Investigation of the effect of filling level on the wear and vibration of a SAG mill by DEM

Semi-autogenous grinding (SAG) mill is widely used in the grinding process of coal and ores because of its strong applicability,large capacity and low consumpti...     

DEM investigation on conveying of non-spherical particles in a screw conveyor

Screw conveyors are extensively used in modern industry such as metallurgy, architecture and pharmaceutical due to their high-efficiency in the transportation of granular materials. And substantial efforts have been devoted to the study of the screw conveyors. Numerical method is an effective way to study screw conveyor. However, previous studies have mainly focused in the regime of spherical particles while the in-depth investigations for non-spherical particles that should be the most encountered in practical applications are still limited. In view of the above situations, discrete element method (DEM), which has been widely accepted in simulating the discrete systems, is utilized to investigate the conveying process of non-spherical particles in a horizontal screw conveyor, with particles being modeled by super-ellipsoids. In addition, a wear model called SIEM (Shear Impact Energy Model) is incorporated into DEM to predict the wear of screw conveyor. The DEM simulation results demonstrate that the particle shape is influential for the flow behaviors of particles and the wear of conveyor. The conveying performance evaluated quantitatively of both mass flow rate and power consumption is subsequently obtained to investigate the effect of sphericity of particle with different operation parameters. Moreover, particle collision frequency and collision energy consumption are acquired to investigate the possible particle breakage between particles and screw blade. The comparisons between particle–particle collision and particle–wall collision reveal that particles with large shape index have more possibility to be damaged in particle–wall impingement.     

Passive vibration absorber effect on the machining surface quality of a flexible workpiece

This paper presents a study of the vibratory behaviour of a flexible workpiece subject to a milling end operation. Indeed, this vibratory behaviour is critical, especially when the excitation frequency is near to the resonance. For this reason, passive vibration suppression is considered in order to attenuate the dynamic response of the milled workpiece and decrease the dynamic effect on the resulting machined surface roughness and flatness. In order to confirm the efficiency of the passive vibration suppression, the vibratory behaviour and the quality (roughness and flatness) of a machined surface are studied without and with passive absorber (TMD) using a finite-element model.     

地应力水平对深埋隧洞爆破振动频谱结构的影响

爆破振动的频谱特性对隧洞安全施工具有重要意义。采用动力有限元方法,分析了不同地应力水平条件下围岩爆破振动频率特征,通过对实测爆破振动信号的时域和频域联合分析,研究了不同频带上的振动能量分布。结果表明,爆破振动的主频及各个振动能量优势频带都有随地应力水平升高而降低的趋势,伴随爆破破岩过程而发生的地应力瞬态卸载动力效应是产生这一现象的主要原因。地应力水平越高,爆破振动信号中20～100 Hz的低频振动能量比重越大。当爆区的地应力为20 MPa时,20～100 Hz频带内的振动能量可达到总振动能量的35%左右;当爆区的地应力为30～50 MPa时,20～100 Hz频带内的振动能量可达到总振动能量的50%以上。除地应力水平外,应力卸载速率及岩体的力学特性也对爆破振动主频具有显著影响,卸载速率越高,低频振动能量比重越大。卸载速率取决于掏槽爆破方式,直孔掏槽导致岩体应变能释放速率最高。岩体弹性模量越大,爆破振动的主频越高。     

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.     

Numerical study of sliding wear caused by a loaded pin on a rotating disc

A computational approach is proposed to predict the sliding wear caused by a loaded spherical pin contacting a rotating disc, a condition typical of the so-called pin-on-disc test widely used in tribological studies. The proposed framework relies on the understanding that, when the pin contacts and slides on the disc, a predominantly plane strain region exists at the centre of the disc wear track. The wear rate in this plane strain region can therefore be determined from a two dimensional idealisation of the contact problem, reducing the need for computationally expensive three dimensional contact analyses. Periodic unit cell techniques are used in conjunction with a ratchetting-based failure criterion to predict the wear rate in the central plane strain region. The overall three dimensional wear rate of the disc is then determined by scaling the plane strain wear rate with a conversion factor related to the predicted shape of the wear track. The approach is used to predict pin-on-disc test data from an Al-Si coating using a tungsten carbide pin. The predicted results are found to be consistent with measured data.     

Design and evaluation of a low-power mobile shaker for vibration tests on heavy wheeled vehicles

In the field of mobile agricultural and off-road machinery, there is a growing interest to examine the dynamic behaviour of the vehicle under construction with a view to improve passenger comfort and machine performance. As many of these machine constructors are small sized, specialised companies are required to execute vibration tests and to evaluate vibration levels. Because most of these machines are heavy constructions with exceptional proportions, it is obvious to perform vibration tests on the factory floor by means of a low power mobile excitation device such as an electro-hydraulic shaker. This paper shows that an air spring, parallel to the actuator of an electro-hydraulic shaker, results in considerable power savings. The behaviour of the shaker is discussed at its resonance frequencies. For small band excitation signals, extra power savings can be achieved by tuning the spring stiffness and by using the air spring at constant pressure. Experiments on a one degree of freedom vertical shaker show good agreement with the theory and demonstrate that the different mode shapes of an agricultural tractor can be sufficiently excited with a nominal hydraulic power of 500 W.     

Application of a screw conveyor with axial tilt blades on a shearer drum and investigation of conveying performance based on DEM

Screw conveyors are widely employed in industrial fields for conveying bulk materials. The shearer drum which uses the screw conveying principle is responsible for excavation and conveying coal particles onto the chain conveyor. Screw conveyor performance is affected by potential factors, such as the blade axial tilt angle and style, core shaft form and diameter. The effect of blade axial tilt angle on the conveying performance was investigated with the help of DEM. In the case of the screw conveyor, the mass flow rate, and particle axial velocity increased with increasing positive axial tilt angle, and declined with increasing negative axial tilt angle. In the case of the drum, the mass flow rate, particle axial velocity, and loading rate first increased and then decreased with increasing positive axial tilt angle, and decreased with increasing negative axial tilt angle. These results can be considered as a benchmark for screw conveyor and drum structural designs with axial tilt screw blades.     

The effect of the geometric parameters of the corrugation shape on the vibration analysis of 3D structured beams

This paper deals with the vibration analysis of 3D structured beams with double sinusoidal pattern. The corrugation depends on different parameters such as orientation, amplitude and wave length of the double sinusoid shape. First, a numerical modeling was built using the Finite Element method. Then, experimental tests of bending vibration were conducted on planar and corrugated beams. These data validated our model and proved that the resonant frequencies generally increase due to corrugated shape. A parametric study demonstrated that the optimal values of the corrugation shape can be found to increase the resonant frequencies.     

Deformation and vibration of upright loops on a foundation and of hanging loops

The deformation and vibration of vertical flexible loops are investigated theoretically and experimentally. Both upright and hanging loops are considered. Potential applications include nanorings and carbon nanotubes as force sensors or structural components. The upright tubes rest on a rigid or linearly elastic (Winkler) foundation, and cases with adhesion and nonlocal elasticity are included in the analysis. The hanging loops are suspended by a clamp with zero or finite length. The effects of self-weight, foundation stiffness, work of adhesion, and nonlocal elasticity on the loop height or depth are determined, as well as the effects of self-weight and foundation stiffness on the lowest frequency for in-plane symmetric vibration. Good agreement is attained between theoretical results (based on an inextensible-elastica model) and experimental data.     

Free vibration analysis of a plate on foundation with completely free boundary by finite integral transform method

The theoretical solutions of eigenfrequencies and vibration modes of a rectangular thin plate on an elastic foundation with completely free boundary are derived by using a double finite cosine integral transform method. In the analysis procedure, the elastic foundation is regarded as a Winkler elastic foundation model. Because the basic dynamic elasticity equations of the thin plate on elastic foundation are only used, it is not needed to select the deformation function arbitrarily. Therefore, the solution developed in the present paper is more reasonable and more accurate. To prove the correctness of the solutions, numerical results obtained using the present solutions are compared with those in the literatures.     

Effect of open spaces between grousers on the gross traction of a track shoe for lightweight vehicles analyzed using 2D DEM

The purpose of this study is to investigate the effect of open spaces between grousers on gross traction using the discrete element method (DEM). We used a quasi-2D track shoe model in which we could control the open spacing between track shoes to observe the tractive performance experimentally. The gross traction and the sinkage of the grouser were measured on artificial sand. Moreover, we applied a 2D DEM analysis to the interaction between the open-spaced track shoes and the model soil. We confirmed the accuracy of the DEM analysis using the experiments. The analysis with the model dry sand could recreate the characteristic region of the soil under the shearing action, which depends on the track shoe spacing. The DEM also showed that the gross traction decreased with the increase in open spacing of the grousers. From the result of a 2D DEM analysis of a grouser for a prototype mesh crawler for the Japan Aerospace Exploration Agency, we estimated a thrust coefficient of approximately 0.4 for a wider grouser pitch-to-height ratio of 4.0–7.75 because of the constant sinkage of the grouser, neglecting the role of the meshed belt.     

基于HHT能量谱的高精度雷管短微差爆破降振效果分析

为揭示高精度雷管短微差爆破干扰降振机理,选取紫金山金铜矿露天爆破实测的单段波形信号,利用Matlab分析了不同微差间隔下两段叠加信号的时频特征; 综合考虑爆破振动三要素并结合HHT(Hilbert-Huang transform)能量定义降能率,分析了段数、相邻振幅比和最大段药量位置对短微差爆破叠加信号降振效果的影响。根据研究成果,爆破设计时应避免出现前后段数药量差距过大,并尽量将较大药量的段数靠后起爆。研究表明:相同微差间隔下随着段数的增加,叠加信号降能率逐渐增大,当段数达到一定数量后增加分段数,微差爆破的降振效果并不明显; 微差爆破中相邻振幅比越接近1,降振效果越明显; 最大段药量靠后的叠加信号降能率大于其他顺序。     

Thermal gradient effect on the free vibration of a cardioid cross-section cylindrical shell

For the first time, a new cross-section profile and efficient method are developed for the vibration analysis of isotropic and orthotropic cylindrical shells having circumferentially varying profile of a cardioid cross-section expressed as an arbitrary function, under thermal gradient effect. The governing equations of orthotropic cylindrical shells with varying thermal gradient around its circumference are derived as a boundary-value problem and solved numerically as an initial-value problem, based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method. As a semi-analytical procedure, the trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction and also to reduce the two-dimensional problem to one-dimensional one. The thermal gradient is assumed to arise due to the variation of Young's moduli and shear modulus, along the circumferential direction of the shell. The results are obtained to indicate the effects of cardioid cross-section on the natural frequencies and corresponding mode shapes in the thermal environment as well as the sensitivity of the vibration behavior to the thermal gradient ratio and the orthotropy of the shell is also investigated for different types of vibration modes. In general, close agreement between the obtained results and those of other researchers has been found.     

Investigation of the effect of the added mass fluctuation and lateral vibration absorbers on the vertical nonlinear vibrations of the offshore wind turbine

Nonlinear Dynamics - In this article, the effects of the changes in the mass of the floating wind turbine (as a multi-body system) on its nonlinear vertical vibrations are investigated. The...     

The mullins effect in uniaxial extension and its influence on the transverse vibration of a rubber string

This paper presents a study of the stress softening effect encountered in uniaxial extension and explores its effect on the small amplitude transverse vibration of a stretched rubber cord. An idealization of the uniaxial stressstrain behavior of a stress softening material is presented, the importance of the deformation history is emphasized, and parameters are introduced to track the deformation history. An extended investigation of a model proposed by Mullins and Tobin to quantify stress softening by introduction of a strain amplification factor is then presented. A major result derived from this model is shown to be consistent with results reported by others. The uniaxial stress softening theory is used to describe the transverse vibration behavior of a rubber string subjected to repeated stretching. This appears to be the first application of the softening model of Mullins and Tobin to a dynamical problem. Analytical results are compared with uniaxial stress-strain and transverse vibration experiments performed with buna-n, neoprene, and silicone rubber cords. Both types of experiments provide a simple and novel method to evaluate the predictive success of our uniaxial theory without the need for a specific constitutive model. The pseudoelastic response found in biological tissues is discussed in light of results obtained in the transverse vibration experiments.     

Investigation of the effect of the Coriolis force on a thin fluid film on a rotating disk

The effect of the Coriolis force on the evolution of a thin film of Newtonian fluid on a rotating disk is investigated. The thin-film approximation is made in which inertia terms in the Navier–Stokes equation are neglected. This requires that the thickness of the thin film be less than the thickness of the Ekman boundary layer in a rotating fluid of the same kinematic viscosity. A new first-order quasi-linear partial differential equation for the thickness of the thin film, which describes viscous, centrifugal and Coriolis-force effects, is derived. It extends an equation due to Emslie et al. [J. Appl. Phys. 29, 858 (1958)] which was obtained neglecting the Coriolis force. The problem is formulated as a Cauchy initial-value problem. As time increases the surface profile flattens and, if the initial profile is sufficiently negative, it develops a breaking wave. Numerical solutions of the new equation, obtained by integrating along its characteristic curves, are compared with analytical solutions of the equation of Emslie et al. to determine the effect of the Coriolis force on the surface flattening, the wave breaking and the streamlines when inertia terms are neglected.     

Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton's principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.     

Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

In this paper we present a three‐dimensional Navier–Stokes solver for incompressible two‐phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third‐order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second‐order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first‐order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three‐dimensional results with those of quasi‐two‐dimensional and two‐dimensional simulations. This comparison clearly shows the need for full three‐dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd.