Multi-response optimization on single-point incremental forming of hyperbolic shape Al-1050/Cu bimetal using response surface methodology

In present work, experimental and numerical investigations were carried out on single-point incremental forming of explosive bonded clad sheets. The sheets were produced by explosion welding from 1050 aluminum alloy and C10100 copper alloy sheets. A generatrix of hyperbolic curve was utilized as profile of final shapes formed by SPIF process. During some investigations, the interaction and main effect of the process parameters viz. tool diameter, step down, rotational speed, and sheet arrangement were evaluated on the fracture depth and wall thickness at fracture using ANOVA method. For experimentation, a customized design table was built with three quantify and one qualify factors in two levels. The design table totally provides four input factors and two responses in 12 runs. The responses are fracture depth and wall thickness. A multi-response optimization was conducted to find optimum values for input parameters using response surface methodology (RSM) and the confirmatory experiment revealed the reliability of RSM in this regard. Moreover, predictive models were presented in confidence interval of 95% to formulate the relationship between the responses and the input factors using RSM approach. Additionally, a finite element analysis was carried out on the SPIF based on optimal input parameters to depict reaction force changing, thickness variation, and stress distribution.     

考虑接触演变的板材回弹过程建模与优化

回弹是由工件在卸载后的弹性变形引起的。板料成形过程中为了控制成形件的最终形状,必须进行回弹设计优化。准确预测回弹对于板料成形过程的模具设计非常重要。降低回弹模拟结果与试验结果的偏差是设计过程中的难题。基于NUMISHEET’02的自由弯曲标准考题考虑板材与模具间的接触演变过程,建立了一个有限元模型来预测回弹。采用一个常规的优化方法对有限元分析中的材料和单元模型进行了分析,研究发现不同模型对回弹结果有较大影响。模拟结果与参考文献中的试验结果比较表明了模型的正确性和可行性。     

Improving profile accuracy in SPIF process through statistical optimization of forming parameters

In single-point incremental forming (SPIF) process, a number of parameters are involved and need to be adjusted before the commencement of the forming operation. The inappropriate selection of these parameters could be detrimental to process accuracy. In this paper, the effect of five parameters, namely, sheet thickness, tool radius, step size, wall angle, and pre-straining level of sheet, on the profile accuracy of the produced part of AA1060 with SPIF is experimentally investigated. A response surface method is employed for the experimental design and regression analysis. The experimental results are presented in the form of graphical three-dimensional response surfaces. The results of ANOVA show that the sheet thickness, wall angle, step size, and the interaction between the sheet thickness and wall angle are extremely significant in terms of their effect on profile accuracy. Furthermore, an empirical model is proposed to achieve improved profile accuracy in terms of the optimized parameters.     

Deformation mechanics in single-point and accumulative double-sided incremental forming

Single-point incremental forming (SPIF) uses one small hemispherically ended tool moving along a predefined toolpath to locally deform a completely peripherally clamped sheet of metal such that the sum total of the local deformations yields the final desired shape of the sheet. While SPIF is characterized by greater formability than conventional forming processes, it suffers from significant geometric inaccuracy. Accumulative double-sided incremental forming (ADSIF) is a substantial improvement over SPIF in which one hemispherically ended tool is used on each side of the sheet metal. The supporting tool moves synchronously with the forming tool, therefore acting as a local but mobile die. ADSIF results in considerably enhanced geometric accuracy and increased formability of the formed part as compared to SPIF. In light of the aforementioned advantages of ADSIF as compared with SPIF, an investigation of the mechanics associated with the ADSIF process, which has yet to be presented in the literature, is warranted. The present study sheds light on the differences in deformation mechanisms between SPIF and ADSIF. Finite element analyses are performed to simulate deformation in the two processes, and a detailed analysis of the deformation history is presented. It is shown that the presence of the supporting tool in ADSIF elicits substantial differences in the plastic strain, hydrostatic pressure, and shear strains as compared to SPIF. The implications of these trends on the prevalent modes of deformation in ADSIF along with possible explanations for increased formability observed in the process arediscussed.     

Effects of three parameters on forming force of the single point incremental forming process

This research has examined the effects of three parameter groups on the forming force of single point incremental forming (SPIF) process. The parameters under study include the material types (sheet aluminum, brass and copper), the forming angles (30°, 40° and 50°), and the tool revolution speeds (200, 400 and 600 rpm). The metal forming was carried out using a spherical edge tool which was pressed onto the metal surface to form work pieces of truncated pyramid shape. In the experiment, the forming forces were measured and analyzed to determine an optimal parameter combination, with regard to the material type, forming angle and revolution speed, for the SPIF process. The experimental results showed that all three parameter groups exerted varying influences over the forming force of the SPIF process. The findings indicated that the sheet brass exhibited the highest force value and that the smaller forming angle contributed to the greater forming force. In addition, the higher tool revolution speed resulted in the lower forming force.

     

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.     

The formability of annealed and pre-aged AA-2024 sheets in single-point incremental forming

The formability of AA-2024 sheets, an aerospace grade material, in the annealed and pre-aged conditions has been investigated in the single-point incremental forming (SPIF) process. The major operating parameters, namely step size, tool radius, and forming speed, of SPIF process were varied over wide ranges, and their effect on the formability was quantified through a response surface method called as central composite rotational design. It was found that the interaction of step size and tool radius is very significant on the formability. Moreover, a variation in the forming speed does not affect the formability of annealed AA-2024 sheet. However, the formability of pre-aged AA-2024 sheet decreases with the increase in the forming speed. Furthermore, the annealed sheet shows higher formability than the pre-aged sheet.     

Formability evaluation of a pure titanium sheet in the cold incremental forming process

Owing to its ability to deform a sheet metal locally, the single point incremental forming (SPIF) process produces larger deformations as compared to the conventional forming processes. In the present study, we investigated the effect of some process parameters – pitch, tool diameter, feed rate and friction at the interface between the tool and blank – on the formability of a commercially-pure titanium sheet. Trends between the process parameters and formability are presented in this paper.     

Analytical modeling and numerical simulation for three-roll bending forming of sheet metal

The three-roll bending forming of sheet metal is an important and flexible manufacturing process due to simple configuration. It is suitable for forming large sheet parts with complex, curved faces. Most researches on roll bending forming of large workpiece are mainly based on experiments and explain the process through macroscopic metal deformation. An analytical model and ABAQUS finite element model (FEM) are proposed in this paper for investigating the three-roll bending forming process. A reasonably accurate relationship between the downward inner roller displacement and the desired springback radius (unloaded curvature radius) of the bent plate is yielded by both analytical and finite element approaches, which all agree well with experiments. Then, the three-roll bending forming process of a semi-circle-shaped workpiece with 3,105 mm (length)?×?714 mm (width)?×?545 mm (height) is simulated with FEM established by the optimum tool and process parameters. Manifested by the experiment for three-roll bending forming of this workpiece, the numerical simulation method proposed yields satisfactory performance in tool and process parameters optimization and workpiece forming. It can be taken as a valuable mathematical tool used for three-roll bending forming of large area sheet metal.     

Investigating the temperature from friction stir in the SPIF process via an infrared imager

Single point incremental forming (SPIF) is a highly flexible forming process for sheet metal. It has low production costs be-cause the process does not use a die. It is suitable for prototyping and made-to-order production. Currently, the SPIF process employs the concept of heat to increase formability. The idea is to generate heat from friction caused by sliding the tool against the workpiece, called “friction stir”. This research proposed to study the behavior of temperature that occurs when affected by the tool rotation speed and the feed rate, which are both variables affecting friction stir. This research adopted the method of detecting temperature with infrared cameras and online recording data. The camera sensor received data as 8-bit images containing data from 0 to 255. The value of each position represented the temperature level. In this research, the mini-mum-maximum temperature range was set at 80–300 degrees Celsius for forming the hot dipped zinc coat roll steel sheet at a thickness of 0.2 mm using the SPIF process. The variable parameters were the tool rotation speed and feed rate. The tool rotation speed was categorized as high and used no sliding friction with feed rates of 500, 1000, 1500 mm/min. Concerning the results analysis, this study used the relationships between tool rotational speed and feed rate, shown as relative sliding velocity. The results showed with significance that the increase of the maximum temperature in the process corresponded to an increase in relative sliding velocity using a tool rotational speed and feed rate with no relative sliding velocity. The process temperature was close to room temperature. Relative sliding velocity at approximately 6000 and 10000 mm/min caused a maximum temperature of approximately 160–180 and 200–250 degrees Celsius, respectively. Another issue found in the experiment was that not turning the tool reduced the formability of the process.

     

Comparison between three optimization methods for the minimization of maximum bending load and springback in wiping die bending obtained by an experimental approach

The sheet metal bending process is widely used in the automotive industries, and it is actually one of the most important manufacturing processes. The robustness and the reliability of the bending operation, like many other forming operations, depend of several parameters (geometry, material, and process). In this paper, the die radius and the clearance between the punch and the sheet are optimised in order to reduce the maximum bending load and the springback. Two optimization problems are formulated, and three optimization procedures based on the response surface method are proposed and used to find the optimum solutions. Global and local approximations are used to replace the initial optimization problem, which is implicit by an explicit problem, and the optimum is localised using two algorithms: a sequential quadratic programming and an evolution strategies. The objective functions are evaluated experimentally into a limited points number, which are defined using a design of experiments technique. Good results are obtained from the three optimization procedures. The ability of each technique to find the optimal solution is evaluated, and the results show a good agreement between those three methods.     

Optimization of the structural and process parameters in the sheet metal forming process

The quality of the sheet metal forming product is determined by defects such as wrinkling, springback, etc. Optimization techniques can avoid such defects while the desired final shape is obtained. The design variables of the optimization process consist of the structural parameters and process parameters. The structural parameters are the initial blank shape, geometry, etc. and the process parameters are the blank holding force (BHF), the drawbead restraining force (DBRF), etc. In this paper, the two groups of parameters are separately optimized. The structural parameters are optimized by the equivalent static loads method for non linear static response structural optimization (ESLSO) and the process parameters are optimized by the response surface method (RSM). A couple of examples are solved by the iterative use of ESLSO and RSM, and the solutions are discussed.     

瑞风商务车托架拉延成形数值模拟及工艺参数优化

基于逆向工程建立瑞风商务车托架零件的几何模型,并基于Dynaform软件平台对不同工艺参数下该零件的拉延成形过程进行数值模拟。在此基础上,以压边力、拉延筋高度和拉延筋圆角半径作为设计变量,以零件不发生破裂为优化目标,以有限元数值模拟结果作为虚拟样本,建立目标函数的人工神经网络预测模型;将人工神经网络预测模型作为优化算法的知识源,采用遗传算法对压边力、拉深筋几何参数等工艺参数进行了优化设计。试验结果表明,数值模拟、神经网络预测和工艺优化是可靠的,从而可为制定金属板料最佳的冲压成形工艺提供一条先进、合理的途径。     

Prediction and control of pillow defect in single point incremental forming using numerical simulations

Pillows formed at the center of sheets in Single point incremental forming (SPIF) are fabrication defects which adversely affect the geometrical accuracy and formability of manufactured parts. This study is focused on using FEA as a tool to predict and control pillowing in SPIF by varying tool size and shape. 3D Finite element analysis (FEA) and experiments are carried out using annealed Aluminum 1050. From FEA, it is found out that the stress/strain state in the immediate vicinity of the forming tool in the transverse direction plays a determinant role on sheet pillowing. Furthermore, pillow height increases as compression in the sheet-plane increases. The nature of in-plane stresses in the transverse direction varies from compressive to tensile as the tool-end geometry is changed from spherical to flat. Additionally, the magnitude of corresponding in-plane stresses decreases as the tool radius increases. According to measurements from the FEA model, flat end tools and large radii both retard pillow formation. However, the influence of changing tool end shape from hemispherical to flat is observed to be more important than the effect of varying tool radius, because the deformation zone remains in tension in the transverse direction while forming with flat end tools. These findings are verified by conducting a set of experiments. A fair agreement between the FEM and empirical results show that FEM can be employed as a tool to predict and control the pillow defect in SPIF.

     

基于几何补偿的高强板汽车覆盖件回弹优化控制

利用板料成形CAE软件DynaForm对高强板汽车覆盖件地板中通道进行回弹仿真分析,结合模具几何补偿,通过对成形工艺参数的正交优化,找到了最优参数组合及各因素对回弹的影响程度,有效地控制了零件在多工序冲压成形过程中产生的回弹.     

Study on the driver plate for electromagnetic forming of titanium alloy Ti-6Al-4V

In order to improve energy efficiency, a driver plate made from high-conductivity material is normally used in the electromagnetic forming process of high-strength but low-conductivity sheet metal. The choice of driver plate significantly influences final deformation of the workpiece. In this paper, the electromagnetic free bulging process of Ti-6Al-4V titanium alloy sheet, widely used in aerospace, was studied by both experimental means and numerical simulation. The forming efficiency and quality of the workpiece under different types of driver plates were investigated in detail. The results show that by using high-conductivity and easily deformed materials such as aluminum alloy, with a skin depth in thickness, high efficiency and uniform deformation can be achieved. The results of this study can provide guidance on the choice of process parameters such as the material and thickness of a driver plate.     

A study on optimal design of process parameters in single point incremental forming of sheet metal by combining Box–Behnken design of experiments,response surface methods and genetic algorithms

Incremental forming is a sheet metal forming process characterized by high flexibility; for this reason, it is suggested for rapid prototyping and customized products. On the other hand, this process is slower than traditional ones and requires in-depth studies to know the influence and the optimization of certain process parameters. In this paper, a complete optimization procedure starting from modeling and leading to the search of robust optimal process parameters is proposed. A numerical model of single point incremental forming of aluminum truncated cone geometries is developed by means of Finite Element simulation code ABAQUS and validated experimentally. One of the problems to be solved in the metal forming processes of thin sheets is the taking into account of the effects of technological process parameters so that the part takes the desired mechanical and geometrical characteristics. The control parameters for the study included wall inclination angle (α), tool size (D), material thickness (Th_ini), and vertical step size (In). A total of 27 numerical tests were conducted based on a 4-factor, 3-level Box–Behnken Design of Experiments approach along with FEA. An analysis of variance (ANOVA) test was carried out to obtain the relative importance of each single factor in terms of their main effects on the response variable. The main and interaction effects of the process parameters on sheet thinning rate and the punch forces were studied in more detail and presented in graphical form that helps in selecting quickly the process parameters to achieve the desired results. The main objective of this work is to examine and minimize the sheet thinning rate and the punch loads generated in this forming process. A first optimization procedure is based on the use of graphical response surfaces methodology (RSM). Quadratic mathematical models of the process were formulated correlating for the important controllable process parameters with the considered responses. The adequacies of the models were checked using analysis of variance technique. These analytical formulations allow the identification of the influential parameters of an optimization problem and the reduction of the number of evaluations of the objective functions. Taking the models as objective functions further optimization has been carried out using a genetic algorithm (GA) developed in order to compute the optimum solutions defined by the minimum values of sheet thinning and the punch loads and their corresponding combinations of optimum process parameters. For validation of its accuracy and generalization, the genetic algorithm was tested by using two analytical test functions as benchmarks of which global and local minima are known. It was demonstrated that the developed method can solve high nonlinear problems successfully. Finally, it is observed that the numerical results showed the suitability of the proposed approaches, and some comparative studies of the optimum solutions obtained by these algorithms developed in this work are shown here.     

Ideal forming—II. Sheet forming with optimum deformation

A method is proposed for the design of ideal forming processes. The objective is to directly determine ideal configurations for both the initial and the intermediate stages that are required to form a specified final shape. At the start, it is assumed that formability of local material elements is optimum when they deform in minimum work paths. The ideal global process is then defined as the one having such local deformations optimally distributed in a final shape. Mathematical procedures for implementing these conditions are derived. Primary emphasis is placed upon forming of sheet (membrane) materials under plane-stress conditions, although many of the ideas are applicable to more general forming processes. Sample results illustrate optimum process parameters which the ideal forming theory can provide.     

冲压件成形计算机模拟工艺参数优化方法研究

分析了常规有限元金属板料成形模拟的不足，提出了参数化有限元分析的概念，在对人工神经网络、遗传算法进行深入分析研究的基础上，采用参数化有限元分析方法进行分析，得到了训练样本。提出了采用人工神经网络技术建立冲压件成形多参数映射关系模型，采用遗传算法进行多参数组合优化，实现冲压件成形计算机模拟工艺参数优化的方法。实际应用结果表明，优化结果与试验结果基本吻合，该优化方案实用可行。     

Numerical and experimental analysis of wall thickness variation of a hemispherical PMMA sheet in thermoforming process

In thermoforming, a heated plastic sheet is stretched into a mold cavity by applying pressure, eventually assisted by direct mechanical loading. Since upon its contact with the cold surface of the mold the sheet is prevented from undertaking any further deformation, the forming sequence induces a thickness variation in the final part. This fundamental inherent defect of thermoforming technology highly affects the optical characteristics of optical products. Therefore, the more uniform the wall thickness, the less chance optical defects will occur. In this research, the production process of a hemispherical transparent PMMA sheet as an optical product was numerically simulated. The simulated process is a two-step process comprising a combination of free forming and plug-assisted forming. In the simulation, the acrylic sheet is assumed to undergo a nonlinear and large elastic deformation which merits application of hyperelastic models. Mooney–Rivlin hyperelastic model is used as the constitutive equation. The obtained numerical results are validated with those achieved from the experiments. Different combinations of free forming and plug-assisted forming methods are studied based on what percentage of total height of the final part is produced by each method. Finally, an optimum combination of the two-step forming process is proposed. With this optimum combination, satisfactorily uniform wall thickness and minimal mold marks on the product surface will be achieved.