Multi-objective optimization of forming parameters for tube hydroforming process based on the Taguchi method

Tube hydroforming is an attractive manufacturing technology which is now widely used in many industries, especially the automobile industry. The purpose of this study is to develop a method to analyze the effects of the forming parameters on the quality of part formability and determine the optimal combination of the forming parameters for the process. The effects of the forming parameters on the tube hydroforming process are studied by finite element analysis and the Taguchi method. The Taguchi method is applied to design an orthogonal experimental array, and the virtual experiments are analyzed by the use of the finite element method (FEM). The predicted results are then analyzed by the use of the Taguchi method from which the effect of each parameter on the hydroformed tube is given. In this work, a free bulging tube hydroforming process is employed to find the optimal forming parameters combination for the highest bulge ratio and the lowest thinning ratio. A multi-objective optimization approach is proposed by simultaneously maximizing the bulge ratio and minimizing the thinning ratio. The optimization problem is solved by using a goal attainment method. An example is given to illustrate the practicality of this approach and ease of use by the designers and process engineers.     

Multi-objective optimization and sensitivity analysis of tube hydroforming

Tube hydroforming is a manufacturing process used to produce structural components in cars and trucks, and the success of this process largely depends on the careful control of parameters such as internal pressure and end-feed force. The objective of this work was to establish a methodology, and demonstrate its effectiveness, to determine the optimal process parameters for a tube hydroformed in a die with a square cross section. The Taguchi method was used to establish a design of virtual hydroforming experiments, and numerical simulations were carried out with the finite element code LS-DYNA®. A sensitivity analysis was also carried out with analysis of variance. Multi-objective functions that consider necking/fracture, wrinkling, and thinning were formulated, and the response surface methodology was used with the most sensitive factors to obtain a defect-free part. An objective function, based on the final corner radius in the part, was also included in the optimization model. The forming severity of virtual hydroformed parts was evaluated using the forming limit stress diagram and the forming limit (strain) diagram. Finally, the normal-boundary intersection method and the L ₂ norm were used to obtain the Pareto-optimal solution set and the optimal solution within this set, respectively. The hydroforming process for this part was also optimized using the commercial optimization software LS-OPT®, with two different single-objective algorithms. However, the optimum load path predicted with the proposed methodology was shown to achieve a smaller corner radius. The proposed optimization technique helped to define a process window that leads to a robust manufacturing process and improved part quality.     

Numerical and experimental investigation of inward tube electromagnetic forming

In this work, experimental and numerical simulation of high-speed inward forming of tubes on a die in electromagnetic forming (EMF) system using a compression coil is presented. A 2D axi-symmetric electromagnetic model is used to calculate magnetic field and magnetic forces. Modified loose-coupled simulations of electromagnetic and structural aspects of EMF process are reported and emphasized in this paper. During the simulation, in each time step, the transient magnetic forces are obtained from the electromagnetic model and used as input load to the mechanical model. Based on the calculated deformation, in each step, the tube geometry in the electromagnetic model is updated to calculate the electromagnetic forces in proceeding step. Tube material, AA 6061-T6, is assumed to obey the Johnson-Cook (J-C) rate-dependent model. Displacement and thickness variations of workpieces along the tube length are presented and discussed experimentally and numerically. The results demonstrate that various workpiece zones could be thickened or thinned based on various process parameters. In addition, it is seen that the increase of discharge voltage decreases the thickness at die radius and reverses the thickening trend at tip of the bead.     

3D Multi-physics field simulation of electromagnetic tube forming

Numerical simulations of electromagnetic forming process offer the opportunity to overcome the multi-physics filed coupling problems. The purpose of this work is to establish a three-dimensional (3D) finite element model which can be used for non-axisymmetrical 3D models. And the simulation method will serve as a guide to analyze arbitrary complex 3D models in the future. In each time step, the transient magnetic forces and the joule heat generated by electromagnetic code are used as the loading condition to predict the deformation of the tube by mechanical code and the temperature variation of the tube by thermal code, respectively. Whereafter, the tube geometry is updated according to the deformation result. The simulation result of displacement at the center of the tube with time and the final tube profile are in better agreement with the experimental ones. The lows of the strain, stress, strain rate, and the temperature variation are analyzed. The changes of the magnetic force on the tube are also analyzed.     

Multi-objective optimization of sheet metal forming die using FEA coupled with RSM

Present study describes the approach of applying response surface methodology (RSM) with a Pareto-based multi-objective genetic algorithm to assist engineers in optimization of sheet metal forming. In many studies, finite element analysis and optimization technique have been integrated to solve the optimal process parameters of sheet metal forming by transforming multi objective problem into a single-objective problem. This paper aims to minimize objective functions of fracture and wrinkle simultaneously. Design variables are blank-holding force and draw-bead geometry (length and diameter). Response surface model has been used for design of experiment and finding relationship between variables and objective functions. Forming limit diagram (FLD) has been used to define objective functions. Finite element analysis applied for simulating the process. Proposed approach has been investigated on a cross-shaped cup drawing case and it has been observed that it is more effective and accurate than traditional finite element analysis method and the ‘trial and error’ procedure.     

Analysis of the electromagnetic forming process

As a result of the mathematical analysis of the electromagnetic forming process, an approximate solution and a more exact numerical solution of a set of differential equations are presented. Both methods permit the investigation of the influence of a variety of parameters of the discharge unit, the forming coil, and of the workpiece on the attainable forming result. Three conditions for an optimum design of the forming machine are derived from the approximate solution, one of them being an expression for the optimum frequency, for which maximum deformation is achieved. The numerical solution was verified by comparison with selected experimental results.     

On the forming uniformity during a single layer forming of electromagnetic incremental forming

Aiming to the precise control of forming quality in electromagnetic incremental forming (EMIF), deformation behaviors of a spherical crown-shaped thin-wall     

多目标的装夹方案优化及变夹紧力优化

夹具布局和夹紧力大小影响切削变形的大小和分布.基于遗传算法和有限元方法,提出一种夹具布局和夹紧力优化设计方法.该方法将同步优化夹具布局和夹紧力大小以及施加变夹紧力相结合,首先以加工变形最小化和变形分布最均匀为目标同步优化夹具布局和夹紧力大小,然后在优化后的夹具布局的基础上求解使得加工变形最小的变夹紧力大小.使用该方法进行底座薄壁零件的夹具优化设计,结果表明优化得到的设计优于经验设计和多目标优化方法,该方法有效地降低了加工过程中工件的变形,提高变形均匀度.     

Analysis of forming limit in tube hydroforming

The automotive industry has shown increasing interest in tube hydroforming. Despite many automobile structural parts being produced from cylindrical tubes, failures frequently occur during tube hydroforming under improper forming conditions. These problems include wrinkling, buckling, folding back, and bursting.We perform analytical studies to determine forming limits in tube hydroforming and demonstrate how these forming limits are influenced by the loading path. Theoretical results for the forming limits of wrinkling and bursting are compared with experimental results for an aluminum tube.     

Improved workability using preheating in the electromagnetic forming process

Journal of Mechanical Science and Technology - Electromagnetic forming (EMF) is a high-speed method used to shape metals using a high-energy magnetic field generated by a forming coil. In this...     

Multi-objective optimization of multipass turning processes

In this paper, a methodology is proposed for the multi-objective optimization of a multipass turning process. A real-parameter genetic algorithm (RGA) is used for minimizing the production time, which provides a nearly optimum solution. This solution is taken as the initial guess for a sequential quadratic programming (SQP) code, which further improves the solution. Thereafter, the Pareto-optimal solutions are generated without using the cost data. For any Pareto-optimal solution, the cost of production can be calculated at a higher level for known cost data. An objective method based on the linear programming model is proposed for choosing the best among the Pareto-optimal solutions. The entire methodology is demonstrated with the help of an example. The optimization is carried out with equal depths of cut for roughing passes. A simple numerical method has been suggested for estimating the expected improvement in the optimum solution if an unequal depth of cut strategy would have been employed.     

平板件电磁成形工艺研究

介绍电磁成形原理及其在平板件冲压工艺中的应用,分析平面螺旋线圈在加工平板件毛坯中的磁场分布,设备参数对工艺性能的影响及电磁成形工艺的优缺点。     

管材成形技术综述

与板材一样，管材也是工业生产中广泛使用的重要原料。随着技术的进步，各种管材加工技术得到了快速发展。其中，具有低能耗、省材料、高效率等优点的塑性成形，逐渐成为管材加工的主要手段。本文以广泛应用的典型管成形工艺方法为重点，介绍了各种管成形的工艺、设备等内容。     

网络环境下制造资源的多目标优化及仿真

制造资源优化是网络化制造的核心问题。针对生产企业在利用外部资源方面的三类需求,这里提出了两种可行的制造资源优化方法。详细论述了优化的步骤,建立了产品交货期、成本以及加工质量的三目标优化模型,并给出了求解模型的有效算法。最后,通过具体的计算实例进行了数值仿真。     

混合陶瓷球轴承多目标优化

混合陶瓷球轴承(Hybrid Ceramic Ball Bearing,HCBB)用Si3N4陶瓷球替换钢球,这两种材料性能差距较大,导致轴承寿命和发热量发生显著变化,需对HCBB进行多目标优化设计。提出高速HCBB多目标优化模型,目标函数为疲劳寿命和直接表征发热的自旋摩擦功率。用Ioannides-Harris理论计算HCBB寿命,用非劣排序遗传算法-II求解该多目标优化问题。结果显示优化的HCBB显著优于当前设计。     

钢铝双帽型保险杠横梁多目标优化

为了保证保险杠横梁优良的碰撞性能,并使其质量更小和结构简单,研究了一种钢铝双帽型保险杠横梁.使用LS-DYNA软件对保险杠横梁进行摆锤正面冲击数值模拟,经对比发现,钢铝双材横梁相比相同结构单一材料的横梁在正面碰撞中显示出良好的平衡性和碰撞性能;使用控制变量法研究发现,横梁前后帽的厚度和法兰的位置对其碰撞性能有显著影响;...     

Multi-objective optimization of an axial compressor blade

Numerical optimization with multiple objectives is carried out for design of an axial compressor blade. Two conflicting objectives, total pressure ratio and adiabatic efficiency, are optimized with three design variables concerning sweep, lean and skew of blade stacking line. Single objective optimizations have been also performed. At the data points generated by D-optimal design, the objectives are calculated by three-dimensional Reynolds-averaged Navier-Stokes analysis. A second-order polynomial based response surface model is generated, and the optimal point is searched by sequential quadratic programming method for single objective optimization. Elitist non-dominated sorting of genetic algorithm (NSGA-II) with ε-constraint local search strategy is used for multi-objective optimization. Both objective function values are found to be improved as compared to the reference one by multi-objective optimization. The flow analysis results show the mechanism for the improvement of blade performance.