外文翻译--绝热高速切削有限元模型

附录1绝热高速切削有限元模型摘要二维正交切削过程的有限元模型正在发展。仿真是使用标准的有限元软件结合一个特殊的电动机，这种电动机是能够以网捕捉的形式用有规律的四边形和三角形在剪切区域完整的捕捉事物。重现事物和确保数据收敛的这种技术已经寻找到了。分割碎片有序排列和分割过程还在研究过程中。令人特别关注的是剪裂带产生的问题。弹性性能和切割速度的影响也正在讨论。 Elsevier公司2002科技有限公司保留所有***。 关键词：加工； 有限元； 格； 芯片分割；绝热剪切带 1、言 钛合金Ti6Al4V被广泛应用于航空航天及其他工业应用。这些合金大部份是应用于机械加工。 因此设计具有更好的可加工性钛合金是一个值得研究的目的。为了达到这一目的/找出严重影响材料可加工参数是非常必要的。这项工作可以利用有限元计算机模拟的参数研究方法来完成。一旦这最有前途的设计方法被肯定/实现合金改用的最后的一步材料设计过程就完成了。这种方式类似于标准的CAE生产周期，只有仅有少量几个原型被建立。创造一个金属切削过程的可靠的计算机模型在这个过程中是一个关键步骤。在本文中，我们在一些细节描述了这种模型。它使用标准的有限元软件来计算，从而保证可移植性和灵活性。随着啮合算法的要求迫切，特别预处理器已经研制成功，这个特别的处理器是用C+编程，且可能应用于不同平台。 本文安排如下；第2部分在对模型要求的一个简短说明之后，第3部分对有限元模型进行详细介绍。第4简述了一些模型的加工成果，重点放在细节的切屑形成过程。第5总结工作，并指出今后的研究目标。 2、问题 在金属切削过程中，材料被切割工具从工件表面切除，碎屑形成。 这个问题涉及塑性大变形，随着***和工件、工具和碎屑之间的摩擦产生大量的热量。在***前端工件材料的分离也已经被模拟。随着材料参数的影响对材料设计的考虑比对加工过程本身更重要。这个切削过程的模拟就是指正交切削。这个过程是用二维模拟的/这大大减少了计算机所需要的计算时间。更进一步简化是做非常严格的假设的工具。在仿真中摩擦与热流进入工具已经被忽略，但是可以很容易被包括在内。 这种忽略的原因是，有必要尽可能简化切削过程，像下文将作解释那样，***其背后的机制。 另外，毫无塞尔马辐射从表面上的碎屑产生，在材料边界也没有的热传导。综上所述，高速切削是一个非线性问题。它已经被一个完全热力耦合有限元模型模拟。 因此，编制了有限元法处理金属切削加工时的划伤问题就成为一个艰巨的任务，利用商业有限元软件是一个有吸引力的替代方案。 现代有限元软件可以在原则处理这类强非线性问题。在我们的研究中，我们决定用ABAQUS中/标准程式系统，这种系统允许定义复杂的接触状况，尽量避免定义材料属性，在多方面保证程序可定制的，包括由用户自定义子程序。我们假定以下大部分的方法可以应用于同样大的有限元包。 由于使用的标准化软件，方程公式(有限元法，热耦合，一体化计划，等)可以在别的非常详细的资料中找到3。金属切削过程中许多有限元模拟所用明确的方法(例如见17 )都能被演示。这些公式方法都是有保证的。 (概述了切削过程中有有限元能够被在16中好到)。尽管如此，决定用一个隐码/ 在模拟过程中汇总被检查，但迭代过程不再保证衔接。利用ABAQUS /标准内含编码有一个好处，实行模拟过程中允许用户在很大的范围内灵活的自定义子程序。 这种套路/可以用来执行复杂的材料分离准则。 此外，如果本地网有细化的需要，隐码有较好的标度行为。如果狭窄剪切带形式/ 命令执行的单元尺寸为1镑或不足1镑是必要的(见第4/2 节)优势，在CPU 使用时间有明确的算法，将大大降低。如果摩擦的影响较大，一个明确的方法可能是上好的，然而，并非如此。另一方面，明确方法往往需要改变一些物理参数，如密度或工具的速度，或用人工粘性。 我们认为/ 如果衔接能够达到，没有任何理由去考虑的一个隐模拟不亚于一个明确的。 也不同于许多其他的模拟/我们充分利用综合阶四边形，它有优于三角元素更好的收敛性能/ 这个问题的进一步讨论在第3/3节。 当正交切削时，钛合金形式分割碎屑 (见图 9 )。金属切削过程中任何详细的模拟都必须能够借此分割考虑。碎屑分割背后的机制仍然没有完全弄懂12，15，25，26。显然，所谓的绝热剪切在分割过程起了突出的作用/ 剪切带材料热软化导致在这个区域产生变形。在软化和变形之间的反馈引起狭长区域附加巨大变形/ 而周围的材料只产生微小变形。然而，不知道绝热剪切带是否是由裂缝延伸到材料中引起的成的，这在25是作为假设。如果这是正确的，应力集中在裂纹尖端诱引起剪切带形变(见例如 5 )。 在这里通过对该模型描述/我们假定碎屑分割是由纯绝热剪切/不是裂缝引起的。很显然/ 剪切带材料点的有效塑性流动曲线必须表明最大值。我们选用一个使温流动曲线出现最大值曲线流场，详细解释见4/1节。 如果分割碎屑形式/集中应力导致了碎屑(近似)连续变形。必须采取措施，以避免有限元网格因扭曲太大而变形，尤其是在用四边形元素仿真的的过程中。综上所述/模拟需满足下列要求/ 尽可能定期使用四边形，避免极端网格扭曲；剪切带内高密度网格； 碎屑连续变形(分割)； 隐式算法收敛； 为得到可移植性和灵活性使用标准软件。在金属切削模拟，为自动形成网格算法的选用是固定的，如用拉格朗日方算法，元素扭曲变大，尤其是分割碎屑形式。频繁重复分割以避免分子扭曲太大。在材料移出的剪切带它也可以用来制造精确网格(见插图6)。 然而/标准网格发电机是不能处理复杂的任务。因此，预处理程序已经编辑了能够分割曲率很大的被用四边形剪切生成的区域程序。剪切带的位置是用几何判据和网格细化自动决定的。预处理程序将在下一节描述。随后，对网格生成过程和建模的分割的详细内容作解释。3/有限元模型3/1网发电的原理过去的预处理程序(被称为pre+ )都是用标准数据库在C+中写的，因此，可以移植到不同的平台。 预处理程序被用来计算几何参数数据，使模型参数轻松改变。它适用于二维三维空间中各种各样的问题。生成四边形最简单的办法是划分组件的物理区域，组件是被四条线和一个映射单位正方形***的。单位正方形有规律的啮合可以映射回用等角投影的该地区本身。细节的详细叙述见23，24。如果我们在真实空间内用(x/y)，在平面内用（，）定义坐标，一般曲线坐标系可以通过解拉普拉斯方程来定义 （1） （2）这里的表示，等等。这个方程系统的物理解释/当两个对立边携带不同的电压，坐标协调电场区域的等势线。 把坐标（，）作为***变数，这当然是很容易求解的方程。在这种情况下方程已被颠倒过来，求解 （3） （4）这是一个半椭圆形的线性方程组求解，可以解决使用标准方法。啮合算法通常是用来制造网在一个物理地区，是经过了一个有限元计算的结果，因为它被用来自动生成网格的过程。 因此，界限被计算步骤定义，因此已经离散。求解方程，定期矩形网使用的网格大小的选择应小于最小距离，使等量的旧与新网相同。 由于不规则形状的区域解点数目已是一个相当大的数据，谨慎选择算法是有优势的。我们已经制定了一个多重算法，详细介绍见勃兰特7。 这种算法的优点是快速，稳定，而且也给出一个截断误差的估计。这种计算方法可以起到数值误差是可比的截断误差。 由于方程是非线性的，只能用近似格式( FAS )的方法来进行。多重技术依赖的事实标准松弛方法(如高斯-赛德尔)非常有效地减少振荡解决部分误差，而畅顺，大部份波长不影响不大。因此，我们经过几个步骤放宽任何涉及方程的误差可以代表以及对粗网少点。放松对这个粗格再次降低小波长组成，其中， 现在有一个较大的绝对波长为电网是粗糙。因此，递归计划是用在错误的，是有效降低对所有尺度。 这种算法是一个标准的工具/用于解决椭圆型方程使读者可参考文献进一步的详细内容20。它只需约一分钟，一个标准的工作站，即使格数点约为250 000只要界限的区域不是太强烈弯曲。插图1( a )显示坐标系在一个简单的区域被用描述算法创建。附录2A finite element model of high speed metal cutting with adiabatic shearingAbstract A finite element model of a two-dimensional orthogonal cutting process is developed/ The simulation uses standard finite element software together with a special mesh generator that is able to mesh the chip completely with regular quadrilateral elements and a strong mesh refinement in the shear zone for continuous and segmented chips/ The techniques of remeshing and to ensure convergence of the implicit calculation is described/ Results for the formation of segmented chips are presented and the segmentation process is studied/ Of special interest is the occurrence of split shear bands/ The influence of the elastic properties and of the cutting speed is also discussed/Keywords/ Machining/ Finite elements/ Remeshing/ Chip segmentation/ Adiabatic shear bands 1/ Introduction Titanium alloys like Ti6Al4V are widely used in aerospace and other industrial applications/ A large fraction of the production costs for components made of these alloys is due to machining/ The design of titanium alloys with better machinability is therefore a worthwhile research aim/ To achieve this/ it is necessary to identify the important material parameters that critically influence the machinability of the material/ This can be done by parameter studies using finite element computer simulations/ Once the most promising design avenues are determined/ the actual alloy modification can be done/ which is thus only the final step of the material design process/ This approach is similar to the standard CAE production cycle/ where only a few prototypes are built/ * Corresponding author/ E-mail addresses/ martin/baekertu-bs/de (M/ Baker)/ j/roeslertu-bs/de (J/ Rosler)/ c/siemerstu-bs/de (C/ Siemers)/ 1 Work supported by Deutsche Forschungsgemeinschaft/ Creating a reliable computer model of the metal cutting process is the first and crucial step in this process/ In this paper/ we describe such a model in some detail/ It uses standard finite element software for the calculations/ thus ensuring portability and flexibility/ As the requirements on themeshing algorithm are quite strong/ a special preprocessor has been developed/ which is programmed in Ctt and is thus also portable to different platforms/ The paper is organized as follows/ after a short description of the requirements on the model in Section 2/ the details of the finite element model are given in Section 3/ Some results produced with the model are shown in Section 4/ focussing on the details of the chip formation process/ Section 5 summarizes the work and points out future research aims/ 2/ The problem In the metal cutting process material is removed from the surface of the workpiece by a cutting tool and a chip is formed/ The problem involves large plastic deformations which generate a considerable amount of heat/ as does the friction between tool and workpiece and also between tool and chip/ The separation of workpiece material in front of the tool also has to be modeled/ As the influence of the material parameters is more important for material design considerations than are the details of the process itself/ the cutting process simulated here is that of orthogonal cutting/ The process is simulated as two-dimensional/ which strongly reduces the computer time needed for the calculation/ A further simplification is done by assuming the tool to be perfectly rigid/ Friction and heat flow into the tool have been neglected so far in the simulations/ but can easily be included/ The reason for this omission is that it is necessary to simplify the cutting process as much as possible to gain insights into the underlying mechanisms as will be explained below/ Also/ there is no thermal radiation from the free surface of the chip and no heat transfer at the boundary of the material is allowed/ Rapid machining is a strongly non-linear problem due to the effects described above and it has to be simulated using a fully coupled thermomechanical finite element model/ It is therefore a formidable task to develop a finite element code to deal with the metal cutting problem from scratch/ so that the use of commercial FE software is an attractive alternative/ Modern finite element software can in principle handle such strongly non-linear problems/ For our studies we have decided to use the ABAQUS/Standard program system/ which allows the definition of complex contact conditions/ leaves many possibilities to define material behaviour/ and can be customized in many regards by including user-defined subroutines/ We suppose that most of the methods described below would work with any similarly powerful FE package/ Due to the use of standardized software/ the formulation of the equations (finite element formulation/thermomechanical coupling/ integration scheme/ etc/) can be found in great detail elsewhere 3/ Many finite element simulations of the metal cutting process are performed using the explicit method (see for example 17)/ which is guaranteed to converge/ (An overview over finite element simulations of the cutting process can be found in 16/) Nevertheless/ we have decided to use an implicit code/ Here convergence is checked during the simulation/ but the iterative solution process is no longer guaranteed to converge/ One advantage of using the implicit code ABAQUS/Standard is that this allows a great range of flexible user-defined subroutines to be introduced in the simulation/ Such routines can be used to implement complicated material separation criteria/ In addition to that/ the implicit code has a better scaling behavior if local mesh refinement is needed/ If narrow shear bands form/ element sizes of the order of 1 lm or less are necessary (see Section 4/2) and the advantage in CPU time of using an explicit algorithm will strongly diminish/ An explicit method is probably superior if frictional effects are large/ which is/ however/ not the case here/ On the other hand/ explicit methods often need to change some physical parameters like density or tool velocity/ or have to use artificial viscosity/ In our opinion/ there is no reason to consider an implicit simulation inferior to an explicit one/ if convergence can be achieved/ Also differently from many other simulations/ we use fully integrated first-order quadrilateral elements/ which have better convergence properties than triangular elements/ This is discussed further in Section 3/3/ Titanium alloys form segmented chips when cut orthogonally (see Fig/ 9)/ Any detailed simulation of the metal cutting process must be able to take this segmentation into account/ The mechanisms behind chip segmentation are still not completely understood 12/15/ 25/26/ It is clear that so-called adiabatic shearing plays a prominent role in the segmentation process/ Thermal softening of the material in the shear zone leads to an increased deformation in this zone/ which produces heat and leads to further softening/ This positive feedback between softening and deformation causes a narrow band of extremely strong deformation/ while the surrounding material is only slightly deformed/ It is/ however/ not known whether the adiabatic shear bands are caused by cracks growing into the material/ as assumed in 25/ If this is true/ the stress concentration at the crack tip can then induce the formation of the shear band (see e/g/ 5)/ For the model described here/ we assume that chip segmentation is caused by pure adiabatic shearing/ without cracks occurring/ It is quite clear that the effective plastic flow curve of a material point in the shear band must show a maximum for this mechanism to hold/ We have used a flow curve field where even the isothermal flow curves show a maximum/ This is further detailed in Section 4/1/ If segmented chips form/ the shear concentration leads to a (nearly) discontinuous deformation of the chip/ Measures have to be taken to ensure that the finite element mesh is not too much distorted due to this deformation/ especially in a simulation using quadrilateral elements/ To summarize/ the simulation has to meet the following requirements/ / use of quadrilateral elements/ as regular as possible/ avoiding extremely distorted meshes/ / high mesh density in the shear zone/ / discontinuous deformation (segmentation) of the chip/ / convergence of the implicit algorithm/ / use of standard software for portability and flexibility/ The use of an algorithm for automatic remeshing is mandatory in a simulation of metal cutting/ as element distortions become large in a Lagrangian approach/ 2 especially if segmented chips form/ A frequent remeshing ensures that the elements never become too distorted/ It can also be used to create a refined mesh in the shear zone that moves with the material (see Fig/ 6)/ However/ standard mesh generators are not able to handle the complex tasks involved in this problem without difficulties/ Thus a preprocessor has been programmed that can mesh the strongly curved regions created by the cutting process using quadrilaterals/ The position of the shear zone is automatically determined using a geometric criterion and the mesh is refined there/ The preprocessor is described in the following section/ Afterwards/ details of the mesh creating process and of the modeling of the segmentation are explained/ 3/ The finite element model 3/1/ Principles of mesh generation The used preprocessor (called Pre+) is written in Ctt using standard class libraries and is thus portable to different platforms/ The preprocessor can be used to calculate parametrized geometry data/ so that model parameters can easily be changed/ It is applicable to a wide range of problems in two and (with some restrictions) in three dimensions/ The easiest way of generating quadrilateral elements is to divide the physical region to be meshed into parts that are bounded by four lines and can be mapped onto the unit square/ A regular meshing of the unit square can then be mapped back onto the region itself using a conformal map/ as described in some detail in 23/24/ If we define the coordinates in real space with (x/ y) and those on the square with (n/ g)/ a general curvilinear coordinate system can be defined by solving the Laplace equation （1） （2）Here nxx denotes the partial derivative o2n=ox2/ etc/ This system of equations has a physical interpretation/ the coordinates correspond to the equipotential lines of an electric field on the region when two opposing sides are held on a different voltage/ It is of course much easier to solve the equation using the coordinates （n/ g） as independent variables/ In this case the equation has to be inverted/ resulting in （3） （4）This is a quasi-linear elliptic system of equations/ which can be solved using standard methods/ The meshing algorithm is usually used to create a mesh on a physical region that is the result of a finite element calculation/ as it is used to automatize the remeshing process/ Therefore/ the bounding lines are defined by the node positions of the previous calculation step and are thus already discretized/ To solve the equations/ a regular rectangular mesh is used where the grid size is chosen to be smaller than the smallest distance between nodes on the bounding surfaces/ so that the contour of the old and the new mesh closely agree/ As the nu

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