Rolling Resistance Model Research Articles

Influence of Rolling Resistance and Particle Size Distribution in the Simulation of Sand Infiltration into the Static Gravel Bed

Fine sediment infiltration and subsequent clogging in a gravel bed affect several fluvial, ecological, and biological processes, resulting in the degradation of the river ecosystem. Despite many experimental and a few numerical studies, the process is yet to be entirely understood. We employed a pure Lagrangian framework, called the Discrete Element Method (DEM), to numerically investigate the infiltration process. Special attention is given to tackling the issue of non-spherical and irregular particle shapes and particle size distributions (PSDs) in numerical simulations. Due to computational limitations, these aspects were either not considered or simplified in previous numerical studies. We implicitly included non-spherical and irregular shape effects through rolling resistance models, which do not cause excessive computational overhead. Our study shows that rolling resistance models greatly influence packing and fine sediment infiltration. However, they may also lead to unphysical particle behavior; thus, they should be carefully used in numerical simulations. Oversimplified PSDs do not mirror natural systems, and full PSDs pose computational challenges. Sufficient grain classes are needed to mimic the non-homogeneity and poly-dispersity found in natural fluvial sediments. The infiltrating characteristics of sand concerning PSD and shape effects are linked to size ratio D15,Gravel/D85,Sand, assuring physical and realistic modeling of the infiltration process.

Research on Material Viscoelasticity and Its Influence on Indentation Rolling Resistance

Viscoelastic materials are applied in several fields, and their relaxation characteristics are intricately related to the failure mechanism of sealing components and the generation of indentation rolling resistance in belt conveyors. Therefore, it is imperative to explore the relaxation characteristics of viscoelastic materials using characterization models. This article focuses on exploring these characterization models and the indentation rolling resistance of viscoelastic materials. The research comprises the following aspects: (1) A 2N + 2 element generalized Maxwell constitutive model is proposed for the relaxation behavior of viscoelastic materials to address the limitations of conventional relaxation models. (2) We conducted numerical calculations based on the relaxation modulus to solve the relaxation spectrum using several relaxation spectrum models. The findings showed that the model parameters were dependent on the testing time range. (3) The relationship between the indentation rolling resistance and relaxation model parameters was evaluated based on the theoretical foundation of the indentation rolling resistance calculation.

Parametrisation of a rolling resistance model for extending the brush tyre model

Parametrisation of a rolling resistance model for extending the brush tyre model

Parametrisation of a rolling resistance model for extending the brush tyre model

Parametrisation of a rolling resistance model for extending the brush tyre model

A semi-physical thermodynamic transient rolling resistance model with nonlinear viscoelasticity

Rolling resistance dictates a large part of the energy consumption of trucks. Therefore, it is necessary to have a sound understanding of the parameters affecting rolling resistance. This article proposes a semi-physical thermodynamic tyre rolling resistance model, which captures the essential properties of rolling resistance, such as transient changes due to temperature effects and the strain-amplitude dependency of the viscous properties. In addition, the model includes cooling effects from the surroundings. Both tyre temperature and rolling resistance are obtained simultaneously in the simulation model for each time step. The nonlinear viscoelasticity in rubber is modelled using the Bergström–Boyce model, where the viscous creep function is scaled with temperature changes. The cooling of the tyre is considered with both convective and radiative cooling. Moreover, the article explains different material parameters and their physical meaning. Additionally, examples of how the model could be used in parameter studies are presented.

Flowability of Crumbler Rotary Shear Size-Reduced Granular Biomass: An Experiment-Informed Modeling Study on the Angle of Repose

Biomass has potential as a carbon-neutral alternative to petroleum for chemical and energy products. However, complete replacement of fossil fuel is contingent upon efficient processes to eliminate undesirable characteristics of biomass, e.g., low bulk density, variability, and storage-induced quality problems. Mechanical size reduction via comminution is a processing operation to engineer favorable biomass flowability in handling. Crumbler rotary shear mill has been empirically demonstrated to produce more uniformly shaped particles with higher flowability than hammermilled biomass. This study combines modeling and experimentation to unveil fundamental understandings of the relation between granular particle characteristics and biomass flow behavior, which elucidate underlying mechanisms and guide selection of critical processing parameters. For this purpose, the impact of critical material attributes, including particle size (2–6 mm), particle shape (briquette, chip, clumped-sphere, cube, etc.), and surface roughness, on the angle of repose (AOR) of milled pine chips were investigated using discrete element method (DEM) simulations. Forest Concepts Crumbler rotary shear system is used to produce milled pine particles within the same size range considered in DEM simulations. AOR of different sets of these particles were measured experimentally to benchmark DEM results against experimental data. Specific energy consumption for the comminution of biomass with different particle size and moisture content are measured for technoeconomic analysis. Our results show that the smaller size (2 mm) of pine particle achieves better followability (i.e., smaller AOR) while the energy cost of comminution is significantly higher and bulk density is almost the same as the 6-mm pine particles. For the 2-mm particle size, Crumbles from veneer have better flow properties than Crumbles from chips. Contrarily, no significant difference was observed between the AOR of the two materials for the 6-mm particle size. Furthermore, from DEM simulations, mechanical interlocking between particles was found as a dominant factor in determining AOR of complex-shaped particles such as milled pine, which cannot be accurately captured by using simple particle shapes (e.g., mono-sphere) with a rolling resistance model. Conversely, clumped-sphere model alleviates this limitation without increasing computational cost significantly and can be used for accurate representation of biomass granular particles when simulating free-flow behavior.

Rolling resistance model for estimation of friction fluctuation in linear ball guideways

Linear ball guideways are widely employed in machine tool drive systems. Friction fluctuation of linear ball guideways causes fluctuations in the feed rate that results in contour errors in synchronous motions while using several feed drives. In this study, a practical model of rolling resistance is proposed for a model-based design of the raceway profile that realizes a smooth feed motion. In the proposed model, the rolling resistance is obtained from the preload and two contact angles at the upper and lower raceways. The preload variation is represented by a simplified spring model. The validity of the proposed model is experimentally verified. The variation in the rolling resistance is influenced by the phase difference between the upper and lower raceway profiles. The resistance variation can be decreased by setting the phase difference to the half period of the profile component. The experimental results indicate that the fluctuation components of the rolling resistance, with a wavelength longer than the contact diameter between the ball and raceway, can be correctly estimated. The estimation error for the shorter-wavelength component is not a crucial issue because the rolling resistance fluctuation is small for such a component. The verification results show that the proposed model can provide an effective guideline for the raceway profile design to reduce the rolling resistance fluctuation to an acceptable level.

Effect of Particle Size Distributions and Shapes on the Failure Behavior of Dry Coke Aggregates.

Carbon anodes participate in chemical reactions to reduce alumina in the Hall–Héroult process, of which coke aggregates make up a major part. The failure analysis of coke aggregates not only leads to a better understanding of the deformation mechanisms of anode paste under compressive loading but also can identify potential causes of structural defects in carbon anodes, such as horizontal cracks. The coke aggregates are composed of particles with different size distributions and shapes, which may strongly affect the failure behavior of the anode during compaction. In this paper, the effects of particle size distributions and shapes on the mechanical behavior and the failure of coke aggregates are investigated using the discrete element method modeling technique. The numerical results reveal that, although the mechanical behavior of coke mixtures is generally dependent on larger particles, the presence of fine particles in the coke aggregates reduces fluctuations in the stress–strain diagram. In addition, the rolling resistance model is employed as a parameter representing the effect of particle shape. It is shown that the rolling resistance model can be an alternative to the overlapped spheres model, which has a higher computational cost than the rolling resistance model. The second-order work criterion is used to evaluate the stability of the coke aggregates, the results of which indicate that the addition of fine particles as well as increasing the rolling resistance between the particles increases the stability range of the coke aggregates. Moreover, by using the analysis of micro-strain contour evaluations during the compaction process, it is shown that, both by adding fine particles to the coke mixture and by increasing the rolling resistance between the particles, the possibility of creating a compression band in the coke aggregates is reduced. Since the presence of the compaction bands in the anode paste creates an area prone to horizontal crack generations, the results of this study could lead to the production of carbon anodes with fewer structural defects.

Experimental method for identifying constitutive parameters of rolling resistance between particles in discrete element method

A method to identify the parameters of rolling resistance between particles in the discrete element method is proposed in this paper. Experiments revealed that a free rolling particle would swing back and forth marginally before it stops. We assume that the restoring force of the swing is mainly rolling resistance. An optical experimental system was designed to obtain the rolling resistance in the DEM model. A method to identify the parameters using the time history curve of the swing is proposed. We measured the time history of the angular displacement of cylindrical samples made of rubber and aluminum. In addition, the rolling stiffness and damping coefficients were identified. The identified parameters were applied to the discrete element model to simulate the experimental process. The results show that the time-history curve of swing obtained by DEM is in good agreement with the experimental curve. This verifies that the particle swings back and forth because of rolling resistance and that the parameters of the rolling resistance model can be determined by this experimental method

A NOVEL DISCRETE ELEMENT ROLLING RESISTANCE MODEL BASED ON HYSTERESIS SPRING ENERGY DISSIPATION

The rolling resistance between particles plays an important role in the stability of the particulate systems. In a conventional discrete element method, the rolling resistance model between particles is usually made of springs, dashpots, and sliders in the rotational direction. The particles rolling kinetic energy is dissipated by the viscous (moment) and friction forces. With this model, the viscous force (moment) is directly related to the rolling velocity. Consequently, the dynamic dissipation capacity of particles close to the static state becomes weaker with the rolling velocity decreasing. It is known that the time required to simulate a particle rolling with a velocity close to zero by using the traditional discrete element method is longer than the experimental results. To solve this problem, the mechanism of rolling resistance caused by material hysteresis is analyzed based on tribological principle, and a new discrete element model of hysteresis rolling resistance (HDEM) is established. A hysteresis spring with velocity-independent kinetic energy dissipation is proposed, and its constitutive law’s formula is derived. To verify the new rolling resistance model, the free-rolling of a single round particle specimen on a flat surface is measured through a physical experiment. The measured data are compared with the results simulated by the new rolling resistance model HDEM and the conventional rolling resistance model. The results show that the results based on HDEM are more consistent with the experimental data, and the particle oscillation frequency is in better agreement with the experimental phenomenon observed.

Comparative 3D DEM simulations of sand\u2013structure interfaces with similarly shaped clumps versus spheres with contact moments

Three-dimensional simulations of a monotonic quasi-static interface behaviour between initially dense cohesionless sand and a rigid wall of different roughness during tests in a parallelly guided direct shear test under constant normal stress are presented. Numerical modelling was carried out by the discrete element method (DEM) using clumps in the form of convex non-symmetric irregularly shaped grains. The clumps had an aspect ratio of 1.5. A regular grid of triangular grooves (asperities) along the wall with a different height at the same distance was assumed. The numerical results with clumps were directly compared under the same conditions with our earlier DEM simulations using pure spheres with contact moments with respect to the peak and residual interface friction angle, width of the interface shear zone, ratio between grain slips and grain rotations, distribution of contact forces and stresses. The difference between the behaviour of clumps and pure spheres with contact moments proved to be noticeable in the post-peak regime due to a different particle shape. The rolling resistance model with pure spheres was proved to be limited for capturing particle shape effects. Three different boundary conditions along the interface were proposed for micropolar continua, considering grain rotations and grain slips, wall grain moments and wall grain forces, and normalized interface roughness. The numerical results in this paper offer a better understanding of the interface behaviour of granular bodies in DEM and FEM simulations.

Tire/Road Rolling Resistance Modeling: Discussing the Surface Macrotexture Effect

This paper deals with the modeling of rolling resistance and the analysis of the effect of pavement texture. The Rolling Resistance Model (RRM) is a simplification of the no-slip rate of the Dynamic Friction Model (DFM) based on modeling tire/road contact and is intended to predict the tire/pavement friction at all slip rates. The experimental validation of this approach was performed using a machine simulating tires rolling on road surfaces. The tested pavement surfaces have a wide range of textures from smooth to macro-micro-rough, thus covering all the surfaces likely to be encountered on the roads. A comparison between the experimental rolling resistances and those predicted by the model shows a good correlation, with an R2 exceeding 0.8. A good correlation between the MPD (mean profile depth) of the surfaces and the rolling resistance is also shown. It is also noticed that a random distribution and pointed shape of the summits may also be an inconvenience concerning rolling resistance, thus leading to the conclusion that beyond the macrotexture, the positivity of the texture should also be taken into account. A possible simplification of the model by neglecting the damping part in the constitutive model of the rubber is also noted.

Discrete element simulation of super-ellipse systems

There are two key problems in discrete element simulations of super-ellipse systems. One is the determination of contact point, and the other is the mechanical equilibrium with almost zero kinetic energy. The Newton–Raphson method or its modification used to determine the contact point is only sufficiently numerically stable for suitable deformation parameters, and the state of all particles with almost zero velocity is difficult to reach. In this paper, a novel contact detection method for all deformation parameters is used to determine the contact point, and a rolling resistance model is used to dissipate rotational kinetic energy for mechanical equilibrium. A series of tests are investigated to verify the validity of this method. For random packing under gravity, no residual kinetic energy (or almost 0) is observed, and the force that acts on the bottom is equal to the gravity, meaning that the system reaches mechanical equilibrium. After equilibrium, the process of hopper discharge, in which the kinetic energy remains stable for shape and material parameters, is also modeled. Furthermore, direct shear tests at different shear rates are simulated, and the results meet the rate independence, which is in agreement with experiments. The method is also suitable for investigation of sound propagation properties in the super-ellipse system, and the velocities of compressional and shear waves are calculated in uniaxial compression tests. In addition to super-ellipses, the method can be applied to other particle systems once the shape functions are given. After reaching the equilibrium state, a hole is opened at the bottom, and its width is 15 times the width of the particle. Figure shows the snapshots of particle flow at different times. Then, 0.372 seconds later, after 136 particles drop through the hole, a semi-circular structure of force arch occurs, and the particle flow stops. These findings are different from the results of the previous research and show that the shape has a significant effect on the flow rate.

Influence of various DEM shape representation methods on packing and shearing of granular assemblies

Realistic yet efficient representation of particle shape is a major challenge for the Discrete Element Method. This paper uses angle-of-repose and direct-shear test simulations to describe the influence of several shape representation methods, and their parameters, on the bulk response of granular assemblies. Three rolling resistance models, with varying coefficient of rolling friction, are considered for spherical particles. For non-spherical particles, superquadrics with varying blockiness and multi-spheres with varying bumpiness are used to model cuboids and cylinders of several aspect ratios. We present extensive quantitative results showing how the various ways used to represent shape affect the bulk response, allowing comparisons between different approaches. Simulations of angle-of-repose tests show that all three rolling friction models can model the avalanching characteristics of cube/cuboid and cylindrical particles. Simulations of direct-shear tests suggest that both the shear strength and the dilative response of the considered non-spherical particles (but not their porosity) can only be predicted by the elasto-plastic rolling resistance model. The quantitative nature of the results allows identifying values of the shape-description parameters that can be used to obtain similar results when using alternative shape representation methods.Graphical abstract

Effect of particle rolling resistance on drained and undrained behaviour of silty sand

This paper explores the effect of particle rolling resistance on the mechanical behaviour of silty sand under various shearing conditions. The elastic–plastic spring–dashpot rolling resistance model was employed, and drained and undrained triaxial tests were conducted on silty sand with various fines contents and rolling resistance. It was found that the rolling resistance of fines contents had a strong impact on the critical state, peak state, phase transformation state as well as zero-dilatancy state of silty sands. Moreover, depending on the correlation between rolling resistance of coarse and fine particles, fines can positively or negatively contribute to the overall structure of silty sand. Increasing the rolling resistance of fines enhances the liquefaction resistance of silty sands. Thus, the presence of fines of high rolling resistance in the sand can result in a marked decrease in collapsibility or liquefaction susceptibility compared with the presence of fines of lower rolling resistance.

The influence of the first integrals and the rolling resistance model on tippe top inversion

In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is described not only by the force applied at the contact point, but also by the additional rolling resistance torque. We show that the possibility or impossibility of tippe top inversion depends on the existence of specific integrals of the motion of the system. In this paper, we consider an example of the law of rolling resistance by which the area integral is preserved in the system. We examine in detail the case where the action of all dissipative forces reduces to the horizontal rolling resistance torque. This model describes fast rotations of the top between two horizontal smooth planes. For this case, we find permanent rotations of the system and analyze their linear stability. The stability analysis suggests that no tippe top inversion is possible under fast rotations between two planes.

Calibration of cohesive DEM parameters under rapid flow conditions and low consolidation stresses

Discrete Element Method (DEM) is a well-established and validated tool for the simulation of bulk materials. However, a lot of questions still need answering in the domain of cohesion and adhesion. This paper will present a calibration approach using the draw down test. This test generates several test results which could be used for the calibration and is one of the standard tests for the calibration of cohesionless materials. For the bulk material wet sand (10% moisture) is used. It is shown how the draw down test can be used to determine a unique set of friction, rolling resistance and cohesion values to reproduce the real behaviour of wet sand. For the DEM simulation the JKR model, one of the most widely used cohesion models, was used. It considers surface energy density and increased particle overlap to explain cohesion. The ambiguity associated with surface energy or interfacial energy is tackled by developing thorough calibration procedures which will help in fine tuning these parameters. Further, the rolling resistance model used for the simulation of cohesive materials is discussed. Calibration results for the very widely used modified elastic-plastic spring dashpot rolling resistance model are compared to an adhesive hysteric rolling resistance model.

A Numerical Based Approach to Calculate Ore Dilution Rates Using Rolling Resistance Model and Upside-Down Drop Shape Theory

The chief characteristic of the caving mining method is that caved ores, surrounded by overlying rocks, are drawn from the drawpoint. And the ultimate objective of investigating the draw problems is to forecast the ore loss and dilution. In this paper, the rolling resistance model in the Particle Flow Code was used to simulate the effect of actual shape of different materials flowing towards a drawpoint under the near-field condition and improve the computational efficiency at the same time. The reliability of the rolling resistance model was validated against experimental results, and the new empirical equations were deduced for calculation of the ore dilution rates based on the upside-down drop shape theory (UDDS theory). Within the precision and range of values considered in this paper, the results show that when the height of IEZ is in the range of 30–80 m, the particle size, the drawpoint size and the column height have no significant influence on the (isolated extraction zone) IEZ’s shape and maximal width. And regardless of near-field gravity flow with one or two granular materials, the shape of IEZ was coincident with the upside-down drop shape.

Discrete Element Modeling of Seed Metering as Affected by Roller Speed and Damping Coefficient

Abstract. The development of highly efficient seed metering is required to meet the demands of modern seeding equipment. The discrete element method (DEM) was used to simulate metering of seeds with a fluted roller meter. This approach was chosen due to its capability to accurately represent granular material flow. The contact model selected for the DEM simulation was the linear rolling resistance model. Angle of repose experimental tests and simulations were performed to calibrate the rolling friction coefficient for peas. The calibrated value for the rolling friction coefficient was 0.016. A 192 mm cross-section of an air cart seed roller and housing was defined as the domain of the simulation. Sensitivity analysis showed that simulated mass flow rates were not sensitive to the selected damping coefficients (0.2, 0.5, and 0.8). Sensitivity indicator values varied between -0.049 and 0.088 for the range of damping coefficients and roller speeds studied. The simulated geometry of the seed meter and housing resulted in a steady flow of seeds, with discharged mass increasing linearly. The simulated mass flow rates were 34.0, 72.3, 110.4, 147.3, and 182.0 g s-1 for roller speeds of 10, 20, 30, 40, and 50 rpm, respectively. An experiment was performed to validate the simulation results. The predicted mass flow rate values of the simulation were within 10 g s-1 of the experimental results, with the largest relative error being 16.5%. Keywords: DEM, Damping, Metering, Peas, Rolling friction coefficient, Seed, Simulation.

Rolling Resistance of a Hard Sphere on Rubber Sheets: Limitations of Linear Viscoelastic Modeling and Influence of Nonlinearities

A growing body of evidence suggests that limited accuracy can be expected from analytical and computational tools relying on linear viscoelasticity for the prediction of rolling resistance in real systems presenting material and geometric nonlinearities. A set of experimental data for the viscoelastic resistance to motion incurred by a rigid sphere rolling between two parallel sheets of rubber, in realistic in-service conditions, was determined, in a previous work [Zéhil and Gavin, 2019]. The tests involved different elastomers (a Urethane rubber and a Neoprene rubber) and different sheet thicknesses, ball diameters, loading levels and rolling speeds. The accuracy of linear models in predicting such practical data is assessed in this work. To this aim, the elastomers are described by general linear viscoelastic models whose master-curves are characterized by: (i) High Frequency Thermo-Viscoelastic Spectroscopy, under very small strain amplitudes and (ii) Dynamic Mechanical Analysis under relatively larger deformations. In both cases, rolling resistance predictions are obtained using computational tools based on linear viscoelasticity [Zéhil and Gavin, 2013a, 2013b] and compared to the measurements. Conclusions are drawn regarding: (i) the practical limitations of linear rolling resistance models and (ii) influences of nonlinearities such as those due to large deformations, to the Mullins effect [Mullins, 1969] and to the Payne effect [Payne, 1962], on predictions.