铝型材挤压非正交网格有限体积数值模拟关键技术研究
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摘要
随着我国国民经济的快速发展和人民生活水平的迅速提高,铝合金挤压型材在生产和生活中得到了广泛应用。铝型材挤压模具是实现型材生产的关键技术装备,目前我国型材挤压模具的设计主要依赖类比设计和经验设计方法,所设计的模具必须经过反复的试模和修模才能满足工艺要求。这种依赖经验设计和试模返修的传统生产模式已不能满足铝型材工业快速发展的需要,迫切需要科学的设计分析工具,从而使铝型材挤压模具的设计由经验设计上升到科学设计。计算机数值模拟技术已经成为材料成形过程工艺与模具设计的有力工具,铝型材挤压成形属于剧烈塑性大变形过程,常规分析方法往往不能对其进行有效分析。因此,发展适合于剧烈大变形的塑性变形分析理论模型及其数值计算方法,研究铝型材挤压成形过程中的金属流动规律以及模具结构参数和工艺参数对型材质量的影响规律,对挤压工艺和模具的合理设计、减少试模时间和提高型材质量都具有十分重要的意义。
有限元法在金属塑性成形数值模拟中应用广泛,但在模拟变形量极大的挤压过程时却遇到了瓶颈:网格易发生严重畸变,需要不断重划网格,甚至无法将模拟进行下去。有限体积法导出的离散方程具有良好的守恒性,而且离散方程系数物理意义明确,计算量相对较小,是目前计算流体力学中应用最为广泛的一种方法,其突出的优点是所采用的欧拉网格是背景网格,不随材料一起运动,网格在模拟过程中不发生畸变,避开了网格再划分问题,因而可以更好地模拟铝型材挤压这类大变形问题。目前研究人员使用的有限体积法软件多为通用软件,没有考虑铝型材挤压工艺的特点,同时由于有限体积法数值模拟理论及其关键技术在塑性成形中的应用尚未完善,所以出现了模拟时间过长、所挤出件表面质量不好等一系列问题,不能有效指导铝型材的挤压工艺与模具设计。
本文旨在根据铝合金材料的特性及铝型材挤压过程材料变形机理、模具结构、工艺条件等,将计算流体力学中广泛应用的有限体积法引入到塑性成形领域,建立一种高效、灵活、可靠的铝型材挤压成形过程数值模拟方法及其关键技术,开发相应的模拟分析系统,重点实现大挤压比薄壁型材挤压、具有流动再分配作用的导流模挤压、具有复杂模具结构和复杂流动规律的空心壁板型材平面分流模挤压等挤压过程的非正交网格有限体积法数值模拟,根据获得的速度场、应力场、应变场等场量分布规律实现模具结构和工艺参数的优化,为铝型材制造提供理论指导。
针对铝型材挤压过程数值模拟现状及存在的问题,将适合大变形问题的有限体积法引入塑性成形领域,研究了有限体积法的基本理论,给出了有限体积法的基本控制方程和有限体积网格的构成特点。研究了控制方程的离散方法,讨论了有限体积法中各种常用的插值格式。研究了三维非稳态问题中的时间积分方案和控制方程的离散过程。介绍了有限体积法中变量的存储方式,深入研究了基于压力速度耦合求解的SIMPLE算法的实施过程。
研究了铝合金挤压过程的模具结构、工艺条件、材料变形机理和流动特点,铝合金材料的力学性能特点和本构关系。应用刚(粘)塑性模型,忽略材料的弹性变形,将高温下的铝合金材料视为一种刚(粘)塑性、各向同性、不可压缩的非牛顿流体。研究了铝合金材料变形过程中的动力粘度变化与应力、应变速率及温度的关系,建立了动力粘度方程,为将有限体积法引入铝合金型材挤压等塑性成形领域奠定基础。
结合铝型材挤压过程的工艺特点和有限体积法基本理论,研究建立了铝型材挤压过程非正交网格有限体积法数学模型。针对有限体积法中传统的正交结构网格对不规则区域的适应性差和难于施加边界条件的缺点,采用非正交网格划分不规则计算区域,实现了对曲面边界的准确拟合,更易于合理地施加边界条件;将控制方程采用直角坐标形式直接在非正交网格上离散,避免了适体坐标法中复杂的坐标变换过程;研究了非正交网格的特点及网格的非正交性带来的网格中心节点连线不垂直于界面和不通过界面中心点的问题,研究了非正交网格上控制方程的离散格式,推导建立了非正交网格上三维非稳态问题离散方程,消除了网格非正交性带来的误差:针对基于交错网格的SIMPLE算法在非正交网格上难于实现的问题,推导建立了基于非正交同位网格的SIMPLE算法,采用延迟修正方法处理界面插值,引入相邻节点压力差,解决了同位网格SIMPLE算法的压力震荡无法检测的问题;采用二次压力修正方法,解决了网格的非正交性带来的压力修正方程无法写成通用离散形式的问题;针对铝合金型材挤压过程的变形工艺特点和金属流动规律,建立了非正交网格有限体积法模拟铝型材挤压过程的初始条件和边界条件;基于铝型材挤压非正交网格有限体积法数学模型,进行了系统开发,给出了模拟分析步骤和程序流程。
研究建立了三维非稳态铝型材挤压非正交网格有限体积法的关键技术。研究建立了非正交同位网格的节点编号和网格信息的数据存储。建立了非正交网格上摩擦边界的施加方法;建立了非正交网格上自由表面追踪的VOF方法,针对网格的非正交性,改善了流体体积函数的计算公式,提出了一种简单的流体方位确定方法,便于自由表面方向的确定。研究了非正交网格有限体积法所形成的代数方程组的特点和数值求解方法、内部迭代和外部迭代的收敛准则、时间步长的自动调整关键技术。根据以上关键技术,进一步完善了铝型材挤压非正交网格有限体积法模拟分析程序。
针对空心铝型材挤压过程,建立了块结构化非正交网格有限体积法数值模拟关键技术。研究建立了块结构化网格的块分界面数据结构;研究了块结构化网格有限体积法的求解方式,建立了联合整体求解的强隐方法;实现了块与块之间的界面信息传递;研究了VOF方法在块界面处的处理方法,建立了块结构化非正交网格上自由表面追踪的VOF方法。基于以上关键技术,进一步开发了铝型材挤压块结构化非正交网格有限体积法模拟分析程序,实现了空心铝型材平面分流模挤压过程数值模拟分析。
对所建立的数学模型、关键技术及其所开发的数值模拟系统进行了一系列算例验证,包括与有限元软件Deform、有限体积法软件SuperForge等计算结果的对比验证和试验验证。通过对比分析,表明本文建立的铝型材挤压有限体积法数值模拟数学模型正确、高效,特别适用于大变形挤压过程的数值模拟分析。利用所开发系统,实现了大变形薄壁型材导流模挤压,空心型材平面分流模具挤压等挤压过程的数值模拟分析,进一步研究模具结构对金属流动的影响,并根据模拟结果优化模具结构,为实践提供理论指导。
With the fast development of national economy and people's living level, aluminum profile products are getting wider employment in production and living fields. Extrusion die is the key equipment of aluminum profile extrusion production. At present, design of profile extrusion die is mainly based on engineering analogy and experience accumulation in our nation, the designed die has to be tested and repaired frequently in order to adjust process parameters. The traditional production mode which depend on experimental design, die testing and repairing has been not satisfied the rapid development of aluminum profile industry. The scientific design and analysis tools are urgently needed to develop the design of aluminum profile extrusion die from experienced design up to scientific design. Computational numerical simulation has been a powerful tool for the die and process design of material deformation process. Aluminum profile extrusion process is the large deformation process. It usually can not be effectively analyzed by conventional analysis method. Therefore, developing the theoretical model and numerical calculation method to suit severe plastic deformation process, and researching the flowing law of metals and the effect of relative parameters on quality of profile in aluminum profile extrusion process has a great significance on reasonable design of extrusion process and die structure, reducing testing time of die, and improving quality of profile.
Finite element method (FEM) is widely used in numerical simulation of metal plastic forming process, but it has a big problem in simulating extrusion process with severe deformation: the mesh is easily distorted and need to be remeshed frequently, which sometimes cause the simulation even impossible to go on. Finite volume method (FVM) is the most popular method used in computational fluid dynamics at present. Its discrete equations have good conservation and clear physical meaning, and its computational cost is relatively small. The prominent advantage of FVM is that the Euler grids employed by this method is the background grids which don't move with the materials and don't be distorted. So FVM is more suitable for the large deformation problems such as aluminum extrusion process because the grids can avoid to be remeshed. At present, FVM software used by researchers is mainly the general-purpose software, which doesn't consider the process characteristics of aluminum extrusion process. At the same time, the theories and key technologies of FVM numerical simulation of plastic deformation process have not been perfect yet. There are some problems such as longer time cost, lower surface quality and so on. These problems cause these FVM software can not guide the process and die design of aluminum profile extrusion process effectively.
This paper is aimed to introduce FVM which is widely used in computational fluid dynamics into plastic deformation process based on characteristics of aluminum alloy and deformation mechanism, die structure, process conditions and so on of aluminum extrusion process, establish a efficient, flexible and stable numerical simulation method and its key technologies of aluminum profile extrusion process, then develop the numerical analysis system, primarily realize the non-orthogonal grids based FVM simulation of extrusion process, including the thin walled profile extrusion process with the large reduction, the pocket die extrusion process with effect on redistribution of flow, the hollow profile porthole die extrusion process with complex die structures and flow patterns, and so on. Then optimize the die structure and process parameters based on obtained velocity fields, stress fields, strain fields and so on, and provide the theoretical guidance of profile extrusion process.
Aiming at the research status and mainly existing problems of numerical simulation of aluminum extrusion process, FVM method which is suitable for large deformation problems is introduced into the plastic deformation field. The base theories of FVM are researched, the governing equations and grid character of FVM are given. The discrete methods of governing equations are researched, and the common used interpolation schemes of FVM are discussed. The variable storage arrangement of FVM is introduced, and the implementation process of SIMPLE algorithm which is a coupling solution of solving pressure and velocity is researched.
Die structure, process conditions, deformation mechanism and flow character of materials, mechanical properties and constitutive relation of aluminum alloy are researched. By applying the rigid-viscoplastic model and neglecting the elastic deformation of materials, the aluminum alloy under high temperature can be regard as a kind of rigid-visoplastic, isotropic, incompressible non-newtonian fluid. The relationship of viscosity, stress, strain rate and temperature of aluminum alloy deformation process is researched, and the dynamic viscosity equation is established in order to lay the foundation of introducing FVM into aluminum alloy profile extrusion process.
By combining process character of aluminum profile extrusion process and FVM base theories, the mathematical model of FVM simulation of aluminum profile extrusion process based on non-orthogonal grids has been researched and established. Aiming at the poor adaptation of irregular calculation domain and the difficult treatment of friction boundary conditions bring by using traditional orthogonal grids which is commonly used in FVM, non-orthogonal grids are used to adapt to irregular calculate domain, realize the exactly fitting of curved face boundary, and make the reasonable implementation of boundary conditions become more easily. The governing equations are discretized on non-orthogonal grids by Cartesian coordinate directly, so the complicated coordinate transformation which used by body-fitted method is avoided. The problems casused by girds' nonorthogonality are researched, such as the connecting line of adjacent center points don't vertical to the interface, and don't pass through the center point of interface. The discrete schemes of governing equations based on non-orthogonal grids are researched, the discretization equations of 3D unstable problems based on non-orthogonal grids are deduced and established, and effect caused by grids' nonorthogonality has been eliminated. Aiming at the difficulty of implementing SIMPLE algorithm using staggered variable arrangement based on non-orthogonal grids, SIMPLE algorithm using collocated variable arrangement based on non-orthogonal grids is deduced and built. The deferred correction approach is used to interpolate values on interface. This approach can bring in pressure difference of neighbor nodes, so the pressure oscillation can be filtered out. The pressure correction equation can't be written into unified form of general discrete equation because of the grids' nonorthogonality, so twice pressure correction method is used to solve this problem. Aiming at the process character and flow law of aluminum extrusion process, the initial and boundary conditions of FVM simulation of aluminum extrusion process based on non-orthogonal grids are built. The simulation system is developed base on above mathematical model, and simulation steps and flow chart of the system are given.
The key technologies of 3D unsteady FVM simulation of aluminum extrusion process base on non-orthogonal grids are researched and built. Nodes numbering and data storage on non-orthogonal collocated grids are researched, and the friction boundary is implemented on non-orthogonal grids. VOF method which is used to tracking flow's free surface is built on non-orthogonal grids, the calculate formulas of VOF method are developed by aiming at the grids' nonorthogonality. A simple method is used to determining the orientation of free surface conveniently. Some key technologies, such as the character and solution method of algebraic equations obtained by FVM based on non-orthogonal grids, the convergence criterion of inner and outer iteration, time step auto control, and so on, are researched. Then the simulation system of FVM simulation of aluminum extrusion process based on non-orthogonal grids has been further developed by above key technologies.
Aiming at the hollow profile extrusion process, key simulation technologies of FVM based on non-orthogonal block structured grids are established. Data structure of block interface is researched and built. Solution method of FVM based on is researched and the strong implicit procedure is built to solve algebraic equations on the global calculation domain unitively. The treatment of VOF method on block interface is researched and VOF method is built on non-orthogonal block structured grids. FVM simulation system of aluminum extrusion process based on non-orthogonal block structured grids is developed based on above key technologies, and the numerical simulation of hollow profile extrusion process using porthole die is realized.
Some numerical cases are simulated to verify the feasibility and exactness of the mathematical model, key technologies and relative numerical system, and the simulation results are compared with the results obtained by FEM software Deform, FVM software SuperForge and experiment under the same conditions. These results comparisons indicate that the mathematical model of FVM simulation of aluminum extrusion process is correct and efficient, and it has a good applicability for extrusion process with large deformation. The developed system can realize extrusion process including thin walled profile pocket die extrusion with large deformation, hollow profile porthole die extrusion. The die structure's effect to flow law of metals has been researched, and the extrusion die structure has been optimized by the simulation, which can provide theoretical guidance of practice of extrusion process.
有限元法在金属塑性成形数值模拟中应用广泛,但在模拟变形量极大的挤压过程时却遇到了瓶颈:网格易发生严重畸变,需要不断重划网格,甚至无法将模拟进行下去。有限体积法导出的离散方程具有良好的守恒性,而且离散方程系数物理意义明确,计算量相对较小,是目前计算流体力学中应用最为广泛的一种方法,其突出的优点是所采用的欧拉网格是背景网格,不随材料一起运动,网格在模拟过程中不发生畸变,避开了网格再划分问题,因而可以更好地模拟铝型材挤压这类大变形问题。目前研究人员使用的有限体积法软件多为通用软件,没有考虑铝型材挤压工艺的特点,同时由于有限体积法数值模拟理论及其关键技术在塑性成形中的应用尚未完善,所以出现了模拟时间过长、所挤出件表面质量不好等一系列问题,不能有效指导铝型材的挤压工艺与模具设计。
本文旨在根据铝合金材料的特性及铝型材挤压过程材料变形机理、模具结构、工艺条件等,将计算流体力学中广泛应用的有限体积法引入到塑性成形领域,建立一种高效、灵活、可靠的铝型材挤压成形过程数值模拟方法及其关键技术,开发相应的模拟分析系统,重点实现大挤压比薄壁型材挤压、具有流动再分配作用的导流模挤压、具有复杂模具结构和复杂流动规律的空心壁板型材平面分流模挤压等挤压过程的非正交网格有限体积法数值模拟,根据获得的速度场、应力场、应变场等场量分布规律实现模具结构和工艺参数的优化,为铝型材制造提供理论指导。
针对铝型材挤压过程数值模拟现状及存在的问题,将适合大变形问题的有限体积法引入塑性成形领域,研究了有限体积法的基本理论,给出了有限体积法的基本控制方程和有限体积网格的构成特点。研究了控制方程的离散方法,讨论了有限体积法中各种常用的插值格式。研究了三维非稳态问题中的时间积分方案和控制方程的离散过程。介绍了有限体积法中变量的存储方式,深入研究了基于压力速度耦合求解的SIMPLE算法的实施过程。
研究了铝合金挤压过程的模具结构、工艺条件、材料变形机理和流动特点,铝合金材料的力学性能特点和本构关系。应用刚(粘)塑性模型,忽略材料的弹性变形,将高温下的铝合金材料视为一种刚(粘)塑性、各向同性、不可压缩的非牛顿流体。研究了铝合金材料变形过程中的动力粘度变化与应力、应变速率及温度的关系,建立了动力粘度方程,为将有限体积法引入铝合金型材挤压等塑性成形领域奠定基础。
结合铝型材挤压过程的工艺特点和有限体积法基本理论,研究建立了铝型材挤压过程非正交网格有限体积法数学模型。针对有限体积法中传统的正交结构网格对不规则区域的适应性差和难于施加边界条件的缺点,采用非正交网格划分不规则计算区域,实现了对曲面边界的准确拟合,更易于合理地施加边界条件;将控制方程采用直角坐标形式直接在非正交网格上离散,避免了适体坐标法中复杂的坐标变换过程;研究了非正交网格的特点及网格的非正交性带来的网格中心节点连线不垂直于界面和不通过界面中心点的问题,研究了非正交网格上控制方程的离散格式,推导建立了非正交网格上三维非稳态问题离散方程,消除了网格非正交性带来的误差:针对基于交错网格的SIMPLE算法在非正交网格上难于实现的问题,推导建立了基于非正交同位网格的SIMPLE算法,采用延迟修正方法处理界面插值,引入相邻节点压力差,解决了同位网格SIMPLE算法的压力震荡无法检测的问题;采用二次压力修正方法,解决了网格的非正交性带来的压力修正方程无法写成通用离散形式的问题;针对铝合金型材挤压过程的变形工艺特点和金属流动规律,建立了非正交网格有限体积法模拟铝型材挤压过程的初始条件和边界条件;基于铝型材挤压非正交网格有限体积法数学模型,进行了系统开发,给出了模拟分析步骤和程序流程。
研究建立了三维非稳态铝型材挤压非正交网格有限体积法的关键技术。研究建立了非正交同位网格的节点编号和网格信息的数据存储。建立了非正交网格上摩擦边界的施加方法;建立了非正交网格上自由表面追踪的VOF方法,针对网格的非正交性,改善了流体体积函数的计算公式,提出了一种简单的流体方位确定方法,便于自由表面方向的确定。研究了非正交网格有限体积法所形成的代数方程组的特点和数值求解方法、内部迭代和外部迭代的收敛准则、时间步长的自动调整关键技术。根据以上关键技术,进一步完善了铝型材挤压非正交网格有限体积法模拟分析程序。
针对空心铝型材挤压过程,建立了块结构化非正交网格有限体积法数值模拟关键技术。研究建立了块结构化网格的块分界面数据结构;研究了块结构化网格有限体积法的求解方式,建立了联合整体求解的强隐方法;实现了块与块之间的界面信息传递;研究了VOF方法在块界面处的处理方法,建立了块结构化非正交网格上自由表面追踪的VOF方法。基于以上关键技术,进一步开发了铝型材挤压块结构化非正交网格有限体积法模拟分析程序,实现了空心铝型材平面分流模挤压过程数值模拟分析。
对所建立的数学模型、关键技术及其所开发的数值模拟系统进行了一系列算例验证,包括与有限元软件Deform、有限体积法软件SuperForge等计算结果的对比验证和试验验证。通过对比分析,表明本文建立的铝型材挤压有限体积法数值模拟数学模型正确、高效,特别适用于大变形挤压过程的数值模拟分析。利用所开发系统,实现了大变形薄壁型材导流模挤压,空心型材平面分流模具挤压等挤压过程的数值模拟分析,进一步研究模具结构对金属流动的影响,并根据模拟结果优化模具结构,为实践提供理论指导。
With the fast development of national economy and people's living level, aluminum profile products are getting wider employment in production and living fields. Extrusion die is the key equipment of aluminum profile extrusion production. At present, design of profile extrusion die is mainly based on engineering analogy and experience accumulation in our nation, the designed die has to be tested and repaired frequently in order to adjust process parameters. The traditional production mode which depend on experimental design, die testing and repairing has been not satisfied the rapid development of aluminum profile industry. The scientific design and analysis tools are urgently needed to develop the design of aluminum profile extrusion die from experienced design up to scientific design. Computational numerical simulation has been a powerful tool for the die and process design of material deformation process. Aluminum profile extrusion process is the large deformation process. It usually can not be effectively analyzed by conventional analysis method. Therefore, developing the theoretical model and numerical calculation method to suit severe plastic deformation process, and researching the flowing law of metals and the effect of relative parameters on quality of profile in aluminum profile extrusion process has a great significance on reasonable design of extrusion process and die structure, reducing testing time of die, and improving quality of profile.
Finite element method (FEM) is widely used in numerical simulation of metal plastic forming process, but it has a big problem in simulating extrusion process with severe deformation: the mesh is easily distorted and need to be remeshed frequently, which sometimes cause the simulation even impossible to go on. Finite volume method (FVM) is the most popular method used in computational fluid dynamics at present. Its discrete equations have good conservation and clear physical meaning, and its computational cost is relatively small. The prominent advantage of FVM is that the Euler grids employed by this method is the background grids which don't move with the materials and don't be distorted. So FVM is more suitable for the large deformation problems such as aluminum extrusion process because the grids can avoid to be remeshed. At present, FVM software used by researchers is mainly the general-purpose software, which doesn't consider the process characteristics of aluminum extrusion process. At the same time, the theories and key technologies of FVM numerical simulation of plastic deformation process have not been perfect yet. There are some problems such as longer time cost, lower surface quality and so on. These problems cause these FVM software can not guide the process and die design of aluminum profile extrusion process effectively.
This paper is aimed to introduce FVM which is widely used in computational fluid dynamics into plastic deformation process based on characteristics of aluminum alloy and deformation mechanism, die structure, process conditions and so on of aluminum extrusion process, establish a efficient, flexible and stable numerical simulation method and its key technologies of aluminum profile extrusion process, then develop the numerical analysis system, primarily realize the non-orthogonal grids based FVM simulation of extrusion process, including the thin walled profile extrusion process with the large reduction, the pocket die extrusion process with effect on redistribution of flow, the hollow profile porthole die extrusion process with complex die structures and flow patterns, and so on. Then optimize the die structure and process parameters based on obtained velocity fields, stress fields, strain fields and so on, and provide the theoretical guidance of profile extrusion process.
Aiming at the research status and mainly existing problems of numerical simulation of aluminum extrusion process, FVM method which is suitable for large deformation problems is introduced into the plastic deformation field. The base theories of FVM are researched, the governing equations and grid character of FVM are given. The discrete methods of governing equations are researched, and the common used interpolation schemes of FVM are discussed. The variable storage arrangement of FVM is introduced, and the implementation process of SIMPLE algorithm which is a coupling solution of solving pressure and velocity is researched.
Die structure, process conditions, deformation mechanism and flow character of materials, mechanical properties and constitutive relation of aluminum alloy are researched. By applying the rigid-viscoplastic model and neglecting the elastic deformation of materials, the aluminum alloy under high temperature can be regard as a kind of rigid-visoplastic, isotropic, incompressible non-newtonian fluid. The relationship of viscosity, stress, strain rate and temperature of aluminum alloy deformation process is researched, and the dynamic viscosity equation is established in order to lay the foundation of introducing FVM into aluminum alloy profile extrusion process.
By combining process character of aluminum profile extrusion process and FVM base theories, the mathematical model of FVM simulation of aluminum profile extrusion process based on non-orthogonal grids has been researched and established. Aiming at the poor adaptation of irregular calculation domain and the difficult treatment of friction boundary conditions bring by using traditional orthogonal grids which is commonly used in FVM, non-orthogonal grids are used to adapt to irregular calculate domain, realize the exactly fitting of curved face boundary, and make the reasonable implementation of boundary conditions become more easily. The governing equations are discretized on non-orthogonal grids by Cartesian coordinate directly, so the complicated coordinate transformation which used by body-fitted method is avoided. The problems casused by girds' nonorthogonality are researched, such as the connecting line of adjacent center points don't vertical to the interface, and don't pass through the center point of interface. The discrete schemes of governing equations based on non-orthogonal grids are researched, the discretization equations of 3D unstable problems based on non-orthogonal grids are deduced and established, and effect caused by grids' nonorthogonality has been eliminated. Aiming at the difficulty of implementing SIMPLE algorithm using staggered variable arrangement based on non-orthogonal grids, SIMPLE algorithm using collocated variable arrangement based on non-orthogonal grids is deduced and built. The deferred correction approach is used to interpolate values on interface. This approach can bring in pressure difference of neighbor nodes, so the pressure oscillation can be filtered out. The pressure correction equation can't be written into unified form of general discrete equation because of the grids' nonorthogonality, so twice pressure correction method is used to solve this problem. Aiming at the process character and flow law of aluminum extrusion process, the initial and boundary conditions of FVM simulation of aluminum extrusion process based on non-orthogonal grids are built. The simulation system is developed base on above mathematical model, and simulation steps and flow chart of the system are given.
The key technologies of 3D unsteady FVM simulation of aluminum extrusion process base on non-orthogonal grids are researched and built. Nodes numbering and data storage on non-orthogonal collocated grids are researched, and the friction boundary is implemented on non-orthogonal grids. VOF method which is used to tracking flow's free surface is built on non-orthogonal grids, the calculate formulas of VOF method are developed by aiming at the grids' nonorthogonality. A simple method is used to determining the orientation of free surface conveniently. Some key technologies, such as the character and solution method of algebraic equations obtained by FVM based on non-orthogonal grids, the convergence criterion of inner and outer iteration, time step auto control, and so on, are researched. Then the simulation system of FVM simulation of aluminum extrusion process based on non-orthogonal grids has been further developed by above key technologies.
Aiming at the hollow profile extrusion process, key simulation technologies of FVM based on non-orthogonal block structured grids are established. Data structure of block interface is researched and built. Solution method of FVM based on is researched and the strong implicit procedure is built to solve algebraic equations on the global calculation domain unitively. The treatment of VOF method on block interface is researched and VOF method is built on non-orthogonal block structured grids. FVM simulation system of aluminum extrusion process based on non-orthogonal block structured grids is developed based on above key technologies, and the numerical simulation of hollow profile extrusion process using porthole die is realized.
Some numerical cases are simulated to verify the feasibility and exactness of the mathematical model, key technologies and relative numerical system, and the simulation results are compared with the results obtained by FEM software Deform, FVM software SuperForge and experiment under the same conditions. These results comparisons indicate that the mathematical model of FVM simulation of aluminum extrusion process is correct and efficient, and it has a good applicability for extrusion process with large deformation. The developed system can realize extrusion process including thin walled profile pocket die extrusion with large deformation, hollow profile porthole die extrusion. The die structure's effect to flow law of metals has been researched, and the extrusion die structure has been optimized by the simulation, which can provide theoretical guidance of practice of extrusion process.
引文
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