On the optimal die curvature in deep drawing processes

The paper presents an attempt to increase the limit drawing ratio of deep drawing processes by searching an optimal die curvature, which minimizes the drawing load. The search done here for an optimal die curvature is based on experimental observations and followed by a detailed upper bound analysis. The analysis takes into account the non-steady character of the process (from a 2D circular plane blank into a 3D axisymmetric cup). The plastic flow along the die curvature is expressed in a toroidal coordinate system which seemingly describes more naturally a smooth velocity field along the real toroidal profile of the die. The outcome provides more closely the relationship between the energy dissipation rate and the die curvature so that a preferred die curvature is obtainable by energy minimization.Circular sheet blanks, made from aluminum and copper, were drawn through dies with different radii of curvature (with at least five repetitions at each radius) to capture the features of the optimal dies whenever exists.The main result is that under certain circumstances an optimal die curvature does exist. It depends largely on the drawing ratio and the blank/die interfacial friction, m, but appears quite insensitive to the initial thickness of the blanks. The optimal die curvature is pronounced in the cases where the frictional resistance is relatively low, otherwise it is indistinctable and remains practically undeterminable by designers.     

圆锥形凹模径向分块压边拉深工艺实验研究

采用圆锥形凹模拉深工艺可以提高成形极限,但需要用压边圈将板坯先压成与凹模面吻合的形状,当变形程度较大时,板坯很容易起皱。为了克服这一缺点,提出了将圆锥形凹模与径向分块压边方法结合的工艺,该工艺可有效改善压边圈与板坯的约束状态,从而达到抑制起皱的目的。对圆筒形件的拉深成形,采用了刚柔复合的径向分块压边圈结构,设计了圆锥形凹模径向分块多压边圈拉深模,取不同凹模半锥角的圆锥形凹模进行了圆筒形件的拉深成形实验。实验表明,新的压边方法能有效克服初始成形过程的起皱,可与锥度较小的凹模一起使用。采用凹模半锥角为45°的凹模,得到AA5754、AA6061和08Al三种板材的极限拉深系数分别为0.410、0.431、0.373,显著提高了成形极限。对圆锥形凹模的拉深成形,给出了理论计算成形极限的方法,理论与实验结果非常接近。     

Hydro-rim deep-drawing processes of hardening and rate-sensitive materials

The conventional deep drawing process is limited to a certain limit drawing ratio (LDR) beyond which rupture will ensue. An asymptotic solution of the complete governing equations of this process indicates that this relatively low LDR results from the steep build-up of radial tensile stress with maximum value at the die lip. This tensile stress is significantly enhanced by interfacial friction along the die/flange and by high speed of the operating load and thus holds responsible for premature ruptures. The intention of this work is to examine the possibilities of relaxing the above limitation, aiming towards a process with an ‘unlimited drawing ratio’. The ideas which may lead to this goal are:(a) exerting an external fluid pressure on the outside rim of the blank (“Hydro-rim process”) to reduce radial stress and to decrease, in parallel, the interfacial friction,(b) increasing the blank temperature to a level at which the material is more rate sensitive, and thus less prone to early failure. The benefits of these ideas are examined via parametric analysis of the solution and with experiments in deep drawing processes.A clear outcome from the solution is that if changes in the material properties (strain hardening, strain-rate sensitivity, yield stress, etc.) can be controlled, say, by controlling the temperature and/or the operating speed, the process can reach higher drawing ratios with substantially less assisted fluid pressure.     

混合压边液体内向流动动态充液拉深

为抑制液体内向流动动态充液拉深中凸缘增厚而造成的拉深阻力急剧增长,提出混合压边液体内向流动动态充液拉深新方法。对定间隙下设定恒定压边力的混合压边充液拉深压边形式实质进行分析,采用有限元研究混合压边方式下压边间隙、压边力以及径向压力的变化对成形过程的影响。研究结果表明:定间隙下设定恒定压边力的混合压边充液拉深压边形式的实质是设定压边间隙和设定压边力压边方式的混合;采用混合压边方式可以降低实际最大压边力,降低凸缘区的摩擦阻力,减少第二个谷底点的减薄率;压边力影响零件直壁部分壁厚分布,较大的压边力得到的零件直壁壁厚较薄;压边间隙的变化影响成形零件直壁壁厚分布,较小的压边间隙成形零件直壁较薄,第二个谷底点越接近零件底部。     

The effect of a multistep deep-drawing process with circular and rectangular shapes on the deformation of AZ31 magnesium sheets

This study has mostly focused on the forming limit, microstructural change, and anisotropy that arise from rectangular and circular deep drawing of magnesium sheets. Moreover, this study predicts the change in the material thickness and the forming depth at the first forming process that produces the rectangular cup by the deep drawing of the rectangular blank. Further, by using the rectangular cup that is formed by the first forming process, when the circular and square cups in the rectangular cup are simultaneously manufactured in the so-called second forming process, the effect of the clearance between the die and punch on the change in the product thickness according to forming depth associated with microstructural analysis is investigated. The forming temperature is optimized to maximize formability. The results obtained in this study are utilized as data for predicting the die clearance and the change in the thickness.     

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.     

NUMERICAL SIMULATION AND EXPERIMENTAL RESEARCH ON HYDRAULIC COUNTER-PRESSURE DEEP DRAWING OF CONICAL PART

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The effect of die/blank holder and punch radiuses on limit drawing ratio in angular deep-drawing dies

Deep-drawing is one of the most important methods used to form sheet metal. The radius of die/blank holder and punch is important for deep-drawing dies because of an effective way to promote deep drawability sheet metal. This paper presents an attempt to determine the effect of various radiuses of die and punch on the limit drawing ratio and was investigated using DIN EN 10130–91 sheet metal. The die/blank holder profile with angles of α?=?0°, α?=?2.5°, α?=?7.5°, α?=?12.5°, α?=?15° and die/punch profile with radiuses for R?=?10, R?=?8, R?=?6, R?=?4 and R?=?0 mm were analyzed to determine the influence of punch force on the limit drawing ratio. The aim of this study is to investigate the effect of radius and angle variables on drawability in the deep-drawing process and to obtain useful data from the industrial field. The experiments show that the limit drawing ratio increased with increasing radius of punch (R), die/blank holder angle (α).     

Buckling prevention by lateral fluid pressure in deep-drawing

An instability analysis of flange buckling against lateral fluid pressure in deep drawing is considered. It is intended to explain the experimental fact that relatively low fluid pressure when applied to the flange area can suppress buckling. The analysis is based on the approximate ‘energy method’ with the inclusion of the work against the fluid. The attention is focused on the initiation of the deep drawing process, where buckling (of non-hardening material) is most susceptible. A special apparatus which enables the replacement of a rigid blank-holder by a lateral fluid-pressure was used for testing. A general solution to the critical pressure, above which the deep drawing can be terminated without buckling, is provided. The prediction of the critical pressure and the number of the associated buckling ‘waves’ (wrinkles) agree very well with the experiments. The pertinent geometrical and material variables (as blank thickness, drawing ratio, Young modulus, yield strength, etc.) are grouped in nondimensional form and plotted for various parameters to provide an engineering-type solution for potential users.     

数值模拟分析工艺参数与拉深件壁厚变化的关系

在分析板料拉深成形有限元理论的基础上建立数值模拟的分析模型,利用数值模拟技术系统地对拉深过程进行模拟。主要研究模具圆角半径、摩擦因数、压边力与模具间隙等工艺参数与拉深件壁厚最大变薄率的内在关系。     

Deep drawing with internal air-pressing to increase the limit drawing ratio of aluminum sheet

The effects of internal air-pressing on deep drawability are investigated in this study to increase the deep drawability of aluminum sheet. The conventional deep drawing process is limited to a certain limit drawing ratio(LDR) beyong which failure will occur. The intention of this work is to examine the possibilities of relaxing the above limitation through the deep drawing with internal air-pressing, aiming towards a process with an increased drawing ratio. The idea which may lead to this goal is the use of special punch that can exert high pressure on the internal surface of deforming sheet during the deep drawing process. Over the ranges of conditions investigated for Al-1050, the local strain concentration at punch nose radius area was decreased by internal air-pressing of punch, and the deep drawing with internal air-pressing was proved to be very effective process for obtaining higher LDR.     

On the hydrodynamic deep-drawing process

The feasibility of deep-drawing aided by hydrodynamic flow beneath the blank is demonstrated. The analytical background for directing the design of the process is based on the limit analysis in plasticity theory coupled with flow analysis of viscous, non-inertial fluid. It is done for isotropic non-hardening material with inclusion of constant friction coefficient as an additional parameter acting on plastic/rigid interfaces.The main attention is focused on approximating the Limit Drawing Ratio (LDR) via upper and lower bound and comparing the conventional process to the suggested hydrodynamic-aided process. The unique features of the process along with its limitations (geometrical and material-wise) are exhibited. The prominent role of the die curvature with regard to LDR is emphasized. A non-dimensional number combining fluid viscosity, punch speed, material strength and a characteristic length of the process (identified as Sommerfeld Number) appears as a useful measure for the clearance height through which the fluid flows. The study is corroborated with experiments.     

正交试验设计在TA2筒形件拉深成形过程中的应用

研究了TA2筒形件的拉深成形过程,对无压边圈情况下拉深成形的5个因素(凹模入口圆角、凸凹模间隙、模具与板坯之间润滑系数、凸模圆角、坯料直径)进行了有限元数值模拟及其正交试验,提出了采用成形后板坯最大厚度与最小厚度之差Δt的概念来作为描述零件成形结果的评价标准,且论证了采用该评价标准的合理性。对试验结果进行了直观分析和方差分析,得出了各因素对拉深成形过程的影响次序及显著性。     

拉深工艺变压边力控制数值模拟研究

根据实际生产中压边力的控制状况和理论分析确定了几种压边力变化曲线，以非轴对称抛物面车灯反光罩的成形为例，采用Dynaform软件对多种变压边力控制的成形工艺分别进行了数值模拟计算，分析了各种变压边力控制对成形的影响，并确定了对成形最为有利的压边力的变化趋势。     

A study on high ratio cup drawing by Maslennikov’s process

Deep drawing of sheet metals using Maslennikov’s technique has been analyzed by analytical and finite element simulation approaches. A new friction model based on local contact conditions has been used in the finite element (FE) simulations of the process. Compared to traditional Coulomb friction model, the results of FE simulations with the new friction model show good correlation with analytical calculations. The effects of key process parameters such as rubber ring thickness, ring inner diameter, die hole diameter, and die profile radius on the results have been investigated. The results showed that very deep cups without thinning in the side wall portion can be achieved with this process. Based on the results of FE analysis, it was found that the maximum drawing ratio can be achieved by adopting a combination of process parameters which correspond to points nearest to the fracture limit.     

Study on process parameters and its analytic application for nonaxisymmetric rectangular cup of multistage deep drawing process using low carbon thin steel sheet

Multistage deep drawing process is widely used to obtain various nonaxisymmetric rectangular cups. This deep drawing scheme including drawing and ironing processes consists of several tool sets to carry out a continuous production within one progressive press. To achieve the successive production, design and fabrication of the necessary tools such as punch, die, and other auxiliary devices are critical, therefore, a series of process parameters play an important role in performing the process design. This study focuses on the tool design and modification for developing the rectangular cup with an aspect ratio of 5.7, using cold-rolled low carbon thin steel sheet with the initial thickness of 0.4 mm. Based on the design results for the process and the tools, finite element analysis for the multistage deep drawing process is performed with thickness control of the side wall in intermediate blanks as the first approach. From the results of the first approach, it is shown that the intermediate blanks could experience failures such as tearing, wrinkling, and earing by excessive thinning and thickening. To solve these failures, the modifications for the deep drawing punches are carried out, and the modified punches are applied to the same process. The simulation results for the multistage rectangular deep drawing process are compared with the thickness distributions before and after the punch shape modifications, and with the deformed shape in each intermediate blank, respectively. The results of finite element reanalysis using the modified punches show significant improvement compared with those by using the original designed punch shapes.     

盘形件增量拉深成形过程的数值模拟

增量拉深成形由于旋转的模具与坯料接触区域的不断变化而一直是数值模拟的难点,为此用Deform-3D有限元软件对为A1100铝合金的盘形件增量拉深过程进行了数值模拟.结果表明:增量拉深成形凸模的受力与传统拉深工艺相比大大降低,据此得到了凸模受力图和板料应变云图,每一步凸模受力峰值和坯料等效应变值与已有的盘形件工艺试验研究结果一致.     

汽车横梁拉深成形的有限元分析

建立了汽车横梁拉深的有限元三维模型，对其拉深成形过程进行了数值模拟，并与实验结果对比分析，说明数值模拟方法的可行性。在此基础上讨论了摩擦润滑条件、压边力和凸模的虚拟冲压速度对板料拉深过程的影响。通过有限元模拟分析方法得到最佳压边力数值，然后通过综合分析数值模拟结果和拉深实验结果确定了实际拉深过程中的最佳压边力。结果表明，在实际拉深过程中要尽量减小模具和板料的摩擦；在模拟拉深成形时，当虚拟冲压速度大于一定值时，会使模拟结果严重失真，因此，汽车横梁拉深数值模拟时最大虚拟冲压速度不要大于2000mm／s。     

薄壁深抛物线形零件固体颗粒介质成形工艺

薄壁抛物线形壳体成形过程为拉深和胀形两种变形模式的复合,极易发生起皱和破裂。固体颗粒介质成形是采用固体颗粒代替刚性凸模或凹模(或弹性体、液体)对板料进行成形的工艺。板材在颗粒介质内压的作用下成形,可以有效防止抛物线形件拉深成形过程中侧壁的起皱;由于颗粒内压是非均匀分布的,故可以有效控制抛物线形件成形过程中的破裂,提高板材的成形极限。根据固体颗粒介质成形工艺的特点,提出了两次成形薄壁深壳体零件的工艺,建立了数值分析模型,通过数值模拟和试验对该成形过程和工艺参数进行了分析。结果表明,采用固体颗粒介质成形工艺过程简单、成形工件壁厚分布均匀、表面质量好、回弹小。     

The influence of ultrasonic vibration-assisted micro-deep drawing process

Micro-deep drawing process combined with ultrasonic vibration were performed on three stainless steel 304 foils of different thicknesses to determine the influence of ultrasonic vibrations on micro-cup formability and the limit drawing ratio (LDR). An ultrasonic system that applies 20 kHz of oscillation at various amplitudes was developed, and a concentrator was used to transfer the oscillation from the transducer to the die. The LDRs of these foils were obtained with and without ultrasonic variations. The experimental results in this study showed that using ultrasonic vibration following the deep drawing processes increased the LDR from 1.67 to 1.83, from 1.75 to 1.92, and from 1.83 to 2 for thicknesses of 50, 75, and 100 μm, respectively. The oscillation amplitudes had a significant effect on different thicknesses. An amplitude of 8.6 μm could not be appropriately applied to foils because of the excessive oscillated force. The punch force also decreased as the oscillation amplitude increased because of reduced friction between the die and the blank. Based on these experimental results, this study showed that ultrasonic vibrations can be used to produce micro-cups that exhibit high application flexibility in miniaturization technology.