Optimal process design of sheet metal forming for minimum springback via an integrated neural network evolutionary algorithm

The process of sheet metal forming is characterized by various process parameters. Accurate prediction of springback is essential for the design of tools used in sheet metal forming operations. In this paper, an evolutionary algorithm is presented that is capable of handling single/multiobjective, unconstrained and constrained formulations of optimal process design problems. To illustrate the use of the algorithm, a relatively simple springback minimization problem (hemispherical cup-drawing) is solved in this paper, and complete formulations of the algorithm are provided to deal with the constraints and multiple objectives. The algorithm is capable of generating multiple optimal solutions in a single run. The evolutionary algorithm is combined with the finite element method for springback computation, in order to arrive at the set of optimal process parameters. To reduce the computational time required by the evolutionary algorithm due to actual springback computations via the finite element method, a neural network model is developed and integrated within the evolutionary algorithm as an approximator. The results clearly show the viability of the use of the evolutionary algorithm and the use of approximators to derive optimal process parameters for metal forming operations.     

Computer-aided engineering for sheet metal forming: definition of a springback quality function

Computer-aided engineering methods are extensively applied to sheet metal forming integrated design. The adoption of a new class of materials, the advanced high strength steels, has increased the occurrence of springback, and consequently the request for tools oriented to springback reduction and optimization. This paper presents an approximated formulation to compute the springback field after stamping through the finite element analysis of the process. This can be found assuming that the residual field of nodal forces after stamping produces a springback shape referable to a linear combination of n modes of vibration of the nominal shape of the component. The aim of this formulation is not that of substituting the finite element analysis of the springback but rather to make use of the coefficients of the linear combination, so to define a global quality function for springback. In this way, Robust Design methods or other current optimization procedures to improve the stamping process as for structural defects (such wrinkling, necking and flatness) can be applied also for the reduction of springback. The meaning of these coefficients will be shown through three test cases and the consistency of the formulation will be discussed according to the number of modes of vibration included in the computation.     

响应面法优化波纹巴非蛤酶解工艺的参数

应用响应面分析法分别优化波纹巴非蛤蛋白2段酶解的条件,第一段酶解使用胰蛋白酶,以蛋白质利用率为响应值;第二段酶解用木瓜蛋白酶,以肽得率为响应值.最终确定第一段酶解的最优条件为:酶与底物质量比为0.4:100,酶解时间为3h,酶解温度为52.0℃;第二段酶解的最优条件为:酶与底物的质量比为0.25:100,酶解时间为7.62 h,酶解温度为57.0℃,在此条件下,肽得率为54.35％,与模型的预测值55.67％接近.经2段酶解的上清液中小分子肽平均含量为2.25％.     

Auto-tuning and adaptive control of sheet metal forming

This paper describes the design and implementation of automatic controller tuning and model reference adaptive control (MRAC) to improve part quality in stamping and extends previous work on a manually-tuned fixed-gain process controller. Automatic tuning is described with a discussion of implementation issues in the presence of plant disturbances. Design of a direct MRAC, whose controller gains are continuously adjusted to accommodate changes in process dynamics and disturbances, is investigated, including simulation-based robustness analysis of the adaptation law and a consideration of constrained estimation in the recursive least squares algorithm to address practical implementation issues. The performance of the MRAC process controller designed through simulation is experimentally validated. Good tracking of the reference process variable (i.e., punch force), and significant part quality improvement in the presence of disturbances, is achieved.     

Tool path optimization for single point incremental sheet forming using response surface method

Incremental sheet forming (ISF) process is based on localized plastic deformation in a thin sheet metal blank. It consists to deform progressively and locally the sheet metal using spherical forming tool controlled by a CNC machine-tool. Although it is a slow process compared to conventional forming technique such as stamping. The cost reduction linked to the fact that punches and dies are avoided which makes it a very attractive process for small batch production and rapid prototyping. However, ISF process depends strongly on the forming tool path which influences greatly the part geometry and sheet thickness distribution. A homogeneous thickness distribution requires a rigorous optimization of the parameter settings, and an optimal parameterization of the forming strategy. This paper shows an optimization procedure tested for a given forming strategy, in order to reduce the manufacturing time and homogenize thickness distribution of an asymmetric part. The optimal forming strategy was determined by finite element analyses (FEA) in combination with response surface method (RMS) and sequential quadratic programming (SQP) algorithm.     

响应面分析法优化水提取甜叶菊苷工艺的研究

为优化水提取甜叶菊苷的工艺,在单因素试验基础上,选择料液比,提取温度,提取时间为自变量,甜叶菊苷提取率为响应值,利用Box-Benhnken中心组合试验和响应面分析法,研究各自变量交互作用及其对甜叶菊苷提取率的影响,模拟得到二次多项式回归方程的预测模型,并确定水提取甜叶菊工艺最佳条件为:选取料液比为1:26,提取温度为72℃,提取时间为118 min.在此优化条件下提取率达到21.02%。     

Response surface methodology for constrained simulation optimization: An overview

This article summarizes ‘generalized response surface methodology’ (GRSM), extending Box and Wilson’s ‘response surface methodology’ (RSM). GRSM allows multiple random responses, selecting one response as goal and the other responses as constrained variables. Both GRSM and RSM estimate local gradients to search for the optimum. These gradients are based on local first-order polynomial approximations. GRSM combines these gradients with Mathematical Programming findings to estimate a better search direction than the steepest ascent direction used by RSM. Moreover, these gradients are used in a bootstrap procedure for testing whether the estimated solution is indeed optimal. The focus of this paper is the optimization of simulated (not real) systems.     

磁致位移传感器在板材成型控制系统中的应用

介绍了磁致伸缩线性位移传感器的原理及使用方法,给出了该传感器在板材成型控制系统中的应用实例,并对系统的静态特性及系统控制精度进行了分析与评价.对测试系统进行标定,其相关系数为0.9999,回程误差为0.2880V,满量程电压为7.0154V,滞后优于4%FS,分辨力达0.002%FS,灵敏度达65.3mV/mm,控制信号的滞后误差最大为0.33mm.     

Robust design of sheet metal forming process based on adaptive importance sampling

Optimization methods have been widely applied in sheet metal forming area. However, the existence of variations during manufacturing processes significantly may influence final product quality, rendering non-robust optimal solutions. In this paper, experiments were conducted to investigate how a stochastic behavior of noise factors affected stamping quality. Robust design models for sheet metal forming process integrated adaptive importance sampling with response surface method, in order to minimize impact of the variations and achieve reliable process parameters. Support Vector Machine with nonlinear capability in both pattern recognition and regression was adopted to map the relation between input process parameters and part quality. A cup drawing example was employed to verify the feasibility of the proposed method. Comparisons were conducted between different optimization models to demonstrate robustness of the adaptive importance sampling method. Final results showed that the stamping part quality was optimized under the specified constraint requirements.     

A methodology of forming manufacturing cells using manufacturing and design attributes

This study develops a methodology for forming machine cells using part's design and manufacturing dissimilarities. The proposed methodology is divided into two sequential phases. In phase I parts are grouped into families based upon their design and manufacturing attributes. In phase II, the machines are grouped into manufacturing cells based on relevant operational costs and the various cells are assigned part families using an optimization technique.     

Reliability assessment for sheet metal forming operations

Methodology developed for reliability calculations of structures is applied to estimate reliability of sheet metal forming operations. Sheet forming operations are one of the most common technological processes but still the tool and process design is a difficult engineering problem. Product defects are often encountered in the industrial practice. Material breakage, wrinkling, shape defects due to springback are most frequent defects in sheet metal forming operations. Numerical simulation allows us to evaluate product manufacturability and predict the defects at early stages of the design process. In the paper the so-called forming limit diagrams (FLD) are used as a criterion of material breakage in the manufacturing process. A zone of a FLD where good results are guaranteed with sufficient probability is considered as safe zone. Sheet forming operations are characterized with a significant scatter of the results. This can be caused by differences that can occur in forming of each part. Small differences in the contact conditions, for instance, can lead to significant changes in the deformation state of the sheet. In reliability-like approach we try to quantify intuitive terms of probability of failure/success of forming operations given some uncertainty of parameters characterizing a forming process like friction parameters or blankholding force. Since the employment of the gradient-based reliability techniques is very much limited due to the some degree of numerical noise introduced by the explicit dynamic algorithm used to perform sheet stamping simulation the method of adaptive Monte Carlo simulations were chosen for reliability assessment.     

A robust and accurate geometric model for automated design of drawbeads in sheet metal forming

A robust and accurate geometric model of real drawbeads that can be used for the automated design of drawbeads is presented in the paper. A three-dimensional geometric drawbead is a lofted surface, of which the section curves are constructed parallel to the stamping direction on the control points. Adaptive control point interpolation is introduced to simplify the management of the drawbead geometry and avoid unexpected shapes. Given primitive control points on a drawbead curve, dominant control points are adaptively obtained with the shapes of both the drawbead curve and the binder considered. An a priori heuristic parameter adjustment strategy is proposed to correct the parameter errors of section curves, which improves the accuracy and consistency of the drawbead geometry. By incorporating the proposed geometric drawbead with a previously developed intelligent drawbead optimization algorithm, a fully automated design process for drawbeads is realized that includes geometric modeling, finite element analysis, intelligent optimization of the drawbead geometry, and die manufacturing. Finally, a fender example is presented to verify the feasibility and validity of the fully automated drawbead design process. The simulation results with the optimized geometric drawbeads and equivalent drawbeads are compared with the experimental results. The proposed geometric drawbead shows remarkable practicability and accuracy in the automated design of drawbeads in sheet metal forming and demonstrates good consistency with the experimental results while the equivalent drawbead model introduces unneglectable deviations.     

Multi-fidelity optimization for sheet metal forming process

Traditional design optimization for industry problems often requires many runs of costly high-fidelity finite element models. Multi-fidelity techniques offer a means to reducing prohibitive computational cost by combining cheap low-fidelity analyses with more accurate but more expensive high-fidelity solutions. This paper proposes a two-stage multi-fidelity method to better compromise the uses of low-fidelity and high-fidelity solutions. A correction response surface (RS) was first constructed based on the ratio or difference between high-fidelity and low-fidelity solutions at fewer sample points. Then the low-fidelity analysis is further replaced by a moving least square (MLS) approximation to enhance its accuracy. To demonstrate the present design procedure, multiobjective optimization of draw-bead restraining forces for an automobile inner panel is exemplified herein, where the high-fidelity model employs an incremental solver, while the low-fidelity model adopts a one-step solver. The results significantly improved the computational efficiency and accuracy of optimizing sheet-metal formability without wrinkle and fracture.     

曲面三参数binary细分法

在经典四点细分法的基础上,通过在曲线细分过程中引入三个参数,给出一种改进的细分曲线构造的算法,利用生成多项式等方法对细分法的一致收敛性、Ck连续性进行了分析。并把该方法扩展到曲面上,进而提出了曲面三参数binary细分法。在给定初始控制数据的条件下,可以通过对形状参数的适当选择来实现对细分极限曲面形状的调控。数值实验表明该算法较容易控制曲面形状,可方便地应用于工程实际,解决曲线、曲面位置调整和控制问题。     

A control design and calibration reduction methodology for AFR control in gasoline engines

A control architecture for air to fuel ratio (AFR) control of gasoline engines designed to work with switching and/or wide range oxygen sensors, with the goal of minimizing calibration effort while meeting performance requirements, is described. A high bandwidth, dithered inner-loop reference tracking controller with pre-catalyst oxygen sensor feedback coupled with a low bandwidth setpoint tracking outer-loop with post catalyst oxygen sensor feedback, is used to control engine exhaust and O₂ storage in the three-way catalyst (TWC), respectively. A total synthesis inspired design ensures that significant non-linearity in the system is handled through a coordinated and corrective action and expected response blocks in the open-loop, without burdening the closed loop controller. Calibration is achieved offline, through closed loop optimization using genetic algorithms, while simultaneously meeting performance and stability criteria with significantly reduced need for in-vehicle tuning. Experimental results show comparable emissions performance with the stock OEM AFR controller under warmed up conditions over a standard drive cycle.     

响应曲面分析法对青藤碱超临界CO2流体萃取条件的优化

以青风藤药材为原料,在单因素实验研究的基础上,采用Box-Behnken响应曲面分析法对影响青风藤药材中青藤碱超临界CO2萃取得率的关键因素:萃取时间、压力、温度进行了优化,旨在为青藤碱新型、绿色提取分离方法作探讨.根据统计模型进行了工艺参数的优选,以得率为指标,优化后所得青藤碱超临界CO2萃取工艺条件为:萃取压力为27.63 MPa,萃取温度为50.68℃,萃取时间为120.24 mim.该条件下得率为1.372%.验证试验证实了该方程的预测值与试验值之间具有较好的拟合度.     

Parallel boundary and best neighbor searching sampling algorithm for drawbead design optimization in sheet metal forming

In the present paper, a Kriging-based metamodeling technique is used to minimize the risk of failure in a sheet metal forming process. The Kriging-based models are fitted to data that are obtained for larger experimental areas than the areas used in low-order polynomial regression metamodels. Therefore, computational time and memory requirement can be an obstacle for Kriging for data sets with many observations. To improve the usability of the Kriging-based metamodeling techniques, a parallel intelligent sampling approach: boundary and best neighbor searching (BBNS) (Wang et al., J Mater Process Technol 197(1–3):77–88, 2008a) is suggested. Compared with the serial BBNS version, the sampling procedure is performed synchronously. Thus, larger sample size should be considered for real-life problems when multiple processors are available. Furthermore, the parallel strategy is prone to converge based on more samples. The performance of the parallel approached is verified by means of nonlinear test functions. Moreover, the drawbead design in sheet metal forming is successfully optimized by the parallel BBNS approach and Kriging metamodeling technique. The optimization results demonstrate that the parallel BBNS approach improves the applicability of the Kriging metamodeling technique substantially.