Determination of blank shapes for drawing irregular cups using an electrical analogue method

An electrical analogue method is introduced to determine optimum blank shapes for deep-drawing cups of irregular cross-section. Square and rectangular cups were drawn from aluminium and steel blanks having these shapes and required very little trimming. Comparison is made with other methods of developing blanks and although one empirical method gave reasonable results for rectangular cups it is concluded that the electrical analogue method is preferred; it is also applicable to irregularly shaped cups.     

Blank development and the prediction of earing in cup drawing

The article deals with the prediction of blank shapes using the method of plane strain characteristics. In one case the material is assumed to be an incompressible, non-hardening, isotropic solid, and ideal blank shapes are developed when deep drawing prismatic cups. The significance of the study is that the resulting slip line field pattern does not violate the Hencky equations. The earing behaviour when deep drawing cylindrical cups from circular disks has also been predicted based on a particular form of anisotropy which allows for four fold symmetrical earing. The technique permits the blank shape to be calculated throughout the entire drawing operation, and demonstrates how the ears develop.     

Wrinkling control in aluminum sheet hydroforming

In this paper, the wrinkling behavior of 6111-T4 aluminum alloys during sheet hydroforming process was numerically and experimentally investigated. In sheet hydroforming, one or both surfaces of the sheet metal are supported with a pressurized viscous fluid, while a punch forms the part. In sheet hydroforming the use of a matching female die is not needed. The use of the pressurized fluid delays the onset of material rupture (International Journal of Mechanical Science 2003;45:1815–48) and also acts as an active blank-holding force to control wrinkling in the flange area. To form a wrinkle-free deep-drawn hemispherical cup with sheet hydroforming, a theoretical analysis based on the work of Lo et al. (Journal of Materials Processing Technology 1993;37:225–39) was initially used to predict the optimum fluid pressure profile. Simplifying geometrical assumptions and Tresca material model used in the theoretical analysis provided a fluid pressure profile that resulted in premature rupture of the sheet metal. However, an optimum fluid pressure profile generated by the finite element method, using Barlat's anisotropic yield function (Journal of Mechanical Physics and Solids 1997;45(11/12):1727–63), was successfully applied in sheet hydroforming to make the deep-drawn hemispherical cup without tearing and with minimal wrinkling in the flange area. The finite element model was also capable of accurately predicting the location of the material rupture in pure stretch, and wrinkling characteristics of the aluminum alloy sheet in the draw-in process.     

Blank optimization for sheet metal forming using multi-step finite element simulations

The present study aims to determine the optimum blank shape design for deep drawing of arbitrary shaped cups with a uniform trim allowance at the flange, i.e., cups without ears. The earing, or non-uniform flange, is caused by non-uniform material flow and planar anisotropy in the sheet. In this research, a new method for optimum blank shape design using finite element analysis is proposed. The deformation process is first divided into multiple steps. A shape error metric is defined to measure the amount of earing and to compare the deformed shape and target shape set for each stage of the analysis. This error metric is then used to decide whether the blank needs to be modified. The blank geometry change is based on material flow. The cycle is repeated until the converged results are achieved. This iterative design process leads to optimal blank shape. To test the proposed method, three examples of cup drawing are presented. In every case converged results are achieved after a few iterations. The proposed systematic method for optimal blank design is found to be very effective in the deep drawing process and can be further applied to other sheet metal forming applications such as stamping processes.     

先进充液柔性成形技术及其关键参数研究

基于所提出的具有均匀压边力并轴向加压的板材充液柔性成形技术,面向板材液压柔性成形技术的普遍规律,成形出拉深比较高的铝合金筒形件以及其他复杂形状的零件如方锥盒形件、方盒形件、轴对称锥形件等,对其中的关键技术如初始液压加载状态、液压加载最优路径、破裂控制等一些关键参数进行了研究和优化;考虑板平面方向性系数的影响,利用数值模拟的手段对其成形过程进行了分析,指导实验研究,得出了有益的结论。     

The design of blank’s initial shape in the near net-shape deep drawing of square cup

Deep drawing process is very useful in industrial field because of its efficiency. The deep drawing is affected by many process variables, such as blank shapes, profile radii of punch and die, formability of materials and so on. Especially, in order to obtain the optimal products in deep drawing process, blank shape is very important formability factor. In this paper, the finite element method is used to investigate the cup height of the square cup drawing process. In order to verify the prediction of FEM simulation of the product’s height and forming load in the square cup drawing process, the experimental data are compared with the results of the current simulation. A finite element analysis is also utilized to acquire the designed profile of the drawn products, a reverse forming method for obtaining the initial blank’s shape according to the forward square cup drawing simulation is proposed. The design of initial blank’s shape is also certified to obtain the designed profile of drawn cups by experiment. The influences of the blank’s shape on the height of product, the forming load, the maximum effective stress and the maximum effective strain are also examined.     

Development of a hydroforming setup for deep drawing of square cups with variable blank holding force technique

Sheet hydroforming is a process that uses fluid pressure for deformation of a blank into a die cavity of desired shape. This process has high potential to manufacture complex auto body and other sheet metal parts. Successful production of parts using hydroforming mainly depends on design aspects of tooling as well as control of important process parameters such as closing force or blank holding force (BHF) and variation of fluid pressure with time. An experimental setup has been designed and developed for hydroforming of square cups from thin sheet materials. Square cups have been deep drawn using constant and variable BHF techniques. A methodology has been established to determine the variable BHF path for successful hydroforming of the cups with the assistance of programmable logic controller and data acquisition system. Finite element (FE) simulations have also been carried out to predict formability with both of these techniques. It has been found that it is possible to achieve better formability in terms of minimum corner radius and thinning in the case of variable BHF technique than in the case of constant BHF technique (constant force during forming and calibration). The results of FE analysis have been found to be in good agreement with experimental data.     

Optimization of the design parameters of modified die in hydro-mechanical deep drawing using LS-DYNA

The use of a modified die enhances the limiting draw ratio compared to that obtainable in a conventional deep drawing operation. Application of these dies, in conventional deep drawing, eliminated the use of blank holder but enhances the tendency of wrinkling in drawn products. In hydro-mechanical deep drawing process, the punch deforms the blank to its final shape by moving against a controlled pressurized fluid. In this paper, a new concept of the application of modified dies in hydro-mechanical deep drawing is presented. The finite element (FE) simulations of a deep-drawing process using modified dies are performed using the 2-D explicit finite element code LS-DYNA, with the aim of optimization of design parameters and the results are compared with the experimental values. The initial design steps in the design of modified die in finite element simulation were taken from the concept of Tractrix die. The use of Tractrix die enhances the draw ratio but simultaneously increases the tendency of wrinkling. In this paper the design parameters of modified Tractrix die for hydro-mechanical deep drawing are optimized for the successful drawing of cups. It is also experimentally verified that by using such modified dies in hydro-mechanical deep drawing, deeper cups are drawn without wrinkling.     

板坯形状对方截面无模旋压轴向可旋深度的影响

利用实验方法对比了方形和圆形板坯形状对方截面无模旋压轴向可旋深度的影响,并对其影响机理进行了理论分析。首先采用确定初始步长的方法推导了可无限扩展的方截面旋轮路径公式,在此基础上分别模拟了方形和圆形板坯的无模旋压过程,并对模拟结果进行实验验证。然后提出了轴向可旋深度的评估方法,并以此为判据,对比分析了同轴向旋压深度下圆形和方形板坯工况的后续可旋性,发现方形板坯工况优于圆形板坯工况,进而揭示其机理为：方形板坯工况旋压过程中剩余法兰形状与旋轮路径切合性较好,促进了金属径向流动均匀化。     

基于类等势场的粉末高温合金盘件预成形设计及有限元模拟

为了提高产品的质量和工作效率并降低生产成本,需对预制坯进行合理的预成形设计.根据能量最小原理和最小阻力原理,利用塑性变形过程中坯料的流动规律与静电场等势线分布类似这一特性,提出一种能够进行预成形设计的新方法--类等势场法,并采用该方法对粉末高温合金盘件进行预成形设计,从中优选出6组预成形形状,并利用商用有限元软件MSC/SuperForm对上述预制坯的等温成形过程进行数值模拟,得到了6组粉末高温合金盘件终锻结束时各个部分的等效应变分布以及预锻和终锻的变形程度分配.通过对盘件轮毂、辐板和轮缘三部位以及整体盘件最大等效应变和最小等效应变的比较与分析,以及预锻变形量和终锻变形量的比较,并参考模具法向和切向的受载情况,认为选择3号预锻模为最佳方案.结果表明,该方法克服了传统方法精度低、耗时和耗力等缺点,其结果可靠.     

Optimum blank design by the predictor-corrector scheme of SLM and FSQP in the deep drawing process of square cup with flange

This paper presents a more accurate predictor-corrector scheme that combines the stream line method (SLM) and feasible sequential quadratic programming (FSQP) using the explicit dynamic finite element method (FEM) to design the optimum blank in the deep drawing process of square cup with flange. It is clear that faster convergence and better results of calculating optimum blank shape are guaranteed when FSQP uses a better initial guess. But it is not easy to guess the initial blank shape due to the variation of blank thickness, material anisotropy, and friction on the flange area at the beginning in the deep drawing process. SLM can obtain a preliminary prediction of the optimum blank shape with a little computational effort, so with SLM it is feasible to predict the initial guess of optimum blank with the assumption of fixed height of square cup with flange. FSQP can continue to adopt the predictor obtained by SLM to correct the optimum blank efficiently and accurately. Then the optimum blank is used in the final simulation and experiment. From comparison of the target shape between the simulated and experimental results, a good correspondence is confirmed. Other comparisons of the punch load, punch stroke, and wall thickness of the target square cup also show good agreement.     

Blank shape design for a planar anisotropic sheet based on ideal forming design theory and FEM analysis

A sequential design procedure to optimize sheet forming processes was developed utilizing ideal forming design theory, FEM analysis and experimental trials. For demonstration purposes, this procedure was used to design a blank shape for a highly anisotropic aluminum alloy sheet (2090-T3) that results in a deep-drawn, circular cup with minimal earing. All blank shape design methods require a certain number of iterations. However, the sequential procedure can be more effective than the other iterative methods based on FEM analysis in conjunction with experimental trials or on experimental trials alone. For this design demonstration, the anisotropic constitutive behavior of the 2090-T3 sheet was expressed using plastic potentials previously proposed by Barlat et al. The implementation of the anisotropic strain-rate potential in the ideal forming design code is also briefly summarized.     

复杂形状拉深件快速展开与成形模拟

基于UG的CAD技术 ,从UG中导出了零件几何信息数据 ,用文献 [1]提出的方法得到拉深件毛坯猜测值 ;采用大变形理论和理想变形假设 ,给出了用于复杂形状拉深件成形分析的一步法数学公式和有限元表达。在此基础上 ,对拉深件毛坯初始形状进行了优化 ,并就成形中拉深件厚向应变分布进行了分析 ,得到满意结果     

Fluid absorption study in ultra-high molecular weight polyethylene (UHMWPE) sterilized and unsterilized acetabular cups

The weight gain due to fluid absorption was measured in gamma-sterilized, ethylene oxide (ETO) gas-sterilized, and unsterilized ultra-high molecular weight (UHMW) polyethylene acetabular cups. After about 2 months the total average fluid absorption gain of the polyethylene cups was: 1.76 +/- 0.45 mg (average +/- standard deviation) for the unsterilized polyethylene cups, 2.81 +/- 0.95 mg for the gamma-sterilized polyethylene cups and 1.51 +/- 0.34 for the ETO gas-sterilized polyethylene cups. There was little difference in fluid absorption between the sterilized and unsterilized specimens. In particular, the gamma-sterilized acetabular cups absorbed more than the ETO gas-sterilized and the unsterilized cups. However, the weight gain was higher in serum compared with that in water.     

Unsteady potential and viscous flows between eccentric cylinders

This paper presents a newly developed spectral collocation method for the study of the unsteady annular flow between two eccentric cylinders. In order to predict the stability of a system in a confined flow, the formulae and results of added mass and fluid damping are provided in the present paper when a cylinder undergoes oscillatory motion in the plane of symmetry and normal to the plane of symmetry in an eccentric annulus. The potential flow theory has been developed to obtain the added mass for incompressible, inviscid and irrotational fluid. For the viscous fluid, the added mass and the viscous damping are presented. This method is validated by comparison with the available analytical solutions obtained for the unsteady potential flow in the eccentric annular space. Excellent agreement was found between the solutions obtained with the present spectral method and the available analytical solutions. In the present study, the viscous effect on the added mass can be evaluated, comparing the results obtained by potential flow theory with those obtained by the viscous flow theory, and viscous damping is investigated.     

冲压件的智能排样

本文提出针对冲压件的一种基于知识的智能优化排样技术。把数学方法、子目标法、启发式搜索法及符号推理方法有机集成，协同求解。首次将制件下料技术的作业性作为排样的一种约束条件，探讨了智能优化排样的一些关键技术方法。     

Optimum blank design in sheet metal forming by the deformation path iteration method

Optimum blank design methods have been introduced by many researchers to reduce development cost and time in the sheet metal-forming process. Direct inverse design method such as Ideal Forming (Chang and Richmond, Int J Mech Sci 1992; 34(7) and (8): 575–91 and 617–33) [7, 8] for optimum blank shape could play an important role to give a basic idea to designer at the initial die design stage of the sheet metal-forming process. However, it is difficult to predict an exact optimum blank without fracture and wrinkling using only the design code because of the insufficient accuracy. Therefore, the combination of a design code and an analysis code enables the accurate blank design. In this paper, a new blank design method has been suggested as an effective tool combining the ideal forming theory with a deformation path iteration method based on FE analysis. The method consists of two stages: the initial blank design stage and the optimization stage of blank design. The first stage generated a trial blank from the ideal forming theory. Then, an optimum blank of the target shape is obtained with the aid of the deformation path iteration method which has been newly proposed to minimize the shape errors at the optimization stage. In order to verify the proposed method, a square cup example was investigated.     

长颈法兰径向轧制过程中金属的轴向流动

通过对长颈法兰径向轧制过程中金属沿轴向的流动规律进行理论分析和实例计算，提出了径向轧制过程中存在着轴向流动以及流动量取决于环坯与成品截面形状的观点，指出了传统环坯设计方法存在的问题。     

基于有限元网格映射方法的精确反算求解毛坯

以有限元仿真技术为基础,提出了一个新的方法——有限元网格映射方法,解决了薄板冲压成形过程中毛坯反算的一些关键问题。有限元仿真能很好地模拟材料的流动,具体体现在网格上节点的移动,根据映射,确定不同时刻下单元中点的位置变化以及不同时刻位置变化之间的联系,从而能获知初始毛坯中哪些部分参与了零件成形,并最终获得优化的毛坯形状和尺寸。用一个复杂的V形件冲压实例验证了本方法的正确性和快速性。     

板材拉深成形电控永磁压边方法研究

为了克服传统压边方法不能独立施加压边力,电磁压边能耗高且发热量大的问题,提出了一种基于电控永磁技术的压边方法。根据电控永磁技术和拉深成形工艺的特点,研制了带有磁力压边装置的拉深成形模具。采用有限元方法模拟了磁极单元和磁垫的充退磁过程,在进行磁场和力学场耦合分析的基础上,确定了以磁吸力作为压边力施加在成形板坯上的接触压力分布。由有限元软件模拟的电控永磁压边与传统压边作用下板坯的成形效果可知,两种压边方法所得拉深件的应变分布基本一致。采用电控永磁压边方法分别对直径为180 mm和195 mm的08Al板坯（厚度为0.98 mm）进行了拉深实验,拉深高度为48 mm,结果表明,电控永磁压边方法可以实现压边力的独立加载,能够提供足够大的压边力。最后,分别计算了采用传统压边方法、电磁压边方法和电控永磁压边方法的能量消耗,其中,电控永磁压边方法节能效果最好,相对于电磁压边方法,节能高达95%以上。