用DEM模拟和实验模型验证圆锥破碎机的性能评估-毕业论文外文翻译.docx

翻译部分英文原文Cone crusher performance evaluation using DEM simulations and laboratory experiments for model validationKeywords: Cone crusher DEM Validation Experiment Simulation ModellingAbstract： Cone crushers are commonly used for secondary and tertiary crushing stages in the aggregate and mining industry. It has previously been demonstrated that the discrete element method (DEM) can be used to simulate rock breakage in crushers using a variety of modelling techniques. In order to provide confi-dence in the simulation results the DEM models need to be validated against experimental data. Such val-idation efforts are scarcely reported in the existing literature and there are no standardized procedures defined. In this paper a laboratory cone crusher is simulated using DEM and the results are compared with laboratory experiments. The rock material is modelled using the Bonded Particle Model approach calibrated against single particle breakage experiments. Two case simulations have been performed investigating the influence of eccentric speed. The laboratory crusher is a Morgårdshammar B90 cone crusher that has been equipped with custom machined liners, variable speed drive and a National Instruments data acquisition system. The results provide novel insight regarding the stochastic flow behaviour of particles when exited by the mantle at high frequency. The estimated product size distribu-tion matches the experimental results relatively well when evaluating the corresponding coarse region that is feasible to calculate from the DEM product discharge data.1. Introduction The cone crusher is the most common machine type for sec-ondary and tertiary crushing of hard rock materials in the minerals processing industry. During recent years, minerals processing experts and engineers have shown an increased interest in the operation of primary and secondary crushing and potential efforts to optimize the performance and operation have followed. This interest directs focus on modelling and simulation capabilities in order to provide accurate and robust predictions. Models com-monly range from relatively simple empirical analytical models to mechanistic analytical models and numerical models which for instance, utilize the discrete element method (DEM). The required quality and applicability of the different modelling approaches depends on why it is applied. If the model is used in a fast and simple steady state simulation; a fitted empirical size reduction model may be enough, at least if the prediction capabil-ity limitations are well understood and considered. In cases where, for instance, the influence on circuit performance due to a crusher liner design change is evaluated, a more advanced mechanisticmodel is needed. Such mechanistic models have been developed and successfully implemented by e.g. Eloranta (1995) and Evertsson (2000). The Evertsson Cone Crusher model was later adopted and implemented in a dynamic simulation platform based on Simulink, developed by Asbjörnsson, Hulthén and Evertsson (Asbjörnsson, 2015).Even though the advanced mechanistic cone crusher models are derived based on first principle equations there are some assump-tions included in the modelling framework. These assumptions are, for instance, related to how particles flow and where in the crusher they are subjected to a particular type of breakage mode. Further analysis of these assumptions is one of the drivers for developing simulation models that are capable of delivering predictions where the actual machine geometry, dynamics and rock material proper-ties are considered. Other drivers for detailed modelling of com-minution machines are related to, for example, development of new machines, machine design optimization or problem solving. The discrete element method, proposed by Cundall and Strack (1979), has proven to be the most suitable modelling methodology for these purposes. Several authors have contributed to the research field of modelling compressive crushers in DEM. It should be noted that breakage is normally not considered in DEM as the most common simulation applications only involve the flow beha-viour of the granular media. Hence, when modelling a compressive crusher some kind of methodology needs to be applied in order to facilitate a useful description of the actual breakage events and how rock particles break apart. The three most common approaches used for modelling breakage in DEM are listed below: Bonded Particle Model (BPM) - Spheres are arranged in a cluster and bonded together in each contact point using bonding beams (Potyondy and Cundall, 2004). Particle Replacement Model (PRM) - Particles are replaced by a set of progeny fragments at the breakage event (Cleary, 2001). Tetrahedral Element Model (TEM) - Particles are modelled using a tessellated mesh structure using voronoi grains, polyhedrons or trigons (Cundall, 1988; Potapov and Campbell, 1996). All of these three approaches have been used for modelling compressive breakage in cone crushers. Herbst and Potapov (2004) used a version of the TEM method but only displayed results from a 2D simulation of a crusher. The TEM approach was later applied in 3D by the same group for modelling a Morgård-shammar B90 laboratory crusher (Lichter et al., 2009). The PRM method has successfully been implemented for cone crusher sim-ulations by Cleary, Sinnott and Delaney (Cleary and Sinnott, 2015; Delaney et al., 2015). The BPM method has previously been applied for modelling of breakage in cone crushers by the authors in a series of publications (Johansson et al., 2015; Quist and Evertsson, 2016, 2010; Quist et al., 2011). The BPM model is implemented on clusters of sub-particles assembled with the shape from 3D scanned rock particles. The micro properties of the BPM model were calibrated against single particle breakage experiments and the results have been compared to industrial scale experiments. The experiments were conducted on a Svedala H6000 cone crusher and the power draw and pressure signals were measured using a custom data acquisition system with a sampling rate of 500 Hz.These attempts to develop a validated DEM model structure for compressive breakage in cone crushers have been continued in lab-oratory scale experiments using a B90 Morgårdshammar cone crusher by Johansson and Quist (Johansson et al., 2015). In the mentioned work the eccentric speed of the mantle was investi-gated at levels significantly higher than normal for cone crushers. It was found that the original liner design with a distinct short par-allel zone in the CSS region was possibly suitable for laboratory sample size reduction purposes however less suitable for the investigation of high speed crushing. A new liner design CAD model was developed with continuous liner surfaces and this design was evaluated using DEM.In this work new liner components have been machined and two laboratory experiments have been conducted at eccentric speeds 10 Hz and 20 Hz with a close side setting of 2.2 mm.The eccentric throw of the crusher is fixed at 4.3 mm.The corresponding case has been modelled in DEM and the main scope of this paper is to compare the laboratory result with the DEM simulation results. This comparison is both of scientific value in terms of DEM validation but also in terms of understanding the mechanics and phenomena of high speed cone crushing.The motivation for exploring cone crushing at higher speeds is to investigate if it is possible to capitalize on the increased number of single particle breakage compression events. It has previously been shown that single particle breakage is superior in terms of energy utilization when compared to, for instance, single particle impact breakage and interparticle bed breakage (Schönert, 1972).The layout and configuration of this paper follows the IMRDC structure where the methodology of the experiments and DEM modelling is first presented. In the subsequent section the experi-mental results are shown followed by the DEM simulation results. Finally the experimental and simulation findings are discussed and conclusions are proposed.2. MethodIn this section the methodology for both DEM simulations and laboratory experiments is presented. In order to be able to compare particle size distribution results between the simulation and experimental domains a previously developed post processing script has been refined. This methodology is presented in the end of the section.2.1. Laboratory experimentsThe laboratory experiments were carried out in the Chalmers rock processing laboratory in Göteborg, Sweden. Tests were con-ducted using a Morgårdshammar B90 laboratory cone crusher equipped with a variable speed drive to allow control of the eccen-tric speed of the main shaft. The performance of the new liner design has previously been evaluated using DEM simulations (Johansson et al., 2015). The virtually tested liner design was then machined using the material Uddeholm Nimax. The liner design can be seen in Fig. 1 and the experimental setup and feeding arrangement in Fig. 2. A novel feed entrance geometry was mod-elled and 3D printed in order to allow for unrestricted flow into the chamber.The feed rock material was a 5.68 mm granite material from Kållered, Sweden. The feed material was presented to the crusher using a vibrating feeder placed above the crusher. The input feed was controlled by a potentiometer and the speed of the crusher controlled by a variable speed drive. A National Instruments Lab-VIEW graphical interface was used to control and sample power draw and discharge mass flow signals. The discharge mass flow was measured using a custom developed load cell balance placed under the crusher.Before each experiment a set of sequential preparation steps are performed. Firstly the crusher is started and allowed to run for 5 min crushing at 600 rpm. This is done in order for the bearing arrangement to reach operating temperature. The crusher is then stopped for a change of feed material. The feeder is emptied and the test material is placed into the vibrating feeder. Once again the crusher is started and the feed carefully adjusted while the speed is ramped up to the maximum speed of the test series. To utilize the crusher capacity the feed mass flow is adjusted until the power consumption settles, for the tests presented in this paper the power level was aimed to be 3 kW at eccentric speed 20 Hz. When the power level has settled to steady state operation the first product material sampling is performed. The sample con-tainer is placed onto a mass flow balance, tracking the accumulated mass. From the accumulated discharge mass data the mass flow rate can be calculated by linear regression.Fig. 1. Liner geometry design with inner mantle at nominal position for 2 mm CSS.Fig. 2. (Left) Image of the crusher set up and feed arrangement, (right) the crusher inlet when the top is removed. The linearity of the mass flow gives an indication of whether or not the sampling was performed at steady state conditions. After 40 s the sample container is removed and stored for later analysis. The speed is then lowered to the new set point and the power draw is allowed to stabilize once again. At this point a new sampling pro-cedure may be initiated and the process is repeated until all eccen-tric speed set points have been completed. The size distribution of the product samples has been analysed using sieve analysis follow-ing the EN933-1 standard (Standardization, 1998).2.2. DEM model configuration The DEM model has been developed and simulated in EDEM 2.7 provided by DEM Solution Ltd. The rock material is based on two different 3D scanned rock shapes in the size range 68 mm. The scanned particles shapes are used as moulds for a packed cluster of fraction particles that are bonded with beams according to the BPM modelling approach (Potyondy and Cundall, 2004; Potyondy et al., 1996). The full procedure and methodology of the specific approach of using meta-particles is described by Quist (Quist and Evertsson, 2016). According to the framework by Potyondy and Cundall, particles are allowed to overlap given that the overlap is small compared with the particle fraction size. Bonds of finite stiff-ness are created at contact points between two particles and these bonds carry load and break when the calculated stress on the bond exceeds a strength criteria. The bonds fail under tensile or shear loads but not due to compression. The micro-properties of the meta-particles are presented in Table 1. When fraction particles are liberated and are no longer part of a cluster, the interaction with surrounding particles and geometrical elements is controlled by the Hertz-Mindlin no slip contact model. The main limitation and challenge of performing DEM simu-lations of comminution equipment is to balance; the number of meta-particles included in the simulation, the size of the machine section modelled, and operational time needed to be able to draw any useful conclusions. In this work a 40 degree section of the crusher is modelled in order to increase the amount of material in one feeding location with the intention of achieving a choke feeding condition. The section limitation is realised by the boundary wall where the friction parameters are set to low values. The nutational motion of the mantle is created by two sinu-soidal rotations defined from a pivot point where one of the motions is phase shifted p/2 rad. In addition, a third counter rota-tional motion around the vertical axis is added in order to simulate the mantles rolling motion on the concave. In the real crusher the mantle is allowed to freely rotate around the main shaft axis and the interaction between the mantle and concave can be compared with a planetary gear where the rocks act as gear teeth. If this counter rotation is not included the simulated particles will expe-rience a false horizontal force causing particles to report to the boundary wall. Dring the initial iterations of these simulations it was found that the number of meta-particles was not enough to achieve a sat-isfactory choke fed condition. One reason is due to the significantly higher eccentric speed of the mantle that excites the feed particles with a force upwards causing an unstable bed. In order to mitigate this issue a new strategy was tested where a set of large spherical particles were created on top of the meta-particles to apply a choke feeding pressure. The success of this strategy needs to be evaluated further as the interaction between the additional choke feed parti-cles and the meta-particles creates a bias in the simulation results.2.3. DEM post processing The particle size distribution of the surviving clusters of meta-particles has been estimated using the methodology described in Q