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A computational design-of-experiments study of hemming processes for automotive aluminium alloys G Lin1 *, K Iyer1, S J Hu1 , W Cai2 , and S P Marin2 1 Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA 2 Manufacturing Systems Research Lab, General Motors R&D Center, Warren, Michigan, USA The manuscript was received on 2 March 2004 and was accepted after revision for publication on 16 June 2005. DOI: 10.1243/095440505X32661

Abstract: Hemming is a three-step sheet-folding process utilized in the production of automotive closures. It has a critical impact on the performance and perceived quality of assembled vehicles. Using a two-dimensional finite element model, this paper presents a design-of-experiments (DOE) study of the relationships between important hemming process parameters and hem quality for aluminium alloy AA 6111-T4PD flat surface–straight edge hemming. The quality measures include roll-in/roll-out of the hem edge as well as the maximum true strain on the exposed bent surface. The finite element (FE) model combines explicit and implicit procedures in simulating the three forming subprocesses (flanging, prehemming, and final hemming) along with the corresponding springback (unloading). The results show that the pre-hemming die angle and the flanging die radius have the greatest influence on hem edge roll-in/roll-out, while pre-strain and the flanging die radius impact the maximum surface strain significantly. The computational DOE results also provide the basis for process parameter selection to avoid hem surface cracking and particular insights for achieving acceptable formability. Keywords: hemming, aluminium alloy, finite element analysis, DOE, roll-in/roll-out, maximum surface strain

1

INTRODUCTION

Hemming is a three-step sheet-folding process utilized in the final stages of production of automotive closures, e.g. doors, deck lids, etc. Being the last step in the production of closure panels, hemming has a critical influence on the final part and assembly quality. Hemming involves the bending of the edge of a sheet on to itself or another sheet, i.e. the nominal bend angle is 1808. The hemming process is applied to fulfil two functions: (a) to join the inner and outer panels that comprise the abovementioned closures and (b) to impart a uniform, desirable appearance to highly visible auto body panel edges. Figure 1 depicts the three hemming stages: flanging, pre-hemming, and final hemming. Flanging is designed to produce a bend angle that is nominally *Corresponding author: Department of Mechanical Engineering, University of Michigan, Ann Arbor, 2250 GG Brown, 2350 Hayward, MI 48109, USA. email: [email protected]

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908. This is followed by pre-hemming, during which a pre-hemmer forces further deformation of the outer panel to a certain degree. The last stage is completed with a final hemmer that is designed to produce a finished bend angle of approximately 1808. Following each forming step, the sheet is unloaded elastically. Unlike regular bending, in which loads are applied at the extremities of the specimen, the hemming operation is performed sequentially with a number of rigid dies and the majority of the sheet material (blank) is constrained from movement along its own plane. Additionally, the length of the folded sheet section is typically very small,
5–15 mm, in comparison with the overall sheet dimensions. Broadly, two types of hems are found in practice, ‘2t’ and ‘3t’, as shown in Fig. 2. A ‘2t’ hem (Figs 2(a) and (b)) is produced when only a single sheet is involved since the thickness of the final hem is approximately twice the thickness of the sheet. A ‘3t’ hem is produced when a second sheet, referred to as the inner sheet, is involved, as shown in Figs 2(c) and (d). When flat hems (Figs 2(a) and (b)) are not possible, as when Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture

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Fig. 1 Hemming stages and related terminologies of process parameters and parts [1] (Reproduced courtesy of ASME, taken from A study of fundamental mechanisms of warp and recoil in hemming, by G. Zhang, X. Wu, and S. J. Hu. Published in Journal of Engineering Materials and Technology, 2001, 123(4), 436–441)

the bending limit for the material is exceeded before a fully flat hem can be formed, rope hems (as shown in Figs 2(c) and (d)) are used. However, a rope hem is less desirable than a flat hem because it has poorer perceived quality, e.g. gap and flushness imperfectness

between adjacent hemmed components. The major production quality metrics relating to the hem are defined in Fig. 3, including roll-in/roll-out (also referred to as creepage/growing) and warp/recoil.

2

Fig. 2 Different hem types [2] (Reproduced courtesy of Society of Manufacturing Engineers)

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BACKGROUND

Owing to complexities related to the process, different dies involved, and non-linear plastic material behaviours, analytical studies of metal hemming have been very limited. A number of studies of hemming with drawing-quality steels have examined process and geometric conditions to shed light into their influence on the quality of hemmed parts. Computer aided design was used by Livatyali et al. B03604 # IMechE 2005

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Fig. 3 Roll-in/roll-out (creepage/growing) and recoil/warp [2] (Reproduced courtesy of Society of Manufacturing Engineers)

[3] to improve hem quality by optimizing flanging and pre-hemming operations. Zhang et al. [2] performed an experimental investigation of curved surface– straight edge hemming and carried out linear regression analysis for the relationships between input variables (sheet metal thickness, surface curvature, etc.) and hemming quality indices (creepage, recoil, radial springback, etc.). Furthermore, Zhang et al. [1] revealed, through implicit finite element analysis, that reverse bending and springback are the fundamental mechanisms causing surface warp and recoil and proposed a pre-hemming target-ending position based on minimization of the final equivalent warp. Most recently, again through implicit simulations and computational design of experiments, Zhang et al. [4] integrated orthogonal Latin hypercube sampling and the response modelling technique in analysing and optimizing steel hemming processes. In fact, adequate (empirical) guidelines for production of high-quality hems with traditional drawing quality steels can be relatively easily obtained because the forming limit in bending exceeds the deformation induced during hemming and cracking of the exposed bend surface is not an issue. Unfortunately, the experience with traditional steels does not translate directly to modern lightweight automotive aluminium alloys, which exhibit cracking on the exposed bend surface before a full 1808-fold can be achieved. Purely empirical attempts to develop process guidelines for producing crack-free aluminium alloy hems have not met with success. Due to the reduced formability of aluminium alloys, manufacturers are currently obliged to use rope hems in closure panels, which requires changes in vehicle design and creates problems in perceived quality. With regard to aluminium alloys, Muderrisoglu et al. [5] investigated the relationships between flange length, flanging punch radius, springback, and bending load for aluminium alloy AA 1050. The study reported cracking of the exposed hem corner during final hemming, but it did not explore the relationships between process or geometric parameters and the hemming limit in detail. Sarkar et al. [6] B03604 # IMechE 2005

investigated the microstructural evolution of two automotive AA 5754 alloys with decreasing bend radius. The chemical composition of the alloy was found to affect its bending limit and determine the correlation between the reduction in area obtained from a standard tensile test and pre-strain. A recent study by Dao and Li [7] described the localized deformation originating from surface roughness features leading to shear bands that eventually grow and result in macrocracking in AA 6111-T4. The maximum bend angle used in their study is 158. Graf and Hosford [8] obtained the forming limits for aluminium alloy AA 6111-T4 under pure tension as a function of orientation and pre-strain. However, this information is not directly applicable to bending or hemming owing to the through-thickness stress and strain gradients that are absent in pure tension. While it is generally believed that careful selection of process parameters can minimize or overcome most forming defects, including roll-in/roll-out, recoil/warp, and exposed hem corner cracking, the necessary mechanics-based relationships between process parameter values and the accumulation of strain in the region of the bend corner are still unknown. This paper describes a computational design-ofexperiments (DOE) study of the relationships between hemming process parameters and the hem quality, roll-in/roll-out, and maximum surface strain on the exposed hem surface, for automotive AA 6111-T4PD. A 16-run fractional factorial DOE is performed through a two-dimensional finite element (FE) model of flat surface–straight edge hemming, with its advantages of time efficiency and resource savings over traditional physical hemming tests. The process parameters considered are sheet pre-strain, flanging length, flanging die radius, flanging clearance, pre-hemmer angle, and pre-hemmer path. The study numerically evaluates the influence of these parameters on hem roll-in/roll-out and the maximum surface strain, which is related to the formability in bending. The FE model developed for the study uses explicit time integration to simulate the forming (including flanging, pre-hemming, and Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture

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final hemming) procedures and an implicit module for the corresponding springback analyses. The numerical accuracy of the forming simulations is established by converging the explicit simulation to the equivalent implicit one utilizing the mass scaling technique. The validity of the FE model is verified through comparisons between computed and experimentally measured final hem dimensions.

3 3.1

ANALYTICAL PROCEDURES The finite element model

The increased application of FE simulations for sheet metal forming processes is attributable to both the exponential advancing in the computer hardware (CPU (central processing unit) speed, etc.) and the maturing of the FE analysis software. In particular, the emergence of the explicit FE procedure has led to the development of effective software packages for this class of problems. The explicit dynamic algorithm has several key advantages over a conventional implicit algorithm for sheet metal forming problems. First, there is no need for a direct, banded, and linear equation solver. Consequently, the computational cost of an explicit solution generally scales linearly, instead of quadratically, with problem size. Second, large deformation, nonlinear problems, and contact constraints are relatively easy to implement in an explicit procedure. However, the implicit FE program still plays an irreplaceable role in the analysis of sheet metal forming problems, particularly for predictions of springback, which is a quasi-static procedure. The FE model developed for this study is designed for use with the Abaqus/Explicit and Abaqus/Standard (implicit) software packages [9, 10]. Abaqus provides the capability to import deformed meshes and their associated material states between its explicit and implicit schemes. This import analysis technique is particularly useful for simulating entire sheet metal forming processes (which require an initial preloading, forming, and subsequent springback); the initial pre-loading can be simulated using the implicit procedure, while the subsequent forming process can be simulated with the explicit method. Finally, the springback analysis can be performed with the implicit scheme. The combined explicit/ implicit FEA method (referred to as the hybrid method from hereon) used in the hemming simulations is described in the flowchart shown in Fig. 4. The FE model, shown in Fig. 5, consists of a blank (also referred to as the outer panel) with 10 uniform layers of elements and 2000 elements in all, and an inner panel with 5 uniform layers of elements and Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture

Fig. 4 Hybrid FE analysis procedure used for the hemming simulation

500 elements. In anticipation of the steeper strain gradients in the region of the bend corner, the mesh is more refined in the corresponding area. All the tools including punch, flanging die, blank holder, pre-hemmer, and final hemmer are assumed to be rigid and modelled as analytical rigid surfaces, because their stiffness is much higher than the formed metal in reality. In addition to the constraints introduced by the fixed, rigid dies, the blank is fixed in the x direction at its far end. Particularly for flat surface–straight edge hemming simulations, linear quadrilateral plane strain (CPE4R) elements are used to mesh the sheets. Shell elements are not preferred since the deformation is highly localized around the bending corner, throughout the in-plane direction. Reduced integration elements are used owing to their compatibility with both the explicit and standard versions of Abaqus. The material properties are provided by the uniaxial tension test. The materials considered include AA 6111-T4PD and AA X611-T4. Standard tensile properties for the aluminium alloys can be measured up to a strain (true strain by default in this paper) of 23 per cent. However, the strains measured on the exposed hem surface, which are also tensile but constrained from necking by its neighbouring material, can be 70 per cent or even higher. In order to describe the stress–strain diagram in the ‘blank’ range, a power law model is used to extrapolate the actual measured data, as shown in Fig. 6 in terms of true strain and true stress. The other physical properties, including density, elastic module, and Poisson’s ratio, are B03604 # IMechE 2005

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Fig. 5 Finite element model

respectively 2700 kg/m3 , 70 GPa, and 0.31. The Coulomb friction coefficients between contact surfaces are approximated as 0.1 (another magnitude 0.18 is also evaluated but it reveals nearly no difference). In simulations, contact between the blank and rigid tools, including the holder, punch, and flanging die, is removed for evaluating springback after the flanging simulation, and the pre-hemmer and final hemmer are also removed for the same purpose after prehemming and final hemming simulations respectively. The inner panel is introduced between the flanging springback and the pre-hemming step. It is pressed on to the blank by a temporary pad force, which is deactivated for the final hemming springback simulation. The pre-hemmer presses the flange until it reaches the nominal position, i.e. being bent to coincide with the pre-hemmer. In

final hemming, the final hemmer moves downwards and stops at the ‘3t’ position. 3.2

Numerical benchmark of the finite element model

In the practial laboratory and production hemming operations, the tool speed is roughly 50 mm/s. If this forming speed is simulated literally with the FE model, each simulation can take several days. Generally, some sort of artificial timescale is required to be introduced into the analysis to achieve an economical solution. The explicit FE procedure provides two methods for reducing the CPU and turnover time per simulation: either (a) by increasing the tool velocity or (b) by increasing the model mass artificially. Both alternatives yield equivalent results for rate-independent materials, although mass

Fig. 6 True stress–strain curves determined for the aluminium alloys considered

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scaling is preferred if rate dependencies are included in the model because the natural timescale is preserved. In either case, the accuracy of the artificially sped-up calculation must be determined first. In the present study, the mass scaling technique has been adopted in order to reduce explicit forming simulation times. With the explicit time integration scheme, by increasing the mass scaling factor (MSF), p ffiffiffiffiffiffiffiffiffiffi the computation can be speeded up by MSF times. However, some accuracy is invariably lost. The simulation is considered to be numerically accurate if the obtained solution agrees with the equivalent quasi-static solution. A rule of thumb when selecting the appropriate MSF is to try several simulations with different MSFs and monitor the ratio of the kinetic energy over internal energy of the deformed material, making sure that it is less than 5–10 per cent during most of the simulation procedure. However, a more direct way to evaluate the numerical validity of the hybrid FE procedure is to analyse the distribution of the surface plastic strain on the exposed hem surface and computed profiles of the blank after deformation. In fact, noticing that the deformation is dominated by plasticity, the volume strain should be zero, i.e.

"1 þ "2 þ "3  "p1 þ "p2 þ "p3 ¼ 0

ð1Þ

where "1 , "2 , "3 are the total principal strains and "p1 , "p2 , "p3 are the principal plastic strains. With the plane strain assumption, the out-of-plane component "2 ¼ "z vanishes. Hence there is only one independent non-zero principal strain component. Furthermore, the most deformed exposed hem corner, which is a free surface, is subject to biaxial tension. Consequently, the surface strain is identical with the principal strain under this particular circumstance and may be correlated with a future failure criteria study for the generation of localized microcracks around the bending edge. The default speed of the tools in the model is 1 m/s as MSF ¼ 1. Table 1 lists the properties used in the numerical benchmark procedure. In particular, the inner panel is positioned with a 4 mm offset from Table 1

Material Blank Inner panel Inner panel offset Flanging length Punch radius Flanging clearance Flanging die radius Pre-hemmer angle Pre-hemmer path

the bent edge of the outer panel (after flanging) in order not to interfere with the bend corner during pre-hemming and final hemming stages, while maintaining the capability to transmit the pad pressure on to the outer panel. Simulations are performed with 4 MSFs, i.e. 1600, 400, 100, and 25. Figures 7 and 8 show the convergence of the explicit solution to the implicit (quasi-static) result with different MSFs. It is found that the MSFs of up to 400 all provide acceptable results for the entire hemming procedure. The maximum mismatch of the springback predicted by the hybrid method against implicit ones are
10–50,
50–250, and
100–300 mm for flanging, pre-hemming, and final hemming respectively. Correlations of the strain outputs on the exposed bent surface from both hybrid and implicit models are provided in Table 2, which shows quantitatively that with the MSF increasing the hybrid solution accuracy decreases for flanging. The afterward steps do not show as clear an MSF influence, probably due to accumulated error. The MSF of 100 is finally preferred for conservative consideration. With the SUNBLADE1000 Unix workstation and Abaqus 6.2.1, the CPU time consumed by the hybrid method with MSF 100 is 3000.4 s, which is only about 10 per cent of that of the pure quasi-static simulation (28 742.4 s). 3.3

Physical validation of the finite element analysis model

Physical validation of the entire simulation is required because of the uncertainty on the adequacy of the extrapolated uniaxial material property to reflect the multiaxial deformation of the real cold-worked material. A comparison between computed and experimentally measured profiles of the bent blank is made. The simulation conditions are nominally identical with those prevalent in the laboratory tests, as also listed in Table 1. The profiles of the bent specimen are obtained using the image processing technique. The laboratory hemming apparatus drives its punch, pre-hemmer, and final hemmer in curved

Parameters for FE model validations

Numerical

Physical

6111-T4PD 100.0 mm  75.0 mm  2.0 mm 82.9 mm  75.0 mm  2.0 mm 4.0 mm 12.0 mm 2.0 mm 2.4 mm 2.5 mm 458 Vertical

X611-T4, 6111-T4PD 100.0 mm  75.0 mm  0.95 mm 82.9 mm  75.0 mm  0.95 mm 4.0 mm 12.0 mm 2.0 mm 2.4 mm 2.0 mm 458 84.38 (inclined)

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Fig. 7

Principal strain distributions on the exposed hem surface comparisons

trajectories owing to its crank-rod design mechanism. Fortunately, since the curvature radii are fairly large compared to the practical tool trace, declined straight lines (deviated from the vertical direction by about 5.78) can be utilized to fit the real curve locally in simulations. Two different types of aluminium alloys are tested. However, only the results for AA 6111-T4PD are shown for the sake of simplicity. Figure 9 shows the acceptable agreement between computed and measured springback profiles, especially in terms of roll-in/roll-out. The slight difference (
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can be mainly attributed to the following reasons and can be considered to be negligible. 1. The parameters and conditions can be slightly inconsistent for experiments and FE analysis, including some approximations/simplifications, e.g. slight uncertainties in the boundary conditions and friction coefficient values, etc. 2. The intrinsic FE approximations and experimental measurement error. 3. The presence of the microcracking in the hem corner in final hemming. Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture

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Fig. 8 Springback comparisons for the numerical benchmark Table 2 Correlations of strain distributions on the exposed bent surface obtained by the hybrid numerical approach with implicit results Hybrid MSF ¼ 25

MSF ¼ 100

MSF ¼ 400

MSF ¼ 1600

Flanging 0.9998 Pre-hemming 0.9972 Final hemming 0.9960

0.9997 0.9984 0.9949

0.9995 0.9947 0.9792

0.9970 0.9340 0.9365

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3.4

DOE study

This section describes a systematic investigation on the influences of the process variables. Since the study involves several input variables simultaneously, a factorial design is selected for this purpose. Previous experimental evidence reveals that warp/recoil is generally fairly small for aluminium hemming, typically less than 50 mm. The interest lies in the roll-in/roll-out and the B03604 # IMechE 2005

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Fig. 9 Spingback profile comparison for physical validation

maximum principal strain on the exposed hem corner. After a rough surface screening, six variables are suspected to be the primary variables influencing the interested outputs. These variables are: prestrain ("0 ), flanging length (L), flanging die radius (Rd ), clearance (C ), pre-hemmer angle (
), and prehemmer path (P). Here, the pre-hemmer path is considered because a differently approaching prehemmer imposes different shear tractions on contact surfaces between the blank and pre-hemmer. Usually low-order DOE is preferred because it is simple to interpret and has achieved successful applications in many studies. In particular, Zhang et al. [2, 4] have revealed that linear models work well for hemming processes. Technically, two-level designs are utilized to investigate the linear effect of the response over the range of the factor levels chosen. Thus 2k full factorial designs require that 2k runs be performed (which implies a 26 run size in the present case), which is usually far more than necessary, especially for a large number of variables. Consequently, fractional factorial designs, which consist of a subset of full factorial designs, are commonly preferred due to economic considerations, with the estimability of some factorial effects being sacrificed owing to B03604 # IMechE 2005

aliasing. An optimal fraction can be chosen according to the criteria of resolution [11] and minimum aberration [12]. In particular, the computerized DOE has its own characteristics; i.e. no replicates are needed and no environment-related lurking variable exists. Eventually a 26-2 fractional factorial design is adopted for this DOE study, with the defining relation as

L ¼ "0 Rd P ¼ Rd C


ð2Þ

The original settings of the input variable are 0 and 4.88 per cent, 9 and 12 mm, 1 and 3 mm, 1.05 and 1.2 mm, 45 and 608, and horizontal and vertical for "0 , L, Rd , C ,
, and P individually. They are coded as 1 (low level) and þ1 (high level). In particular, the horizontal path of the pre-hemmer is assigned the value 1, while the vertical direction is þ1. The design matrix is shown in Table 3 in the first six columns. Since a 26-2 factorial design has 15 degrees of freedom, 15 factorial effects can be estimated. Based on the effect hierarchy principle, all six main effects should be estimated. Furthermore, an assumption can be made that all interaction effects involving pre-strain ("0 ) are negligible because "0 can be treated as a material property, which usually does not interact with the other process parameters. Additionally, the interactions of the factors belonging Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture

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Table 3

Design matrix and outputs considered in the experimental design

Input variables

Response

"0

L

Rd

C




P

Roll-in/roll-out (mm)

Bend corner maximum surface strain

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1.281 1.353 1.050 0.702 0.919 0.763 1.827 1.895 0.805 1.048 1.475 1.062 2.082 2.136 1.253 1.576

0.530 0.582 0.607 0.548 0.573 0.505 0.517 0.562 0.538 0.596 0.595 0.546 0.559 0.512 0.521 0.572

to the same stage tend to be more important than those from different stages. The three-way interaction pairs LCP=Rd
P and L
P=Rd CP have to be selected fairly arbitrarily because the significance of their effects cannot be easily ranked according to the above rules, but the chance for three-way interactions to be significant is very small. As a result, among all the candidates in the aliasing relations generated from equation (2), the factorial effects to be estimated include: (a) main effect: "0 , L, Rd , C ,
, P; (b) interactions: LP, Rd P, CP, LRd ,
P, LC , Rd C , LCP, L
P. The study deals with the AA 6111 material, with both the blank and inner panel being 1 mm thick. An interfacial program is developed to automate the parametric study, and the statistical software JMP IN is utilized to analyse the data.

4

are relatively few factors that influence the maximum surface strain on the exposed hem surface, and that the pre-strain and flanging die radius are the most significant ones. The pre-hemmer path P has nearly no impact on the final hem profile and the maximum surface strain on the exposed hem surface. After dropping the insignificant effects, the fitted models by least square error (LSE) are given in coded manner as

Roll-in ¼ 1:327  0:312
þ 0:230Rd  0:116LC þ 0:103C þ 0:102Rd C þ 0:098"0 "Surf

max

¼ 0:554 þ 0:027"0  0:014Rd

ð3Þ ð4Þ

These models can be employed for prediction purposes, provided that the settings of the input variables do not exceed the investigated ranges too much.

RESULTS AND DISCUSSION

The half-normal plots revealing the relative effect significance are shown in Figs 10 and 11 for roll-in/ roll-out and maximum surface strain responses respectively. None of the 16 runs exhibit the roll-out phenomenon. As shown in Fig. 10, the significant effects on the roll-in response include
, Rd , L by C, Rd by C, L, "0 ; i.e. those points fall off the straight line through the middle group of insignificant points in the half-normal plot. The most important input variables affecting the roll-in/roll-out response are the pre-hemmer angle, flanging die radius, clearance, pre-strain, flanging length by clearance interaction, and flanging die radius by clearance interaction. From Fig. 11, it is declared that there Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture

Fig. 10 Half-normal plot for the roll-in response

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(b) the pre-strain and flange die radius on the maximum surface strain; (c) the pre-hemmer path having almost no impact on the roll-in/roll-out and maximum surface strain.

Fig. 11 Half-normal plot for the maximum surface strain on the exposed blank bottom

It is worth noting that
, L, and C affect the roll-in/ roll-out response but they do not appear in the maximum surface strain output model. This reveals that the roll-in/roll-out can be controlled under the constraint of the maximum surface strain, implying that the potential optimal design opportunities do exist without increasing the risk of crack generation. For instance, a large flanging die radii and/or a small pre-strain are preferred to minimize the maximum surface principal strain, while suitable settings of flanging length, flanging clearance, and prehemmer angle can be utilized to control the roll-in/ roll-out responses.

5

CONCLUSIONS

A hybrid finite element model is built for a flat surface–straight edge hemming simulation, with the mass scaling technique utilized to achieve computational efficiency. The results from the hybrid model with an appropriate mass scaling factor have been benchmarked against implicit outputs to ensure accuracy. The proposed model is also validated physically by comparing the FE analysis outputs to the experimental tests, obtaining acceptable agreements from both ends. Based on the validated model, a 16-run fractional factorial DOE is conducted to study the responses of the hem roll-in/roll-out and the maximum surface strain on the exposed hem surface. Among six input variables, pre-strain, flanging length, flanging die radius, clearance, pre-hemmer angle, and prehemmer path, the following variable effects are identified to be significant: (a) the pre-hemmer angle and flange die radius on the hem roll-in; B03604 # IMechE 2005

The last finding seems to some extent contradictive to the observations by Livatyali et al. [3]. However, the ‘contradiction’ might be explained by the aforementioned unique criteria for determining the stop position of the pre-hemmer. Future work includes identifying failure criteria to predict the crack generation at the localized bending corner, developing guidelines for designing crack-free flat hems (if they exist) of aluminium alloys by optimizations, and further extending current twodimensional work to the much more complicated three-dimensional case, including curved surface and edge hemming. ACKNOWLEGEMENTS The authors of this paper gratefully acknowledge the financial support provided by General Motor Collaborative Research Lab at the University of Michigan, the hemming apparatus provided by Lamb Technicon, as well as the contributions on physical hemming tests by Mr J. Yao and Dr S. J. Swillo. REFERENCES 1 Zhang, G., Wu, X., and Hu, S. J. A study on fundamental mechanisms of warp and recoil in hemming. J. Engng Mater. Technol., 2001, 123(4), 436–441. 2 Zhang, G., Hao, H., Wu, X., Hu, S. J., Harper, K., and Faitel, W. An experimental investigation of curved surface–straight edge hemming. J. Mfg Processes, 2000, 2(4), 241–246. 3 Livatyali, H., Muderrisoglu, A., Ahmetoglu, M. A., Akgerman, N., Kinzel, G. L., and Altan, T. Improvement of hem quality by optimizing flanging and pre-hemming operations using computer aided die design. J. Mater. Processing Technol., 2000, 98, 41–52. 4 Zhang, G., Hu, S. J., and Wu, X. Numerical analysis and optimization of hemming processes. J. Mfg Processes, 2003, 5(1), 87–96. 5 Muderrisoglu, A., Murata, M., Ahmetoglu, M. A., Kinzel, G., and Altan, T. Bending, flanging and hemming of aluminum sheet – an experimental study. J. Mater. Processing Technol., 1996, 59, 10–17. 6 Sarkar, J., Kutty, T. R. G., Wilkinson, D. S., Embury, J. D., and Lloyd, D. J. Characterization of bendability in automotive aluminum alloy sheets. Mater. Sci. Forum, 2000, 331–337, 583–588. 7 Dao, M. and Li, M. A micromechanics study on strainlocalization-induced fracture initiation in bending using crystal plasticity models. Phil. Mag. A, 2001, 81(8), 1997–2020.

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8 Graf, A. and Hosford, W. The influence of strain-path changes on forming limit diagrams of Al 6111 T4. Int. J. Mech. Sci., 1994, 36(10), 897–910. 9 Abaqus/Standard: User’s Manual, v.6.2 (Hibbitt, Karlsson and Sorenson Inc., Providence, Rhode Island) 2001. 10 Abaqus/Explicit: User’s Manual, v.6.2 (Hibbitt, Karlsson and Sorenson Inc., Providence, Rhode Island) 2001. 11 Box, G. E. P. and Hunter, J. S. The 2k  p fractional factorial designs. Technometrics, 1961, 3, 311–351 and 449–458. 12 Fries, A. and Hunter, W. G. Minimum aberration 2k  p designs. Technometrics, 1980, 22, 601–608.

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APPENDIX Notation

C L P Rd

clearance between the flanging die and punch flanging length pre-hemmer path flanging die radius

"0


pre-strain of the sheet metal pre-hemmer angle

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