Finite element analysis on the V-die coining bend process of steel metal

An elasto-plastic incremental finite element computer code based on an updated Lagrangian formulation was developed to simulate the V-die coining bend process of sheet metal under the plane-strain condition. A modified Coulomb’s friction law was introduced to treat the alternation of the sliding–sticking state of friction at the contact interface. The r-minimum method was used to treat the elastic–plastic stress state and to solve contact problems at the tool–metal interface. V-bends of sheet metals are classified according to the number of contact points of the sheet with the bending die, and include air bends, bottoming bends, and coining bends. The former has three contact points with the bending die at the punch top and die shoulders, and there have been many experimental and analytical research works reported on it. The latter two are in contact at a greater number of points. To clarify the bending characteristics, it is necessary to fully understand the process and stress state in the bent part. The experiment was performed to validate the theoretical formulation and to support the development of the computer code. Simulation was performed on the punch load of the coining bend and the bend angle of the bent part after unloading. Calculated sheet geometries and the forming force agree well with the experimental data. The simulation clearly demonstrates the efficiency of the code to simulate V-die coining bend processes that proceed under contact history.     

The effect of strain-hardening on frictional behavior in tip test

In previous investigation of the tip test using aluminum alloy AL6061-O, it was found that the distance of radial tip from the external side surface of the workpiece deformed has a linear relationship with the maximum forming load measured at a certain punch stroke. In this study, further experiments with aluminum alloys AL2024-O, AL5083-O, AL6061-O, AL7075-O, annealed carbon steel AISI 1010 and pure copper C12100 were carried out to investigate the effect of material properties on frictional behavior by the tip test for the materials commonly used in bulk metal forming. To characterize the relationships among radial tip distance, maximum forming load and shear friction factor, finite element analyses were employed. It was observed that the linear relationships among these three were maintained for the various tested materials. Also, it was found that the friction condition at the punch was always higher than that at the lower die interface such that the ratio of shear friction factors at the die and punch interfaces should be less than one. By examining the material properties currently tested, it was determined that this ratio could be estimated from a logarithmic equation from the value of strain-hardening exponent, depending on the material used.     

Effects of process variables on V-die bending process of steel sheet

This investigation aims to clarify the process conditions of the V-die bending operation of steel sheet. It provides a model which predicts the correct punch load for bending and the precise final shape of products after unloading, in relation to the tensile properties of the material and the geometry of tools. The process variables are punch radius (R_p), die radius (R_d), punch width (W_p), punch speed (V_p), friction coefficient (μ), strain hardening exponent (n) and normal anisotropy (R).This investigation is carried out by performing some experiments and by finite-element simulation. Experiments determine the punch for bending for various process variables, such as punch radius, punch speed and lubrication, were carried out. As a result it was found that punch load increases as punch radius and punch speed increase or lubrication decreases.An elasto-plastic incremental finite-element computer code based on an updated Lagrangian formulation was developed to simulate the V-die bending process of sheet metal under the plane-strain condition. Isotropic and normal anisotropic material behavior was considered including nonlinear work hardening. A modified Coulomb’s friction law was introduced to treat the alternation of sliding–sticking state of friction at the contact interface. Simulation results, such as the punch load of bending and the bend angle of the bent part after unloading, are compared with experimental data; satisfactory agreement was observed. The simulation clearly demonstrates that the code to simulate V-die bending process was efficient.Simulations were made to evaluate the effects of die radius, punch width, strain hardening exponent and normal anisotropy on punch load of bending. The punch load for bending is smaller for materials with a larger strain hardening exponent. The effect of punch width on punch load is limited. The punch load decreases in the early stage and increases in the final stage of the bending process as the die radius increases. The influences of all of the process variables on the final bend angle of the bent parts of sheet after unloading were also evaluated. The effects of process variables except die radius on the bend angle after unloading are also limited. The angle of spring-back is greater for tools with larger die radius.     

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。     

Evaluation of interfacial friction condition by boss and rib test based on backward extrusion

Proper consideration of tribological problems at the contact interface between the tool and workpiece is crucial in metal forming, since interfacial friction condition plays an important role in metal forming by influencing the metal flow, forming load, die wear, etc. In order to quantitatively estimate such friction condition, a new friction testing method “Boss and Rib Test” based on the backward extrusion process is proposed in this work. In boss and rib test, a key design is to use a tube-shaped punch so that the boss and rib at the deforming workpiece along the inner and outer surfaces of the punch are formed during backward extrusion. It was experimentally and numerically revealed that the heights of the boss and rib vary according to the friction condition applied. It was also found that the height of the boss is higher than that of the rib when the friction condition at the contact interface is severe. From this finding, the shear friction factor can be evaluated according to lubricant characteristics assigned. In addition, simulation results revealed that calibration curve demonstrating deformation pattern of the workpiece is affected by strain-hardening exponent of the workpiece.     

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.     

Friction factor evaluation by FEM and experiment for TA15 titanium alloy in isothermal forming process

The friction at die–workpiece interface is an important parameter in metal forming processes, which affects the metal flow, cavity fill, surface quality, etc. The friction in the forming process is influenced by material properties and forming conditions. The friction in forming process of TA15 (Ti–6Al–2Zr–1Mo–1V) titanium alloy under high temperatures (isothermal forming) and low strain rates is studied here by ring compression test. The friction calibration curves are elaborated by means of finite element method. The research on the calibration curves and friction factor at the loading speed v?=?0.1–1.0?mm/s and the conventional forging temperature (950°C) and near-beta forging temperature (970°C) is carried out. The influence of loading speed on friction calibration curves is similar to the influence on friction factor m: at the low (m <about 0.1) or high (m >about 0.7) friction condition, the influence of loading speed can be ignored, however the influence is notable in the midst magnitude (about 0.2–0.5). The temperature variation from 950°C to 970°C has little influence on friction calibration curves, but has notable influence on m under lubricated condition.     

Influence of blank profile on the V-die bending camber process of sheet metal

The finite element simulation is now widely used in the design of stamping tools. A trial and error procedure has been replaced by a simulation in which defects associated with sheet forming processes are predicted and evaluated. This paper aims to clarify the process conditions of the V-die bending of a sheet metal. It provides a model that predicts not only the correct punch load for bending, but also the precise final shape of the products after unloading. An incremental elastic-plastic finite element computer code, based on an updated Lagrangian formulation, was developed to simulate the V-die bending of sheet metal. In particular, the assumed strain field (ASF) element was used to formulate the stiffness matrix. The r-minimum technique was used to deal with the elastic-plastic state and solve contact problems at the tool-metal interface. A series of experiments were performed to validate the formulation in the theory, leading to the development of the computer codes. The predicted punch load in the finite element model agrees closely with the experimental results. The whole history of deformation and the distribution of stress and strain during the forming process were obtained by carefully considering the moving boundary condition in the finite element method .A unique feature of this V-die bending process is the camber after unloading. The computer code successfully simulates this camber. The simulation was performed to evaluate the effects of the size of the blank on the camber process. The results in this study clearly demonstrate that the computer code efficiently simulated the camber process .     

Characterization of Frictional Behavior in Cold Forging

In the present investigation, tip test was utilized to characterize the effects of surface roughness of the specimen and forming tools, rate of deformation, and type of lubricants on friction in solid and solid contact under high contact pressure at room temperature. For the test, a cylindrical specimen made of aluminum alloy of 6061-O was used and grease, corn oil, VG100, and VG32 were applied as lubricants. Single punch and two counter punch sets with different surface roughness of R _a = 0.08 and 0.63 μm were manufactured in order to investigate a frictional behavior during the test. In addition, two different deformation speeds of 0.1 and 5.0 mm/s were used for the test to check their effect on friction as well. Load levels and tip distances obtained from the test were compared to find out any correlation between the two. The change of surface topology of the specimen was monitored by optical measurement technique to better understand a frictional behavior at the punch and counter punch interfaces. Present investigation clearly shows that tip test is easy to apply to experimentally characterize the frictional behavior in cold forging under various processing conditions considered.     

Analysis of deep drawing of sheet metal using the Marform process

This paper deals with the deep drawing of metal cups using the Marform process. Using this technique, higher limiting drawing ratios can be obtained compared with the conventional deep drawing process. The analytical model of the process is presented initially, followed by the finite element simulations using ABAQUS software. A new friction model based on local contact conditions is presented and used in the finite element (FE) simulations of the process. Compared with traditional Coulomb friction model, the results of the FE simulations with the new friction model showed good correlation with experimental results. The results showed that the maximum thinning occurs at the punch profile portion, and by increasing the forming pressure, thinning of the sheet metal propagates from the punch profile portion to the side wall. At low forming pressures, wrinkles appear in the flange, whilst at higher pressures, fracture is the main defect of the Marform process.     

Optimization of processing parameters for double-ridged rectangular tube rotary draw bending based on grey relational analysis

The rotary draw bending of double-ridged rectangular tube is a complex nonlinear physical process with multifactors coupling effects. Processing parameters, especially clearances and friction coefficients between tube and various dies, have a significant effect on the forming quality of the double-ridged rectangular tube in rotary draw bending. If the values of these processing parameters are inappropriate, some defects including cross-sectional deformation, wall thinning, and wall thickening easily occur in the bending process of double-ridged rectangular tube. So optimization of these processing parameters is of great importance to control these defects. Based on the grey relational analysis method combined with the orthogonal experimental design and finite element simulation, a grey relational analysis model was established for the rotary draw bending process of double-ridged rectangular H96 brass tube. With the model, optimization of clearances and friction coefficients between tube and various dies was implemented with consideration of interactive effects of the above defects. The results show that (1) the main factors influencing cross-sectional deformation, wall thickening, and wall thinning are tube–mandrel clearance Δc _m, tube-bending die clearance Δc _b, and tube–mandrel clearance Δc _m, respectively. (2) The optimal values of clearances Δc _m, Δc _p, Δc _w, and Δc _b and friction coefficients μ_m, μ_p, μ_w, and μ_b of tube–mandrel, tube–pressure die, tube–wiper die, and tube-bending die are 0.15, 0.2, 0.2, 0.2, 0.02, 0.3, 0.06 and 0.17 mm, respectively. Furthermore, the verification for the optimal values of these processing parameters was carried out, and the double-ridged rectangular H96 bent tube obtained by using the optimal values of these processing parameters has the minimum values of cross-sectional deformation, wall thinning, and wall thickening and can satisfy the national aviation industry standards.     

Four-ball assessment of deep drawing oils

A comparative study has been made of four-ball friction and wear test results and the cup-drawing performance of a number of commercial fatty drawing oils and mineral oils. A linear correlation was observed between the maximum punch load required to draw a flat-bottomed cup from a lubricated mild steel blank of fixed diameter and the four-ball friction coefficient μ₁₄₂₅ determined at 1425 r.p.m. within a pre-transition load range. Both quantities showed dependence on lubricant density and viscosity, confirming an (elasto)-hydrodynamic mechanism contributed in both the cupdrawing and the 1425 r.p.m. four-ball tests, under conditions that were insufficient to promote chemical action between the lubricant and the sliding metal surfaces. A theoretical equation between the cup wall stress and μ₁₄₂₅ has been derived, of similar form to the empirical equation expressing the observed correlation. Drawing efficiencies of the oils calculated from values of μ₁₄₂₅ were within 1–2% of those estimated from cup-drawing loads. Information on the extreme pressure properties of the oils was obtained from standard four-ball wear-load tests. It is concluded that, overall, fourball friction and wear test data suffice to rate drawing oils for both simple and severe forming of steel sheet, provided that the test conditions allow similar lubrication mechanisms to operate as in the relevant drawing operation.     

Influence of Cone Semi-Angle on the Formability Limitation of the Hole-Flanging Process

A hole-flanging process on a circular plate with a predeter-mined smaller hole in its centre has been analysed using the incremental updated Lagrangian of the elasto-plastic finite-element code. An extended r-minimum technique was employed such that each incremental step size is determined not only by the yielding of an element Gaussian point, but also by the change in the boundary conditions along the tool–metal interface. Coulomb’s friction law was adopted to solve the frictional effect of the tool–metal interface. This work aims to investigate the influence of the cone semi-angle of various truncated conical punches on the limitation of formability in the hole-flanging process. Experimental results, using a low-carbon (BA _ CO2) sheet plate with a thickness of 1.18 mm, have been obtained and compared with the corresponding theoretical results. It was found that the limitation of formability during the forming process is not affected by the cone semi-angle of the truncated conical punch but the finish shape and maximum punch load are dependent on the cone semi-angle.     

铝合金阶梯形件粘性介质压力成形的研究

通过压缩试验得到了粘性介质的应力－－应变关系、压力衰减随冲头加载速率及时间变化的规律。采用有限元软件DEFORM分析了在不同压边力下分别用钢凸模和粘性介质成形铝合金阶梯形件的工艺过程。结果显示，采用VPF可以提高板料的成形性。根据模拟结果，采用VPF成功地制备了阶梯形件，这表明有限元法对VPF试验具有很好的指导意义。     

On the size effects in micro/meso semisolid extrusion–forging of A356 aluminum alloy

Micro/meso forming is an economically competitive process for the fabrication of miniature metallic parts. Scaling conventional metal forming down to micro/meso scale leads to the so-called size effects. In this study, the size effects in micro/meso semisolid extrusion–forging (MSEF) of A356 aluminum alloy were numerically and experimentally investigated. An experimental setup for MSEF was developed, and the mechanical performance of A356 aluminum alloy in the semisolid state was tested. Then, the MSEF with various die-hole diameters and various friction coefficients were numerically investigated to examine the size effects in the processes. With certain punch displacements, it was found that the aspect ratio of the extruded pin decreased and the forging load increased during the miniaturization of the die-hole. In addition, the contact condition and the lubrication became increasing critical when the die-hole got smaller. Furthermore, various experiments were performed using A356 aluminum alloy. When the die-hole shrunk in the experiments, the changes of the pin aspect ratio and the forging load followed similar trends with the numerically simulated results. The size effects in the MSEF experiments mainly belong to the first-order size effect. In addition, no significant defect was found in the formed specimens with a die-hole diameter down to 0.55 mm, indicating great formability of the MSEF. The size effects identified in the MSEF process in this study assist in understanding the material flow and the cavity filling in the micro/meso semisolid forming with complicated geometrical shapes.     

Finite element analysis of tube inversion process with radiused dies

The extended r_min technique has been incorporated in the incremental updated Lagrangian formulation (ULF) of an elasto-plastic finite element computer code in order to handle the contact boundary condition when analyzing the axisymmetric tube inversion process with a quarter fillet die radius. A fillet die applies an axial compressional load onto a thin tube so that the inside or outside of the tube inverts totally making the central axis of the original tube the same as a new double-walled tube. This is called an inside-out or outside-in inversion process. This study employs an elasto-plastic finite element method to simulate and analyze inside-out inversion. The objective is to examine how different process factors, such as the geometry and material modulus, influence metal tube inversion. This study also simulates a quarter fillet radius of the die to analyze the tube forming condition and range that can be applied in engineering under these requirements. In addition, the axial compressional load under inside-out inversion stability to be suitable for a personal computer, so it can be effectively analyzed and evaluated on line instantaneously.     

三维板料成形过程的有限元分析

基于有限变形理论建立了三维金属板料成形过程的弹塑性有限元数学模型。数学模型采用物质坐标系中的Total Lagrange描述、J 2型本构方程和等向强化假设,考虑了板料的厚向异性,对于金属板料与模具的摩擦定律。为简化计算采用薄膜单元。为了改善节点接触状态变化时计算的收敛性,提出了“弹性边界层”方法。采用根据此模型编制的程序模拟了机油收集器基本件的成形过程,并与试验结果进行了比较。     

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.     

7075铝合金和QRO90模具钢在热成形工况下的摩擦磨损行为

铝合金在热成形制造过程中存在严重的模具磨损,不但缩短模具使用寿命,还造成工件表面拉毛和成形偏差。为模拟模具钢与7系铝合金在热成形工况下的摩擦过程,搭建单向高温摩擦磨损试验平台,对热成形工况下的摩擦磨损行为展开研究,并通过光学轮廓仪和扫描电镜分析模具钢与铝合金磨损表面形貌。结果发现,热成形过程中黏结磨损和磨粒磨损同时存在,磨损颗粒在粗糙表面上被压实和堆积,对后续的摩擦磨损行为有显著影响。对单向高温摩擦试验的接触副局部进行有限元建模,分析粗糙接触表面上的局部接触条件,探讨其对后续摩擦学行为的作用。分析表明,摩擦过程中存在黏滑现象,局部接触压力受表面形貌影响,显著大于名义载荷,最大等效应力出现在表面之下。这对进一步分析磨损行为、提出合适的表面工程方案提供了基础。     

Determination of the real contact area for numerical simulation

The knowledge of the real area of contact plays an important role in metal forming processes as it influences friction and heat transfer in the tool-workpiece interface. In accurate finite element analysis, friction and heat transfer have to be faced by numerical interface models that consider the real contact area in dependence of the applied normal load. Up-to-date methods for the calculation of the real contact area-load relation are either oversimplified or too complex to be used in interface models. This paper presents a new method for evaluating the real contact area in dependence of the normal load that takes the material properties and real asperity slopes into consideration, and simplification (compared to e.g. the work of Neumaier [Zur Optimierung der Verfahrensauswahl von Kalt-, Halbwarm- und Warmmassivumformverfahren, Fortschritt-Berichte VDI: Reihe 2, Fertigungstechnik, vol. 637. Düsseldorf: VDI Verlag, 2003] is achieved by making use of the statistical character of real surfaces. The main idea of the new concept is to obtain the real contact area-load relation by combining the bearing area curve and a model asperity with correct representation of the mean asperity slope.