On contact numbers in random rod packings

Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well with experiments on granular packings. Contact numbers are also compared to caging numbers calculated for sphero-cylinders with arbitrary aspect-ratio. The caging number for rods arrested by uncorrelated point contacts asymptotes towards at high aspect ratio, strikingly close to the experimental contact number for thin rods. These and other findings confirm that thin-rod packings are dominated by local arrest in the form of truly random neighbor cages. The ideal packing law derived for random rod–rod contacts, supplemented with a calculation for the average contact number, explains both absolute value and aspect-ratio dependence of the packing density of randomly oriented thin rods.     

A geometric algorithm based on tetrahedral meshes to generate a dense polydisperse sphere packing

In the discrete element method, the packing generation of polydisperse spheres with a high packing density value is a major concern. Among the methods already developed, few algorithms can generate sphere packing with a high density value. The aim of this paper is to present a new geometric algorithm based on tetrahedral meshes to generate dense isotropic arrangements of non-overlapping spheres. The method consists of first filling in every tetrahedron with spheres in contact (i.e., hard-sphere clusters). Then, the algorithm increases the packing density value by detecting the large empty spaces and filling them with new spheres. This new geometric algorithm can also generate a complex shape structure.     

DEM simulation of binary sphere packing densification under vertical vibration

The densification of random binary sphere packings subjected to vertical vibration was modeled by using the discrete element method (DEM). The influences of operating parameters such as the vibration conditions, sphere size ratio (diameter ratio of larger versus small spheres), and composition (volume fraction of large spheres) of the binary mixture on the fractional packing density φ (defined as the volume of spheres divided by the volume of container) were studied. Two packing states, i.e., random loose packing (RLP) and random close packing (RCP), were reproduced and their micro properties such as the coordination number (CN), radial distribution function (RDF), and force structure were characterized and compared. The results indicate that properly controlling vibration conditions can realize the transition of binary packing structure from the RLP to RCP state when the sphere size ratio and composition are fixed, and the fractional packing density for RCP after vibration can reach φ_RCP?≈?0.86. Different packing characteristics from RLP and RCP identify that RCP shows much denser and more uniform structure than RLP. The current modeling results are in good agreement with those obtained from both the physical experiments and the proposed empirical models in the literature.     

Experimental study on the packing densification of mixtures of spherical and cylindrical particles subjected to 3D vibrations

To identify the dense packing of cylinder–sphere binary mixtures (spheres as filling objects), the densification process of such binary mixtures subjected to three-dimensional (3D) mechanical vibrations was experimentally studied. Various influential factors including vibration parameters (such as vibration time t, vibration amplitude A, frequency ω, vibration acceleration Γ) as well as particle size ratio r (small sphere vs. large cylinder), composition of the binary mixtures X_L (volume fraction of cylinders), and container size D (container diameter) on the packing density ρ were systematically investigated. The results show that the optimal vibration parameters for different binary cylinder–sphere mixtures are different. The smaller the size ratio, the less vibration acceleration is needed to form a stable dense packing. For each binary mixture, high packing density can be obtained when the volume fraction of large cylindrical particles is dominant. Meanwhile, increasing the container size can decrease the container wall effect and get higher packing density. The proposed analytical model has been proved to be valid in predicting the packing densification of current cylinder–sphere binary mixtures.     

Dynamic simulation of particle packing influenced by size, aspect ratio and surface energy

The multi-sphere method and JKR model are used in the discrete element method simulation to investigate the effect of the particle size, aspect ratios, and cohesiveness on the packing structure, characterized by porosity, radial distribution function (RDF), coordination number and contact geometry. In the absence of cohesive force, the porosity is nearly invariable with fixed aspect ratio, regardless of the size of the particles. In contrast, as surface energy increases, the porosity increases with decreasing particle size and increasing aspect ratio. The RDF results show that the number of peaks for different aspect ratios changes and show trends similar to the relaxation algorithm, expected for the finer particles. In the case of finer, cohesive particles, the most novel outcome of contact analysis is the existence of single contact, attributed to the formation of a cage structure, which has not been previously reported. The peak position and the width of the contact distributions are affected by higher surface energy because fewer contacts are required to achieve the mechanical equilibrium. Another interesting observation is that higher porosity does not always imply fewer contacts for particles with non-zero aspect ratios and high surface energies. The analysis of the distribution of the contact vector angles is found to better explain increased porosity in spite of higher coordination numbers. The results presented shed light on the packing density and structure, revealing features not easily discerned via experiments, and confirming the important role of the cohesion and aspect ratio in packing.     

An entropy-like parameter of particle size distributions as packing density index in complex granular media

Information entropy dimension (ED) has been used earlier in the characterization of the particle size distribution (PSD) in complex multi-particle granular media. In this work the ED is first proposed as an indicator of the packing density on the basis of the theoretical based interpretation of the ED in the granular media PSD context. A one-parametric exact self-similar PSD model, where the information ED is known, together with a 2-D computational random packing algorithm, are used to test the ability of the ED as an indicator of packing density. It is found that the packing density increases when the ED does. Moreover, results show a strong linear dependence between packing density and the ED. Empirical results from a large soil data base also reinforce the computational results. As ED may be estimated from field or laboratory data, the above mentioned results suggest its use as an indicator of packing density in complex granular media and material science in order to predict their properties.     

局域波时频域多重分形在故障诊断中的应用

提出了一种振动信号时域与时频域的多重分形方法,并将该方法实际应用于故障诊断之中。信号局域波分解的时频域幅值矩阵经过网格划分后,通过最小二乘法计算出广义维数Dq。应用振动信号时频域多重分形方法在往复式压缩机填料泄漏故障进行了实例分析,并分别得出了对于该类故障较为敏感维数。实测往复式压缩机的振动信号分析表明,时域信号的多重分形只对早期填料泄漏故障较为敏感,时频域多重分形方法随着故障程度的增加其广义维数增加,能够较好的区分故障的严重程度。实践证明该方法在实际应用中切实可行。     

A pi-shaped ultrasonic tweezers concept for manipulation of small particles

A pi-shaped ultrasonic actuator is proposed for the noncontact trapping, extraction, and transportation of small particles. In this actuator, two metal plates clamp a multilayer piezoelectric vibrator by a small bolt, and the metal plates are tapered in their lower parts so that a vibration gradient can be obtained. The flexural vibration of the metal plates is used to generate a sound field in the gap between the two tapered metal plates. At a driving frequency of about 152.8 kHz, shrimp eggs, grass seeds, thyme seeds, rice powder, fine salt, and fine sugar, which have an average diameter from several tens of micrometers to several hundreds of micrometers, can be trapped stably without contact with the actuator, and the particles insoluble in water can be extracted from water and transported in water by the actuator. In the noncontact trapping of small particles, the positions of trapped particles as well as the relationship among the number of trapped particles, vibration velocity, and input power are investigated. The number of trapped particles increases as the vibration velocity or input power increases. However, when the vibration velocity or input power is too large, the particles may be ejected out of the actuator and, therefore, cannot be stably trapped. The minimum vibration velocity to trap small particles increases as particle density increases for the particles that have the shape near to a sphere and a proper density. In the extraction of small particles from water, the relationship between the number of extracted thyme seeds and the input power is investigated. Increasing the input power can increase the extracted thyme seeds. However, there is a maximum particle number that can be extracted from water. In the transportation of thyme seeds in water, the dependence of the particle loss during the transportation on the speed and distance of transportation and the input power is experimentally estimated. As the distance and speed of transportation increase, the particle loss during the transportation increases. Increasing the input power increases the trapping effect and, therefore, decreases the particle loss.     

脉动注射保压过程中的压力损失

以低密度聚乙烯(LDPE)为原料,在中心浇口圆盘模腔脉动压力诱导注射成型过程中,测定了模具和喷嘴之间的压力,研究了保压过程中的压力损失,并与稳态注射成型过程做了比较.实验结果表明:存在某一频率和振幅,可使振动力场对保压过程中模腔压力损失最小.在所给实验条件下,频率为4 Hz时压力损失最小.与稳态注射相比,在保压阶段,脉动压力诱导注射模腔中的压力损失要小.脉动压力诱导注射可提高喷嘴压力和模腔压力,有利于保压补缩.     

火工品包装箱抗震性能的线性动力学分析

通过静力学分析,忽略接触摩擦,将火工品包装箱的抗震性能分析转化为线性动力学问题,建立了有限元模型并分析模态,得到了前20阶振动频率,在此基础上对包装箱进行了随机振动和水平冲击测试。该方法对优化火工品包装箱设计以提高箱体结构的抗震性能,具有实际意义。     

CFD-DEM numerical study on air impacted packing densification of equiaxed cylindrical particles

A CFD-DEM model was developed to reproduce the packing densification process of mono-sized equiaxed cylindrical particles under air impact. The effects of operating parameters on packing density were firstly studied. Then various microscopic properties of packing structures such as coordination number (CN), contact types, particle orientations, pore features were characterized and compared. And corresponding densification mechanisms were analysed based on particle motion behaviour, local structure evolution, and forces. Results indicate that the air impact can realize the packing densification of cylindrical particles under appropriate conditions. The pore size distribution in the packing of cylindrical particles shows a tail at larger pore sizes compared with that in the packing of equal spheres. Both the size and the sphericity of the pores decrease in the final dense packing; also, more surface-surface and less surface-edge contacts between two particles therein can be formed. More cylindrical particles tend to be in parallel or perpendicular contact with each other to form more stable local structures during air impact. Most particles at higher position move down (direction of gravity/air impact) with about one particle length during the densification process and most particles exhibit translational motion to realize the local rearrangement for pore filling through air impact induced inter-particle forces.     

Granular packing: numerical simulation and the characterisation of the effect of particle shape

The packing of granular particles is investigated using a combined finite-discrete element approach. One of the aims of this paper is to present an application of a recently improved numerical simulation technique for deformable granular material with arbitrary shapes. Our study is focused on the influence of the effect of the particle shape on (1) the emergent properties of a granular pack (packing density, coordination number, force distribution), and on (2) the spatial distribution of the stress. A set of simulations that mimick the sedimentation process is carried out, with varying input parameters, such as contact friction and particle shape. It is shown that the eccentricity of the particles not only significantly influences the final density of the pack but also the distribution of the stress and the contact forces. The presence of surface friction increases the amount of disorder within the granular system. Stress heterogeneities and force chain patterns propagate through the particles more efficiently than for the frictionless systems. The results also suggest that for the monodisperse systems investigated the coordination number is one of the factors that controls the distribution of the stress within a granular medium.     

压路机激励下重载铁路路桥过渡段动力特性研究

以蒙华重载铁路某路桥过渡区为试验对象,开展压路机激励下过渡区的动力特性试验,研究过渡区动力响应的分布规律;建立考虑振动轮-路基耦合的动力分析数值模型,研究过渡区等效刚度分布及振动轮-路基面接触力变化特性。结果表明:随着路基深度增大,动应力扩散角逐渐减小,埋深0.2~3.0 m处扩散角在78.2°~55.0°,倒梯形过渡段动应力扩散角要大于一般路基扩散角;相比列车荷载,压路机激励引起的竖向动应力在路基中衰减更快,并且在基床表层中衰减最大;压路机驶离桥台方向的基床表层动侧压力系数为0.35~0.53,驶向桥台方向为0.24~0.36,倒梯形过渡段的动侧压力系数要小于一般路基段;过渡段路基等效刚度在74.8~87.2 kN/mm,随离桥台距离增大而呈线性减小趋势;振动轮激励过程中,过渡段内的振动轮-路基面最大接触力峰值比一般路基段大,且随着过渡区刚度差的增大而增大。     

透析器中随机分布纤维管表面定浓度时传质模拟

通过数值模拟,研究了在透析器外壳内壁面的影响下,纤维表面定浓度时,中空纤维分布的随机性对透析器管外流场和浓度场的影响,同时考察了管外流体速度以及中空纤维填充密度对管外传质系数的影响.模拟结果表明:随机排布的方式对传质系数有较大的影响,但相比忽略壁面影响时的影响要小;Reynolds 数越大,传质系数也越大;在所研究的中空纤维填充密度范围内(10%～50%),随着填充密度的增大,透析器的管外传质系数先增大,后减小,变化幅度均较小,与忽略壁面影响的值比较发现,在填充密度小的时候壁面对传质有促进作用,填充密度大的时候则相反.     

Decoupled Control of Carbon Nanotube Forest Density and Diameter by Continuous‐Feed Convective Assembly of Catalyst Particles

The widespread potential application of vertically aligned carbon nanotube (CNT) forests have stimulated recent work on large‐area chemical vapor deposition growth methods, but improved control of the catalyst particles is needed to overcome limitations to the monodispersity and packing density of the CNTs. In particular, traditional thin‐film deposition methods are not ideal due to their vacuum requirements, and due to limitations in particle uniformity and density imposed by the thin‐film dewetting process. Here, a continuous‐feed convective self‐assembly process for manufacturing uniform mono‐ and multi‐layers of catalyst particles for CNT growth is presented. Particles are deposited from a solution of commercially available iron oxide nanoparticles, by pinning the meniscus between a blade edge and the substrate. The substrate is translated at constant velocity under the blade so the meniscus and contact angle remain fixed as the particles are deposited on the substrate. Based on design of the particle solution and tuning of the assembly parameters, a priori control of CNT diameter and packing density is demonstrated. Quantitative relationships are established between the catalyst size and density, and the CNT morphology and density. The roll‐to‐roll compatibility of this method, along with initial results achieved on copper foils, suggest promise for scale‐up of CNT forest manufacturing at commercially relevant throughput.     

Packing of fine particles in an electrical field

A numerical model based on the Discrete Element Method (DEM) is developed to study the packing of fine particles in an electrical field related to the dust collection in an electrostatic precipitator (ESP). The particles are deposited to form a dust cake mainly under the electrical and van der Waals forces. It is shown that for the packing formed by mono-sized charged particles, increasing either particle size or applied electrical field strength increases packing density until reaching a limit corresponding to the density of random loose packing obtained under gravity. The corresponding structural changes are analyzed in terms of coordination number, radial distribution function and other topological and metric properties generated from the Voronoi tessellation. It is shown that these properties are similar to those for the packing under gravity. Such structural similarities result from the similar changes in the competition of the cohesive forces and the driving force in the packing. In particular, it is shown that by replacing the gravity with the electrical field force, the previous correlation between packing density and the ratio of the cohesive force to the packing-driven force can be applied to the packing of fine particles in ESP.     

Superfine cement for improving packing density, rheology and strength of cement paste

Superfine cement is a cement ground to a much higher fineness than ordinary cement. The addition of a small quantity of superfine cement to fill into the voids of ordinary cement can improve the packing density of the cement and thereby reduce the amount of mixing water needed to fill the voids. In this study, the effects of superfine cement on the packing density of cement (directly measured by a wet packing test), the water film thickness of cement paste (taken as the excess water to solid surface area ratio), and the flowability, rheology and strength of cement paste were investigated. The results showed that the addition of 10% to 20% superfine cement can significantly increase the packing density of the cement and the water film thickness of the cement paste. Such increases in packing density and water film thickness would then improve the flowability, rheology and strength of the cement paste. Hence, superfine cement is an effective cementitious filler for improving cement performance.     

Effects of crystal structures and intermolecular interactions on charge transport properties of organic semiconductors

In this study, the effects of the packing configuration and intermolecular interaction on the transport properties are investigated based on density functional theory. Molecular design from the standpoint of a quantum-chemical view is helpful to engender favorable molecular packing motifs. The transfer integral along the orientation with π–π overlap is much larger than other directions without π–π overlap, and the mobility along this orientation is higher than that along other directions. The intermolecular interaction analyses demonstrate that hydrogen bonds play a crucial role with strong electrostatic interactions in charge transfer. There will be a synergistic relationship when the π–π stacking and intermolecular interaction coexist in the same direction. It turns out that intermolecular interactions are responsible for charge transport, while π–π stacking interactions dominate donor–acceptor transport. Incorporating the understanding of the molecular packing motifs and intermolecular interactions into the design of organic semiconductors can assist in the development of novel materials.     

A discrete element analysis of elastic properties of granular materials

The elastic properties of a regular packing of spheres with different tolerances were evaluated using the discrete element method to elucidate the mechanisms behind the discrepancies between laboratory experiments and theoretical predictions of the classic Hertz-Mindlin contact law. The simulations indicate that the elastic modulus of the packing is highly dependent on the coordination number and the magnitude and distribution of contact normal forces, and this dependence is macroscopically reflected as the influence of confining pressure and void ratio. The increase of coordination number and the uniformity of contact normal forces distribution with increasing confining pressure results in the stress exponent $n$ for elastic modulus being higher than 1/3 as predicted by the Hertz-Mindlin law. Furthermore, the simulations show that Poisson’s ratio of a granular packing is not a constant as commonly assumed, but rather it decreases as confining pressure increases. The variation of Poisson’s ratio appears to be a consequence of the increase of the coordination number rather than the increase of contact normal forces with confining pressure.     

球形永磁阵列振动能量收集器设计与优化

为实现多方向环境能量收集,设计球形电磁式振动能量采集器。基于二维Halbach阵列设计的球面Halbach永磁阵列,较传统永磁阵列能提高线圈中磁链变化梯度,从而提高结构输出性能;建立数学解析模型,据解析结果对模型各参数进行优化;对该模型进行有限元仿真分析及实验性能测试。结果表明,该模型能有效响应空间任意方向振动,进而转化为电能;外部激励为10 Hz、激励为水平方向、负载阻值50 Ω时,该球形振动能量采集器输出电能达最大,单个线圈中最大负载功率可达0.8 mW。