The application of abductive networks and FEM to predict the limiting drawing ratio in sheet metal forming processes

The deep drawing process, one of the sheet metal forming methods, is very useful in the industrial field because of its efficiency. The limiting drawing ratio (LDR) is affected by many material and process parameters, such as the strain-hardening exponent, the plastic strain ratio, friction and lubrication, the blank holder force, the presence of drawbeads, the profile radius of the die and punch, etc. In order to verify the finite element method (FEM) simulation results of the LDR, the experimental data are compared with the results of the current simulation. The influences of the process parameters such as the blank holder force, the profile radius of the die, the clearance between the punch and the die, and the friction coefficient on the LDR are also examined. The abductive network was then applied to synthesize the data sets obtained from the numerical simulation. The predicted results of the LDR from the prediction model are in good agreement with the results obtained from the FEM simulation. By employing the predictive model, it can provide valuable references to the prediction of the LDR under a suitable range of process parameters.     

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。     

Hydrodynamic deep drawing process assisted by radial pressure with inward flowing liquid

A radial pressure can reduce drawing force and increase drawing ratio in hydrodynamic deep drawing. However, conventional hydrodynamic deep drawing cannot attain a radial pressure higher than the pressure in the die cavity. In this research, a modified method, named hydrodynamic deep drawing assisted by radial pressure with inward flowing liquid, was proposed and investigated using both primarily experimental and numerical simulation analysis. A radial pressure higher than the pressure in the die cavity was realized by means of the inward flowing of the liquid during this process. After preliminary experimental validation, FEM was used to explore the forming process. The results from the simulation were compared with those from the experiment. The effects of the radial pressure on the wall thickness distribution, punch force, and compressive stress in the blank flange were studied with assistance of numerical simulation. The process window for radial pressures versus drawing ratios was established in 2Al2O alloy experimentally and cups with drawing ratio of 2.85 were successfully formed.     

Deep drawing with anti-lock braking system (ABS)

In this study, for improving the formability and LDR a new method deep drawing with anti-lock braking system (ABS) was developed. The system is based on the blank sliding from the flange into the die cavity continually, which is controlled by the blank holder gap (BHG) and, at the same time by ABS, which moves up and down vertically, conducting anti-lock braking to the blank with the interval of very short time. The experimental results for AI99.8 aluminium sheet showed that higher drawing height and LDR of the cup can be achieved by the use of ABS. It was found that the new system increased surface quality and decreased ear in the top corners of the cup.     

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。     

The role of die curvature in the performance of deep drawing (hydro-mechanical) processes

A hydromechanical deep drawing process (which replaces the conventional rigid blank-holder tool with a hydrostatic fluid pressure) is utilized to study the roles played by die curvature, interfacial friction, material hardening, etc. in deep drawing performance. The analytical study is based on limit analysis in plasticity (applying both the upper and the lower bounds simultaneously) with a special emphasis on the geometry of the die profile. The resulting relationships between the various parameters obtained through the bounds are backed by an independent numerical solution using Woo's finite difference scheme. The associated experiments, with which the limit analysis is compared, were conducted with aluminium blanks at various die radii and with various holding fluid pressures.The relatively close proximity of the above solutions, in describing the observed behaviour of the process, enables one to draw a few general conclusions about the strength of the limit analysis in describing realistic deep drawing processes. Also potential improvements concerning the choice of die radius of curvature and the blank holding force are indicated.     

圆筒形件拉深失稳及各因素影响分析

对板料成形中圆筒形件拉深的破裂失稳及产生破裂失稳的临界压边力进行研究.由于凸、凹模圆角及其间隙的存在,圆筒形件拉深的筒壁区实际为凸、凹模圆角之间的公切线部分.根据Mises-Hill屈服函数及Tresca准则求出凸缘变形区、凹模圆角区和筒壁区的应力分布,得到危险断面处的应力表达式,从而求出不产生破裂失稳的临界压边力的解析表达式,并进一步分析获得拉深比、硬化指数、厚向异性系数、摩擦因数以及径向推力等因素对临界压边力的影响规律.采用液压压边与周缘加径向推力的拉深模具对08Al板料进行拉深试验,试验结果与理论计算结果具有很好的一致性.     

On the dimensional accuracy of deep drawing products by hydroforming processes

In the hydroforming process the punch deforms the blank to its final shape by moving against a controllable fluid-pressure in a pre-determined path. The present work exhibits the fact that the final geometry of the product (mainly the wall thickness variations) depends on the overall history by which the fluid pressure-path is operated during the drawing process. In addition, other phenomena akin to hydroforming processes have been observed, e.g. the shift in the location of the rupture site (if it occurs) from near the bottom of the product to near its lip and the (slight) variation in the final length of the product. In order to explain these occurrences a detailed numerical stress analysis is offered, featured by an ad-hoc “finite difference” scheme. It differs from previous solutions by admitting changes in the thickness of the blank and still accounting for the blank/tool interfacial friction and the out-of-plane curvature of the product. The material behavior of the blank includes exponential strain hardening, normal anisotropy and initial strain. The experiments shown here were carried out on aluminum sheets with a specially built hydroforming machine.     

The effect of nanoparticulate loading on the fabrication and characterization of multi-doped Zn-Al2O3-Cr2O3 hybrid coatings on mild steel

In this paper, an improved approach is proposed to determine the optimal profiles of two controllable process parameters (hydraulic pressure and blank holder force), which improve the forming condition and/or make better use of forming limits in hydromechanical deep drawing (HMD) process. A method based on adaptive finite element analysis coupled with fuzzy control algorithm (aFEA-FCA) was developed using LS-DYNA to determine the optimal loading profiles and thus to maximize the limiting drawing ratio (LDR). Maximum thickness reduction, maximum wrinkle height in the flange region of the sheet metal blank, and position of the nodes in the unsupported portion of the sheet metal blank between punch and die were used as criteria in the fuzzy control algorithm. Different rule-based matrices were compared by considering the maximum thinning occurred in the sheet metal blank, and thus, the most accurate matrices were determined for the control algorithm. The optimal loading profiles could be determined in a single FEA, thus reducing the computation time. The proposed approach enables determining the optimal loading profiles and also could be applied to complex parts easily. In addition, effects of initial blank diameter and coefficient of friction between the sheet-blank holder and sheet-die on the optimal loading profiles were investigated. An attainable LDR of 2.75 for AA 5754-O sheet material in hydromechanical deep drawing process was proven experimentally using the optimal loading profiles determined by adaptive FEA.     

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。     

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。     

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.     

镀层薄板拉深过程中镀层厚度变化影响因素分析

对镀层板料拉深成圆筒件的过程进行模拟及试验研究,得到了圆筒件各部分镀层厚度的变化规律。选取镀层最薄处厚度为镀层质量评价因素,利用LS-DYNA软件,基于正交法分析了拉深过程中的主要工艺参数（压边力、凹模圆角半径、凸模入口圆角半径和摩擦因数）对镀层厚度变化的影响规律,并结合拉深机理对其进行了深入研究,得到了所选工艺参数的最优组合。     

一种测量板料拉深摩擦因数的传感器设计

针对板料拉深成形中如何测量板料法兰处真实摩擦分布情况以及如何评价润滑剂好坏的难题,设计了一套基于电阻应变计和双层悬臂梁原理的探针组合式传感器安装于拉深凹模中,用来实时测量板料法兰上一点处所受的垂向正向力和径向切向力,可计算出该测量点处的实时摩擦因数.试验证明：该传感器能真实地反映板料拉深成形过程中法兰平面上的实际摩擦分布情况.     

Experimental and mathematical analysis of simulation results for sheet metal parts in deep drawing

In this paper, deep drawing of conical and cylindrical cups without blank holder is investigated using a conical die design. These cups are produced by pushing circular blanks by pushing the flat head punch in a single stroke. ANSYS APDL 14.0 was then used to investigate the effects of die and punch geometry, half-cone angle, die and punch fillet radius, and drawing load. The thickness distribution of the cup was numerically investigated to determine the optimal process design, and mathematical analysis was adopted to determine the thickness distribution and longitudinal stress calculation. An experimental set-up was designed to validate the simulation results for conical and cylindrical shaped sheet-metal cups. Tensile tests were carried out to obtain the flow of the stress-strain curve for the simulation. The drawing characteristics of materials were investigated by performing Erichsen cupping and Vickers hardness tests. Experiments were conducted on blanks of aluminum alloys and stainless steel with initial thicknesses of 1.5 mm. A cylindrical cup of ss304 with LDR of up to 2.2 and conical cup of AA1100 with LDR of up to 2.7 were successfully achieved. Finite element simulation results showed good agreement with the mathematical and experimental results.     

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.     

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.     

半球底直筒形拉深件成形极限实验研究

以半球底直筒形拉深件为研究对象,用实验的方法,从压边力、摩擦系数、凹模圆角半径等几个方面对半球底直筒形件进行成形研究,得到了各工艺参数对其成形极限的影响.即压边力、摩擦系数在一定范围内的增大,半球底直筒形拉深件的胀形区域减小,成形极限有降低的趋势.     

Analysis of draw–redraw processes

An analytical model is developed to analyze the draw–redraw processes. Thickening of the flange is modeled using a complete pure radial drawing analysis which takes into account interfacial friction and radial thickness variation. A plastic bending analysis is used to calculate thinning in all forming radii. Material properties, tooling geometry, and process parameters are included in the model. The derivation is then developed into computer subroutines. By arranging the subroutines into the deforming sequence, draw–redraw process can be simulated. The predicted wall thickness profiles agree very well with the experimental measurements. Characterization of wall thickness profile is also discussed.     

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。