Efficient implicit simulation of incremental sheet forming

In single point incremental forming (SPIF), the sheet is incrementally deformed by a small spherical tool following a lengthy tool path. The simulation by the finite element method of SPIF requires extremely long computing times that limit the application to simple academic cases. The main challenge is to perform thousands of load increments modelling the lengthy tool path with elements that are small enough to model the small contact area. Because of the localised deformation in the process, a strong nonlinearity is observed in the vicinity of the tool. The rest of the sheet experiences an elastic deformation that introduces only a weak nonlinearity because of the change of shape. The standard use of the implicit time integration scheme is inefficient because it applies an iterative update (Newton–Raphson) strategy for the entire system of equations. The iterative update is recommended for the strong nonlinearity that is active in a small domain but is not required for the large part with only weak nonlinearities. It is proposed in this paper to split the finite element mesh into two domains. The first domain models the plastically deforming zone that experiences the strong nonlinearity. It applies a full nonlinear update for the internal force vector and the stiffness matrix every iteration. The second domain models the large elastically deforming zone of the sheet. It applies a pseudolinear update strategy based on a linearization at the beginning of each increment. Within the increment, it reuses the stiffness matrix and linearly updates the internal force vector. The partly linearized update strategy is cheaper than the full nonlinear update strategy, resulting in a reduction of the overall computing. Furthermore, in this paper, adaptive refinement is combined with the two domain method. It results in accelerating the standard SPIF implicit simulation of 3200 shell elements by a factor of 3.6. Copyright © 2011 John Wiley & Sons, Ltd.     

多点复合渐进成形与单点渐进成形的对比分析

为提高金属板材渐进成形的成形质量、成形精度、成形效率和成形极限,了解不同渐进成形工艺对制件成形性能的影响,本文以典型方锥台制件为研究对象,利用有限元软件MSC.Marc对2种渐进成形工艺进行了三维建模,对比分析了单点渐进成形和多点复合渐进成形对制件等效塑性应变、厚度分布和成形精度的影响.数值模拟结果表明:单点渐进成形的等效塑性应变和厚度减薄主要集中在制件相邻侧壁间的拐角处,而多点复合渐进成形的等效塑性应变和厚度减薄均匀地分布在制件成形区;相同成形工艺参数下,相比单点渐进成形,多点复合渐进成形更有利于制件的成形效率、成形质量、成形精度和成形极限的提高,更有利于抑制破裂等失稳现象的产生.2种渐进成形工艺的成形试验表明,数值模拟结果与试验相符.     

Enhancing time efficiency on single point incremental forming processes

Single Point Incremental Forming (SPIF) is a promising manufacturing technology concerning the production of customized products, low batches or prototyping of ready-to-use parts, given its easy implementation and absence of dedicated tooling. The range of application is wide, covering many materials and virtually unlimited geometries. Indeed, nowadays’ process downsides are more related to high forming times and dimensional inaccuracy. There are many processing parameters that can be optimized to circumvent such problems. In this work, focus is given on the effect of increasing tool feed rate. To this end, a dedicated SPIF machine is employed. After forming steel and aluminum sheets, parameters like forming force, maximum wall angle and formability are assessed for a range of velocities from 1500 to 12,000 mm/min. Parameters like step down or tool diameters are kept constant for a clear comparison. It will be shown how the process can be fastened up without seriously compromising its feasibility.     

板料渐进成形数值模拟与实验研究

为提高渐进成形的成形效率和成形质量,了解板料渐进成形的变形规律及工艺参数对成形的影响,采用有限元方法对板料渐进成形过程进行了数值模拟研究,分析了斜壁盒形件渐进成形过程应力分布和厚度变化趋势,通过对不同进给量和不同成形路径进行数值模拟,分析了工艺参数对成形的影响.结果表明,斜壁盒形件最大应力和最大厚度减薄发生在底面拐角处;成形过程中工具头运动轨迹应尽量采用走螺旋线的方式,可以提高成形件的成形能力和成形质量.渐进成形实验表明,数值模拟结果与实验结果基本吻合.     

Analytical prediction of formed geometry in multi-stage single point incremental forming

Single Point Incremental Forming (SPIF) is a die-less forming process that can be economically used for low volume production of sheet metal components. One of the limitations of SPIF is the maximum wall angle that can be formed in a single stage. To overcome this limitation, Multi-stage Single Point Incremental Forming (MSPIF) is used to form components with large wall angles. When the tool is moved from out-to-in during any stage, material present ahead of it (towards the centre of the component) moves down rigidly. If this rigid body displacement is not considered during tool path generation for MSPIF, it leads to stepped/unwanted features. Predicting the component geometry after each stage helps in monitoring the shape being developed and in turn is useful in designing intermediate stages to form required final geometry with desired accuracy. In the present work, a simple methodology is proposed to predict rigid body displacement based on tool path and process parameters (tool diameter, incremental depth, sheet thickness) used. Tool and sheet deflections due to forming force are also considered to predict final geometry of the component. Proposed methodology is validated by comparing predicted profiles with experimentally measured profiles of high wall angle axisymmetric components formed using different materials and sheet thicknesses. Predicted profiles are in good agreement with experimental results.     

Fast simulation of incremental sheet metal forming by adaptive remeshing and subcycling

In order to use incremental sheet forming (ISF) in an industrial context, it is necessary to provide fast and accurate simulation methods for virtual process design. Without reliable process simulations, first-time right production seams infeasible and the process loses its advantage of offering a short lead time. Previous work indicates that implicit finite element (FE) methods are at present not efficient enough to allow for the simulation of AISF for industrially relevant parts, mostly due to the fact that the moving contact requires a very small time step. Finite element methods based on explicit time integration can be sped up using mass or time scaling to enable the simulation of large-scale sheet metal forming problems. However, AISF still requires dedicated adaptive meshing methods to further reduce the calculation times. In this paper, an adaptive remeshing strategy based on a multi-mesh method is developed and applied to the simulation of AISF. It is combined with subcycling to further reduce the calculation times. For the forming of a cone shape, it is shown that savings in CPU time of up to 80 % are possible with acceptable loss of accuracy, and that the simulation time scales more moderately when the part size is increased, so that larger, industrially relevant parts become feasible.     

Experimental investigations and optimization of forming force in incremental sheet forming

Incremental sheet forming process has been proved to be quiet suitable and economical for job and batch type production, which exempts expensive and complex tooling for sheet forming. Investigation of forming forces becomes important for selecting the appropriate hardware and optimal process parameters in order to assure perfection and precision of process. Moreover, lack of available knowledge regarding the process parameters makes the process limited for industrial applications. This research paper aims at finding out effects of different input factors on forming forces in single-point incremental forming (SPIF) process. For operation sustainability and hardware safety, it becomes critical to optimize forming forces for a given set of factors to form a particular shape. In this study, optimization of input factors has been performed to produce conical frustums with helical tool path using Taguchi analysis as design of experiment (DOE) and analysis of variance (ANOVA). The optimal experimental conditions for forming forces have been calculated as sheet thickness (0.8 mm), step size (0.2 mm), tool diameter (7.52 mm), tool shape (hemispherical), spindle speed (1000 rpm), feed rate (1000 mm/min) and wall angle (50^o). Effects of tool shape and viscosity of lubricants have also been investigated. An intensive understanding of the mechanism of forming forces has been presented, which shows that force trend after peak values depends upon instant input factors that can be categorized as a safe, severe and crucial set of parameters.     

Thermal modeling in electricity assisted incremental sheet forming

A thermal model was built to account for the effects of geometrical parameters of sheet specimen, process parameters and material parameters on the temperature increase of the sheet specimen in Electricity-Assisted Incremental Sheet Forming (EISF). In the EISF, the local area of sheet specimen contacting with a forming tool is heated by direct current, which flows through the forming tool to the sheet specimen. EISF experiments of two high strength steel sheets were carried out to validate the thermal model. The thermal model can be integrated into the control program of EISF system to achieve more accurate temperature control.     

大幅面板材渐进折弯成形的本构建模及模拟

为了提高大幅面板材成形的模拟精度,在板材折弯平面应变假设条件下,推导出基于Hill各向异性屈服准则的弹塑性本构方程.借助ABAQUS有限元软件本构模块用户子程序接口,通过编程将上述推导的应力-应变本构关系显示表达式嵌入ABAQUS分析平台.以超长大开口半椭圆形工件成形为例,建立了大幅面钢板渐进折弯的三维弹塑性有限元模型,并数值模拟了多道次渐进折弯成形及回弹全过程.模拟效果和工程应用结果表明,与传统的基于平面应力假设的本构关系模型相比,采用平面应变假设的本构关系模型的模拟结果更接近实验值.     

An assessment of various process strategies for improving precision in single point incremental forming

Single point incremental forming (SPIF) is a process with the capability to form complex geometries using a tool of very simple geometry, without the need for a matching die. However, large elastic springback resulting from the die-less nature of the process can cause problems if high levels of accuracy are required. The aim of this investigation is to use numerical modelling to investigate different strategies to improve the process precision. A finite-element (FE) model has been used to investigate the effects of adding a backing plate, a supporting kinematic tool and modifying the final stage of the tool path. The results show that the backing plate will minimise the sheet bending near to the initial tool contact location; the additional kinematic tool will reduce springback; and the extension of the tool path across the base of the sheet will eliminate the pillow effect. The cumulative effect of introducing these features to the process shows an improvement in the overall accuracy of the profile and in the thickness distributions of the final product. The results contribute to a better understanding of springback in SPIF.     

Titanium based cranial reconstruction using incremental sheet forming

In this paper, we report recent work in cranial plate manufacturing using incremental sheet forming (ISF) process. With a typical cranial shape, the ISF process was used to manufacture the titanium cranial shape by using different ISF tooling solutions with and without backing plates. Detailed evaluation of the ISF process including material deformation and thinning, geometric accuracy and surface finish was conducted by using a combination of experimental testing and Finite Element (FE) simulation. The results show that satisfactory cranial shape can be achieved with sufficient accuracy and surface finish by using a feature based tool path generation method and new ISF tooling design. The results also demonstrate that the ISF based cranial reconstruction has the potential to achieve considerable lead time reduction as compared to conventional methods for cranial plate manufacturing. This outcome indicates that there is a potential for the ISF process to achieve technological advances and economic benefits as well as improvement to quality of life.     

An investigation into thickness distribution in single point incremental forming using sequential limit analysis

Single point incremental forming (SPIF), needing no dedicated tools, is the simplest variant of incremental sheet metal forming processes. In the present work, a simplified model of SPIF of a truncated cone, capable of predicting the thickness distribution, has been developed using sequential limit analysis (SLA). The obtained results were validated experimentally and compared with thickness predictions obtained from an explicit shell FE model implemented in Abaqus. It is shown that SLA is capable to solve the thickness prediction problem more accurately and efficiently than the equivalent FEA approach. As an application of the proposed model, the effect of the diameter of the hemispherical tool tip and the step down on the thickness distribution and the minimum thickness in a 50° cone is studied using SLA. By introducing bending and stretching zones in the wall of the cone, variations of the minimum thickness by changing the tool diameter and the step down are discussed.     

Efficient implicit finite element analysis of sheet forming processes

The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time‐savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton–Raphson iterations. This also applies to quasi‐static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd.     

渐进成形A3003铝板减薄带分析及数值模拟研究

研究渐进成形过程中板料减薄带的变化,可以提供合理的加工参数,提高板料的成形性能和加工利用率,减少零件破裂失效.基于渐进成形过程中金属板料轮廓的变化与理想情况下轮廓的区别,对渐进成形初始成形阶段A3003铝板减薄带的产生原因和剪切力的变化过程进行了理论分析,并通过有限元模拟分别从未变形区金属板料的长度和强度两个角度对板料渐进成形过程中未变形区下沉的影响,以及成形角度和杨氏模量对变形区回弹的影响两个方面,对减薄带的产生原因进行研究.结果表明:板料未变形区的下沉和变形区的回弹使板料在初始加工阶段形成一段平缓区域,工具头在平缓区域的变形性质发生了变化,平缓区域发生剪切变形导致了板料在初始加工阶段形成了减薄带;渐进成形时减小板料未变形区的长度,增大板料与垂直方向的角度可以一定程度上阻碍减薄带的产生,模拟结果与理论分析相符合.     

Towards accuracy improvement in single point incremental forming of shallow parts formed under laser assisted conditions

Single point incrementally formed parts with a low wall angle geometry typically exhibit a manufactured geometry that significantly deviates from the design surface due to accumulated unwanted bulging deformation. Development of the bulge on the bottom of the part might result in wrinkling of the sheet at the bulged region which leads to higher forming forces and can even cease the forming process. In this study, the geometric inaccuracy of low angled parts is investigated by means of both Finite element analysis and an experimental campaign on a conical geometry. Deformation mechanisms in shallow sloped parts have been studied in detail and the tool-sheet contact area has been characterized both for low and high angled geometries. In a second phase, the laser assisted single point incremental forming process and its potential for improving accuracy are investigated. To obtain suitable process parameters for a warm forming condition, a transient heat transfer analysis is developed to simulate the laser movement on the conical geometry. Based on the simulated and experimentally determined tool-sheet contact zone, different laser spot positioning strategies have been used while the accuracy of the part and forming forces were measured. It has been observed that overforming of the cone wall is due to the continuous deformation of the sheet outside the contact zone which changes into underforming upon laser treatment. By selection of a proper laser positioning strategy a reduction of 42 % in bulge height is observed. This shows its effect in reducing radial forming forces.     

Stress based prediction of formability and failure in incremental sheet forming

A strain-based forming limit criterion is widely used in sheet-metal forming industry to predict necking. However, this criterion is usually valid when the strain path is linear throughout the deformation process [1]. Strain path in incremental sheet forming is often found to be severely nonlinear throughout the deformation history. Therefore, the practice of using a strain-based forming limit criterion often leads to erroneous assessments of formability and failure prediction. On the other hands, stress-based forming limit is insensitive against any changes in the strain path and hence it is first used to model the necking limit in incremental sheet forming. The stress-based forming limit is also combined with the fracture limit based on maximum shear stress criterion to show necking and fracture together. A derivation for a general mapping method from strain-based FLC to stress-based FLC using a non-quadratic yield function has been made. Simulation model is evaluated for a single point incremental forming using AA 6022-T43, and checked the accuracy against experiments. By using the path-independent necking and fracture limits, it is able to explain the deformation mechanism successfully in incremental sheet forming. The proposed model has given a good scientific basis for the development of ISF under nonlinear strain path and its usability over conventional sheet forming process as well.     

Single point incremental forming: state-of-the-art and prospects

Incremental sheet metal forming in general and Single Point Incremental Forming (SPIF) specifically have gone through a period of intensive development with growing attention from research institutes worldwide. The result of these efforts is significant progress in the understanding of the underlying forming mechanisms and opportunities as well as limitations associated with this category of flexible forming processes. Furthermore, creative process design efforts have enhanced the process capabilities and process planning methods. Also, simulation capabilities have evolved substantially. This review paper aims to provide an overview of the body of knowledge with respect to Single Point Incremental Forming. Without claiming to be exhaustive, each section aims for an up-to-date state-of-the-art review with corresponding conclusions on scientific progress and outlook on expected further developments.