Energy efficiency of cold roll forming process

Cold roll forming is an important sheet metal forming process for the mass production of a variety of complex profiles out of a wide spectrum of materials and thicknesses. The energy efficiency of such a continuous bending process may lead to a significant reduction in energy consumption. In this paper, the energy efficiency indicator is introduced for the case of roll forming. In order for this indicator to be calculated, analytical models are proposed and developed for the estimation of the energy consumption and the production rate. An application to a U-section profile and the effects of the process parameters on the energy efficiency indicator are discussed. The overall contribution (in percent) of the main process parameters on the energy efficiency indicator is calculated through a matrix of experiments. The results have shown that the most influential process parameters, on the energy efficiency of the cold roll forming process, are the bending angle concept, the line velocity, and the inter-distance among the roll stations.     

Optimization of roll forming process parameters—a semi-empirical approach

The roll forming process parameters play a major role in the quality of the final roll-formed product. Optimum configuration without any cost increase in the roll forming line could present accurate and flawless products. In this paper, a roll forming process experimental modelling of a symmetrical U-section profile from advanced high strength steel (AHSS) material (type DP600) is presented. The factors selected for this study are the roll forming line velocity, the inter-distance between roll stations, the roll gap, and the diameter of the rolls. An optimization procedure for the roll forming line, via statistical design of the experimental simulation runs, is also presented. The optimum values of process parameters are calculated for minimum elastic longitudinal strains and shear strains, at strip edge, for each roll station. A reduction of 20–35% in elastic longitudinal strains could occur for all roll stations, and 30–50% reduction in shear strains occurs for roll stations with a greater folding angle, as this leads to roll-formed products of a better quality. Finally, the contribution of each factor on the longitudinal and shear strains has been calculated, showing that the inter-distance between the roll stations plays a dominant role in the roll forming process.     

基于动态序列响应面方法的钣金成形过程参数优化

为得到钣金成形最佳工艺方案，结合有限元方法将设计转化为特定目标和约束的待优化问题；针对成形模拟易受干扰和强非线性特点，提出采用逐次逼近模型，分解复杂设计函数为显式简单函数组合，进行递进全局寻优，避免出现局部最优解和过程发散现象；并利用动态多项式序列响应面方法构造目标和约束的简单近似响应面，用以去除噪声干扰及最大程度减少精确分析计算量。该方法无需求解复杂函数敏度，经实例验证具有很高的精度和效能。     

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.     

汽车前轴精密辊锻成形过程的数值模拟

汽车前轴的精辊-模锻工艺是一种用小成形力锻造设备成形较大型前轴锻件的塑性加工技术,其工艺关键在于精密辊锻。前轴的精密辊锻分4个道次,是典型的局部成形工艺。辊锻工艺由于旋转的模具与辊锻件之间的接触区域在不断变化,一直以来成为数值模拟的难点。对4个道次的模具建立了模型,采用三维刚塑性有限元程序DEFORM-3D模拟了前轴精密辊锻工艺,分析了辊锻过程中金属变形的规律,研究了模具参数对成形质量的影响以及辊锻力矩的变化规律。模拟结果对于改进辊锻工艺设计、提高模具设计水平具有指导作用。     

Robust design of roll-formed slide rail using response surface method

Roll-formed slide rail used as a linear guide in the smooth movement of drawers and electric home appliances requires geometric accuracy because of a high slenderness ratio and repetitive usage. The slide rail members are generally manufactured by the roll forming process. The members need to be improved through optimization of the roll forming process instead of the designer’s experience. The aim of this study is to determine the optimal roll forming parameters by using robust optimization technique which simultaneously satisfies three criteria such as the shape difference factor, bowing factor and modified inverse safety factor. In analyzing the roll forming process of a slide rail, the pass in which the largest deformation occurred is designated as the target pass. The positions and the curvature of rolls are set as the design variables in the target pass. The cost function, which is comprised of the shape difference factor, the bowing factor, and the modified inverse safety factor, is obtained using design-of-experiments of the response surface method. The cost function is minimized by using robust optimization techniques and showed the improved the straightness and the durability value. Using robust design methodology, it is able to be constructed a multi-objective function, and optimized three criteria, simultaneously.     

基于实验设计与数据分析的金属热挤压成形比能耗优化

为降低金属挤压成形阶段能耗,以挤压成形比能耗为目标,建立热平衡约束条件等价方程,以铝棒起始温度、铝棒长度、挤压速度、挤压筒温度、模角等为控制变量,以热导率、材料强度系数为扰动变量,集成利用实验设计（DOE）与数据分析等方法构建热平衡约束的挤压成形比能耗鲁棒优化模型。结果表明,在热平衡约束以及多参数控制环境下,通过鲁棒优化可降低挤压成形比能耗,而且可以保证产品质量的稳定性。     

Investigation of the effect of roll forming pass design on main redundant deformations on profiles from AHSS

The tooling design in the roll forming process plays a major role in the quality and successful mass production of a variety of complex profiled products, in many industrial sectors. The roll forming line is comprised of consecutive forming passes. Each roll forming pass consists of a set of rotating rollers able to bend the material as it passes through them. The roll forming pass design plays a major role in the production of profiles. The introduction of advanced high strength steels (AHSS), such as the DP-series and TRIP-series, has also posed new challenges for the design of the roll passes. The current paper exploits explicitly the finite elements (FE) method and investigates the effect of the roll forming passes design on main redundant deformations, such as longitudinal stains at the edge of the profile, shear strains on strips plane, thickness reduction, and final produced cross section with springback. The profiles discussed are symmetrical V- and U-sections from the AHSS Dual Phase series (DP780). The gradual lowering of the flower pattern design, known as ??downhill pass flow??, is discussed. The calculated decrease in the peak longitudinal strains of up to 28%, and the decrease in thickness of up to 38% are also presented and discussed.     

Evolutionary bi-criteria optimum design of robots based on task specifications

The optimum robot structure design problem based on task specifications is an important one, since it has greater influence on manipulator workspace design, vibrations of the manipulator during operation, manipulator efficiency in the work environment and power consumption. In this paper, an optimization robot structure problem is formulated with the objective of determining the optimal geometric dimensions of the robot manipulators considering the task specifications (pick and place operation). The aim is to minimize torque required for motion and maximize manipulability measure of the robot subject to dynamic, kinematic, deflection and structural constraints with link physical characteristics (length and cross-sectional area parameters) as design variables. In this work, five different cross-sections (hollow circle, hollow square, hollow rectangle, C-channel and I-channel) have been experimented for the link. Three evolutionary optimization algorithms namely multi-objective genetic algorithm (MOGA), elitist nondominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) are used for the optimum structural design of 2-link and 3-link planar robots. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best optimal solution. Two multiobjective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the Pareto optimal fronts. Two more multiobjective performance measures namely optimiser overhead and algorithm effort, are used to find computational effort of optimization algorithm. The results obtained from various techniques are compared and analyzed.     

On the prediction of side-wall wrinkling in sheet metal forming processes

Prediction and prevention of side-wall wrinkling are extremely important in the design of tooling and process parameters in sheet metal forming processes. The prediction methods can be broadly divided into two categories: an analytical approach and a numerical simulation using finite element method (FEM). In this paper, a modified energy approach utilizing energy equality and the effective dimensions of the region undergoing circumferential compression is proposed based on simplified flat or curved sheet models with approximate boundary conditions. The analytical model calculates the critical buckling stress as a function of material properties, geometry parameters and current in-plane stress ratio. Meanwhile, the sensitivities of various input parameters and integration methods of FEM models on the prediction of wrinkling phenomena are investigated. To validate our proposed method and to illustrate the sensitivity issue in the FEM simulation, comparisons with experimental results of the Yoshida buckling test, aluminum square cup forming and aluminum conical cup forming are presented. The results demonstrate excellent agreements between the proposed method and experiments. Our model provides a reliable and effective predictor for the onset of side-wall wrinkling in sheet metal forming processes.     

基于鲁棒性的概率优化设计在薄壁构件耐撞性中的应用

汽车结构的耐撞性及碰撞吸能优化是现代汽车工业重要的研究内容。耐撞性的优化涉及材料与结构的众多参数，传统的确定性优化设计、碰撞仿真及实验往往只能在一定程度上改善结构的碰撞性能，而无法评估设计参数的可靠性和目标函数的鲁棒性，以及在给定可靠性约束条件下使目标函数的鲁棒性达到最优状态。将实验设计、响应面模型和蒙特卡罗模拟技术相结合，构造了基于产品质量工程的6σ鲁棒性优化设计方法，实现了对设计目标的优化，并提高了设计变量的可靠性和目标函数的鲁棒性。     

Simulation of the continuous casting process by a mathematical model

A computational three-dimensional (3D) heat transfer model has been developed and applied to calculate the temperature distribution and solid shell thickness profile of a continous cast slab in a steel plant. This developed model includes non-linear material properties of specific heat and thermal conductivity as well as phase changes during solidification. A general thermo-fluidmechanics computer program, PHOENICS, was employed to numerically solve the heat transfer equation with the associated source terms. The thermal profile and solid shell thickness calculated by mathematical model agree with those predicted by an industrial model and experimental measurements. The model could also be used to predict the optimum process parameters on casting speed, heat removal rates and associated water flow rates and roll force. These parameters could be monitored by suitable sensors and controlled through a feed back system that interfaced with the mathematical model and the sensors.     

扭杆弹簧计算与优化

扭杆弹簧是车辆悬架装置中常用的弹性元件。文中利用有限元方法对扭杆弹簧进行了建模和优化计算。给出了扭杆弹簧的优化参数和结构应力分布规律，并对优化结果进行了实验测试与比较。分析结果表明，扭杆弹簧过渡区的结构对其应力分布具有较大影响，通过优化设计改进扭杆弹簧结构，有利于提高其性能。     

Robust optimization of the billet for isothermal local loading transitional region of a Ti-alloy rib-web component based on dual-response surface method

Billet optimization can greatly improve the forming quality of the transitional region in the isothermal local loading forming (ILLF) of large-scale Ti-alloy rib-web components. However, the final quality of the transitional region may be deteriorated by uncontrollable factors, such as the manufacturing tolerance of the preforming billet, fluctuation of the stroke length, and friction factor. Thus, a dual-response surface method (RSM)-based robust optimization of the billet was proposed to address the uncontrollable factors in transitional region of the ILLF. Given that the die underfilling and folding defect are two key factors that influence the forming quality of the transitional region, minimizing the mean and standard deviation of the die underfilling rate and avoiding folding defect were defined as the objective function and constraint condition in robust optimization. Then, the cross array design was constructed, a dual-RSM model was established for the mean and standard deviation of the die underfilling rate by considering the size parameters of the billet and uncontrollable factors. Subsequently, an optimum solution was derived to achieve the robust optimization of the billet. A case study on robust optimization was conducted. Good results were attained for improving the die filling and avoiding folding defect, suggesting that the robust optimization of the billet in the transitional region of the ILLF was efficient and reliable.     

高鲁棒性两阶段激光雷达惯性测量单元外参在线标定算法

针对车辆在近似平面上运动时,退化的传感器数据难以标定外参的问题,提出了一种高鲁棒性两阶段激光雷达惯性测量单元(LiDAR-IMU)外参在线标定算法。标定算法包括剔除外点的解析解初值计算和非线性滑窗在线迭代优化两个阶段。第一阶段剔除预数据集中的外点,以滑动窗口的形式多次求解只包含旋转分量的手眼标定模型,并改进解析解筛选的条件,求解出多解加权旋转外参的SVD解析解。第二阶段最小化包含外参的残差函数,以旋转解析解为初值滑动窗口迭代优化六自由度外参,使外参快速收敛,并在退化运动和错误历史约束过大时固定外参,避免外参退化。与原始算法对比,该算法对退化的传感器数据具有鲁棒性,可在无外参初值的情况下实现精准鲁棒地在线标定外参。     

Optimization of bending sequence in roll forming using neural network and genetic algorithm

In the roll forming process, the bending sequence plays a major role in the product quality. The optimal bending sequence results in the smallest number of passes and the flawless process. This paper presents a new optimization procedure of bending sequence in a roll forming process. The multilayer perceptron is used to build the neural network (NN), which models the variation of longitudinal strain in process while the genetic algorithm (GA) is employed to optimize the bending sequence. The data used for training the network is automatically obtained by the integration between CAD and CAE. The values of peak longitudinal strains are maximized while the number of passes is reduced to the smallest and the constraint conditions being set on the maximal longitudinal strain to avoid buckling. The overbending at final pass after spring back is also considered in this paper. Two roll forming processes are optimized in order to prove applicability and efficiency of the optimization procedure. This method maintains the longitudinal strain less than the buckling limit, whereas reducing the number of passes to the smallest. Thus, the advantages of the proposed method show the high applicability in designing and optimizing the bending sequence in the roll forming process.     

角度与运动约束下串联式机械臂工作空间求解与结构优化

深水作业机械臂通常采用串联式结构,机械臂每个关节的转动角度与长度会受到相应的限制,这些参数会直接影响到机械臂的运动轨迹规划和作业效率。机械臂的有效工作空间的求解是一个多目标多约束的优化问题。通过数学分析建立机械臂的运动学模型,分析影响有效工作空间的相关参数,利用图解法来分析机械臂工作空间的边界曲线,得到机械臂的有效工作空间的截面。针对机械臂有效工作空间的截面积建立数学解析模型,最后运用遗传算法求得满足约束条件下的机械臂有效工作空间最优解和能够实现高效作业的最优结构参数。仿真结果表明,该模型能够有效求解角度与运动约束下的串联式机械臂结构优化问题。     

Simulation and experimental verification of flexible roll forming of steel sheets

Roll forming is a sheet metal forming process that has been used for decades. Usually roll-formed sections have a constant cross section. Flexible roll forming is a brand new forming process that produces parts with variable cross sections, in which the rollers translate back and forth in a direction that is perpendicular to the sheet feeding direction. Theoretical analysis gives an explanation of the plane strain state, compressive stresses, tensile stresses, and shear stresses in flexible roll forming. In order to analyze the mechanics and the deformation characteristics of flexible roll forming, the finite element method (FEM) model of a 17-step flexible roll forming process is established. The yield criterion used in the FEM simulation is Hill 48, and the parameters of which are solved with the yield stresses under different loading conditions and are firstly verified with a plane strain tensile test. The complicated roller paths are realized with data extracted from the computer-aided design (CAD) files with VC++ programs developed by the authors. We developed the first flexible roll forming prototype machine in China, with which the roll forming experiment of a side door beam is performed. Final shapes of the experimental and numerical results are compared. It is shown that the numerical results based on Hill 48 yield criterion that is solved with yield stresses agree well with the experimental results, which indicates that the simulation model can well reflect the real forming process. Detailed analysis of the distribution and history of plastic strain, longitudinal strain, shear strain, and thickness of both the constant cross section and the variable cross section is performed, which is of great help to understand this forming process.     

Dynamic analysis on laser forming of square metal sheet to spherical dome

Laser forming (LF) is a new die-less forming technique that employs the energy from a laser beam to modify and adjust the curvature of sheet metals. In order to advance the LF process further for realistic application industry, it is necessary to consider large scale three-dimensional laser forming (3DLF). The main problem of 3DLF is the understanding of the mechanism and the planning of laser scanning strategy. This paper illustrates the temperature field, stress–strain field, and deformation field in the process of 3DLF of square sheet to spherical dome with spider-lines strategy with a finite element method (FEM). The explicit dynamic integral is used in the work presented in the paper rather than implicit method for improving the computational efficiency and accuracy. The FEM results showed that the inner stress induced by the laser beam propagates through the sheet as a stress wave, and the thermal stress and the stress wave in the sheet are the main influence factors in 3DLF. Also, the FEM results have been verified against experimental data, and a reasonable correlation has been found. The work showed in the paper would be beneficial of the parameter optimization of laser scanning strategy and the control of the formed precision of the sheet in 3DLF.     

Reliability-based design optimization of slider air bearings

This paper presents a design methodology for determining configurations of slider air bearings considering the randomness of the air-bearing surface (ABS) geometry by using the iSIGHT. A reliability-based design optimization (RBDO) problem is formulated to minimize the variations in the mean values of the flying heights from a target value while satisfying the desired probabilistic constraints keeping the pitch and roll angles within a suitable range. The reliability analysis is employed to estimate how the fabrication tolerances of individual slider parameters affect the final flying attitude tolerances. The proposed approach first solves the deterministic optimization problem. Then, beginning with this solution, the RBDO is continued with the reliability constraints affected by the random variables. Reliability constraints overriding the constraints of the deterministic optimization attempt to drive the design to a reliability solution with minimum increase in the objective. The simulation results of the RBDO are listed in comparison with the values of the initial design and the results of the deterministic optimization, respectively. To show the effectiveness of the proposed approach, the reliability analyses are simply carried out by using the mean value first-order second-moment (MVFO) method. The Monte Carlo simulation of the RBDO’s results is also performed to estimate the efficiency of the proposed approach. Those results are demonstrated to satisfy all the desired probabilistic constraints, where the target reliability level for constraints is defined as 0.8.