【作者】 娄淑梅；

【导师】 赵国群；

【作者基本信息】 山东大学 ， 材料加工工程， 2007， 博士

【摘要】 随着国民经济的快速发展,铝型材在各个领域得到了越来越广泛的应用。但是由于铝型材品种规格多种多样,铝型材挤压过程材料的变形量大,流动规律复杂,挤压模具承受载荷状况恶劣,使得铝型材挤压产品开发和模具的设计成为决定挤压件质量的关键环节。依赖经验设计和试模返修的传统生产模式已无法满足铝型材快速发展的需要。在效率就是生命,质量就是关键的市场经济环境下,铝型材企业最重视的就是模具设计加工成功率的提高,所以迫切需要可靠的科学理论来指导工艺及模具设计。使用数值模拟方法能够模拟铝型材挤压过程中金属流动状况,包括速度、应力、应变、压力等各种物理场量的分布及变化情况,由此可以预测可能产生的缺陷,评价工艺及模具结构参数是否合理,并对其进行及时修改,从一定程度上避免了费时、费力、高成本的试模返修过程,从而能够快速合理地进行工艺与模具设计,缩短生产周期。金属塑性成形领域应用最为广泛的数值模拟方法是拉格朗日有限元方法,但是由于铝型材挤压的变形剧烈,挤压比通常比较大,用拉格朗日有限元法模拟铝型材挤压,会遇到严重的网格畸变和频繁的网格再划分,带来CPU计算时间增加、体积损失较大、误差严重、模拟结果失真等问题,甚至当挤压比达到一定数值时,模拟计算会最终因严重的网格畸变和体积损失而难以进行下去。相对于拉格朗日有限元法,基于欧拉网格的有限体积数值模拟方法,因其网格的欧拉描述而能够避免网格畸变和网格再划分,在大变形的体积成形过程的模拟上显示出其优越性。商品化软件Msc/SuperForge是目前唯一基于有限体积法,应用于金属塑性成形领域的数值模拟工具,国内外许多研究者利用其进行了铝型材挤压过程的模拟。但是SuperForge不是专门针对铝型材挤压的软件,并且通过对该软件的应用发现,与有限元软件相比,Superforge在大变形比的铝型材挤压过程模拟方面具有优越性,但计算的精度和模拟的效率之间的平衡问题是Msc/SuperForge软件的瓶颈。Msc/SuperForge使用类似于有限元网格的三角面片包裹金属表面的方法来描述边界,跟踪自由表面,所以当网格比较稀疏的时候,虽然计算速度较有限元方法快,但是模拟结果比较粗糙,三角面片带来的毛刺现象比较严重。要使模拟的挤压件表面质量提高,就要增加网格数量,但是由于Msc/SuperForge中欧拉背景网格尺寸是统一的,不能对用户感兴趣的关键区域进行局部加密,因此模拟质量的少许提高便会带来网格数目的三次方增长,造成计算效率严重下降。本文针对铝型材挤压这种大变形过程,旨在根据热挤压工艺条件下铝合金材料的性质和成形过程的特点,研究铝型材挤压有限体积法模拟的关键技术,寻找适合的途径和方法,建立铝型材挤压有限体积法数值模拟模型,将适合大变形过程模拟的欧拉网格以及有限体积法灵活地引入铝型材挤压过程模拟中来,为铝型材挤压生产实际提供简便高效的理论指导工具。本文细致研究了热挤压工艺条件下金属材料的性质,尤其是铝合金的本构关系,认为,不考虑铝型材挤压中的弹性变形,可以将铝合金视为刚塑性或粘塑性材料,并且铝型材热挤压一般是在铝合金的再结晶温度以上进行,因此金属的动力学粘度主要取决于应变速率与温度,所以将挤压中的铝合金视为非线性牛顿流体,可采用流体力学中简单高效的SIMPLE算法迭代计算铝型材挤压中的速度场、压力场,利用能量守恒方程求解温度场,继而根据铝型材挤压的本构方程,利用求解出的温度和等效应变速率对铝合金的动力学粘度进行更新。铝型材的挤压一般根据材料性质、挤压坯料高径比的不同,分为稳态挤压和非稳态挤压。而实际的挤压过程也分为稳态挤压阶段和非稳态挤压阶段,当坯料的高径比比较大时,稳态挤压在整个挤压过程中所占比重很高。在工业生产中,铝型材的生产一般都是连续挤压,有效的挤压件都是在挤压的稳态阶段成型的,因此对铝型材挤压稳态过程或状态进行模拟非常必要。所以,本文首先进行了铝型材挤压稳态流动过程的有限体积数值模拟。结合铝型材挤压材料的本构方程及材料的特性,研究了铝型材挤压稳态流动过程有限体积法数值模拟的关键技术,推导建立了铝型材挤压过程中动量守恒方程、连续性方程、能量守恒方程的三维离散格式,得到了稳态SIMPLE算法的三维公式和求解流程,提出了铝型材挤压过程中材料粘度的迭代更新方法。给出了迭代收敛的判据,并且实现了网格的局部加密,不仅提高了计算效率,而且保证了模拟质量。在此基础上,利用Virual C++程序平台,编制了程序,建立了铝型材挤压稳态过程有限体积法数值模拟模型,利用该模型进行了稳态算例模拟,并且与有限元软件DEFORM-3D、CASFORM,有限体积软件SuperForge的模拟结果进行对比验证,证明了本文建立的铝型材挤压三维稳态过程有限体积数值模拟模型的正确性和高效性。挤压过程进行到稳态之前的阶段从一定程度上会影响稳态阶段金属的流动,并且决定着挤压制品的前端形状、应变的积累等,而这些都是制品是否发生翘曲、开裂等缺陷的重要因素;为了使数值模拟能够真实反映铝型材挤压的实际过程,增强铝型材挤压数值模拟软件对实际生产的指导作用,有必要对铝型材挤压由非稳态到稳态整个变化的过程进行研究,得到挤压中重要物理场量随时间的变化规律。因此本文在稳态研究的基础上,拓展建立了铝型材非稳态挤压过程中动量守恒方程、连续性方程、能量守恒方程的三维离散格式,得到了三维非稳态SIMPLE算法的公式和算法流程。针对材料的非稳态流动,将计算流体领域广泛应用的VOF方法引入铝型材挤压过程中的金属流动前沿的动态捕捉中来,真实地模拟了金属前沿流动趋势,得到了良好的表面质量。基于VOF方法,提出根据自由表面位置,自动识别金属流体区域,流场计算采用局部计算方法,即:用控制方程求解金属单元变量,在自由表面单元施加动力学以及运动学条件,空气单元跳过不参与计算,提高了计算效率。提出局部采用“动网格技术”的方法,既解决了挤压垫片移动引起的计算区域变化问题,又避免了全局网格变化带来的计算时间的浪费。根据计算的稳定性条件,提出用时间步长的自动调节方法来进一步提高模拟计算的效率。利用以上关键技术,建立了铝型材挤压三维非稳态过程有限体积数值模拟模型,自主开发了铝型材挤压三维非稳态过程有限体积数值模拟软件,并且利用典型的铝型材挤压非稳态实例验证了铝型材挤压三维非稳态过程有限体积法数值模拟模型是正确、高效的。以上稳态及非稳态模型均是在三维笛卡尔正交网格上建立的,笛卡尔正交网格虽然能够模拟任何形状区域的流动,程序适应性强,但是正交网格对复杂边界或曲线边界采用“阶梯状”近似逼近,在网格较粗的情况下会带来计算误差和边界施加的困难。为了使计算网格边界与流体区域边界更加吻合,使边界条件的施加更加方便、科学,计算更加贴合实际挤压过程,本文研究了适体网格的生成技术,在此基础上着重研究了网格的非正交性对铝型材挤压控制方程中对流项、扩散项的影响,推导建立了三维适体网格下各控制方程的离散公式,基于正交网格下的VOF方法和移动网格技术,充分考虑网格非正交性的影响,拓展建立了适体网格下的VOF方法和移动网格技术。非正交边界上采用剪切摩擦模型,并在此基础上提出了适体网格下边界条件的施加方法。以上述关键技术为依托,建立了更加贴合挤压实际,更加适应复杂区域挤压过程模拟的适体网格下的铝型材挤压有限体积法数值模拟数学模型,对三维铝型材挤压过程有限体积法数值模拟软件进行了网格适体性优化,对典型的稳态以及非稳态挤压过程实例进行了模拟、对比与分析,验证了该模型的有效性。实验是检验数值模拟结果是否正确的最具说服力的工具。为了进一步验证本文所建立的铝型材挤压有限体积数值模拟模型的正确性,本文结合铝型材挤压的工艺和模具设计知识,针对十字花形件的挤压设计了一组挤压模具,进行了挤压实验。通过模拟结果与实验结果的比较,进一步验证了本文建立的铝型材挤压有限体积法数值模拟模型的正确性。更多还原

【Abstract】 With the fast development of national economy, aluminum profile products are getting wider employment in various fields. For the aluminum profiles’ variant specifications and extrusion dies’ fierce working condition due to complex material flow status and the large deformation, the product development and the mould design are more and more important. The traditional product pattern relying on experience design and trial-correct courses can’t satisfy the fast development of the aluminum alloy profile product. Under the economic entironment where the efficiency and the quality are the most important factors, the enterprises think much of the improvement of the efficiency of the die design and machining. Reliable and effective numerical simulation methods are required. They can predict the metal flow pattern, including the distribution and the development of the physical fields, such as velocity, stress, strain and pressure, etc. and then forecast the defect that possibly appears, evaluate if the process and mould conductive parameter are rational and if not. These parameters will be amended, and the trial-correct courses wasting time, manpower and money will be avoided on some degree. And then the process and die design will be completed rapidly and rationally, shortening the product cycle. The most popular numerical simulation method in the metal plastic deformation fields is the finite element method based on Lagrangian mesh. But if the Lagrangian based finite element method is used to simulate the extrusion processes with severely large deformations, serious mesh distort and frequent remeshing will happen. The remeshing will bring the waste of the CPU time, volume loss, the distortion of the results and serious error, etc. When the Reduction ratio in area is pretty large, the simulation can’t continue because of the severe mesh distortion and calculation error.Compared with Laglanrian based finite element method, Eulerian based finite volume method can avoid mesh distort and remeshing for its Euler mesh, and shows its advantages in simulating bulking forming with large deformations. Commercial software Msc/SuperForge is the only tool based on finite volume method to simulate bulking metal forming processes. But SuperForge is not a software that specially aims at aluminum alloy profile extrusion. Many researchers in the world simulate the aluminum alloy profile extrusion with SuperForge. It was found that the SuperForge has many advantages in simulating process with large deformation such as extrusion over finite element softwares, but the balance of the calculation accuracy and the simulation effective is the bottleneck of the SuperForge software. SuperForge uses triangular facets encapsulating the FVM grid to track the free surface and the wall boundary of the deforming body. When the FVM mesh is pretty sparse, the simulation speed is relative high, at the same time, the simulation results are very coarse, and the serious burr brought by the triangular facets is serious. A thick mesh is required if the improvement of the simulated surface finish is needed. But because the Eulerian background mesh is unit and can’t be locally refined at the interested place, improvement of the surface property will bring the increase of the mesh number in cubic way, decreasing the simulation effective.According to aluminum alloy extrusion with large deformation, based on the character of the aluminum alloy during the hot extrusion, this paper aims to study the key technologies of the aluminum alloy profile extrusion simulation by finite volume method, to find suitable and effective methods to build aluminum alloy profile extrusion simulation model by using finite volume method, and introduce the finite volume method and the Euler mesh suitable for large deformation simulation to the aluminum alloy profile extrusion simulation, supplying a simple and effective academic instruct tool to the real aluminum alloy extrusion product.In this paper, the characteristics of the material in aluminum alloy profile extrusion processes are studied carefully, especially the constitutive equation of the metal. The elastic deformation of the processes is ignored and then the material is assumed to be rigid-plastic or visco-plastic material. Isotropic material properties are assumed. The dynamic viscosity is prominently influenced by the equivalent strain-rate and temperature, for the aluminum alloy profile extrusion processes always takes place above the recrystal temperature. So hot aluminum alloy material is described as a non-linear Newtonian fluid material, and the SIMPLE algorithm can be used to iteratively calculate the velocity, pressure fields, and then the temperature is calculated by the energy equation. After that, the dynamic viscosity is updated based on the constitutive equation using the calculated temperature and effective strain-rate.Aluminum profile extrusion includes steady extrusion and unsteady extrusion. The actual extrusion processes is also divided into steady stage and unsteady stage. Because in the industrial production, aluminum profile product is always a continuous processes. The valid extrudate takes shape in the steady stage, further more, when the ratio of the height and the radius is large, the proportion of the steady stage is higher. So the steady flow pattern of the aluminum alloy profile extrusion is studied and simulated by the finite volume method. Combined with the material characters and the constitutive equation, the key technologies of the aluminum profile steady extrusion processes simulation by finite volume method are studied. The three-dimensional discretised forms of the momentum conservation equation, continuity equation and energy conservation equation are obtained. The three dimensional equations and the flow program of the SIMPLE algorithm are given. The method to update the dynamic viscosity of the material in the aluminum alloy profile extrusion is yielded. The convergence criterion is also discussed. Local refinement of the mesh is realized improving the simulation effective, and at the same time, insuring the simulation quality. On the base of above, the code is programmed on Virual C++ plat, and the steady aluminum alloy profile extrusion simulation model using finite volume method is built. Some steady cases are simulated by the model, and the results are compared with those simulated by FEM software DEF0RM-3D and CASFORM, FVM software SuperForge. The comparisons prove the accuracy and the effectiveness of the steady aluminum alloy profile extrusion simulation model using finite volume method.The starting unsteady process before the extrusion reaches its steady state can influence the steady flow and decide the forehead shape and the accumulation of the strain etc., which are the important factors determining if the defects such as bend and craze will happen. To make the simulation model match the real processes of the aluminum extrusion, and reinforce the instruct function of the software to the actual extrusion product, it is necessary to study the change of the physical fields versus the time. On the base of the research of the steady-state flow, the three-dimensional discretised forms of the momentum conservation, continuity equation and energy conservation equation for unsteady-stat aluminum alloy profile extrusion are obtained. The equations and the flow chart of the three-dimensional unsteady SIMPLE algorithm are also got. According to the unsteady flow of the metal, the VOF method which is widely used in the Computational Fluid Dynamics is induced into the catch of the metal free surface. The flowing trend of the metal free surface is simulated factually and good surface finish is obtained. Based on the VOF method, the flowing fields are calculated by a ’part calculation method’, that is, the variables on the elements full of metal fluid are calculated by the government equation, the dynamic and kinematic boundary conditions are implemented on the free surface elements, and the air elements are skipped. This ’part calculation method’ can improve the calculation efficiency. The ’Moving grid system’ is advised to locally used, which can not only solute the calculation domain changing problem rising by the moving of the punch, but also avoid the time waste if all the mesh is changed. The auto-control of the time step is put forward to improve the efficiency of the calculation, based on the stability command of the calculation. On the base of the key technology above, three-dimensional unsteady aluminum alloy profile extrusion finite volume method simulation model is built, and the software is programmed. Several unsteady extrusion cases are simulated to prove the accuracy and the efficiency of the aluminum alloy profile extrusion simulation model by finite volume method.All the above steady and the unsteady extrusion models are build under Cartesian orthogonal grid which can adapted to flow caluculation with all kinds of boundaryes. But when the mesh is corse, the "Stepwise approximation" will introduce error and make the boundary condition treatment difficulty. To make the boundary of the numerical grid match the flowing domain for the convenience of the implement of the boundary condition, fitting the calculation to the actual extrusion process, the body-fitted mesh generation technology is researched, on the base of which, the influence of the grids’ non-orthogonal to the conductive term and the diffusion term etc. is studied, the three dimensional discretised forms of the governing equations on body-fitted grid are built. On the base of the VOF method and the moving grid system, combining the influence of the grid’s non-orthogonal, the VOF method and the moving grid system technology on the non-orthogonal grid system are built, too. Shear friction model are used on the boundary, and then the velocity boundary condition implement method is brought forward. By these key technologies, the aluminum alloy profile extrusion model by finite volume method on the body-fitted mesh system is built, and the according software is coded, too. Typical steady and unsteady extrusion cases are used to prove the efficiency of the model.Experiment is the most powerful tool improving the accuracy of the simulation. So to prove the accuracy of the aluminum alloy profile extrusion finite volume method model, a set of extrusion dies for aα-shaped extrudate are designed on the base of the extrusion arts and the dies. The experiment is done successfully and the comparing between the experiment results and the simulation ones proves that the aluminum alloy profile extrusion finite volume method model built in this paper is accurate again.更多还原