Analysis of hydrofilm extrusion of three-dimensional shapes from round billets

A new method of die construction is proposed, which enables the exact geometrical control of die shape and ensures the initial sealing between billet and die. Using the modified method of die construction the internal metal deformation is analyzed with the aid of a special transformation combined with the upper-bound method. Based on a concept of equivalent friction factor the energy dissipation in fluid film is calculated approximately for three-dimensional hydrofilm extrusion. Computations are carried out for hydrofilm extrusion of various sections such as squares, rectangles, ellipses and clover shapes and various factors affecting the process are discussed. Experiments are performed for clover and square sections using the dies from NC manufacture based on the suggested theoretical design. A reliable sealing system is developed between punch and container. The experimental results are compared with the theoretical prediction and it is shown that the theory is in reasonable agreement with the experimental observation. Various aspects are discussed from the experiment.     

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.     

Axisymmetric extrusion through adaptable dies—Part 3: Minimum pressure streamlined die shapes

In Part 1 of this series of papers, six kinematically admissible velocity fields, as well as the power terms, were developed for use in upper bound models for arbitrarily shaped dies for axisymmetric extrusion. Part 2 compared the results obtained in upper bound models for the six velocity fields through a spherical die shape and demonstrated that the sine-based velocity field was the best. In this final part, the application of the sine-1 field to extrusion through streamlined dies is developed. By fixing the values of two additional constants in the radial flow flexibility function, the two surfaces of velocity discontinuity, which separate the deformation zone from the incoming and outgoing material, will have no shear. In effect, the analysis for streamlined dies can be modeled without the surface of velocity discontinuity power terms. The results for an arbitrarily curved streamlined die, as proposed by Yang and Han, using the sine-1 velocity field and the cylindrical velocity field from the work by Yang and Han are compared. It is found that the upper bound model using the sine-1 velocity field predicts lower values for the extrusion pressure. A method to determine a streamlined die shape is proposed. The method allows flexibility between the entrance and exit by the use of a Legendre polynomial series for representation of the die surface. The method is termed an adaptable die design. The adaptable die design method is used to determine streamlined die shapes, which will minimize the pressure required for the extrusion process.     

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 die design model for thin section extrusions

In an extrusion plant, the die design procedure is very often a trial-and-error process which requires a number of extrusion trials before reaching a satisfactory design. If the die is not corrected or tuned appropriately, the product may be twisted and warped. In this work, a model is proposed which should guide the preliminary design of extrusion dies. The model is focused on the distortions of the extruded product due to exit velocity variations. The die design model is limited to the extrusion of thin sections through solid dies. Since the die opening is assumed to be long and slender, asymptotic approximations have been used in the analysis. Some die design examples are discussed.     

Evaluation of a pyramid die extrusion for a hollow aluminum profile using FE simulation

The pyramid die extrusion for a hollow aluminum profile was analyzed to investigate the potential of such innovative dies. For this purpose, the pyramid and conventional porthole dies were respectively designed for a given hollow aluminum profile. And the extrusion process was comprehensively studied by performing different types of finite element simulation, such as the analysis of steady state, transient state and billet skin tracking. The effects of pyramid angle on the evaluation parameters of extrusion, such as extrusion load, material flow, exit temperature, length of transverse weld, quality of longitudinal weld, back end defect and die stress were overall analyzed and compared with the conventional porthole die. Through this study, the advantages and shortcomings of pyramid die were well concluded, which should be important information for die designers and makers.

     

陶瓷浆料微流挤压成形关键问题研究

利用流体力学理论,针对基于微流挤压成形的陶瓷浆料挤出过程的关键部件挤压凹模的流道形状进行了设计,使用ANSYS软件对挤压凹模出口横截面的流速和流道内部压力场的分布情况进行模拟,分析了四种不同流道形状挤压凹模内部压力场和出口流速的分布规律。研究结果为解决陶瓷浆料挤压成形工艺的难点问题提供了理论依据,具有重要的参考价值。     

Extrusion of non-symmetric T-shaped sections, an analysis and some experiments

In the present study, previously developed analytical approach (Int. J. Mech. Sci. 42 (2000) 273), based on the upper-bound theory, for the design of three-dimensional off-centric extrusion of arbitrarily shaped dies was applied to the extrusion of T-shaped sections from initially round billets with the experimental verifications. Here, non-symmetric T-shaped sections as well as symmetric ones were considered. A computer program was written to obtain optimum die design which yield the lowest upper-bound for a given reduction in area, die length, its off-centric positioning and the frictional conditions. Computations were carried out both for the converging (ruled-surface) and the smooth curved (advanced-surface) dies. Curvature of the extruded product and simulated deforming grid pattern were also predicted. A sophisticated CAD/CAM package was used in conjunction with the CNC and EDM processes to manufacture the streamlined dies for the extrusion of T-shaped sections. The theoretical predictions were observed to be in good agreement with the experimental results.     

钢塑共挤模具导入角变化对聚合物熔体流动行为影响的数值模拟分析

以聚合物挤出过程有限元模型为基础,采用自主开发的有限元分析软件对幂律型流体在钢塑共挤模具分流段的流动过程进行了非等温模拟,获得了聚合物熔体在模具分流段内的速度场和温度场分布;分析了导入角变化对聚合物熔体流动行为影响的一般规律。结果表明:仅考虑导入角变化对流动行为的影响时,速度场和温度场的分布趋势基本不变;在垂直于流动方向的截面上的速度分布和在流动区域内的最大温升会略有改变。给出的如何合理选择导入角度的建议,对模具设计与优化具有一定的指导意义。     

An analytical formulation as an alternative to FEM software giving strain and stress distributions for the three-dimensional solution of extrusion problems

A new improved analytical method based on the upper bound theorem is presented for the solution of extrusion problems. This method has been formulated in such a way as to eliminate the deficiencies in the previous works in order to enable it as a powerful analytical tool as an alternative to finite element software. The proposed formulation is a general method of solution, which could be used for the analysis of many bulk forming processes. However, in this paper, the forward extrusion of a square section from a round billet has been presented as an example. Kinematically admissible velocity fields were computed which gave a more physically realistic material flow patterns as compared to previous works. The distribution of strain and stress as well as the results for the effect of process parameters on the extrusion load and die geometry was also given. These results were compared with FEM data to observe the accuracy and effectiveness of the present method. For the extrusion of square sections from round billets, detailed analysis of strain distribution on the exit section was carried out using the components of the power due to internal deformation, interface friction, and velocity discontinuities at the entry and exit surfaces. Comparison with experimental data was made, and verification of the theoretical results was carried out. The improvement of the results computed using the present method was shown by comparison with the previous works.     

Application of an upper bound method to off-centric extrusion of square sections, analysis and experiments

The previously given analytical method [1], which was based on the upper-bound theory, was used to design the streamlined dies and to investigate the three dimensional off-centric extrusion of circular sections from initially circular billets through linearly converging (ruled-surface) and smooth curved (advancedsurface) dies. For a reasonably correct upper-bound to the load, a set of generalised kinematically admissible velocity fields were derived on the assumption of Bezier-type streamlines by incorporating a special velocity function that takes care of the non-uniform material flow. Based on the present method, for a given reduction in area, material property, friction condition and off-centric positioning of the exit cross-section, computations were carried out to predict the upper-bound to the extrusion pressures, the deforming grid patterns and curvature of the extruded product. Experiments were carried out for some off-centric circular sections with varying die lengths and reduction in areas. A sophisticated CAD/CAM package was used in conjunction with the CNC and EDM processes to manufacture the streamlined dies for the off-centric extrusion of circular rods. Both the solid and split-type specimens made of tellurium lead under both the lubricated and the dry conditions were used for experimental investigations in order to assess pressures, deformation modes and to visualise the deforming grid patterns. The theoretical predictions were observed to be in good agreement with the experimental.     

分流组合模挤压过程数值模拟及模具应力分析

采用有限体积数值模拟方法研究分流组合模中焊合室的深度对铝型材挤压过程的影响,分别采用21mm、26mm和31mm三种焊合室深度对挤压过程进行了模拟,得到了应力、应变、挤压力等各种物理场量的变化规律,并采用有限元法对模具受力及变形情况进行了分析。研究结果表明,焊合室深度对载荷影响不大,但焊合室深度为26mm时质点流速最均匀。模具变形分析结果表明,随着焊合室深度增加,模芯变形程度增大,对应力分布来说,存在一个最佳的焊合室深度。从型材产品质量和模芯变形量综合考虑,应合理设计焊合室深度。     

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。     

Further investigation into extrusion of trocoidal gear sections considering three-dimensional plastic flow

In the present study, theoretical development proposed in previous work carried out in extrusion of clover sections in relation to a generalized die design method is presented in the extended scope for three-dimensional extrusion of trocoidal gear sections from round billets with experimental verification. Computations are carried out for clover and trocoidal gear sections. The CAD/CAM of the suggested dies is introduced for the experiments. Experiments are carried out for a clover section and a trocoidal gear section with eight teeth. Al 2024 aluminum billets were used as the working material. Half-cut specimens are used for flow visualization of the extrusion process. The theoretical predictions are in good agreement with the experimental results in extrusion load and metal flow.     

Upper bound analysis of extrusion from square billets through circular and square/rectangular dies

Upper bound elemental technique (UBET) for prediction of extrusion pressure in three-dimensional forward extrusion process is presented. Using square/rectangular billets, the study of the effect of die land length has been extended for the evaluations of extrusion pressures to extrude sections such as circular, square and rectangular shaped sections with power of deformation due to ironing effect at the die land taken into account. The extrusion pressure contributions due to the die land evaluated theoretically for these shaped sections considered are found to increase with die land lengths for any given percentage reduction and also increase with increasing percentage die reductions at any given die land length. The effect of die land lengths on the extrusion pressures increases with increasing complexity of die openings geometry with rectangular section giving the highest extrusion pressure followed by circular with square section die opening, giving the least extrusion pressure for any given die reduction at any given die land lengths. The proper choice of die land length is imperative if excessive pressure buildup at the emergent section is to be avoided so as to maintain good quality and metallurgical structure of the extrudates. This paper was recommended for publication in revised form by Associate Editor Youngseog Lee Ajiboye, Joseph S. received his B.Eng, M.Eng, and PhD degrees in Mechanical Engineering from the University of Ilorin, Nigeria, in 1988, 1995 and 2006 res-pectively. Dr. Ajiboye is a lecturer in the Department of Mechanical Engineering, Uni-versity of Lagos, Nigeria. He is currently a Contract Research Scientist at KAIST Valufacture Institute of Mechanical Engineering, School of Mechanical, Aerospace & Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305 - 701, Korea. Dr. Ajiboye’s research interests include ECAE/P, determination of frictional effects in metal forming operations, upper bound and finite element in plasticity.     

口模压缩段对塑料挤出流动影响的有限元分析

在塑料挤出成形过程中，压缩段是调节模头流道各部分流量(流速)的主要区段，对熔体的流动具有重要影响。本文采用有限元数值分析方法，计算了熔体在口模内流动的速度场和压力场，定量分析了压缩比和压缩角等压缩段模具结构参数对挤出速度分布、挤出流量和挤出流动均匀性等的影响规律，为优化流道结构参数，提高挤出流动均匀性的研究提供了基础。     

基于数值分析的塑料挤出模优化设计方法研究

以比例间隔法和射线法相结合的办法建立面向CAE的挤出口模的参数化模型,在对其进行三维数值分析得出流道内压力和速度分布的基础上,以口模出口处型材截面上各子区域平均流速相等为优化目标,基于有限元分析结果和参数化流道模型建立目标函数的数学模型,对模具的一些重要结构参数进行设计优化,优化结果可以直接映射到参数化模型,实现了CAE/CAD的直接集成。通过一个算例的分析,验证了该方法的正确性和有效性。     

聚合物气体辅助挤出中气体流动对熔体截面的影响

将聚合物熔体和低速热空气均视作不可压流体,针对一聚苯乙烯（PS）片材的全气体辅助挤出,建立了描述其气体-熔体两相分层流动的三维有限元模型,采用黏弹应力分离法（EVSS）和非协调流线迎风法（SU）等有限元方法,利用PolyFlow求解器对气体辅助流道中气体和熔体流动进行了计算,分析了熔体截面变化的规律及原因。研究结果表明：气体辅助流道内,气体对熔体有拖曳作用;沿挤出方向,熔体速度逐渐增大,而截面积逐渐减小,都在口模出口面上达到极值,同时截面形状有微小改变;口模出口面上熔体沿挤出方向的速度随入口气体体积流率的增大而近似线性增大,熔体截面积则近似线性减小。     

Die design optimization for axisymmetric hot extrusion of metal matrix composites

Strain rate sensitive materials such as Ti alloys, superplastic materials and metal matrix composites (MMCs) can be deformed only in very narrow range of strain rate. In this work, a new process design method for controlling strain rate in workpiece during hot extrusion process is proposed. In this approach, a coupled numerical approach of finite element analysis and optimization technique to optimal profiled die which yields more uniform strain rate distribution in the deforming region is applied to the hot extrusion process of MMCs. Extrusion die profiles are defined by Bezier curves, and FPS (flexible polyhedron search) method is used as optimization technique. The change of relative deviation of strain rate, the progressive development of die profiles with increase of iteration for optimization and the corresponding strain rate distributions are investigated. In addition, the die profiles by optimization scheme for different extrusion ratios are compared with those by analytical solution.     

Numerical and experimental study on the three-dimensional extrusion of square section from square billet through a polynomial shaped curved die

The geometry of die profile plays a major role in reducing the extrusion pressure and ensuring the smooth flow of material. In general, the extrusion process is mostly affected by billet geometry, die geometry, and interface frictional force at the die billet geometry. In the present investigation, an analysis using three-dimensional upper bound method using fifth-order die profile function has been carried out for extrusion of square sections from square billet. The extrusion pressure and optimum die length have been computed by multivariable optimization technique. The present die shape profile is found to be superior to many other profiles. The results obtained will help in design of optimum die profile and investigation of its performance.