任意边界域映射建模理论及模具设计应用

工程实际中任意非规则边界问题的数学模型建立困难,导致参数不易求解和优化。应用近代复变共形映射理论,利用三角插值和法线迭代收敛方法,将任意复杂边界域转化为单位圆域,系统地建立了二者间的共形映射函数。针对挤压（拔制）异型材模具精密快速加工设计问题,求解了模具相似成形塑性流动的数学模型,建立了圆角方型材精密挤压（拔制）模具模腔数学模型及优化函数方程,使模腔快速CAD/CAM一体化成为可能。     

金属塑性成形过程再生核质点无网格方法数值模拟

应用微可压缩材料的流动法则,采用再生核函数无网格方法,自行开发了求解方棒压缩、圆棒压缩、反向挤压和轧制等金属塑性成形过程应用程序。应用再生核质点无网格方法计算得到纯铝和铝合金材料金属塑性成形过程的速度场和应力场解析结果,并与自行开发的I-Form有限元程序得到的计算结果以及试验数据进行了分析比较,结果符合良好。再生核质点无网格方法具有求解金属大变形特点,解决了有限元法中的网格重划问题,为复杂金属变形分析提供了良好的研究手段。     

DEFORM金属挤压成形工艺数值模拟技术

金属挤压成形是用压力机和模具对放置在模具腔内的金属坯料施加强大的压力使金属坯料产生定向塑性变形,从挤压模的模孔中挤出而获得所需断面形状、尺寸且具有一定力学性能的零件或半成品的塑性加工方法.挤压成形的种类很多,例如按照金属塑变流动方向可分为正挤压、反挤压、复合挤压及径向挤压.按照金属坯料温度分冷挤压、温挤压和热挤压等.     

汽车轮毂轴承套圈冷挤压数值模拟分析研究

对某型号汽车轮毂轴承内圈冷挤压模具进行三维建模,利用Deform软件,设定挤压条件后,对内圈挤压成形过程进行了数值模拟。分析了挤压过程中金属的流动与速度分布,挤压速度和摩擦因子对模具载荷的影响,并对凹模的应力进行了分析,指出应力集中导致模具容易损伤的部位。通过数值模拟分析,提出了减小摩擦因子,提高表面质量的方法,减小应力集中和载荷过大造成的模具损伤,通过优化工艺参数提高挤压成形质量。     

不同靴座扩展出口宽度下大宽厚比铜扁线连续挤压过程的数值模拟

基于DEFORM3D软件,采用刚粘塑性有限元理论,运用三维有限元技术详细研究了不同靴座扩展出口宽度对铜扁线连续挤压成形过程的影响。得出了不同靴座扩展出口宽度对模口处的流速均方差、模具载荷、金属等效应场和平均应力场的影响规律。     

模孔偏置位置参数对型材挤压成形影响的数值研究

通过引进流速均方差作为评价塑形变形时金属流动速度不均衡性指标，来有效地控制型材挤压成形时金属流动的不均匀性。通过采用有限变形弹塑性有限元方法，对不同模孔偏置位置参数下型材挤压过程进行了数值模拟研究，获得了挤压力、流速均方差和型材件内部应力应变场随其变化的规律，为进一步实现型材挤压工艺参数优化提供了理论参考。     

多腔壁板铝型材挤压过程数值模拟及模具优化

挤压模具在铝型材挤压生产中起着至关重要的作用,挤压模具设计的优劣直接影响挤压产品的质量。然而实际生产中,挤压模具的设计更多依赖传统设计经验,需要多次试模和修模,无法满足产品开发需求。以典型的多腔壁板铝型材为例,应用UG建立分流组合模几何模型,采用基于任意拉格朗日—欧拉(Arbitrary Largrang-Euler,ALE)算法的HyperXtrude软件对多腔壁板铝型材的挤压成形过程进行数值模拟,获得挤压过程中速度场、温度场、应力场及金属流动情况。针对初始模具设计的不足,提出多腔壁板铝型材挤压模具优化三步曲(开设引流槽、增设阻流块、优化工作带),有效地解决了初始模具设计中速度分布不均的问题。利用数值模拟方法可以优化模具结构,提出的多腔壁板铝型材挤压模具优化三步曲对同类铝型材挤压模具结构设计具有一定的指导意义。     

小型轴承套圈温挤压工艺及模具设计

以6203轴承套圈为例,通过对套圈的温挤压成形工艺过程、成形性能及工艺设计进行理论分析和设计计算,完成了锻件毛坯尺寸、温挤压成形凸模和预应力组合凹模的设计。基于DEFORM体积塑性成形软件,模拟了轴承套圈温挤压的成形过程,并对变形速度、成形性能、成形质量和温挤压应力进行了分析计算。     

柱塞体变形模式转换的成形工艺分析与研究

在柱塞体复合挤压成形过程中,金属的流动方式为过渡方式,其金属的流动规律非常复杂,对柱塞体零件成形的三种不同工艺方案进行了数值模拟分析.并运用滑移线场理论对其流动规律进行了讨论,给出了塑性变形的滑移线场和速端图,预测了金属的流动方向、流动速度等.指出了成形工艺缺陷产生的原因,确定了正确的工艺方案.     

扁挤压筒过渡曲面建模

为改善铝型材挤压过程中金属流动状况,通过引入流函数法建立基于流曲线的扁挤压筒型腔到模口之间过渡曲面的边界条件;同时采用保角映射方法,描述扁挤压筒型腔及模口处轮廓分别向单位圆的映射关系,构造过渡曲面入口和出口复杂图形的解析函数,解决了复杂三维模型向准三维对称模型的转换问题。两者结合得到过渡曲面上各点的流线方程,完成对过渡曲面的数学描述。为验证新构建曲面的合理性,对一矩形壁板成形过程进行模拟。结果表明：流线型过渡曲面有利于金属流动,并且有利于降低型腔面上的法向压力,可减少磨损、提高模具寿命。     

The use of generalised deformation boundaries for the analysis of axisymmetric extrusion through curved dies

A generalised kinematically admissible velocity field is derived for axisymmetric extrusion through curved dies by employing rigid-plastic boundaries expressed in terms of arbitrarily chosen continuous functions. The corresponding upper-bound extrusion pressure is related directly to boundary functions for the plastically deforming region when the die shape, lubrication condition and material characteristics of the billet are given. The proposed method of analysis makes it possible to predict the deformation pattern as well as extrusion pressure. In computation a third-order polynomial is chosen for the die boundary and the bounding function for the plastic region is chosen to be a fourth-order polynomial. The workhardening effect is considered in the formulation. The plastic boundaries as well as stream lines are affected by various process parameters. The theory predicts the relatively faster axial flow at the center than near the die boundary for greater friction factor even with the same die shape. The effects of area reduction and die length are also discussed in relation to extrusion pressure and deformation. Experiments are carried out for steel billets at room temperature. Deformation patterns are measured for several area reductions by the photoetching technique and the extrusion pressure is measured using a load-cell. The predicted extrusion pressure is in excellent agreement with the value computed by the finite element method. The deformation patterns agree well with the experimental observation.     

An analysis for extrusion of helical shapes from round billets

A method of analysis is proposed for three-dimensional extrusion of a helical shape from a round billet. It is reported that a helical shape can be made by hot extrusion through a square die. In this paper, it is suggested that a helical shape be effectively cold extruded through a continuous die with appropriate lubrication. The extrusion of helical shapes can find practical application in some useful products. However, the analytical method regarding this kind of extrusion has not been attempted so far.A kinematically admissible velocity field is derived for the extrusion model where a round billet is extruded into a twisted helical section with a long elliptic cross section. The axis of the cross section is rotating during extrusion. By assuming proper stream surfaces, the velocity field is obtained by deriving the equation of a stream line. Then, an upperbound solution is formulated for the rigid-perfectly plastic material. Computation for the upperbound pressure is carried out for various process variables such as reduction of area, friction, rotation of axis, aspect ratio of a product, die length and overall die profiles.     

A new formulation for three-dimensional extrusion and its application to extrusion of clover sections

The metal flow in the extrusion process is an important factor in controlling the mechanical property of the extruded products. It is, however, difficult to predict the metal flow in three-dimensional extrusion of complicated sections due to the difficulty in representing the geometry of the die surface and in expressing the corresponding velocity field. In this study a new kinematically admissible velocity field for a generalized three-dimensional flow is derived, in which the flow is bounded by the die surface expressed by an analytic function. Then, by applying the upper-bound method to the derived velocity field, the flow pattern as well as the upper-bound extrusion pressure are obtained. As a computational example, extrusion of clover sections from round billets is chosen. A new method of die surface representation is proposed by which there is a smooth transition of die contour from the die entrance to the die exit. Computation is carried out for work-hardening materials such as aluminium and steel. The analysis takes into account the effect of product shape complexity, lubrication condition and reduction of area on extrusion pressure, average effective strain and distribution of effective strains on the cross-section of the extruded product.     

塑料异型材制品的面域造型及口模生成

采用面域造型的方法,建立了塑料异型材挤出制品的塑件模型,由此转换得到机头的口模模型,进而实现型腔型芯的分离.     

基于数值分析的挤出流动规律研究

采用有限元数值分析和最优化设计理论相结合的方法。以挤出流动的均匀性为评价指标，把基于参数化建模和有限元分析结果的优化设计方法作为分析工具，深入系统地分析了模具结构对塑料异型材挤出流动均匀性的影响规律．研究了型材截面形状、模具结构和挤出流动均匀性三者之间的内在联系和相互制约关系，为模具优化设计和生产实践提供指导。     

基于共形映射的壁板型材挤压模具型腔建模

针对复杂铝合金壁板导流模挤压过程中出现的挤压力大、变形不均等缺陷,采用流函数理论建立扁挤压筒型腔到型材出口之间过渡曲面的边界条件。根据复变函数共形映射理论,讨论Schwarz-Christoffel积分变换的正反求解过程;应用Taylor级数凸凹分级展开技术,处理映射精度问题。最终,构造壁板外形单连通域到单位圆周的映射函数,并以此建立壁板挤压模型腔曲面数学方程,利用三维造型软件完成了复杂型材挤压“流线型”过渡曲面的三维建模。     

Analysis of three-dimensional extrusion of sections through curved dies by conformal transformation

A new method of analysis is proposed for the extrusion of arbitrarily shaped sections through curved die profiles. A kinematically admissible velocity field is found by deriving the equation of a stream line. Conformal transformation of a unit circle onto a section is utilized in the derivation. The upper-bound method is then applied to determine the extrusion pressure for the rigid-perfectly plastic material. The redundant work relating to the velocity discontinuities at the entrance and the exit is included in the formulation. The general formulation for an arbitrary cross section is obtained by use of conformal transformation. The upper-bound pressure for extrusion through curved die profiles is computed for a complex section with a curved boundary. Two curved die profiles widely used are chosen to compare the effects of die profiles. From the derived velocity field, the upper-bound extrusion pressures are also computed for the extrusion of regular polygons and rectangles of various aspect ratios. The effects of sectional shape, die profile and interfacial friction at the die surface are discussed.     

A generalized method for analysis of three-dimensional extrusion of arbitrarily-shaped sections

Despite increasing demand for and application of three-dimensional extrusion of various sections through continuous dies, so far very little work has been done by systematic and general analysis to predict the plastic flow properly. For effective die design, efficient design method and the related method of theoretical analysis are required for extrusion of complicated sections. In generalized three-dimensional extrusion of sections through continuous dies, a new method of die surface representation, using blending function and Fourier series expansion, is proposed by which smooth transitions of die contour from the die entrance to the die exit are obtained. The flow patterns as well as the upper-bound extrusion pressures are obtained on the basis of the derived velocity field. The effects of area reduction, product shape complexity, die length and frictional condition are discussed in relation to extrusion pressure, the distorted grid pattern and distribution of the final effective strain on the cross-section of the extruded billet. As computational examples for arbitrarily-shaped products rounded rectangles and ellipses are chosen for the extruded sections. Experiments are carried out for aluminum alloys at room temperature for a rounded square section and an elliptic section. In order to visualize the plastic flow, the grid-marking technique is employed. The theoretical predictions both in extrusion load and deformed pattern are in good agreement with the experimental results.     

An investigation of fracture criteria for predicting surface fracture in paste extrusion

In the extrusion of pastes, fractures may be found on the surface of product. Such fractures compromise strength and are often unacceptable aesthetically. Here some theoretical criteria for predicting the onset of surface fracture, using the elastic–plastic finite element method are evaluated and the success of these criteria in predicting recent observations is assessed. Two criteria based on stress fields successfully predicted an increase in the depth of fracture cracks with extrusion ratio. However these criteria, which are dependent on the deforming zone stresses and extrudate residual stresses, respectively, do not successfully predict the increase in fracture with increasing die entry angle observed experimentally. Three criteria based on ductile fracture are also investigated and difficulties associated with their accurate evaluation in extrusion problems highlighted. However, all three successfully predict the increase in fracture with increasing die entry angle. In considering the effect of extrusion ratio on surface fracture, two of these criteria should be at least qualitatively correct while for the third this is unlikely.     

Round-to-channel section extrusion through linearly converging die: a three-dimensional analysis

Metal flow in the extrusion process is an important factor in controlling the mechanical properties of the extruded products. It is, however, difficult to predict the metal flow in three-dimensional extrusion of sections due to the involvement of re-entrant corners. The present work is an attempt to find an upper bound solution for the extrusion of channel section from round billet through the taper die. The rigid-perfectly plastic model of the material is assumed, and the spatial elementary rigid region (SERR) technique is presented for which the kinematically admissible velocity field is found out by minimizing the plastic dissipation of power. The presented analysis allows for specification of process control parameters and their relation to extrusion load, equivalent die angle, reduction ratios and friction factor.