型材挤压过程工艺参数优化模型

提出了一种集数值仿真、人工神经网络和遗传算法为一体的工艺参数优化模型,用于型材挤压成形过程工艺参数优化,合理配置了非对称角铝型材模模孔位置。通过现场试验,验证了提出的工艺参数优化模型是行之有效和正确的。并在模孔位置优化配置结果基础上对其挤压成形过程进行数值仿真,分析了挤压成形过程中各阶段网格畸变情况,给出了挤压变形时应力和应变分布,对指导型材挤压工艺和模具优化设计具有重要意义。     

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.     

凹模型线对挤压过程的数值模拟和试验研究

本文用数值拟和试验研究相结合的方法分析凹模型线对挤压过程变形状态的影响。模拟计算采用刚塑性有限元法,试验研究用坐标网格法和密栅云纹技术。文章对文献中提出的圆锥凹模、余弦曲线凹模、等应变率曲线凹模、双曲线凹模、椭圆曲线凹模和最短流线凹模,以及另外新设计的正弦曲线凹模,进行数值模拟,得到了各种型线模挤压时的速度场、应力场和应变场,以及由于变形热效应引起的试件和模具温升。并用光刻网格法和密栅云纹法进行试验校核。计算结果与实验结果相互吻合良好,研究结果表明七种曲线凹模中,以新设计的正弦曲线凹模最佳,余弦曲线凹模次之,这两种型线凹模的挤压力低,而且内部应变分布均匀。     

Analytical,numerical and experimental approach for design and development of optimal die profile for the cold extrusion of B4C DRMM Al 6061 composite billet into hexagonal section

Aluminium based matrix composites with boron carbide as particle reinforcement called Discontinuous reinforced metal matrix composites (DRMMs) possess high specific strength, high elastic modulus, good wear resistance, damping capacity and thermal stability. But during the development of DRMM composites, compression process like extrusion is an advisable secondary process for homogenous structure. This research work investigates the metal flow behavior of Al-B₄C based DRMM composite through six different die profiles namely third order polynomial, fourth order polynomial, cosine, elliptical, hyperbolic and conical geometry. Extrusion load, stress and strain distribution, and metal flow for above said die profiles are predicted by using analytical approach upper bound technique and compared with finite element method. Cosine and third order polynomial profiles are found to be most optimal in terms of homogenous and minimal extrusion load requirement. To validate the results, specially made Al-B₄C composite through stir casting route was extruded from round to hexagon through an exclusively fabricated cosine die. Results observed from the experiment have good agreement with both analytical and numerical.

     

悬臂铝合金型材伪分流挤压模具结构设计及其强度分析

铝型材挤压工艺和模具设计不仅需要保障挤出型材质量,还要保障模具强度和寿命,但对于大而长的悬臂铝合金型材,常规平模或导流模结构设计往往导致模具悬臂部位损坏,即使将模具相应部位加厚,也很难达到提高模具强度的要求。以某大悬臂铝型材为例,研究伪分流模具结构设计方法及长悬臂梁分解技术,对比分析常规模具设计与伪分流模具设计对型材挤压速度分布、温度分布、材料粒子运动轨迹等的影响规律,研究不同结构的模具强度。研究表明,采用伪分流模具不仅能够大幅度降低模具应力,而且通过材料流动优化可获得良好的材料流动规律和型材质量。总结给出伪分流结构的设计原则。     

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.     

Optimal Shape Design of an Extrusion Die Using Polynomial Networks and Genetic Algorithms

Designing the optimal shape for an extrusion die to produce a high-quality extrusion product is often required by industry. Design from experience is unsatisfactory for achieving the flexibility and precision requirements in die design. In this paper, a design method has been developed for the optimum shape design of extrusion die. The extrusion process was modelled and analysed by using the finite-element method to obtain the extrusion force and effective strain for different die shapes. A polynomial network was applied to identify the force and strain models in terms of the geometric parameters of the extrusion die. An improved genetic algorithm was used to optimise the identified model for optimal shape with minimum force and strain. It has been verified that the modelling error is extremely small. The designer can quickly and accurately access the optimal shape of an extrusion die through this new approach. RID=" ID=" <E5>Correspondence and offprint requests to</E5>: Dr Y.-C. Hsu, Department of Mechanical Manufacturing Engineering, National Huwei Institute of Technology, 64 Wun-Hua Road, Huwei, Yunlin, Taiwan. E-mail: jasonych&commat;sunws.nhit.edt.tw     

铝合金轴固定件热挤压成形的有限体积法模拟研究

由于变形剧烈，复杂铝型材挤压成形有限元模拟会因网格不断重划分而精度欠佳。文中基于可以有效避免网格重划分难题的有限体积法，对铝合金门轴固定产品的热挤压过程进行数值模拟，详细分析挤压成形中各个阶段金属流动情况以及应力、应变、温度、速度等场量的分布变化情况。棒料进人模口至完全流出工作带这段时间是型材挤压最为困难的阶段，材料在工作带处的应力、应变最大，温度最高，因而对模具工作带处造成的磨损也最为严重。进人到最终稳定挤压阶段时挤压方向金属流速计算值与理论挤出速度吻合很好。模拟结果表明所用有限体积法是有效的，可以为铝型材挤压的模具设计与工艺参数的选择提供理论指导。     

弹塑性有限元法分析不同型线凹模静液挤压时的应力和应变状态

静液挤压时,如凹模的型线不同,变形区的应力和流动状态是不同的。目前,静液挤压时,广泛采用圆锥模,但在挤压脆性金属时,产品经常会出现缺陷。为了研究产生缺陷的原因,应用弹塑性有限元法计算和分析了等应变型线模、余弦型线模、最短流线模、椭圆型线模及圆锥模等五种不同型线凹模在静液挤压时的应力和应变状态。结果表明,等应变型线凹模挤压时的应力和应变分布最为均匀,挤压力和塑变区内的拉应力最小,适用于挤压脆性金属。计算结果与实验比较,符合很好。计算结果对设计挤压凹模有很大的参考价值。     

Microstructure analysis of aluminum extrusion: grain size distribution in AA6060, AA6082 and AA7075 alloys

Microstructure and material flow of aluminum alloys have a significant influence on the mechanical properties and surface quality. In extrusion of aluminum billets at high temperatures the microstructure is dependent on the alloy and the forming and temperature history. A prediction of grain size and precipitation is of increasing importance in order to design the process by adjustment of parameters such as punch speed, temperatures, and quenching. To give references for microstructure prediction based on material flow, and with it strain and strain rate history, this paper deals with the microstructure during the extrusion process of AA6060, AA6082, and AA7075 alloys. Billets have been partly extruded to axisymmetric round profiles and the microstructure of the press rests consisting of the billet rests in container and die has been considered. Furthermore, these rests have been analyzed to show the material flow, dynamic and static recrystallization based on macro etchings and visible microstructure under different conditions, e.g. as in the area of high strain rate near the container wall, or in dead zones [1]. To allow an accurate simulation of the extrusion process, punch force and temperature conditions during the tests have been measured and are presented in this paper, too.     

Design and analysis of streamlined extrusion die for round to hexagon using area mapping technique,upper bound technique and finite element method

Extrusion is one of the most important metal forming process commonly used for the manufacturing of the hexagonal rods. Extrusion of metal through a conventional shear faced die experiences few practical limitations such as dead metal zone, more redundant work etc. Most of the research works have proved that the streamlined die used for extrusion is more efficient than the conventional shear faced die. Design of streamlined die using arbitrarily shaped curves and conventional curves have been done by many researchers. In this study, a new approach of transforming the peripheral point on the surface of round to corresponding point on the extruded hexagon has been obtained by an analytical method. Further the prediction of force required to extrude, the development of stresses and strain have been solved with a combined approach of upper bound theorem and finite element technique by considering the profile as cosine curve. Later the experimental study has been conducted for validating these approaches to register the benefit of cosine profile.     

基于变形均匀性的锻造模具形状优化设计方法

以直接设计预成形模具形状为目标,提出并建立了一种控制变形均匀性的灵敏度分析理论和模具形状优化设计方法。以任意单元的等效应变与所有单元的平均等效应变的差值的平方和作为目标函数,Ｂ样条曲线表示模具形状,Ｂ样条曲线控制点坐标作为优化设计变量,优化设计的目标是通过设计预成形模具形状使目标函数最小,即使整个工件的变形尽可能均匀。给出了目标函数的表达形式,详细推导了目标函数、单元等效应变率和单元各应变率分量对优化设计变量的灵敏度,给出了优化设计的步骤。应用该方法对圆柱体平模镦粗工艺进行预成形优化设计,给出了相应的优化设计结果,并提出了一种检验优化结果的变形均匀因子,优化与未优化结果的比较表明优化取得了良好的效果。     

多目标质量的粉末包套等通道挤扭成形致密工艺参数优化

剧烈塑性变形法—挤扭以剪切塑变为主变形方式,成形工艺复杂,影响因素很多,难以精确地建立工艺参数与成形质量之间的关系;选取优化合理的工艺参数匹配是材料尤其是粉末材料成形无破裂、塑性好、致密化程度高等成形质量的关键。以等通道横截面扭转角、螺旋角、摩擦因子、挤压速度、初始相对密度为自变量,正交试验为设计方案,对纯铝粉末烧结材料进行一道次包套等通道扭挤数值模拟,获得以等效塑性应变、静水压力、最大损伤值、相对密度数据,通过层次分析法计算多质量目标的权重,运用追踪点法和灰色系统理论的灰色关联度优化工艺参数,使设计目标值达到等效应变最大、静水压力最大、最大损伤值最小、相对密度最大。模拟和试验结果表明,运用多目标优化组合参数进行等通道挤扭成形能使纯铝粉末体材料迅速地形变累积,静水压力提高,损伤值显著地减小,致密效率高,晶粒明显细化,提高了材料综合质量。     

混合多目标遗传算法及其在热挤压模具型腔形状优化设计中的应用

将复合形法引入遗传算法来反映决策者对多目标问题中各目标函数的偏好信息，提出一种新的结合复合形法的混合多目标遗传算法。针对热挤压模具型腔轮廓形状优化问题，结合刚-粘塑性有限元模拟和神经网络技术，利用三次样条函数插值来表达凹模型腔轮廓形状，以表面载荷沿凹模型腔轮廓表面均匀分布和挤压力最小为目标，建立了多目标优化的数学模型，对挤压模具型腔轮廓形状进行多目标优化设计，得到了最优的凹模形状。对几种不同模具凹模型腔采用MARC／AutoForge有限元软件进行数值模拟对比研究，结果表明，结合复合形法的多目标遗传优化算法是一种较好的模具型腔形状多目标优化设计方法，其优化结果是有效的和显著的。研究结果说明，通过优化型腔形状来提高模具寿命的效果十分显著。     

Finite element analysis considering fracture strain of sheath material and die lubricant in extrusion process of Al/Cu clad composites and its experimental investigation

Clad composite materials consist of stacks of different materials. During the extrusion process of clad composites, fracture of the sheath or core materials frequently occurs because of the discontinuity of deformation caused due to the differences in the flow stress of the sheath material and core material. In order to predict fracture of the sheath material with oxygen-free high conductivity copper, the theory of ductile fracture has been applied. The effect of lubrication behavior on fracture of core material has been investigated. A technique to predict the fracture strain rate has been proposed. The calculated interface bonding force between the core material and the sheath material has been used to assist in die design for the indirect and direct extrusion processes.     

Selection of optimal process parameters in WEDM while machining Al7075/SiCp metal matrix composites

Aluminium metal matrix composites (MMCs) reinforced with silicon carbide particulate (SiCp) find several applications due to their improved mechanical properties over the conventional metals for a wide variety of aerospace and automotive applications. However, the presence of discontinuously distributed hard ceramic in the MMCs made them as difficult-to-cut materials for conventional machining methods. The wire electrical discharge machining (WEDM), as a widely adopted non-traditional machining method for difficult-to-cut precision components, found an appropriate metal removal process for MMCs to enhance quality of cut within the stipulated cost. While machining the advanced materials like MMCs, a clear understanding into the machining performance of the process for its control variables could make the process uncomplicated and economical. In light of the growing industrial need of making high performance-low cost components, the investigation aimed to explore the machining performance characteristics of SiCp reinforced Al7075 matrix composites (Al7075/SiCp) during WEDM. While conducting the machining experiments, surface roughness, metal removal rate, and wire wear ratio are considered the responses to evaluate the WEDM performance. Response surface methodology is used to develop the empirical models for these WEDM responses. SiC particulate size and volume percentages are considered the process variables along with pulse-on time, pulse-off time, and wire tension. Analysis of variance (ANOVA) is used to check the adequacy of the developed models. Since the machining responses are conflicting in nature, the problem is formulated as a multi-objective optimization problem and is solved using the Non-dominated Sorting Genetic Algorithm-II to obtain the set of Pareto-optimal solutions. The derived optimal process responses are confirmed by the experimental validation tests, and the results are analyzed by SEM.     

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.     

Mechanical property changes in drawing/extrusion of hardening viscoplastic materials with damage

This paper is concerned with the mechanical property changes in drawing/extrusion operations of hardening viscoplastic materials with damage. The process model in this study includes two state variables, the hardness for strain hardening from slip dominated plastic distortion and the porosity for damage from growth of microvoids. The decrease in apparent density in strip drawing of aluminum for several die angles are computed and compared with that from experiments. Simulations of axisymmetric drawing/extrusion have shown that the accumulated porosity in drawing is much bigger than that in extrusion while the difference between the hardness distributions in these processes are insignificant. The effects of the process conditions, such as conical die angle, friction and drawing/extrusion speed, on the mechanical property changes are also examined.     

Die optimization design and experimental study of a large wallboard aluminum alloy profile used for high-speed train

The extrusion die plays a crucial role in the quality control of aluminum alloy profile production. But in practice, the design of extrusion die is mainly dependent on the experience and intuition of die designers; thus, many times of modifications and experiments should be undergone until an acceptable product is gained. In this paper, the extrusion process of a large wallboard aluminum alloy profile used for high-speed train was simulated by means of HyperXtrude software, and the flow behavior of material and deformation mechanism in the die cavity were investigated. With the simulation results of the initial die design scheme, a nonuniform velocity distribution in cross-section of the extrudate was observed. For optimizing the die design scheme, two optimal schemes (adoption of double-step welding chamber and introduction of baffle plate) were proposed. Through optimization, the velocity differences in the extrudate for optimal schemes are decreased from 39.9 to 12.2 and 10.8 mm/s, respectively. Thus, the uniformity of velocity distribution was improved in optimal schemes. The extrusion die design methods for large wallboard profiles were summarized and proposed, including the design methods of baffle plate and double-step welding chamber. Through trial production, a sound wallboard aluminum profile with good geometric shape and high dimensional accuracy was gained. Additionally, the mechanical properties of the extrudate were examined by means of experimental method. It is found that the test results stratified the practical engineering requirements.     

An optimization strategy for die design in the low-density polyethylene annular extrusion process based on FES/BPNN/NSGA-II

An optimization strategy for die design in the polymer extrusion process is proposed in the study based on the finite element simulation, the back-propagation neural network, and the non-dominated sorting genetic algorithm II (NSGA-II). The three-dimensional simulation of polymer melts flow in the extrusion process is conducted using the penalty finite element method. The model for predicting the flow patterns in the extrusion process is established with the artificial neural network based on the simulated results. The non-dominated sorting genetic algorithm II is performed for the search of globally optimal design variables with its objective functions evaluated by the established neural network model. The proposed optimization strategy is successfully applied to the die design in low-density polyethylene (LDPE) annular extrusion process. A constrained multi-objective optimization model is established according to the characteristics of annular extrusion process. The minimum of velocity relative difference, δu, and the minimum of swell ratio, S _w, that, respectively, ensure the extrinsic feature, mechanical property, and dimensional precision of the final products are taken as optimization objectives with a constrained condition on the maximum shear stress. Three important die structure parameters, including the die contraction angle α, the ratio of parallel length to inner radius L/R _i, and the ratio of outer to inner radius R _o /R _i, are taken as design variables. The Phan-Thien–Tanner constitutive model is adopted to describe the viscoelastic rheological characteristics of LDPE whose parameters are fitted by the distributions of material functions detected on the strain-controlled rheometer. The penalty finite element model of polymer melts flowing through out of the extrusion die is derived. A decoupled method is employed to solve the viscoelastic flow problem with the discrete elastic-viscous split-stress algorithm. The simulated results are selected and extracted to constitute the learning samples according to the orthogonal experimental design method. The back propagation algorithm is adopted for the training and the establishment of the predicting model for the optimization objective. A Pareto-optimal set for the constrained multi-objective optimization is obtained using the constrained NSGA-II, and the optimal solution is extracted based on the fuzzy set theory. The optimization for die parameters in the annular extrusion process of low-density polyethylene is performed and the optimization objective is successfully achieved.