Angle of repose in the numerical modeling of ballast particles focusing on particle-dependent specifications: Parametric study

The discrete element method (DEM) is widely used in the realistic simulation of the shapes of particles. Researchers have considered the simplification of particle shapes owing to the high computational cost of such simulation. In this regard, the modeling of calibrated particles is a major challenge owing to the simultaneous effects of particle properties. The angle-of-repose test is a standard test method used to calibrate the bulk behavior of simulated particles. In the present study, the hollow-cylinder (slump) test was modeled for the verification of discrete element simulations. In this regard, a sensitivity analysis was conducted for all effective parameters, namely the static friction, rolling friction, restitution coefficient, sphericity, roundness, particle size distribution, and number of ballast particles. The results indicate that the rolling friction, roundness, number of particles, and size of particles are the most important parameters in the determination of the angle of repose (AOR). For particles in the range of ballast (20–60 mm), the effect of the number of particles on the angle of repose is reduced when the number is greater than 426. Additionally, it is concluded that angular particles can be replaced with sub-angular particles (R ≈ 0.2–0.45) with a higher rolling friction coefficient (μ_r > 0.14).     

Discrete element parameter calibration and the modelling of dragline bucket filling

The Discrete Element Method (DEM) is useful for modelling granular flow. The accuracy of DEM modelling is dependent upon the model parameter values used. Determining these values remains one of the main challenges. In this study a method for determining the parameters of cohesionless granular material is presented. The particle size and density were directly measured and modelled. The particle shapes were modelled using two to four spheres clumped together. The remaining unknown parameter values were determined using confined compression tests and angle of repose tests. This was done by conducting laboratory experiments followed by equivalent numerical experiments and iteratively changing the parameters until the laboratory results were replicated. The modelling results of the confined compression tests were mainly influenced by the particle stiffness. The modelling results of the angle of repose tests were dependent on both the particle stiffness and the particle friction coefficient. From these observations, the confined compression test could be used to determine the particle stiffness and with the stiffness known, the angle of repose test could be used to determine the particle friction coefficient. Usually DEM codes do not solve the equations of motion for so-called walls (non-granular structural elements). However, in this study a dynamic model of a dragline bucket is developed and implemented in a commercial DEM code which allows the dynamics of the walls to be modelled. The DEM modelling of large systems of particles is still a challenge and procedures to simplify and speed up the modelling of dragline bucket filling are presented. Using the calibrated parameters, numerical results of bucket filling are compared to experimental results. The model accurately predicted the orientation of the bucket. The model also accurately predicted the drag force over the first third of the drag, but predicted drag forces too high for the subsequent part of the drag.     

A study of influence of gravity on bulk behaviour of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method （DEM）. Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions. The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.     

A study of influence of gravity on bulk behavior of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method (DEM). Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions.The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.     

不同尺度分布散粒材料砂堆形成过程的二维离散元模拟

用作者开发的离散元程序,模拟不同尺寸分布的砂堆形成过程.把散体颗粒简化为圆形颗粒,模拟过程分三步:首先利用参考网格生成颗粒的松散堆积结构;为了避免颗粒下落的冲击作用对砂堆安息角的影响,先模拟颗粒在重力作用下在圆柱容器内的自由下落与堆积,直至堆积达到稳定;最后,移除容器,只保留一个底部边界,模拟颗粒体系的散落过程,直至形成一个稳定的砂堆.模拟结果表明,在其他参数保持相同的情况下,随着颗粒尺寸的减小,砂堆的安患角逐步减小并趋向于一常值.对模拟中的两组颗粒体系进行相同条件下的砂堆形成实验,结果表明,模拟与实验所得安息角大体相当.     

Effect of rolling friction on wall pressure,discharge velocity and outflow of granular material from a flat-bottomed bin

The present paper provides both experimental and DEM analyses of the filling and discharge of pea grains from a 3D flat-bottomed bin. In the DEM model, the fixed mean values of the experimentally determined single particle data, such as the particle density, Young's modulus, Poisson's ratio as well as the sliding and rolling friction coefficients were incorporated to analyse their effects on the macroscale indicators, such as the wall pressure, discharge velocities and material outflow parameters. The effect of rolling friction was studied based on the experimentally measured single particle rolling friction coefficient. This analysis is aimed at the quantitative prediction of flow parameters as related to the identification of material parameters.     

Investigation of elemental shape for 3D DEM modeling of interaction between soil and a narrow cutting tool

Discrete Element Method (DEM) has been applied in recent studies of soil cutting tool interactions in terramechanics. Actual soil behavior is well known to be inexpressible by simple elemental shapes in DEM, such as circles for 2D or spheres for 3D because of the excessive rotation of elements. To develop a more effective model for approximating real soil behavior by DEM, either the introduction of a rolling resistance moment for simple elemental shape or the combination of simple elements to form a complex model soil particle shape cannot be avoided. This study was conducted to investigate the effects of elemental shape on the cutting resistance of soil by a narrow blade using 3D DEM. Six elemental shapes were prepared by combining unit spheres of equal elemental radius. Moreover, cutting resistance was measured in a soil bin filled with air-dried sand to collect comparative data. The elemental shape, with an axial configuration of three equal spheres overlapped with each radius, showed similar results of soil cutting resistance to those obtained experimentally for the six elemental shapes investigated.     

散料在料仓内流动特性的实验研究

用振动筛测量多种散料的筛分尺寸，测量散料的容积密度、安息角，用应变直剪仪进行散料内摩擦角、壁面摩擦角的测量，分析了散料颗料的形状、尺寸对散料的安息角、内摩擦角、壁面摩擦角的影响。用示踪法进行了圆筒内散料重力场中颗粒流线和等时线的试验，以及出口直径与流量的关系、筒仓内散料高度对流量的影响的试验，流量与筒仓内散料高度关系的试验。分析了散料各物性参数对散料流动性的影响，为散料存贮和运输设备的结构设计提供实验依据。     

Evaluation of link-track performances using DEM

A two-dimensional discrete-element model for the interaction between link-track and soil is presented. The model was developed using commercial PFC2D code. Two different particles, sphere and clump of two spheres, were used to represent the soil. The soil parameters of the model were determined using Hertzian contact theory. Based on the model and soil parameters, simulations of biaxial tests and calculations of the internal angle of friction and cohesion were preformed. The simulation results showed that the internal angle of friction should not exceed the value of 0.65 when using the spherical particles. Based on the clumped particles model, simulations of shear tests with two grouser plates (lengths 100 and 150 mm) were performed under different soil conditions, normal pressures, and cleat heights. A curve fitting of the simulation results was performed using three semi-empirical models from Bekker, Janosi, and Wong for representing the shear stress–displacement relationship. The best fitting was achieved using Wong’s approach. The simulation results of the cleat effects were compared with Bekker’s grouser approach and McKyes’s formulation for soil–blade interaction. In most of the cases, the results of Bekker’s model were the lower bound and McKyes’s model, the upper bound of the DEM simulation results. The properties of the soil model for the DEM were determined using simulation results of shear tests by grouser plate. In the range investigated, the size of the shearing grouser plate is not significant in determining the soil model properties.     

锥体料斗内散料流动相对速度分布的实验研究

用示踪法进行了散粒体在圆锥料斗内不同出口直径条件下流动时相对速度分布的试验，并以此对Jenike轴向应力和共轴理论进行了实验验证，发现有些散料与Jenike轴向应力和共轴理论符合较好，而有些与之偏差较大。分析了内摩擦角、壁面摩擦角对最大主应变率方向的影响。     

Effect of wall rougheners on cross-sectional flow characteristics for non-spherical particles in a horizontal rotating cylinder

Discrete-element-method （DEM） simulations have been performed to investigate the cross-sectional flow of non-spherical particles in horizontal rotating cylinders with and without wall rougheners. The non-spherical particles were modeled using the three-dimensional super-quadric equation. The influence of wall rougheners on flow behavior of grains was studied for increasing particle blockiness. Moreover, for approximately cubic particles （squareness parameters [555]）, the rotational speed, gravitational acceleration and particle size were altered to investigate the effect of wall rougheners under a range of operating conditions. For spherical and near-spherical particles （approximately up to the squareness parameters [344]）, wall rougheners are necessary to prevent slippage of the bed against the cylinder wall. For highly cubic particle geometries （squareness parameters larger than [3441）, wall rougheners resulted in a counter-intuitive decrease in the angle of repose of the bed. In addition, wall rougheners employed in this study were demonstrated to have a higher impact on bed dynamics at higher rotational speeds and lower gravitational accelerations. Nevertheless, using wall rougheners had a comparatively small influence on particle-flow characteristics for a bed composed of finer grains.     

Numerical and experimental studies of gravity effect on the mechanism of lunar excavations

In this paper, the mechanism of soil excavation in partial gravity conditions is investigated by experimental model and numerical study. Experiments were conducted in a parabolic flight, which generated different gravity conditions, focusing on the bearing capacity problem using two soil samples: Toyoura sand and Japanese lunar soil simulant (FJS-1). Corresponding numerical studies were performed by the discrete element method (DEM) for reduced gravity conditions. Herein, the DEM method was modified to include the apparent cohesion that was found in the lunar soil simulant. Two case studies were investigated by the numerical simulations: bearing capacity and soil pushing (as by a bulldozer), and for the former case comparison was made with experiment. Results show that the gravity greatly affects the ultimate bearing capacity of the Toyoura sand; however, such effect becomes insignificant in the lunar soil when the gravity is small or the soil was densely packed. By using the numerical model, this paper suggests that the ultimate bearing capacity observed in the lunar soil simulant was dominated by the apparent cohesive component, rather than gravity or friction. However, gravity causes similar effects on both soil models in the soil pushing problem.     

Influence of rolling friction on single spout fluidized bed simulation

In this paper we study the effect of rolling friction on the dynamics in a single spout fluidized bed using Discrete Element Method (DEM) coupled to Computational Fluid Dynamics (CFD). In a first step we neglect rolling friction and show that the results delivered by the open source CFD–DEM framework applied in this study agree with previous simulations documented in literature. In a second step we include a rolling friction sub-model in order to investigate the effect of particle non-sphericity. The influence of particle–particle as well as particle–wall rolling friction on the flow in single spout fluidized bed is studied separately. Adequate rolling friction model parameters are obtained using first principle DEM simulations and data from literature. Finally, we demonstrate the importance of correct modelling of rolling friction for coupled CFD–DEM simulations of spout fluidized beds. We show that simulation results can be improved significantly when applying a rolling friction model, and that experimental data from literature obtained with Positron Emission Particle Tracking (PEPT) technique can be satisfactorily reproduced.     

Calibration of granular material parameters for DEM modelling and numerical verification by blade-granular material interaction

The discrete element method (DEM) is a promising approach to model blade-granular material interactions. The accuracy of DEM models depends on the model parameters. In this study, a calibration process was developed to determine the parameter values. The particle size was the same as the real material and the particle shape was modelled using two spherical particles rigidly clumped together to form a single grain. Laboratory shear tests and compressions tests were used to determine the material internal friction angle and stiffness, respectively. These tests were replicated numerically using DEM models with different sets of particle friction coefficients and particle stiffness values. The shear test results are found to be dependent on both the particle friction coefficient and the particle stiffness. The compression test results show that it is only dependent on the particle stiffness. The combination of shear test and compression test results can be used to determine a unique set of particle friction and particle stiffness values. The calibration process was validated experimentally and numerically by modelling a blade moving through granular material. Results show that the forces acting on the blade can be accurately modelled with DEM and the maximum error is found to be 26%. The relative particle-blade displacements were used to predict the position and shape of the shear lines in front of the blade. A good qualitative correlation was achieved between the experiments and the DEM simulations.     

Prediction of draft forces in cohesionless soil with the Discrete Element Method

The Discrete Element Method (DEM) is applied to predict draft forces of a simple implement in cohesionless granular material. Results are compared with small-scale laboratory tests in which the horizontal force is measured at a straight blade. This study is focused on the case of cohesionless material under quasi-static conditions.The DEM requires the calibration of the local contact parameters between particles to adjust the bulk material properties. The most important bulk property is the angle of internal friction ?. In the DEM, the shear resistance is limited in the case of spherical particles due to excessive particle rotations. This is cured by retaining rotations of the particles. Although this is known to prevent the material from developing shear bands, the model still turns out to be capable of predicting the reaction force on the blade.In contrast to empirical formulas for this kind of application, the DEM model can easily be extended to more complex tool geometries and trajectories. This study helps to find a simple and numerically efficient setup for the numerical model, capable of predicting draft forces correctly and so allowing for large-scale industrial simulations.     

Three-dimensional discrete element models for the granular statics and dynamics of powders in cavity filling

Rapid granular flow from a moving container and angle of repose formation were investigated by numerical simulations using the discrete element method (DEM) and experiments. Grain models of various geometrical complexity were studied and their ability to reproduce the experiments in those regimes was explored. The predictive power of the most realistic model for gravity driven cavity filling was assessed. Good agreement between computed and measured density distributions within the filled cavities provides a basis for numerical process variations aiming at homogenized density distributions. The effect of numerical coarse graining was found to be negligible for all properties of interest provided that force laws are scaled properly and corrections for boundary effects are taken into account. The proposed scaling was tested for a certain set of force laws but could be applied to different DEM forces as well. An analytic mass flow law for powder discharge from a moving container was derived and verified by our DEM simulations.     

沙水润滑下纳米改性NBR材料的摩擦学性能

丁腈橡胶(NBR)是一种优异的水润滑减摩耐磨材料,但硬质颗粒的介入对其产生较大的材料损失. 利用硅烷偶联剂TESPT改性纳米SiO₂颗粒,并填充至NBR基体,获得改性纳米SiO₂/NBR标记为NBR-1. 改性后的纳米SiO₂颗粒在NBR基体中均匀分散. 将纳米SiO₂颗粒、微米SiO₂颗粒填充至NBR基体标记为NBR-2、NBR-3作为对照组. 三种复合材料在武汉理工大学自制的SSB-100型摩擦磨损试验机上进行沙水润滑工况下的摩擦磨损试验. 结果表明:三种复合材料在沙水工况下摩擦系数均随载荷和转速的增加而下降. 在相同的载荷和转速条件下,NBR-1的摩擦性能最为优异. 对比三种材料的耐沙磨损性能,沙粒对NBR表面的磨损主要为犁沟磨损,NBR-2和NBR-3材料磨损量远远大于NBR-1,NBR-1材料更适用于含沙水区域.      

不同润滑材料对轮轨磨损与滚动接触疲劳的影响

通过轮轨滚动接触模拟试验研究了干态、施加轨顶摩擦调节剂、润滑油和润滑脂工况下的轮轨摩擦、磨损和损伤行为,分析了不同润滑材料对轮轨滚动接触疲劳损伤的影响. 结果表明:施加轨顶摩擦调节剂可将轮轨摩擦系数调控至0.1~0.3范围内,车轮和钢轨试样磨损率较干态下分别降低了54.9%和26.3%,轮轨表面损伤、塑性变形和滚动接触疲劳损伤明显降低;施加润滑油和润滑脂具有更加显著的润滑和减磨效果,摩擦系数降低至0.1以下,磨损率降低85%以上,但润滑油和润滑脂会进入裂纹内部产生“油楔效应”,导致严重的滚动接触疲劳损伤,而轨顶摩擦调节剂的固体润滑特性则避免了该问题的产生.      

Rigid body impact with moment of rolling friction

In this paper, the impact between a rigid pendulum and rough surfaces is studied. The rolling friction moment and the coefficient of rolling friction are introduced, and an improved mathematical model of the planar impact with friction is presented. The influence of the moment of rolling friction on the energy dissipated by friction during the impact is analyzed. For a simple pendulum, using the energetic coefficient of restitution, more energy is dissipated for larger values of the coefficient of kinetic friction and contact radius, and for smaller values of the length of the beam. For a double pendulum using the kinematic coefficient of restitution, some energetically inconsistent results can be solved for some values of the coefficient of rolling friction.     

煤仓内煤散料流动状态与力学行为影响因素

针对煤仓内煤散料流动问题及其力学行为,采用三维颗粒流模拟程序PFC3D建立了某型号煤仓与某种煤散料的离散元模型,简述了其力学模型与求解步骤,模拟分析了煤仓内煤散料卸料流动状态。通过分析水平向侧压力、颗粒速度场和接触力场,重点讨论了煤仓下部锥体内壁面摩擦系数、锥仓倾角和卸料口径等对煤散料颗粒流动状态和力学行为的影响。结果显示,深仓卸料流动为整体流动与中心流动混合状态,煤仓内壁摩擦系数、锥体倾角和卸料孔开口半径均对煤散料流动和水平侧压力有较大影响。