although increasing panel roughness leads to a smaller fluid drag due to the larger gap imposed by rougher panels, the drag due to rolling resistance increases more rapidly. This leads to an increase in total drag with increase in the panel roughness. Additionally, increasing panel roughness is observed to have a significant effect on the sphere wake, leading to irregular wake shedding and increase in the Strouhal number.

Multi-body dynamics modeling and energy consumption optimization of electromagnetic mechanical fully variable valve system

Electromagnetic Mechanical Variable Valve Actuation (EMVVA) technology has the capability to improve engine performance and decrease pollutant emissions. A new type of EMVVA composed of electromagnetic driver and mechanical transmission is proposed to realize the flexible adjustment of valve parameters whether the valve is open or closed process. The geometric mathematical model of the mechanical transmission is developed based on the motion laws of the valve and the geometrical construction of the mechanical transmission, and the conjugate cam curve is solved. A multi-body dynamic model is constructed to calculate the driving torque and energy consumption needed by the mechanical transmission based on the mass, rotational inertia, centroid position of the parts, combining the normal contact force model and the friction model of the clearance contact pair at the same time. Based on the geometric model and multi-body dynamics model, the test platform is established. The test results demonstrated that within the specified valve lift, EMVVA system could accomplish variable valve lift, variable valve timing, and variable valve duration at maximum lift. The maximum timing error does not exceed 1° crank angle, and the maximum valve lift error does not exceed 0.25 mm at 11 mm valve lift. In addition, the error of driving torque between the multi-body dynamics model and the test is less than 0.3 [Formula: see text].Low energy optimization of mechanical transmission was completed using the NSGA-II method and multi-body model. According to the results of the optimization, energy consumption was reduced by 14%, and the peak driving torque was decreased by 54.3%.

Modeling of the Particle Abrasion Process and a Discrete Element Method Study of Its Shape Effect.

This study introduces a novel method for particle abrasion derived from fundamental natural phenomena and mechanical principles, allowing precise control over the degree of abrasion and more accurately mimicking natural processes. The method's validity is confirmed using a specific shape index. Through conventional triaxial tests, the mechanical behavior of granular aggregates with varying degrees of abrasion was analyzed. The findings indicate that increased particle abrasion leads to a decrease in the average coordination number and sliding amount, while the rotation amount increases. This suggests an inverse relationship between the degree of abrasion and the structural stability and interlocking of the particle aggregate. The fabric anisotropy of the system is mainly attributed to the anisotropy of the contact normal force, which decreases as particle abrasion increases. The partial stress ratio of the particle system is influenced by fabric anisotropy and remains independent of particle shape. Additionally, the internal friction angle may be overestimated in conventional triaxial tests.

Dynamic modeling and analysis of 3-RRCPR parallel pointing mechanism with clearance

In order to study the influence of kinematic pair clearance on the dynamic characteristics and pointing accuracy of 3-RRCPR parallel pointing mechanism, the dynamic model of spatial mechanism with three-dimensional revolute pair clearance is established. Firstly, the revolute pair mode considering three-dimensional clearance is established, and the normal and tangential contact force models between the kinematic pair elements are established based on Flores contact model and modified Coulomb friction model. Secondly, the dynamic model of parallel mechanism with clearance is established according to Lagrange multiplier method. Finally, the effects of different clearance sizes and loads on the dynamic characteristics and pointing accuracy of the mechanism are analyzed by numerical simulation. The results show that the increase of clearance size and load will reduce the pointing accuracy, and the decrease of clearance size and the increase of load will enhance the motion stability of the mechanism. Reasonable clearance and load matching is conducive to improving the accuracy of the mechanism. This study provides a theoretical basis for the study of the nonlinear dynamic characteristics and accuracy of the mechanism considering the clearance.

PC-Kriging-powered parallelizing Bayesian updating for stochastic vehicle-track dynamical system with contact force measurements and Gaussian process discrepancy model

High-precision vehicle-track coupled dynamical models play a vital role in assessing the running safety of the vehicle, tracking fatigue behavior, and establishing a digital twin for high-speed railways. This study established a high-fidelity vehicle-track coupled dynamical model as a forward solver, which was then updated in a Bayesian inference framework based on the field tests of rail irregularities and wheel/rail normal contact forces. The prediction errors corresponding to different time steps were represented through a Gaussian process (GP) model characterized by a covariance function with the Gaussian kernel to incorporate the correlation between different time steps. To cope with the considerable expense of the likelihood function calculations with large-scale loop operations and the computational burden due to the large batch of repetitive evaluations of the high-fidelity forward model involved in the stochastic sampling from the posterior probability distribution, a metamodel-powered parallelizing stochastic sampling scheme was adopted. The posterior distribution could be formulated by replacing the expensive explicit model evaluation involved in the likelihood function with a Polynomial-Chaos-Kriging (PC-Kriging) predictor providing a surrogate mapping between the wheel/rail normal contact forces and physical parameters. Finally, a parallelizing computing scheme running across multiple CPU cores on high-performance computers was realized to sample from the vectorized formula of the emulator-powered posterior distribution. Field test data from a high-speed railway in China was adopted to demonstrate that the Bayesian inference scheme can quantify the uncertainties of the core physical parameters of the high-fidelity vehicle-track coupled dynamical system by efficiently trading off accuracy and computational efficiency.

Characterisation of discharge and flow rate predictions for asymmetric wedge-shaped hoppers

It is important to understand the flow behaviour inside wedge-shaped hoppers and accurately predict the discharge rate for the processing and handling of granular materials, regardless of whether the wedge hopper is symmetric or asymmetric. In this paper, the discrete element method (DEM) was used to reveal the flow behaviour of pellet feed in an asymmetric wedge-shaped hopper from the discharge rate, flow pattern, velocity distribution, normal contact force between particles and free-fall arch. The results showed that, with the hopper angle decreasing, the area of the active region of the particles increased, the stagnation zone decreased, and the free-fall arch became unstable. When the unilateral hopper angle was less than 45°, the discharge rate of the wedge-shaped hopper increased, and the average discharge rate reached the maximum value of 1.070 kg s−1 when the left and right hopper angles were equal to 15°. In addition, using the discharging mass proportion coefficient to represent the size of the region in which the unilateral hopper angle affected the flow of particles in the hopper, the hopper angle term in the Brown and Sellers model was corrected. The predictive errors of the corrected discharge rate model were less than 7.6% and 3.3% in the simulated and actual discharging tests respectively, which was better than that of the Brown and Sellers model. The results of the study could provide a theoretical basis for the intelligent upgrading of feed accurate handling equipment, and provide a reference basis for the design of asymmetric wedge-shaped hopper.

Periodic Rolling and Bumping

Abstract We consider a sphere that rolls down an inclined corrugation of identical, frictional circular cylinders in contact. We assume that the motion is a periodic succession of rolling and bumping that results in a velocity that is, on average, steady. We use balances of force and moment and impulse and momentum change to calculate the instantaneous and average velocities, the tangential and normal contact forces, and their ratio in rolling regimes that involve no sliding, some sliding and a transition between these at contact. We compare the predictions for the steady average velocity versus the inclination for different sphere to cylinders radii ratio and the predictions for the angle of inclination versus the radii ratio for stopping, initiation of sliding and loss of contact with the results of numerical simulations.

Force model of ultrasonic empowered minimum quantity lubrication grinding CFRP

As a weight-reducing material in aerospace applications, carbon fiber reinforced polymer (CFRP) requires precision grinding to ensure the accuracy and assembly of mating positioning surfaces. However, achieving low-damage machining of CFRPs remains challenging. Flood cooling reduces the mechanical properties, while dry grinding deteriorates the surface integrity, making minimum quantity lubrication (MQL) a viable alternative. However, nanolubricants struggle to penetrate the grinding area due to gas barrier obstruction. Consequently, a new CFRP grinding approach using multiangle 2D ultrasonic vibration-empowered nanolubricant MQL was proposed. An analytical force model is crucial for optimizing machining strategies and adjusting parameters. The aim is to reveal grinding mechanics and develop a force model under different ultrasonic and lubrication-cooling conditions. First, a uniform random fiber distribution model and a grinding wheel model were established, and the mechanical properties of the interface were predicted. Then, the intermittent grinding behavior and dynamic stiffnesses of the multiangle 2D ultrasonic vibration-assisted grinding (UVAG) system were investigated based on the geometric kinematics of the grains' trajectory. Furthermore, based on the deformation deflection curve, bending fracture force models for 45°, 90°, and 135° fibers were established with different contact and boundary conditions. The material removal mechanisms of shear and tension-compression buckling in 0° CFRP grinding were revealed, and an elliptical contact normal force model was established. The interlayer shear in 45° CFRPs was analyzed. The longitudinal compressive matrix cracking and fiber shear fracture in the 90° CFRPs were elucidated. Fiber microbuckling and fiber bundle removal of 135° CFRPs were investigated. Finally, grinding force models with different fiber orientation angles (FOAs) were interconnected and experimentally assessed. Experimental assessments demonstrated that the grinding force model has acceptable estimation error and effectively captures the mechanics of CFRPs with different FOAs.

Experimental and numerical studies of breakage and fractal characteristics of silica sands in high-pressure triaxial tests

Triaxial compression tests were performed on silica sands with confining pressure ranging from 0.5 to 60 MPa. A multigenerational DEM model was employed parallelly to investigate how micromechanical behaviors evolve with particle breakage. Prediction of the relative breakage considering the influence of axial strain and confining pressure is proposed. A strong correlation between the relative breakage and the input work is proposed regardless of the shear path. A nonlinear relationship is proposed to correlate the relative breakage and the volumetric strain. As the input work goes to infinity, the fractal dimension has an ultimate value approaching 2.66, which is greater than the values from previous theoretical and experimental studies. The mean coordination number in an uncrushable sample is higher than the crushable one during whole shearing. The normal contact force distribution is sensitive to the shear path, and particle breakage makes the contact force more inhomogeneous.

3D DEM investigation of shear behavior and interaction mechanism of woven geotextile-sand interfaces

This paper presents a numerical study on the investigation of microscopic mechanism governing the interaction of woven geotextile and angular sand employing the 3D discrete element method (DEM). The surface texture and tensile properties of the geotextile were simulated using overlapping spherical particles, and the angular sand was simulated using rigid blocks. The DEM models were fully calibrated based on previous experimental data. The shear and dilation zones of sand near the interface were quantitatively determined based on particle displacement gradients. Analysis of contact forces was conducted to explain the microscopic mechanism behind the macroscopic strength evolution. The influence of geotextile surface roughness on the shear strength of the geotextile-sand interface is also discussed. The results show that the failure mode of the woven geotextile-sand interface is a combination of particle sliding failure along the geotextile surface and shear failure of the sand within the shear zone above the interface. There is a rapid redistribution of contact forces prior to reaching peak shear resistance, and the average normal contact force within the shear zone remains relatively constant after the peak shear stress is achieved. A completely developed shear zone stabilizes soil deformation, typically after achieving the peak shear resistance.

DEM analysis of constrained modulus nonlinearity and damping factor of dry granular soils

The seismic site response analysis requires the dynamic soil properties (i.e., the modulus and damping). While it is well understood that the shear modulus and damping ratio are nonlinearly shear-strain dependent, the knowledge on the constrained modulus and damping ratio of compressional waves is still very limited due to lack of laboratory testing equipment. This study aims to simulate cyclic tests of constrained compression for granular specimens by discrete element method (DEM) to understand the dynamic soil properties of compressional waves, i.e., the nonlinearity in constrained modulus and damping ratio with the compression strain. The evolution in microstructure of granular specimens is revealed to provide micromechanical interpretations for the compressional soil nonlinearity. The results show that the dependency of constrained modulus on compression strain is different in compression and extension stages, and the modulus reduction is only observed in the extension path. The damping ratio of samples under cyclic constrained compression is smaller than that of cyclic shear. The nonlinear soil behavior is more obvious at lower confining pressure and for dense sample. The nonlinearity of constrained modulus depends on the coordination number, contact normal force and fabric anisotropy, while the associated damping ratio is only related to fabric anisotropy.

Effect of the Height of a 3D-Printed Model on the Force Transmission and Thickness of Thermoformed Orthodontic Aligners.

This research aims to investigate the influence of model height employed in the deep drawing of orthodontic aligner sheets on force transmission and aligner thickness. Forty aligner sheets (Zendura FLX) were thermoformed over four models of varying heights (15, 20, 25, and 30 mm). Normal contact force generated on the facial surface of the upper right central incisor (Tooth 11) was measured using pressure-sensitive films. Aligner thickness around Tooth 11 was measured at five points. A digital caliper and a micro-computed tomography (µ-CT) were employed for thickness measurements. The normal contact force exhibited an uneven distribution across the facial surface of Tooth 11. Model 15 displayed the highest force (88.9 ± 23.2 N), while Model 30 exhibited the lowest (45.7 ± 15.8 N). The force distribution was more favorable for bodily movement with Model 15. Thickness measurements revealed substantial thinning of the aligner after thermoforming. This thinning was most pronounced at the incisal edge (50% of the original thickness) and least at the gingivo-facial part (85%). Additionally, there was a progressive reduction in aligner thickness with increasing model height, which was most significant on the facial tooth surfaces. We conclude that the thermoplastic aligner sheets undergo substantial thinning during the thermoforming process, which becomes more pronounced as the height of the model increases. As a result, there is a decrease in both overall and localized force transmission, which could lead to increased tipping by the aligner and a diminished ability to achieve bodily movement.

Rope–sheave contact transient analysis in hoisting operations with a bristle model and an arbitrary Lagrangian–Eulerian approach

AbstractThis paper describes the development of a computational model for the rope–sheave contact interaction in reeving systems when the ropes are modeled with an arbitrary Lagrangian–Eulerian approach. This discretization approach has been developed in previous publications as a general and systematic method for the modeling and simulation of reeving systems. However, the rope–sheave contact model was avoided assuming the no-slip contact condition. The contact model developed in this paper introduces specialized ALE-ANCF-cubic rope contact elements that are used to discretize the rope segment winded at the sheave. The contact is modeled using a set of virtual discrete bristles attached to material points in the mid-line of the rope in one end and in contact with the sheave in the other end. Therefore, a second Lagrangian mesh, apart of the ALE mesh used to discretize the rope, is used to define the fixed ends of the bristles. The kinematics and dynamics used to calculate the normal and tangential contact forces are described in detail. The contact model is 3D and can be used to analyze the contact with a sheave groove with arbitrary shape. The tangential contact force model can be used to describe stick and slip contact conditions and, to improve the simulation performance of the model, an LuGre regularization tangential contact force model is used. The rope-sheave contact model is used to analyze the behavior of a simple elevator system. The numerical results show that the static rope-sheave contact interaction agrees well with an analytical solution of the problem. Finally, the same elevator system is analyzed dynamically for a cabin ride of 8 meters with a steady velocity of 1 m/s. Results show that the normal and tangential contact forces during the steady velocity period are not so different from the static solution, but very different from the classical Creep Theory and Firbank’s Theory.

Effect of thermomechanical ageing on force transmission by orthodontic aligners made of different thermoformed materials: An experimental study.

Investigating the impact of thermal and mechanical loading on the force generation of orthodontic aligners made from various thermoplastic materials and different compositions. Five distinct materials were utilized including, three multi-layer (Zendura FLX, Zendura VIVA, CA Pro) and two single-layer (Zendura A and Duran). A total of 50 thermoformed aligners (n = 10) underwent a 48-hour ageing protocol, which involved mechanical loading resulting from a 0.2 mm facial malalignment of the upper right central incisor (Tooth 11) and thermal ageing through storage in warm distilled water at 37°C. The force exerted on Tooth 11 of a resin model was measured both before and after ageing using pressure-sensitive films and a biomechanical setup. Before ageing, pressure-sensitive films recorded normal contact forces ranging from 83.1 to 149.7 N, while the biomechanical setup measured resultant forces ranging from 0.1 to 0.5 N, with lingual forces exceeding facial forces. Multi-layer materials exhibited lower force magnitudes compared to single-layer materials. After ageing, a significant reduction in force was observed, with some materials experiencing up to a 50% decrease. Notably, multi-layer materials, especially Zendura VIVA, exhibited lower force decay. The force generated by aligners is influenced by both the aligner material and the direction of movement. Multi-layer materials exhibit superior performance compared to single-layer materials, primarily because of their lower initial force, which enhances patient comfort, and their capability to maintain consistent force application even after undergoing ageing.

DEM simulation of effects of particle size distribution on meso-mechanical properties of slip zone soil

Particle Size Distribution (PSD) exerts a substantial influence on the mechanical properties of geological materials such as rocks and soils, which can be viewed at a microscale as an assembly of discrete particles. An exploration into the effects of particle gradation on the properties of these materials provides valuable insights into their nature. In the study, the Discrete Element Method (DEM) was used to conduct numerical shear tests on eight distinct groups of slip zone soil, each characterized by a different particle gradation. The aim was to examine the meso-mechanical properties and shear evolution laws of slip zone soil numerical samples with both optimal and sub-optimal PSDs. Findings underscore the pivotal role that PSD plays in various aspects, including dilatancy, the evolution of the displacement field, the network of contact force chains, the principal stress, and the distribution of normal and tangential contact forces within the slip zone soil. It was observed that the network of contact force chains in the numerical samples with an optimal PSD was more complex than in those samples with a sub-optimal PSD. Additionally, the distribution of principal stresses before and after shear was more uniformly balanced. This particle size-based study offers significant reference value for future investigations into the impact of PSD on the macroscopic and meso-mechanical properties of slip zone soil. By augmenting this knowledge, a more comprehensive understanding of the fundamental behavior of these materials can be attained, leading to improved prediction and management of geological risks.

Modeling Density Waves and Circulations in Vertical Cross-Section in Adhesive Contacts

This work continues the study of the process of friction between a steel spherical indenter and a soft elastic elastomer previously published in our paper. It is done in the context of our previous experimental results obtained on systems with strongly pronounced adhesive interaction between the surfaces of contacting bodies during the process of friction between a steel spherical indenter and a soft elastic elastomer. In the present paper, we concentrate on the theoretical study of the processes developing in a vertical cross-section of the system. For continuity, here the case of indenter motion at a low speed at different indentation depths is considered as before. The analysis of the evolution of normal and tangential contact forces, mean normal pressure, tangential stresses, as well as the size of the contact area is performed. Despite its relative simplicity, a numerical two-dimensional (2D = 1 + 1) model, which is used here, satisfactorily reproduces experimentally observed effects. Furthermore, it allows direct visualization of the motion in the vertical cross-section of the system, which is currently invisible experimentally. Partially, it recalls two-dimensional (2D = 1 + 1) models recently proposed to describe the “turbulent” shear flow of solids under torsion and in cellular materials. The observations extracted from the model help us to understand better the adhesive processes that underlie the experimental results.