全膜润滑金属成形工艺的有限元仿真分析

到目前为止,全膜润滑的金属成形的数值分析非常少,这主要是由于求解润滑模型的方法只适用于轴对称和平面应变情况.因此,提出了全润滑膜润滑和金属成形有限元法相结合的方法,适用于稳态和非稳态的三维成形工艺,当然也适用于轴对称和平面应变情况.用一个轴对称拉深成形作为一个试验样板,用该法理论计算出的润滑膜厚与实测值相一致,并与其他方法的计算值进行比较,证明这种方法不仅是正确的,还提高了精度.     

全膜润滑金属成形工艺的有限元分析

针对求解润滑模型的方法只适用于轴对称和平面应变情况，提出了全润滑膜润滑和金属成形有限元法相结合的统一方法，既适用于稳态和非稳态的三维成形工艺，也适用于轴对称和平面应变情况。采用轴对称拉深成形实验，证明这种方法是正确的。该法大幅度增加了仿真的精度，且理论计算的润滑膜厚与实测值相一致。     

Investigation of the strain distribution with lubrication during the deep drawing process

A lubrication/friction model can be implemented in FEM codes to predict the contact area ratio, friction coefficient and strain distribution in lubricated deep drawing process. In the lubrication analysis, the surface roughness effect on lubrication flow is included by using Wilson and Marsault's average Reynolds equation that is appropriated for mixed lubrication with severe asperity contact. With regard to the asperity contact theory, the well-known flattening effect is considered. Friction is expressed in terms of variables such as lubricant film thickness, sheet roughness, lubricant viscosity, interface pressure, sliding speed, and strain rate. The proposed lubrication/friction model combined with a finite element code of deep drawing process to predict the contact area ratio, friction coefficient and strain distribution. Numerical results showed that the present analysis provides a good agreement with the measured strain distributions.     

An analysis of hemispherical punch stretching by the energy method

An approach using the energy method in which the total deforming region is divided into several sections of different geometric shapes is suggested for the analysis of axisymmetric sheet metal forming with friction boundary condition. The corresponding solutions are found through optimization of the total energy dissipation with respect to some parameters assumed in the velocity field as well as in the corresponding geometric profile. Computations are carried out for hemispherical punch stretching of normal anisotropic work-hardening materials for several lubrication conditions. The punch load vs stroke relation, geometric configuration and strain components are determined from the computation. The comparison of the computed results with finite element solutions and corresponding experiments shows good agreements of solutions in load vs stroke, deformed profiles and strain distribution for various lubrication conditions. It is thus shown that the present simple approach can be effectively employed for the analysis of axisymmetric sheet metal working processes.     

A static friction model for tube bulge forming using a solid bulging medium

In a metal working process, the friction between the material and the tools influences the process by modifying the strain distribution of the workpiece. From a numerical point of view, a constant coefficient of friction (Coulomb’s friction) is commonly used in finite element simulations to model the frictional behaviour of contacting solids. However, friction coefficient varies in time and space with many parameters. We presented here a theoretical model of static friction in rubber/metal contact which allows the determination of the static coefficient of friction as a function of local contact conditions. Simulations using finite element software ABAQUS/Explicit were carried out for an axisymmetric tube bulging operation using the defined friction model. We compared the computed tube thickness related to the constant coefficient of static friction with the defined friction model. The results clearly showed that the new friction model provides better agreement between experiments (Girard, Grenier, Mac Donald, J Mater Process Technol 172:346–355, 2006) and results of numerical simulations.     

复杂冲压件成形过程的截面分析技术

基于有限变形虚功率增量型原理的弹塑性大变形有限元理论,建立了高精度的八节点四边形单元平面应变状态下的截面分析模型,并应用非均匀有理B样条曲线描述模具截面线进行接触判断。旨在用很短的计算时间,获得较理想的板料冲压成形的模拟结果。方模具圆坯料胀形和深拉延成形过程以及发动机油底壳深拉延的模拟与试验结果,表明了该截面分析技术的正确性、可行性和高效性。     

润滑条件下铝合金板成形模拟中摩擦模型的研究

对润滑条件下铝合金薄板筒形件拉深成形过程进行了工艺分析，在作出一些简化和假设的基础上，建立了基于流体润滑的筒形件拉深成形过程摩擦模型；将该模型运用到板料成形过程有限元分析中，计算出筒形件成形时摩擦系数动态变化的数值；开发出基于探针测试的铝合金板温成形动态过程摩擦测试系统，并对筒形件成形时的摩擦系数进行了测试实验。计算结果与实验数据表明，板料成形过程中的摩擦系数不是一个常数，随着凸模行程的增加，摩擦系数具有增加的趋势。     

SIMULATION OF CHIP FORMATION IN ORTHOGONAL METAL CUTTING PROCESS: AN ALE FINITE ELEMENT APPROACH

Lagrangian and Eulerian finite element formulations have been traditionally used for modeling of the orthogonal metal cutting process. In this paper it is shown that a more general formulation, the arbitrary Lagrangian-Eulerian method (ALE), may be used to combine the advantages and avoid the drawbacks of both methods in a single analysis. Due to the characteristics of the cutting process, ALE formulation offers a very efficient modeling approach for the cutting process. A comprehensive ALE model along with strain rate and temperature dependent constitutive equations and a contact/friction algorithm is used to analyze the thermo-elasto-plastic process of plane strain orthogonal cutting. Simulation results for cutting of low carbon free cutting steel are presented and compared with available experimental data obtained under similar cutting conditions. Good agreement between the numerical and experimental results is observed.     

A Friction Evaluation Method Based on Barrel Compression Test

To further understand the tribological performance in metal forming, it is critical to accurately evaluate the friction between tool and workpiece. However, the unclear contact conditions at the interfaces and the complex mechanisms of the tribology lead to challenges to assess friction in metal forming processes. In this study, a friction evaluation method by the barrel compression test and its principle model were proposed based on the theoretical analysis and the numerical simulations. Besides the friction factor at the die–specimen interfaces and the initial aspect ratio of the specimen, the strain hardening exponent of the specimen was found to affect the barreling profiles based on the theoretical analysis. Furthermore, the effects of the three influencing factors, including the friction factor at the interfaces, the initial aspect ratio and the strain hardening exponent of the specimen, on the defined barreling factor were numerically analyzed by the finite element method. A predictive model of the barreling factor accounting for these three factors was developed. A friction evaluation method, proposed based on this model, was implemented by various cylinder compression experiments of CuZn40 brass. The method proposed in this study provided a convenient means to identify the contact friction in metal forming processes.     

Elasto-plastic contact problem of laying wire rope using FE analysis

The three-dimensional elasto-plastic contact model, formulated with variational equalities, has been described for laying wire rope in this paper. The augmented Lagrangian multiplier method has been applied to calculate both the normal contact force and friction contact force, and the radial return mapping algorithm has been employed to handle stick/slip phases of friction. With a graphical user interface (GUI), a program for calculating boundary conditions of a three-dimensional finite element modelling is developed to create external files, which are in the format of the ANSYS parametric design language (APDL) and the external files can be accessed by ANSYS for nonlinear analysis. FE simulation of a simple wire strand has been given and the effects of friction coefficient and self-rotating ratio on the contact stress have been analysed. Also the effects of them on the forming stress and strain have been discussed.     

确定拉延筋约束阻力的一种数值模拟方法

利用率形式的虚功原理和考虑弯曲影响的 Mindlin曲壳单元 ,根据塑性变形体积不可压缩的假设 ,将大变形弹塑性有限元应用于板料成形过程中 ,建立了接触摩擦模型。在此基础上 ,利用自行开发的软件 Sheet Form模拟板料流经拉延筋的过程 ,确定板料成形数值模拟中建立等效拉延筋模型需要的拉延筋约束阻力、塑性厚向应变和最小压边力 3个边界条件 ,并与Nine等人的实验结果进行对比 ,证明了该方法的有效性     

Analysis of drawbead process by static-explicit finite element method

The problem analyzed here is a sheet metal forming process which requires a drawbead. The drawbead provides the sheet metal enough tension to be deformed plastically along the punch face and consequently, ensures a proper shape of final products by fixing the sheet to the die. Therefore, the optimum design of drawbead is indispensable in obtaining the desired formability. A static-explicit Finite element analysis is carried out to provide a perspective tool for designing the drawbead. The finite element formulation is constructed from static equilibrium equation and takes into account the boundary condition that involves a proper contact condition. The deformation behavior of sheet material is formulated by the elastic-plastic constitutive equation. The finite element formulation has been solved based on an existing method that is called the static-explicit method. The main features of the static-explicit method are first that there is no convergence problem. Second, the problem of contact and friction is easily solved by application of very small time interval. During the analysis of drawbead processes, the strain distribution and the drawing force on drawbead can be analyzed. And the effects of bead shape and number of beads on sheet forming processes were investigated. The results of the static explicit analysis of drawbead processes show no convergence problem and comparatively accurate results even though severe high geometric and contact-friction nonlinearity. Moreover, the computational results of a static-explicit finite element analysis can supply very valuable information for designing the drawbead process in which the defects of final sheet product can be removed.     

Finite element analysis of tube flaring process with a conical tool

The extended r_min technique is incorporated into an incrementally updated Lagrangian formulation (ULF) of an elasto-plastic finite element computer code in order to handle contact boundary conditions to analyse the axisymmetric tube flaring process with a conical tool. A modified Coulomb friction law was adopted to calculate the influence of the friction coefficient on the tube flaring process. The effects of size and mechanical properties of tubes, as well as lubricants and tool semi-angle on flaring load were studied. It was found that good lubrication is effective in reducing flaring load. An optimum tool semi-angle (tool load is lower) in flaring is determined by frictional and bending activity at the tool inlet. In addition, the forming behaviour of the tube end is investigated to understand whether outward curling takes place and how much influence the tool semi-angle and tube size (initial thickness/initial mean diameter of tube) have on outward curling mode.     

Sectional finite element analysis of forming processes for aluminum-alloy sheet metals

The sectional finite element analysis of the forming processes for the aluminum-alloy sheet metal known to be planar anisotropic was performed. The two-dimensional rigid-viscoplastic FEM formulation based on the bending augmented membrane theory as well as the anisotropic yield criteria was introduced. For modeling the anomalous behavior of aluminum-alloy sheet metals, Barlat's strain rate potential and Hill's (Journal of the Mechanics and Physics of Solids 1990;38:405–17) non-quadratic yield theory with an isotropic hardening rule were employed. Furthermore, a new method to determine anisotropic coefficients of Barlat's strain rate potential was proposed. For evaluating bending effects in the forming process of aluminum-alloy sheet metals, the bending equivalent forces were calculated in terms of the changes in the interior angle at a node between two linear finite elements and were augmented to the membrane stretch forces. In order to verify the validity of sectional finite element formulation based on the bending augmented membrane theory, the plane strain stretch/draw forming processes of a square cup test were simulated and simulation results are compared with experimental measurements. Friction coefficient was obtained from drawbead friction test. The properties of selected material were obtained from uniaxial tensile tests. Simulation shows good agreement with measurements. For the application of the sectional finite element formulation introduced in this research, the drawing process of a rear seat back upper bracket of passenger cars is simulated assuming plane strain condition. The thinning distribution of the simulation agreed well with that of the measurement, so that the sectional analysis is acceptable in the design and analysis of aluminum-alloy sheet stamping dies.     

Surface asperity deformation under bulk plastic straining conditions

The paper is concerned theoretically and experimentally with the flattening of asperities by tools in metal-forming processes, a topic important to lubrication in metal forming. It specifically studies the plane strain compression process. It proposes kinematically admissible velocity fields for the crushing of asperities on a plastically flowing foundation and by adjusting independent variables of the fields predicts the actual flows by an energy minimization method. The theoretical predictions are compared with plane strain compression tests on aluminium samples with surfaces abraded in the direction of bulk plastic flow (the condition that the modelling describes). Both theory and experiment predict that asperities are crushed at the start of bulk plastic compression, to generate a real area of contact a certain fraction of the tool area depending on the contact friction and aspect ratio of the flow field, between 0.75 and 0.95 according to theory and between 0.6 and 0.8 according to experiment; but that with further bulk compression these contact fractions do not change. Despite these quantitative differences, it is felt that the method developed in this paper could usefully be extended to study asperity behaviour in other forming processes such as drawing or rolling.     

Finite element analysis on neck-spinning process of tube at elevated temperature

Tube spinning process is a metal forming process used in the manufacture of axisymmetric products and has been widely used in various applications. Finite element analysis has been successfully applied to the tube spinning processes, but no temperature effects have been considered on neck-spinning. For this reason, the aim of this research is to investigate numerically the neck-spinning process of a tube at elevated temperature. The commercial software Abaqus/Explicit was adopted in the simulation. For the construction of the material model, special uniaxial tensile tests were conducted at elevated temperature and various strain rates, since the material is sensitive to strain rates at high temperature. Comparisons between experimental and simulation results on thickness distribution and the outer contour of the spun tube are discussed. During the final stage, the average deviations between the simulation and experiment were 10.65% in thickness and 3.03% in outer contour. Good agreement was found between experimental and simulation results. The influence of the coefficient of friction, roller translation speeds, and the tip radius of the rollers were also investigated through numerical simulation.     

Effect of variable friction coefficient on sheet metal drawing

A variable friction model that relates the parameters of sheet metal drawing to the local lubrication conditions taking place during the deformation, has been integrated to a finite element program. Variable friction coefficients for the contacting surfaces are determined from the friction model, which uses the related parameters obtained at each time step of the finite element program as inputs. A number of numerical runs have been performed and the strains are compared with the experimental results for circular blanks. A good agreement is obtained between the numerical and experimental results for the variable friction model used.     

金属板料冲压成形的数值模拟

本文采用有限元动力显式算法模拟金属板料冲压成形的加工过程。四结点蜕化壳单元和刚体壳单元分别用来建立权和模具的有限元模型;更新Ｌａｇｒａｎｇｅ法和速率型本构关系被用来处理板料变形中的大应变和大转动;材料模型采用塑性各向异性屈服与等向强化模型;通过主从面模型定义板料和模具的接触,接触算法采用运动约束法,摩擦力用库仓定律计算;并利用动力松弛法对回弹过程进行了计算。模拟结果和实际零件比较,证明模型合理,算法稳定,结果可靠,具有良好的应用价值。     

Computational Mixed TEHL Model and Stribeck Curve of a Journal Bearing

The aim of this article is to propose a model capable of estimating the friction along a heavily loaded journal bearing under mixed and hydrodynamic lubrication. The finite element analysis–computational fluid dynamics (FEA-CFD) model takes into consideration the effect of solid deformations, the asperity contact phenomena, and the influence of metal–metal contact in the Reynolds equation. The Stribeck curve for a plain journal bearing under different operational conditions is calculated and compared to experimental results. The major contribution of the article is the novelty of including mixed lubrication, high-load conditions, and thermal effects in a single computational steady-state model. This comprehensive model, not limited to a specific range of operational conditions, can help during design and for health condition monitoring.     

Modelling of kinetic friction in V-bending of ultra-high-strength steel sheets

The Stribeck friction model was investigated in this study to predict springback of high-strength steel sheets. The coefficient of friction in Stribeck curve depends on sliding velocity and contact pressure. The plane-strain bending process is simulated in ABAQUS/Standard. The influence of forming speed, over-pressing and holding time on springback behaviour of sheets was studied numerically. By plotting the variation of bending angle with punch stroke, we found that the loading curve of finite element analysis showed similar results to the experiments. The unloading curves of FE analysis with friction models based on Stribeck curve and Coulomb law showed good agreement with experiments with error less than 1.5%. Forming speed of up to 50 mm/s does not have significant effect on springback. The effect of holding time on reducing springback is small, but over-press has large effect on reducing springback. The results showed that Stribeck model is suitable for sheet metal forming simulations, especially at higher forming speeds and pressures.