机械产品设计中的颗粒离散元仿真技术及实现
|
摘要
离散单元法是一种求解颗粒及散体物料动力学行为的数值方法。在颗粒制备与处理装置的结构设计与分析方面,颗粒离散元仿真技术得到了普遍的认可,并取得了一系列有价值的研究成果。与其它工程领域相比,针对机械产品的颗粒离散元仿真需要着重考虑并实现以下三个方面的技术问题：边界模型的表面形状、运动及磨损的描述问题；颗粒与复杂的边界模型间的接触判断问题,以及仿真软件的设计及实现问题。
首先,颗粒离散元仿真中的边界模型通常表示某个可运动的机械部件。边界模型具有特定的表面形状与结构,并按照既定的运转方式作刚体运动。利用基本的几何图元对边界模型的形体建模,虽然可以准确地表达某些具有规则形状的机械部件,但是对于复杂的边界模型而言,这样的建模方法显得不够灵活。
机械部件的运动可以通过速度合成定理进行描述。但是,对于沿特定的轨迹运动的机械部件,其运动参数的大小和方向将随时间不断改变。所以,需要研究更加合适的方法描述这类部件的运动形式。
机械部件的表面磨损是由大量颗粒频繁撞击和摩擦所造成的,它是机械产品设计中考虑的重要问题。基于颗粒离散元方法的表面磨损预测,主要是利用离散元仿真得到的微观数据定量地计算部件表面材料的磨损量,并以某种可视化的方法展现出磨损表面的几何特征。目前,相关文献对于这些问题的阐述很有限。
其次,散料处理机械通常涉及到复杂的受力条件。颗粒单元快速而频繁地碰撞机械部件的同时,单元的运动和受力方向在极短的时间内发生改变。离散元仿真采用接触判断算法捕捉颗粒单元与复杂的边界模型之间的碰撞,而通常接触判断算法是制约离散元仿真速度的最大的瓶颈之一。所以,有必要进一步改进和提高现有算法的执行效率,从而在整体上提高仿真计算的速度。
最后,各项离散元仿真技术需要整合到一套功能完备的仿真软件中来。一套通用性强的离散元仿真软件,可以让研究人员从繁重的程序开发工作中解脱出来,将主要精力投入到设计和实施各种数值实验、分析和解释计算结果等方面的工作中来。仿真软件需要提供方便快捷的前处理功能,还需要具备功能丰富的数据后处理功能,以便更好地揭示隐藏于数据背后的规律。然而,目前很少有文献资料系统而完整地说明颗粒离散元仿真软件的设计与实现方法。
本文从以下五个方面深入研究这些仿真技术问题的解决方案和实现方法。
第一,结合颗粒离散元仿真在散料处理机械产品设计与分析过程中的应用特点,归纳总结出离散元仿真应用过程中的三个主要技术问题。
第二,首先使用三角网格对边界模型进行几何建模,以便简化离散元仿真的建模过程；随后,基于这种三角网格边界建模方法,实现了边界模型的运动轨迹规划方法,并以物料挖掘的仿真算例验证了该方法的有效性；最后,研究了一种基于三角网格边界的表面磨损描述方法,该方法在相应的算例中很好地预测了边界模型的表面磨损特征。
第三,提出并实现了一种新的基于几何关系推理的接触判断算法。该算法改进了球形颗粒与复杂的三角网格边界间的相交检测方法；物料混合过程的仿真算例验证了该算法的有效性和稳定性。
第四,开发了一套三维颗粒离散元仿真软件,并以螺旋输送机的仿真算例验证了该仿真软件的有效性。
第五,以球磨机为例,详细地阐述了本文所研究的各项仿真技术在球磨机的工作参数设计和分析中的应用；分别从球磨机内部研磨介质的运动形态分析、磨机功率分析、磨机碰撞能量谱及能量分布,以及磨机衬板的表面磨损预测等几个方面,说明了颗粒离散元仿真在球磨机以及其它相关机械产品设计中的应用价值。
Discrete Element Method (DEM) is an effective numerical method for solving the dynamical problems of granular media and block systems under movable boundary conditions. DEM simulation has been widely applied to the fields of mechanical design for the particle preparation and processing equipment, and has achieved a serial of valuable research conclusions. Compared to its application in other engineering fields, the DEM simulation in the mechanical product design should specially consider the following problems and how to solve the problems.
Firstly, the boundary model usually represents a movable machine component in the DEM simulation. The boundary model occupies a spatial volume with a certain surface geometry, and moves as a rigid body in the prescribed manner. Although the regular boundary can be exactly described by using the elementary geometries, such as cuboids, tetrahedrons and cylinders, this representation method is not convenient enough to describe those boundary surface which have more complex shapes.
Generally, the velocity combination principle of the rigid body can specify the most motion patterns of boundary models. However, for those boundary models which have to continuously move along the predefined paths, the expression of this motion is not suitable due to the instantaneous variation of the kinematical parameters of the boundary models.
The surface wear caused by the highly frequent collisions between the particles and the boundary facets is an important problem in the fatigue failure analysis of components. The objective to predict the surface wear in the DEM simulation is that the volume removed due to the impacting and attrition during a collision should be quantitatively computed by statistics and data analysis from the results of the simulation, and the profile of the worn surfaces of the components should be visually demonstrated. However, these problems have been received limited attention in currently reported literature.
Secondly, most problems in mechanical engineering involve complex mechanics environment where a large number of particles impact the components rapidly and frequently and the directions of kinematic parameters and the collision forces of particles change in a very short time. A contact detection algorithm should accurately capture all kinds of collisions between particles and complex boundary models; meanwhile, a contact detection algorithm needs to have a lower time complexity in order to reduce the whole time consumption of the DEM simulation.
Thirdly, all the related implementation of the DEM simulation techniques should be delicately deployed in a simulation software. A well-designed DEM simulation software enables researchers to concentrate on designing numerical experiments, understanding and interpreting the simulation results, rather than struggling with the heavy programming work. The DEM simulation system should provide a serial of straightforward pre-processing functions and the integral data visualization tools for different problems in the mechanical product design and analysis. However, there is few reported literature to express the implementation of such simulation software.
This dissertation addresses the above three kinds of problems, and the research work mainly focus on the following five aspects.
(1) By studying various DEM application cases, three main problems on the DEM simulation applied in the course of design and analysis of the related mechanical products have been pointed out.
(2) The triangulated mesh is used here to represent the surface geometry of the boundary models. A trajectory planning method has been then completed to express the motion along with the paths, and this method is verified as an effective representation for this kind of motion pattern by a numerical experiment of excavating. At last, a novel wear prediction method based on the triangular mesh boundary has been established, by which the removed volume of the surface material is related to the impact energy, and the profile of the worn component can be reasonably predicted.
(3) A novel contact detection algorithm to find the contacts between spherical particles and triangulated mesh boundaries has been proposed. This algorithm uses the fixed grid subdivision method to search space neighbors for a particle element, and takes less check steps to clarify the contact information than the currently published the intersection check methods. Through simulation cases, the effectiveness and robustness of this algorithm has been verified.
(4) A suit of3D DEM simulation system has been developed and implemented. From the architecture aspect, the entire simulation system is divided into three functional modules. Then, the three modules have been implemented based on the object-oriented programming and the design patterns, respectively. The numerical case for a screw conveyor has been conducted to validate this simulation system.
(5) The above mentioned methods are employed in the DEM simulation application for tumbling ball mills. The numerical experiments have been conducted to analysis the motion pattern of the grinding media in a mill, to measure the power draw, the impact energy spectrum and the collision distribution, and to predict the profile of the worn liner. The results indicate that it is of benefit for the application of the DEM simulation to the related mechanical product design.
首先,颗粒离散元仿真中的边界模型通常表示某个可运动的机械部件。边界模型具有特定的表面形状与结构,并按照既定的运转方式作刚体运动。利用基本的几何图元对边界模型的形体建模,虽然可以准确地表达某些具有规则形状的机械部件,但是对于复杂的边界模型而言,这样的建模方法显得不够灵活。
机械部件的运动可以通过速度合成定理进行描述。但是,对于沿特定的轨迹运动的机械部件,其运动参数的大小和方向将随时间不断改变。所以,需要研究更加合适的方法描述这类部件的运动形式。
机械部件的表面磨损是由大量颗粒频繁撞击和摩擦所造成的,它是机械产品设计中考虑的重要问题。基于颗粒离散元方法的表面磨损预测,主要是利用离散元仿真得到的微观数据定量地计算部件表面材料的磨损量,并以某种可视化的方法展现出磨损表面的几何特征。目前,相关文献对于这些问题的阐述很有限。
其次,散料处理机械通常涉及到复杂的受力条件。颗粒单元快速而频繁地碰撞机械部件的同时,单元的运动和受力方向在极短的时间内发生改变。离散元仿真采用接触判断算法捕捉颗粒单元与复杂的边界模型之间的碰撞,而通常接触判断算法是制约离散元仿真速度的最大的瓶颈之一。所以,有必要进一步改进和提高现有算法的执行效率,从而在整体上提高仿真计算的速度。
最后,各项离散元仿真技术需要整合到一套功能完备的仿真软件中来。一套通用性强的离散元仿真软件,可以让研究人员从繁重的程序开发工作中解脱出来,将主要精力投入到设计和实施各种数值实验、分析和解释计算结果等方面的工作中来。仿真软件需要提供方便快捷的前处理功能,还需要具备功能丰富的数据后处理功能,以便更好地揭示隐藏于数据背后的规律。然而,目前很少有文献资料系统而完整地说明颗粒离散元仿真软件的设计与实现方法。
本文从以下五个方面深入研究这些仿真技术问题的解决方案和实现方法。
第一,结合颗粒离散元仿真在散料处理机械产品设计与分析过程中的应用特点,归纳总结出离散元仿真应用过程中的三个主要技术问题。
第二,首先使用三角网格对边界模型进行几何建模,以便简化离散元仿真的建模过程；随后,基于这种三角网格边界建模方法,实现了边界模型的运动轨迹规划方法,并以物料挖掘的仿真算例验证了该方法的有效性；最后,研究了一种基于三角网格边界的表面磨损描述方法,该方法在相应的算例中很好地预测了边界模型的表面磨损特征。
第三,提出并实现了一种新的基于几何关系推理的接触判断算法。该算法改进了球形颗粒与复杂的三角网格边界间的相交检测方法；物料混合过程的仿真算例验证了该算法的有效性和稳定性。
第四,开发了一套三维颗粒离散元仿真软件,并以螺旋输送机的仿真算例验证了该仿真软件的有效性。
第五,以球磨机为例,详细地阐述了本文所研究的各项仿真技术在球磨机的工作参数设计和分析中的应用；分别从球磨机内部研磨介质的运动形态分析、磨机功率分析、磨机碰撞能量谱及能量分布,以及磨机衬板的表面磨损预测等几个方面,说明了颗粒离散元仿真在球磨机以及其它相关机械产品设计中的应用价值。
Discrete Element Method (DEM) is an effective numerical method for solving the dynamical problems of granular media and block systems under movable boundary conditions. DEM simulation has been widely applied to the fields of mechanical design for the particle preparation and processing equipment, and has achieved a serial of valuable research conclusions. Compared to its application in other engineering fields, the DEM simulation in the mechanical product design should specially consider the following problems and how to solve the problems.
Firstly, the boundary model usually represents a movable machine component in the DEM simulation. The boundary model occupies a spatial volume with a certain surface geometry, and moves as a rigid body in the prescribed manner. Although the regular boundary can be exactly described by using the elementary geometries, such as cuboids, tetrahedrons and cylinders, this representation method is not convenient enough to describe those boundary surface which have more complex shapes.
Generally, the velocity combination principle of the rigid body can specify the most motion patterns of boundary models. However, for those boundary models which have to continuously move along the predefined paths, the expression of this motion is not suitable due to the instantaneous variation of the kinematical parameters of the boundary models.
The surface wear caused by the highly frequent collisions between the particles and the boundary facets is an important problem in the fatigue failure analysis of components. The objective to predict the surface wear in the DEM simulation is that the volume removed due to the impacting and attrition during a collision should be quantitatively computed by statistics and data analysis from the results of the simulation, and the profile of the worn surfaces of the components should be visually demonstrated. However, these problems have been received limited attention in currently reported literature.
Secondly, most problems in mechanical engineering involve complex mechanics environment where a large number of particles impact the components rapidly and frequently and the directions of kinematic parameters and the collision forces of particles change in a very short time. A contact detection algorithm should accurately capture all kinds of collisions between particles and complex boundary models; meanwhile, a contact detection algorithm needs to have a lower time complexity in order to reduce the whole time consumption of the DEM simulation.
Thirdly, all the related implementation of the DEM simulation techniques should be delicately deployed in a simulation software. A well-designed DEM simulation software enables researchers to concentrate on designing numerical experiments, understanding and interpreting the simulation results, rather than struggling with the heavy programming work. The DEM simulation system should provide a serial of straightforward pre-processing functions and the integral data visualization tools for different problems in the mechanical product design and analysis. However, there is few reported literature to express the implementation of such simulation software.
This dissertation addresses the above three kinds of problems, and the research work mainly focus on the following five aspects.
(1) By studying various DEM application cases, three main problems on the DEM simulation applied in the course of design and analysis of the related mechanical products have been pointed out.
(2) The triangulated mesh is used here to represent the surface geometry of the boundary models. A trajectory planning method has been then completed to express the motion along with the paths, and this method is verified as an effective representation for this kind of motion pattern by a numerical experiment of excavating. At last, a novel wear prediction method based on the triangular mesh boundary has been established, by which the removed volume of the surface material is related to the impact energy, and the profile of the worn component can be reasonably predicted.
(3) A novel contact detection algorithm to find the contacts between spherical particles and triangulated mesh boundaries has been proposed. This algorithm uses the fixed grid subdivision method to search space neighbors for a particle element, and takes less check steps to clarify the contact information than the currently published the intersection check methods. Through simulation cases, the effectiveness and robustness of this algorithm has been verified.
(4) A suit of3D DEM simulation system has been developed and implemented. From the architecture aspect, the entire simulation system is divided into three functional modules. Then, the three modules have been implemented based on the object-oriented programming and the design patterns, respectively. The numerical case for a screw conveyor has been conducted to validate this simulation system.
(5) The above mentioned methods are employed in the DEM simulation application for tumbling ball mills. The numerical experiments have been conducted to analysis the motion pattern of the grinding media in a mill, to measure the power draw, the impact energy spectrum and the collision distribution, and to predict the profile of the worn liner. The results indicate that it is of benefit for the application of the DEM simulation to the related mechanical product design.
引文
[1]徐芝纶.弹性力学[M].北京：高等教育出版社,2006.
[2]曾攀.有限元分析及应用[M].北京：清华大学出版社,2004.
[3]Goodman, R.E.. Methods of geological engineering in discontinuous rocks [M]. San Francisco:West Publishing Company,1976.
[4]Crouch, S.L.. Boundary Element Methods in Solid Mechanics:With Applications in Rock Mechanics and Geological Engineering [M]. London:George Allen & Unwin,1983.
[5]Cundall, P.A., Stack, O.D.L.. Discrete numerical model for granular assemblies [J]. Geotechnique,1979,29(1):47-65.
[6]Cundall, P.A., Fairhurst, C.. Correlation of numerical and physical models-an approach to the estimation of rock mass behaviour [J]. Computers and Geotechnics,1987,3(1):62-69.
[7]Starfield, A.M., Cundall, P.A.. Towards a methodology for rock mechanics modelling [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1988,25(3):99-106.
[8]孙其诚,王光谦.颗粒物质力学导论[M].北京：科学出版社,2009,11.
[9]王泳嘉,邢纪波.离散元法及其在岩石力学中的应用[M].沈阳：东北工学院出版社,1986.
[10]王泳嘉,刘国兴,邢纪波.离散元法在崩落法放矿中应用的研究[J].有色金属,1987(02)：20-26.
[11]王泳嘉,陶连金,邢纪波.近距离煤层开采相互作用的离散元模拟研究[J].东北大学学报,1997(04)：30-33.
[12]Jing, L., Stephansson,O. Fundamentals of Discrete Element Methods for Rock Engineering: Theory and Applications:Theory and Applications [M]. London:Elsevier Science,2007, 11.
[13]朱春明.模拟月壤土拱效应试验研究与三维离散元模拟[D].北京：中国地质大学,2010.
[14]Keppler, I., Failure analysis of pebble bed reactors during earthquake by discrete element method [J]. Nuclear Engineering and Design,2013(258):102-106.
[15]于建群.离散元法及其在农业机械工作部件研究与设计中的应用[J].农业工程学报,2005(05)：1-6.
[16]付宏.基于离散元法的玉米脱粒过程分析[J].吉林大学学报(工学版),2012(04)： 997-1002.
[17]Kremmer, M.. Multi-body dynamics simulation of seeds and grains in agricultural engineering applications by use of DEM [A], International Conference of Agricultural Engineering,2003:367-372.
[18]Langston, P.A.. Microstructural simulation and imaging of granular flows in two-and three-dimensional hoppers [J]. Powder Technology,1997,94(1):59-72.
[19]Langston, P.A., Tuziin, U., Heyes, D.M.. Discrete element simulation of granular flow in 2D and 3D hoppers:Dependence of discharge rate and wall stress on particle interactions [J]. Chemical Engineering Science,1995,50(6):967-987.
[20]Van Nierop, M.A.. A discrete element method investigation of the charge motion and power draw of an experimental two-dimensional mill [J]. International Journal of Mineral Processing,2001,61(2):77-92.
[21]Mishra, B.K., Rajamani, R.K.. The discrete element method for the simulation of ball mills. Applied Mathematical Modelling [J],1992,16(11):598-604.
[22]Cleary, P.W.. Predicting charge motion, power draw, segregation and wear in ball mills using discrete element methods. Minerals Engineering [J],1998,11(11):1061-1080.
[23]Cleary, P.W.. DEM simulation of industrial particle flows:case studies of dragline excavators, mixing in tumblers and centrifugal mills [J]. Powder Technology,2000, 109(1-3):83-104.
[24]Morrison, R.D., Cleary, P.W.. Towards a virtual comminution machine [J]. Minerals Engineering,2008,21(11):770-781.
[25]Cleary, P.W.. DEM prediction of industrial and geophysical particle flows [J]. Particuology, 2010,8(2):106-118.
[26]Han, K.. A combined finite/discrete element simulation of shot peening processes-Part I: studies on 2D interaction laws. Engineering Computations [J],2000,17(5):593-619.
[27]Han, K.. A combined finite/discrete element simulation of shot peening processes-Part II: 3D interaction laws [J]. Engineering Computations,2000,17(6-7):680-702.
[28]Fleissner, F., Gaugele, T., Eberhard, P.. Applications of the discrete element method in mechanical engineering [J]. Multibody System Dynamics,2007,18(1):81-94.
[29]Limtrakul, S.. Discrete particle simulation of solids motion in a gas-solid fluidized bed [J]. Chemical Engineering Science,2003,58(3-6):915-921.
[30]Hoffmann, R.. Hierarchical treecode for optimized collision checking in DEM simulations application on electrophotographic toner simulations [A], European Conference on Computational Mechanics Ⅲ, Springer Netherlands:139-139,2006.
[31]付宏,董劲男,于建群.基于CAD模型的离散元法边界建模方法[J].吉林大学学报(工学版),2005(06)：64-69.
[32]付宏.基于图元的三维离散元法边界建模方法[J].计算机集成制造系统,2008(12)：2328-2333.
[33]Munjiza, A., Andrews, K.. NBS contact detection algorithm for bodies of similar size [J]. International Journal for Numerical Methods in Engineering,1998,43(1):131-149.
[34]Perkins, E., Williams, J.R.. A fast contact detection algorithm insensitive to object sizes [J]. Engineering Computations,2001.18(1/2):48-62.
[35]Williams, J.R., Perkins, E., Cook, B.. A contact algorithm for partitioning arbitrary sized objects [J]. Engineering Computations,2004,21(2/3/4):235-248.
[36]Han, K., Feng, Y., Owen, D.. Performance comparisons of tree-based and cell-based contact detection algorithms [J]. Engineering Computations,2007,24(2):165-181.
[37]Mio, H., Cell optimization for fast contact detection in the discrete element method algorithm [J]. Advanced Powder Technology,2007,18(4):441-453.
[38]Munjiza, A., Rougier, E., John, N.. MR linear contact detection algorithm [J]. International Journal for Numerical Methods in Engineering,2006,66(1):46-71.
[39]Bonet, J., Peraire, J.. An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems [J]. International Journal for Numerical Methods in Engineering,1991,31(1):1-17.
[40]Feng, Y., Owen, D.. An augmented spatial digital tree algorithm for contact detection in computational mechanics [J]. International Journal for Numerical Methods in Engineering, 2002,55(2):159-176.
[41]Kremmer, M., Favier, J.F.. A method for representing boundaries in discrete element modelling-part Ⅰ:Geometry and contact detection [J]. International Journal for Numerical Methods in Engineering,2001,51(12):1407-1421.
[42]Su, J., Gu, Z., Xu, X.Y.. Discrete element simulation of particle flow in arbitrarily complex geometries [J]. Chemical Engineering Science,2011,66(23):6069-6088.
[43]Cundall, P.A.. Rational Design of Tunnel Supports:A Computer Model for Rock Mass Behavior Using Interactive Graphics for the Input and Output of Geometrical Data [A], DTIC Document,1974.
[44]Tang, S.K., Egan, G.K., Coulthard, M.A.. Parallelisation of a Distinct Element Stress Analysis Program [A], ASCE:770-777,1991.
[45]Cundall, P.A.. UDEC-A Generalised Distinct Element Program for Modelling Jointed Rock [A], DTIC Document,1980.
[46]Cundall, P.A., Hart, R.D.. Development of generalized 2-D and 3-D distinct element programs for modeling jointed rock [A], DTIC Document,1985.
[47]PFC-2D and PFC-3D Manuals, Itasca Consulting Group,1995.
[48]Hustrulid技术公司网站[EB/OL]. http://www.chutemaven.com/.
[49]Morton, D., Dunstall, S.. Using the Web to increase the availability of DEM-based mill modelling [J]. Minerals Engineering,2004,17(11):1199-1207.
[50]DEM-Solution软件及技术咨询公司网站[EB/OL]. http://www.dem-solutions.com/.
[51]Rockfield软件公司网站[EB/OL]. http://www.rockfield.co.uk/.
[52]Pasimodo软件网站[EB/OL]. http://www.itm.uni-stuttgart.de/research/pasimodo/pasimodoen.php.
[53]LTGGGHTS软件网站[EB/OL]. http://www.liggghts.com/.
[54]LMGC90软件网站[EB/OL]. http://www.lmgc.univ-montp2.fr/LMGC90/LMGC90/Welcome_%21.html.
[55]Yade软件网站[EB/OL]. https://yade-dem.org/wiki/Yade.
[56]王泳嘉,刘连峰.三维离散单元法软件系统TRUDEC的研制[J].岩石力学与工程学报,1996(03)：10-19.
[57]王泳嘉,宋文洲,赵艳娟.离散单元法软件系统2D-Block的现代化特点[J].岩石力学与工程学报,2000(S1)：1057-1060.
[58]刘凯欣,高凌天.离散元法在求解三维冲击动力学问题中的应用[J].固体力学学报,2004(02)：181-185.
[59]GDEM软件网站[EB/OL]. http://gdem-tech.com/.
[60]魏群.拱坝三维可视化设计软件的开发与应用[J].天津大学学报,2008(09)：1087-1090.
[61]杨全文,左树春,徐泳.颗粒离散元法的微机可视化程序设计[J].中国农业大学学报,2002(06)：10-15.
[62]颜辉.离散元法软件与CAD软件集成开发研究[J].现代情报,2007(09)：209-211.
[63]Gyenis, J.. Motionless Mixers in Bulk Solids Treatments-A Review [J]. Kona,2002,20: 9-23.
[64]Fernandez, J.W., Cleary, P.W., McBride, W.. Effect of screw design on hopper drawdown of spherical particles in a horizontal screw feeder [J]. Chemical Engineering Science,2011, 66(22):5585-5601.
[65]Shimizu, Y.. Numerical simulations of bulk handling in screw conveyors by three-dimensional DEM [A]. Massmin 2000, Proceedings. Vol.2000:887-892.
[66]Owen, P.J. Cleary, P.W.. Prediction of screw conveyor performance using the Discrete Element Method (DEM) [J]. Powder Technology,2009,193(3):274-288.
[67]Favier, J.. Industrial application of DEM:Opportunities and Challenges [R], UK,2008.
[68]Cleary, P.W., Sinnott, M.D.. Assessing mixing characteristics of particle-mixing and granulation devices [J]. Particuology,2008,6(6):419-444.
[69]Li, J., Discrete particle motion on sieves-a numerical study using the DEM simulation [J]. Powder Technology,2003,133(1):190-202.
[70]Cleary, P.W., Sinnott, M.D., Morrison, R.D.. Separation performance of double deck banana screens-Part 1:Flow and separation for different accelerations [J]. Minerals Engineering,2009,22(14):1218-1229.
[71]Cleary, P.W., Sinnott, M.D., Morrison, R.D.. Separation performance of double deck banana screens - Part 2:Quantitative predictions [J]. Minerals Engineering,2009,22(14): 1230-1244.
[72]Dong, K., Yu, A., Brake, I.. DEM simulation of particle flow on a multi-deck banana screen [J]. Minerals Engineering,2009,22(11):910-920.
[73]Mishra, B.K., Rajamai, R.K.. Simulation of charge motion in ball mills. Part 2:numerical simulations [J]. International Journal of Mineral Processing,1994,40(3-4):187-197.
[74]Mishra, B.K. and Rajamani, R.K.. Simulation of charge motion in ball mills. Part 1: experimental verifications [J]. International Journal of Mineral Processing,1994,40(3-4): 171-186.
[75]Mishra, B.K. and Ahuja, R.. Cascading mill:A phenomenological design for improved grinding [J]. Minerals Engineering,1998,11(1):77-84.
[76]Rajamani, R.K.. Discrete element analysis of tumbling mills [J]. Powder Technology,2000, 109(1-3):105-112.
[77]Rajamani, R.K., Songfack, P., Mishra, B.K.. Impact energy spectra of tumbling mills [J]. Powder Technology,2000,108(2-3):116-121.
[78]Abd El-Rahman, M.K., B.K. Mishra, and R.K. Rajamani, Industrial tumbling mill power prediction using the discrete element method. Minerals Engineering,2001,14(10): 1321-1328.
[79]Mishra, B.K.. A review of computer simulation of tumbling mills by the discrete element method:Part Ⅰ—Contact mechanics [J]. International Journal of Mineral Processing,2003, 71(1-4):73-93.
[80]Mishra, B.K.. A review of computer simulation of tumbling mills by the discrete element method:Part Ⅱ—Practical applications [J]. International Journal of Mineral Processing, 2003,71(1-4):95-112.
[81]Moys, M.H., Smit, I., Stange, W.. The measurement of forces exerted by the load on liners in rotary mills (wet and dry) [J]. International Journal of Mineral Processing,1996, 44-45(0):383-393.
[82]Moys, M.H., Van Nierop, M.A., Smit, I.. Progress in measuring and modelling load behaviour in pilot and industrial mills [J]. Minerals Engineering,1996,9(12):1201-1214.
[83]Van Nierop, M.A., Moys, M.H.. Measurement of load behaviour in an industrial grinding mill [J]. Control Engineering Practice,1997,5(2):257-262.
[84]Moys, M.H.. Validation of the discrete element method (DEM) by comparing predicted load behaviour of a grinding mill with measured data, in Developments in Mineral Processing [M]. Elsevier:C339-44,2000.
[85]Dong, H., Moys, M.H.. A technique to measure velocities of a ball moving in a tumbling mill and its applications [J]. Minerals Engineering,2001,14(8):841-850.
[86]Monama, G.M., Moys, M.H.. DEM modelling of the dynamics of mill startup [J]. Minerals Engineering,2002,15(7):487-492.
[87]Van Nierop, M.A., Moys, M.H., Axial mixing of slurry in an autogenous grinding mill [J]. International Journal of Mineral Processing,2002,65(3-4):151-164.
[88]Hlungwani, O.. Further validation of DEM modeling of milling:effects of liner profile and mill speed [J]. Minerals Engineering,2003,16(10):993-998.
[89]Kalala, J.T., Bwalya, M., Moys, M.H.. Discrete element method (DEM) modelling of evolving mill liner profiles due to wear. Part Ⅱ. Industrial case study [J]. Minerals Engineering,2005,18(15):1392-1397.
[90]Geary, P.W., Morrisson, R., Morrell, S.. Comparison of DEM and experiment for a scale model SAG mill [J]. International Journal of Mineral Processing,2003,68(1-4):129-165.
[91]Morrison, R.D., Cleary, P.W.. Using DEM to model ore breakage within a pilot scale SAG mill [J]. Minerals Engineering,2004,17(11-12):1117-1124.
[92]Sinnott, M.D., Cleary, P.W., Morrison, R.D.. Is media shape important for grinding performance in stirred mills [J]. Minerals Engineering,2011,24(2):138-151.
[93]Cleary, P.W., Hoyer, D.. Centrifugal mill charge motion and power draw:comparison of DEM predictions with experiment [J]. International Journal of Mineral Processing,2000, 59(2):131-148.
[94]Cleary, P.W.. Recent advances in dem modelling of tumbling mills [J]. Minerals Engineering,2001,14(10):1295-1319.
[95]曹雪丽.介质充填率和料球比对球磨机磨矿效果的影响[D].昆明：昆明理工大学,2011.
[96]田瑞霞,焦红光,白璟宇.离散元法在矿物加工工程中的应用现状[J].选煤技术,2012(01)：72-76.
[97]赵魏.离散元法在磨机设计中的应用[J].矿山机械,2013(02)：66-70.
[98]Geary, P.W.. Large scale industrial DEM modelling [J]. Engineering Computations,2004, 21(2-4):169-204.
[99]Cleary, P.W.. Industrial particle flow modelling using discrete element method [J]. Engineering Computations,2009,26(6):698-743.
[100]Kyle, J., Costello, M.. Comparison of measured and simulated motion of a scaled dragline excavation system [J]. Mathematical and computer modelling,2006,44(9):816-833.
[101]Coetzee, C., Els, D.. Calibration of discrete element parameters and the modelling of silo discharge and bucket filling [J]. Computers and Electronics in Agriculture,2009,65(2): 198-212.
[102]Coetzee, C., Els, D., Dymond, G.. Discrete element parameter calibration and the modelling of dragline bucket filling [J]. Journal of Terramechanics,2010,47(1):33-44.
[103]Tsuji, T., Yabumoto, K., Tanaka, T.. Spontaneous structures in three-dimensional bubbling gas-fluidized bed by parallel DEM-CFD coupling simulation [J]. Powder Technology, 2008,184(2):132-140.
[104]Kremmer, M., Favier, J.F.. A method for representing boundaries in discrete element modelling-part Ⅱ:Kinematics [J]. International Journal for Numerical Methods in Engineering,2001,51(12):1423-1436.
[105]三一重工股份有限公司网站[EB/OL]. http://product.sanygroup.com/products/zh-cn/excavator/.
[106]小原孝之.材料拌和离散元模拟系统的开发与应用[D].北京：清华大学,2007.
[107]Johnson, K.L.. Contact Mechanics [M]. UK:Cambridge University Press,1985.
[108]江旭昌.管磨机[M].北京：中国建材工业出版社,1992.
[2]曾攀.有限元分析及应用[M].北京：清华大学出版社,2004.
[3]Goodman, R.E.. Methods of geological engineering in discontinuous rocks [M]. San Francisco:West Publishing Company,1976.
[4]Crouch, S.L.. Boundary Element Methods in Solid Mechanics:With Applications in Rock Mechanics and Geological Engineering [M]. London:George Allen & Unwin,1983.
[5]Cundall, P.A., Stack, O.D.L.. Discrete numerical model for granular assemblies [J]. Geotechnique,1979,29(1):47-65.
[6]Cundall, P.A., Fairhurst, C.. Correlation of numerical and physical models-an approach to the estimation of rock mass behaviour [J]. Computers and Geotechnics,1987,3(1):62-69.
[7]Starfield, A.M., Cundall, P.A.. Towards a methodology for rock mechanics modelling [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1988,25(3):99-106.
[8]孙其诚,王光谦.颗粒物质力学导论[M].北京：科学出版社,2009,11.
[9]王泳嘉,邢纪波.离散元法及其在岩石力学中的应用[M].沈阳：东北工学院出版社,1986.
[10]王泳嘉,刘国兴,邢纪波.离散元法在崩落法放矿中应用的研究[J].有色金属,1987(02)：20-26.
[11]王泳嘉,陶连金,邢纪波.近距离煤层开采相互作用的离散元模拟研究[J].东北大学学报,1997(04)：30-33.
[12]Jing, L., Stephansson,O. Fundamentals of Discrete Element Methods for Rock Engineering: Theory and Applications:Theory and Applications [M]. London:Elsevier Science,2007, 11.
[13]朱春明.模拟月壤土拱效应试验研究与三维离散元模拟[D].北京：中国地质大学,2010.
[14]Keppler, I., Failure analysis of pebble bed reactors during earthquake by discrete element method [J]. Nuclear Engineering and Design,2013(258):102-106.
[15]于建群.离散元法及其在农业机械工作部件研究与设计中的应用[J].农业工程学报,2005(05)：1-6.
[16]付宏.基于离散元法的玉米脱粒过程分析[J].吉林大学学报(工学版),2012(04)： 997-1002.
[17]Kremmer, M.. Multi-body dynamics simulation of seeds and grains in agricultural engineering applications by use of DEM [A], International Conference of Agricultural Engineering,2003:367-372.
[18]Langston, P.A.. Microstructural simulation and imaging of granular flows in two-and three-dimensional hoppers [J]. Powder Technology,1997,94(1):59-72.
[19]Langston, P.A., Tuziin, U., Heyes, D.M.. Discrete element simulation of granular flow in 2D and 3D hoppers:Dependence of discharge rate and wall stress on particle interactions [J]. Chemical Engineering Science,1995,50(6):967-987.
[20]Van Nierop, M.A.. A discrete element method investigation of the charge motion and power draw of an experimental two-dimensional mill [J]. International Journal of Mineral Processing,2001,61(2):77-92.
[21]Mishra, B.K., Rajamani, R.K.. The discrete element method for the simulation of ball mills. Applied Mathematical Modelling [J],1992,16(11):598-604.
[22]Cleary, P.W.. Predicting charge motion, power draw, segregation and wear in ball mills using discrete element methods. Minerals Engineering [J],1998,11(11):1061-1080.
[23]Cleary, P.W.. DEM simulation of industrial particle flows:case studies of dragline excavators, mixing in tumblers and centrifugal mills [J]. Powder Technology,2000, 109(1-3):83-104.
[24]Morrison, R.D., Cleary, P.W.. Towards a virtual comminution machine [J]. Minerals Engineering,2008,21(11):770-781.
[25]Cleary, P.W.. DEM prediction of industrial and geophysical particle flows [J]. Particuology, 2010,8(2):106-118.
[26]Han, K.. A combined finite/discrete element simulation of shot peening processes-Part I: studies on 2D interaction laws. Engineering Computations [J],2000,17(5):593-619.
[27]Han, K.. A combined finite/discrete element simulation of shot peening processes-Part II: 3D interaction laws [J]. Engineering Computations,2000,17(6-7):680-702.
[28]Fleissner, F., Gaugele, T., Eberhard, P.. Applications of the discrete element method in mechanical engineering [J]. Multibody System Dynamics,2007,18(1):81-94.
[29]Limtrakul, S.. Discrete particle simulation of solids motion in a gas-solid fluidized bed [J]. Chemical Engineering Science,2003,58(3-6):915-921.
[30]Hoffmann, R.. Hierarchical treecode for optimized collision checking in DEM simulations application on electrophotographic toner simulations [A], European Conference on Computational Mechanics Ⅲ, Springer Netherlands:139-139,2006.
[31]付宏,董劲男,于建群.基于CAD模型的离散元法边界建模方法[J].吉林大学学报(工学版),2005(06)：64-69.
[32]付宏.基于图元的三维离散元法边界建模方法[J].计算机集成制造系统,2008(12)：2328-2333.
[33]Munjiza, A., Andrews, K.. NBS contact detection algorithm for bodies of similar size [J]. International Journal for Numerical Methods in Engineering,1998,43(1):131-149.
[34]Perkins, E., Williams, J.R.. A fast contact detection algorithm insensitive to object sizes [J]. Engineering Computations,2001.18(1/2):48-62.
[35]Williams, J.R., Perkins, E., Cook, B.. A contact algorithm for partitioning arbitrary sized objects [J]. Engineering Computations,2004,21(2/3/4):235-248.
[36]Han, K., Feng, Y., Owen, D.. Performance comparisons of tree-based and cell-based contact detection algorithms [J]. Engineering Computations,2007,24(2):165-181.
[37]Mio, H., Cell optimization for fast contact detection in the discrete element method algorithm [J]. Advanced Powder Technology,2007,18(4):441-453.
[38]Munjiza, A., Rougier, E., John, N.. MR linear contact detection algorithm [J]. International Journal for Numerical Methods in Engineering,2006,66(1):46-71.
[39]Bonet, J., Peraire, J.. An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems [J]. International Journal for Numerical Methods in Engineering,1991,31(1):1-17.
[40]Feng, Y., Owen, D.. An augmented spatial digital tree algorithm for contact detection in computational mechanics [J]. International Journal for Numerical Methods in Engineering, 2002,55(2):159-176.
[41]Kremmer, M., Favier, J.F.. A method for representing boundaries in discrete element modelling-part Ⅰ:Geometry and contact detection [J]. International Journal for Numerical Methods in Engineering,2001,51(12):1407-1421.
[42]Su, J., Gu, Z., Xu, X.Y.. Discrete element simulation of particle flow in arbitrarily complex geometries [J]. Chemical Engineering Science,2011,66(23):6069-6088.
[43]Cundall, P.A.. Rational Design of Tunnel Supports:A Computer Model for Rock Mass Behavior Using Interactive Graphics for the Input and Output of Geometrical Data [A], DTIC Document,1974.
[44]Tang, S.K., Egan, G.K., Coulthard, M.A.. Parallelisation of a Distinct Element Stress Analysis Program [A], ASCE:770-777,1991.
[45]Cundall, P.A.. UDEC-A Generalised Distinct Element Program for Modelling Jointed Rock [A], DTIC Document,1980.
[46]Cundall, P.A., Hart, R.D.. Development of generalized 2-D and 3-D distinct element programs for modeling jointed rock [A], DTIC Document,1985.
[47]PFC-2D and PFC-3D Manuals, Itasca Consulting Group,1995.
[48]Hustrulid技术公司网站[EB/OL]. http://www.chutemaven.com/.
[49]Morton, D., Dunstall, S.. Using the Web to increase the availability of DEM-based mill modelling [J]. Minerals Engineering,2004,17(11):1199-1207.
[50]DEM-Solution软件及技术咨询公司网站[EB/OL]. http://www.dem-solutions.com/.
[51]Rockfield软件公司网站[EB/OL]. http://www.rockfield.co.uk/.
[52]Pasimodo软件网站[EB/OL]. http://www.itm.uni-stuttgart.de/research/pasimodo/pasimodoen.php.
[53]LTGGGHTS软件网站[EB/OL]. http://www.liggghts.com/.
[54]LMGC90软件网站[EB/OL]. http://www.lmgc.univ-montp2.fr/LMGC90/LMGC90/Welcome_%21.html.
[55]Yade软件网站[EB/OL]. https://yade-dem.org/wiki/Yade.
[56]王泳嘉,刘连峰.三维离散单元法软件系统TRUDEC的研制[J].岩石力学与工程学报,1996(03)：10-19.
[57]王泳嘉,宋文洲,赵艳娟.离散单元法软件系统2D-Block的现代化特点[J].岩石力学与工程学报,2000(S1)：1057-1060.
[58]刘凯欣,高凌天.离散元法在求解三维冲击动力学问题中的应用[J].固体力学学报,2004(02)：181-185.
[59]GDEM软件网站[EB/OL]. http://gdem-tech.com/.
[60]魏群.拱坝三维可视化设计软件的开发与应用[J].天津大学学报,2008(09)：1087-1090.
[61]杨全文,左树春,徐泳.颗粒离散元法的微机可视化程序设计[J].中国农业大学学报,2002(06)：10-15.
[62]颜辉.离散元法软件与CAD软件集成开发研究[J].现代情报,2007(09)：209-211.
[63]Gyenis, J.. Motionless Mixers in Bulk Solids Treatments-A Review [J]. Kona,2002,20: 9-23.
[64]Fernandez, J.W., Cleary, P.W., McBride, W.. Effect of screw design on hopper drawdown of spherical particles in a horizontal screw feeder [J]. Chemical Engineering Science,2011, 66(22):5585-5601.
[65]Shimizu, Y.. Numerical simulations of bulk handling in screw conveyors by three-dimensional DEM [A]. Massmin 2000, Proceedings. Vol.2000:887-892.
[66]Owen, P.J. Cleary, P.W.. Prediction of screw conveyor performance using the Discrete Element Method (DEM) [J]. Powder Technology,2009,193(3):274-288.
[67]Favier, J.. Industrial application of DEM:Opportunities and Challenges [R], UK,2008.
[68]Cleary, P.W., Sinnott, M.D.. Assessing mixing characteristics of particle-mixing and granulation devices [J]. Particuology,2008,6(6):419-444.
[69]Li, J., Discrete particle motion on sieves-a numerical study using the DEM simulation [J]. Powder Technology,2003,133(1):190-202.
[70]Cleary, P.W., Sinnott, M.D., Morrison, R.D.. Separation performance of double deck banana screens-Part 1:Flow and separation for different accelerations [J]. Minerals Engineering,2009,22(14):1218-1229.
[71]Cleary, P.W., Sinnott, M.D., Morrison, R.D.. Separation performance of double deck banana screens - Part 2:Quantitative predictions [J]. Minerals Engineering,2009,22(14): 1230-1244.
[72]Dong, K., Yu, A., Brake, I.. DEM simulation of particle flow on a multi-deck banana screen [J]. Minerals Engineering,2009,22(11):910-920.
[73]Mishra, B.K., Rajamai, R.K.. Simulation of charge motion in ball mills. Part 2:numerical simulations [J]. International Journal of Mineral Processing,1994,40(3-4):187-197.
[74]Mishra, B.K. and Rajamani, R.K.. Simulation of charge motion in ball mills. Part 1: experimental verifications [J]. International Journal of Mineral Processing,1994,40(3-4): 171-186.
[75]Mishra, B.K. and Ahuja, R.. Cascading mill:A phenomenological design for improved grinding [J]. Minerals Engineering,1998,11(1):77-84.
[76]Rajamani, R.K.. Discrete element analysis of tumbling mills [J]. Powder Technology,2000, 109(1-3):105-112.
[77]Rajamani, R.K., Songfack, P., Mishra, B.K.. Impact energy spectra of tumbling mills [J]. Powder Technology,2000,108(2-3):116-121.
[78]Abd El-Rahman, M.K., B.K. Mishra, and R.K. Rajamani, Industrial tumbling mill power prediction using the discrete element method. Minerals Engineering,2001,14(10): 1321-1328.
[79]Mishra, B.K.. A review of computer simulation of tumbling mills by the discrete element method:Part Ⅰ—Contact mechanics [J]. International Journal of Mineral Processing,2003, 71(1-4):73-93.
[80]Mishra, B.K.. A review of computer simulation of tumbling mills by the discrete element method:Part Ⅱ—Practical applications [J]. International Journal of Mineral Processing, 2003,71(1-4):95-112.
[81]Moys, M.H., Smit, I., Stange, W.. The measurement of forces exerted by the load on liners in rotary mills (wet and dry) [J]. International Journal of Mineral Processing,1996, 44-45(0):383-393.
[82]Moys, M.H., Van Nierop, M.A., Smit, I.. Progress in measuring and modelling load behaviour in pilot and industrial mills [J]. Minerals Engineering,1996,9(12):1201-1214.
[83]Van Nierop, M.A., Moys, M.H.. Measurement of load behaviour in an industrial grinding mill [J]. Control Engineering Practice,1997,5(2):257-262.
[84]Moys, M.H.. Validation of the discrete element method (DEM) by comparing predicted load behaviour of a grinding mill with measured data, in Developments in Mineral Processing [M]. Elsevier:C339-44,2000.
[85]Dong, H., Moys, M.H.. A technique to measure velocities of a ball moving in a tumbling mill and its applications [J]. Minerals Engineering,2001,14(8):841-850.
[86]Monama, G.M., Moys, M.H.. DEM modelling of the dynamics of mill startup [J]. Minerals Engineering,2002,15(7):487-492.
[87]Van Nierop, M.A., Moys, M.H., Axial mixing of slurry in an autogenous grinding mill [J]. International Journal of Mineral Processing,2002,65(3-4):151-164.
[88]Hlungwani, O.. Further validation of DEM modeling of milling:effects of liner profile and mill speed [J]. Minerals Engineering,2003,16(10):993-998.
[89]Kalala, J.T., Bwalya, M., Moys, M.H.. Discrete element method (DEM) modelling of evolving mill liner profiles due to wear. Part Ⅱ. Industrial case study [J]. Minerals Engineering,2005,18(15):1392-1397.
[90]Geary, P.W., Morrisson, R., Morrell, S.. Comparison of DEM and experiment for a scale model SAG mill [J]. International Journal of Mineral Processing,2003,68(1-4):129-165.
[91]Morrison, R.D., Cleary, P.W.. Using DEM to model ore breakage within a pilot scale SAG mill [J]. Minerals Engineering,2004,17(11-12):1117-1124.
[92]Sinnott, M.D., Cleary, P.W., Morrison, R.D.. Is media shape important for grinding performance in stirred mills [J]. Minerals Engineering,2011,24(2):138-151.
[93]Cleary, P.W., Hoyer, D.. Centrifugal mill charge motion and power draw:comparison of DEM predictions with experiment [J]. International Journal of Mineral Processing,2000, 59(2):131-148.
[94]Cleary, P.W.. Recent advances in dem modelling of tumbling mills [J]. Minerals Engineering,2001,14(10):1295-1319.
[95]曹雪丽.介质充填率和料球比对球磨机磨矿效果的影响[D].昆明：昆明理工大学,2011.
[96]田瑞霞,焦红光,白璟宇.离散元法在矿物加工工程中的应用现状[J].选煤技术,2012(01)：72-76.
[97]赵魏.离散元法在磨机设计中的应用[J].矿山机械,2013(02)：66-70.
[98]Geary, P.W.. Large scale industrial DEM modelling [J]. Engineering Computations,2004, 21(2-4):169-204.
[99]Cleary, P.W.. Industrial particle flow modelling using discrete element method [J]. Engineering Computations,2009,26(6):698-743.
[100]Kyle, J., Costello, M.. Comparison of measured and simulated motion of a scaled dragline excavation system [J]. Mathematical and computer modelling,2006,44(9):816-833.
[101]Coetzee, C., Els, D.. Calibration of discrete element parameters and the modelling of silo discharge and bucket filling [J]. Computers and Electronics in Agriculture,2009,65(2): 198-212.
[102]Coetzee, C., Els, D., Dymond, G.. Discrete element parameter calibration and the modelling of dragline bucket filling [J]. Journal of Terramechanics,2010,47(1):33-44.
[103]Tsuji, T., Yabumoto, K., Tanaka, T.. Spontaneous structures in three-dimensional bubbling gas-fluidized bed by parallel DEM-CFD coupling simulation [J]. Powder Technology, 2008,184(2):132-140.
[104]Kremmer, M., Favier, J.F.. A method for representing boundaries in discrete element modelling-part Ⅱ:Kinematics [J]. International Journal for Numerical Methods in Engineering,2001,51(12):1423-1436.
[105]三一重工股份有限公司网站[EB/OL]. http://product.sanygroup.com/products/zh-cn/excavator/.
[106]小原孝之.材料拌和离散元模拟系统的开发与应用[D].北京：清华大学,2007.
[107]Johnson, K.L.. Contact Mechanics [M]. UK:Cambridge University Press,1985.
[108]江旭昌.管磨机[M].北京：中国建材工业出版社,1992.