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An Experimental Investigation of Curved Surface-Straight Edge Hemming
Journal of Manufacturing Processes Vol. 2/No. 4 2000
An Experimental Investigation of Curved Surface-Straight Edge Hemming Guohua Zhang, Hongqi Hao, Xin Wu, and S. Jack Hu, Dept. of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, Michigan, USA Kris Harper and William Faitel, Lamb Technicon Body Assembly Systems, Detroit, Michigan, USA
Abstract
ing, pre-hemming, and final hemming, as illustrated in Figure 1. As the last stage of forming operations, hemming will directly influence product quality. Some of the dimensional inaccuracy introduced during the hemming process, such as creepage/growing (Figure 2), could cause problems in the assembly stage and influ-
In this paper, an experimental investigation of the curved surface-straight edge hemming process is presented. Because hemming is the last stage of automotive panel forming operations, it directly influences the product surface, fitting, and joining qualities. Dimensional accuracy and precision in shape are two major concerns of hemmed parts, and these concerns are usually influenced by a large number of material, geometrical, and process factors. Planned experiments have been carried out according to a fractional factorial design method. Through regression analysis of the experimental results, the hemming quality indices, such as creepage, recoil, and radial springback, as well as hemming loads, can be expressed as a weighted sum of the input variable effects. In addition, the magnitude of each effect can be ranked from the most to the least significant. Using this information, hemming design guidelines can be developed for the optimization of hemming processes.
Outer Panel
Inner Panel
180⬚
90⬚ Flanging
Pre-hemming
Final hemming
Figure 1 Three Stages Considered in the Hemming Process
Keywords: Hemming, Design of Experiment (DOE), Sheet Metal Forming, Creepage, Recoil
Introduction Hemming is a mechanical joining method that is typically used to connect two sheet metal components, such as the inner and outer panels of automobile doors or deck lids. It is also used to create a smooth edge on a sheet metal component by folding the edge of the sheet metal onto itself for appearance and safety considerations. Hemming is widely used in the automobile industry. The appearance of a car depends greatly on the hemmed edges of its external panels, such as doors, hood, and truck lid. Hemming usually consists of pre-hemming and final hemming operations conducted on a preflanged part. However, from the analysis point of view, the deformation of the workpiece is accumulated starting from the flanging operation. Therefore, in this paper, the hemming operation will be considered as three successive processes: flang-
Reference position
Creepage
Growing Creepage: Inward movement of panel edge Growing: Outward movement of panel edge The creepage/growing is measured relative to the reference position, which is defined as the flange line after 90° flanging.
This paper is an original work and has not been previously published except in the Transactions of NAMRI/SME, Vol. XXVIII, 2000.
Figure 2 Creepage and Growing
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Journal of Manufacturing Processes Vol. 2/No. 4 2000
Base plane Warp
Recoil (a) Inappropriate clearance
Recoil: Downward deflection of hemmed surface Warp: Upward deflection of hemmed surface
Level mismatch
Figure 4 Hemming Recoil and Warp Rear door Front door Blank (after springback) Radial springback (⌬R = R1 - R0)
(b) Level-mismatch
Figure 3 Typical Fitting Defects Hemming die
ence fitting quality. Figure 3 shows examples of inappropriate clearance and level-mismatch; these are typical cases of fitting defects that significantly impair the appearance of the vehicle. Creepage/growing introduced in the hemming process is considered the root source of the nonuniform clearance. In the levelmismatch case, dimensional inaccuracy in hemming is one of the major sources. The hemming process is performed under less restraint than most stamping processes, and the outer panel is liable to develop surface defects, which will damage the surface quality. One of the typical surface defects caused by the hemming operation is recoil/warp (Figure 4). Other defects such as wrinkling and splitting may cause failure of hemming. Sheet metal springback is a complex problem, which can lead to other defects, such as recoil/warp. One type of springback that will be discussed in this paper, namely radial springback, is shown in Figure 5. Because hemming is usually the final forming operation, the defects incurred during the process cannot be eliminated in the subsequent operations and may permanently undermine the product quality. Currently, hemming process control is experience-oriented, and die design is based on trial and error. Therefore, understanding the hemming process from the mechanistic point of view, developing predictive modeling capability, and realizing process optimization are important goals in the quest for better design and quality. For analysis purposes, hemming can be classified into four categories according to the geometry: flat surface-straight edge hemming, flat surface-curved
R0
R1
Figure 5 Radial Springback Table 1 Hemming Classification According to Surface and Edge Curvatures
EDGE
Straight
Straight
Concave
RCS
RCE
Concave
SURFACE
Concvex
Convex
edge hemming, curved surface-straight edge hemming, and curved surface-curved edge hemming, as shown in Table 1. For flat surface-straight edge hemming, some researchers1-3 used various finite element (FE) codes to simulate this process under the plane strain condition and compared the predictions with their experimental results. Hao et al.4 conducted a sys-
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Journal of Manufacturing Processes Vol. 2/No. 4 2000
n
Flanging
Surface contour radius (Rs)
A
Sheet A
C
n
B
Sheet
B (a)
(b)
Final hemming
Pre-hemming
Surface contour radius (Rs) B
B
D
D A
Convex
A
Concave
X Y (c)
Figure 7 Definition of Convex and Concave Surfaces
(d)
Figure 6 Experiment Setup and Hemming Process: Flanging, Pre-Hemming, and Final Hemming
Flange die corner radius Rd Pre-hemmer D
tematic experimental study on flat surface-straight edge hemming on AKDQ steel using the orthogonal array design method. These experiments were simulated using a general-purpose finite element code— ABAQUS/Standard.5 The numerical results are quite consistent with the experimental measurements. Muderrisoglu et al.6 conducted an experimental study on flat surface-curved edge hemming using aluminum alloy 1050. They investigated the relationships between the hemming load, springback, bottom deflection, and some input geometry and process factors. Very little information is available in the literature for curved surface-straight edge hemming. This paper presents the results obtained from curved surface-straight edge hemming experiments using the fractional factorial design (FFD).7 Design of experiments (DOE) is employed to obtain the most representative sampling points in the experimental region and provide a systematic approach to analyze the results. The material used in the experiments is AKDQ steel. Its major properties are: Young’s modulus E = 200 GPa, Yield strength Y = 180 MPa, Strength coefficient K = 527 MPa, strain-hardening coefficient n = 0.22, and normal anisotropy coefficient r = 1.6.
Pre-hemmer face angle
Flange die A
Sheet metal thickness (t) L
Flange length
Figure 8 Illustration of Some Design Variables
working surfaces of the hemming dies (A, B, C, and D) are concentric, with the radial difference being equal to the thickness of the sheet metal. According to the curvature of the sheet, the different dies with the corresponding curvature were combined to conduct the flanging, pre-hemming, and final hemming processes. Convex and concave surfaces are defined for consistency according to the outer surface normal of a hemmed part, as shown in Figure 7. Six critical geometric or process variables are selected as the input factors in the experimental design. They are: pre-hemmer face angle (), flange length (L), sheet metal thickness (t), flange die corner radius (Rd) (Figure 8), surface curvature (s: convex or concave surface), and
Experimental Design The experimental setup for the curved surfacestraight edge hemming is shown in Figure 6. The
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Table 2 DOE Design Matrix
Distance from center
L
Rd
t
Levels convex (-1)
127 mm
30°
6.0 mm
0.5 mm
0.76 mm
(+1) concave Run No.
254 mm
60°
12.0 mm 2.0 mm
0.91 mm
⫺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
Edge
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
x
Center
Rs
Factor
s
5
4
3
2
1
Figure 9 Measurement Points Along Bending Line Table 3 Linear Regression Results
Responses Creepage/ Growing (mm)
surface contour radius (Rs) (Figure 7). The response variables are creepage/growing (Figure 2), hemming recoil (Figure 4), radial springback (Figure 5), prehem, and final hem loads. Surface warp is so small under the experimental conditions that it could not be measured with sufficient accuracy. Because there are six factors, a 16-run 26-2 fractional factorial design was employed, which is listed in Table 2, with three replicates for each run.
R2
Regression Model Y = ( −0.650 + 0.36κ s − 0.152 L − 0.128θ
0.9464
−0.0845Rs − 0.0792t ) + (0.42κ s + 0.209θ ⋅ Rd ) ⋅ X L + (0.126κ s + 0.103θ ⋅ Rd ) ⋅ X q
Hemming Y = (0.183 + 0.0523κ s + 0.0242θ ⋅ L + 0.0138Rd recoil −0.0267θ ⋅ κ s ) + (0.0249 + 0.0868κ s − 0.0207 Rs ⋅ κ s (mm)
0.8525
Radial Y = 6.95 − 3.00 L − 2.71t − 2.70 Rs ⋅ L springback −2.68κ s − 2.20θ ⋅ L − 1.97 Rd ⋅ t (⌬R = R1 ⫺ R0) −1.27θ ⋅ R + 1.19 R − 1.16θ ⋅ κ − 0.768θ d d s (mm)
0.9257
Fx = −56.0 + 17.2 Rs + 11.4 L + 8.93Rs ⋅ κ s
0.9169
+0.0159 Rd + 0.0115θ ⋅ L) ⋅ X L + (0.0342 + 0.0539 κ s ) ⋅ X q
Pre-hem load (N/mm)
Results For curved-surface hemming, creepage/growing and recoil are functions of the locations along the bending line. Radial springback can be represented by the curvature change before and after springback, as shown in Figure 5. Because the sheet surface is symmetric about the central line (Figure 9), only half of the part should be considered. Five equally spaced points are chosen along the bending line, from point 1 at the center to point 5 at the edge, as the measurement points for the output responses. To obtain the relationship between the responses (creepage/growing and recoil) and the locations along the bending line, the location (x-coordinate of
Final hem load (N/mm)
+7.89 L ⋅ t − 6.74 κ s − 5.43θ ⋅ L Fy = 72.5 − 25.7θ − 20.1L + 15.5θ ⋅ L
0.8822
+11.3t − 6.36 Rs Fy = 143 − 22.5 Rs + 13.8t + 9.27 L + 7.17θ
0.9453
+6.43Rs ⋅ L − 6.33θ ⋅ L
the five points) is added into the design matrix as the seventh factor. Thus, the original design matrix, Table 2, is expanded five times by including a seventh factor—location, which has five levels. Radial springback is not a function of location, and the radius change can be obtained from the five measurement points. By using regression analysis, the output variables can be expressed as the weighted sum of the select-
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tors. Residual analysis is not presented in this paper, but it was conducted on all the regression models and the results are very supportive.
ed individual effects. The output response Y can be expressed as follows: Y = ΣWi X i
(1)
Discussion
where Xi represents the individual input effects and Wi is the corresponding weight coefficient. Xi includes main effects, two-factor, and three-factor interaction effects. Because a high-degree polynomial model will lack prediction power and be difficult to interpret, the regression models used for creepage/growing and recoil are quadratic models in regard to location; that is, only location linear effect (XL) and quadratic effect (Xq) are included in the regression models. The regression models for the mean values of creepage/growing, recoil, and radial springback are listed in Table 3. Because the maximum values of the pre-hem load and final hem load are very useful for the hemming machine design, the regression models for pre-hem and final hem loads are also included in the table. In the experiment, four load sensors were used to record the load information. An LVDT (linear voltage differential transducer) was used to record the hemmer displacement information. Because the pre-hemmer has a face angle, the two components of pre-hem load Fx and Fy (refer to Figure 6d for the coordinate system) are equally important. For the final hemming, only the vertical component Fy is important. In Table 3, the single symbols, such as s, L, , and so on, represent the main effects of the input factors. XL and Xq represent the location linear effect and quadratic effect, respectively. Two-factor and three-factor interaction effects are denoted by a multiplication of the individual factors. To make the different input factors comparable, all the input effects are normalized and orthogonalized to each other prior to the regression analysis. Thus, the weight coefficient of any effect in the regression model is independent of the other effects. R2 is the correlation coefficient of the regression model. For example, the creepage/growing can be predicted by Eq. (2), whose R2 = 0.9464; that means, 94.64% of the total variation in creepage/growing can be explained by this linear regression model. For all the regression models obtained, the R2 values are very high. This is a proof that the linear regression models can capture most of the characteristics of the relationships between the responses and input fac-
Creepage/Growing From the experimental results, along the bending line from the center to the edge, creepage increases for the convex surfaces and growing increases for the concave surfaces. This is because the surface curvature makes the contact between the flanged part and the hemming dies nonconcurrent. For the convex surface, the pre-hemmer makes contact with the edges first and then with the center. Therefore, there is more creepage at the edge than at the center. The concave surface is just the opposite. From the regression models, the interaction effect (s • XL) between the surface curvature and the location along the bending line has the most significant influence on creepage/growing. This agrees very well with the physical results. Hemming Recoil During the experiments, it was found that the recoil always appears near the bending line and in the gap region between the inner and outer panels. This is caused by the material work hardening around the bending corner and the springback after final hemming. However, surface warp is caused by the horizontal pushing effect and the reverse bending. Therefore, recoil and warp do not necessarily appear together. In these curved surface hemming cases, because of the geometry constraints from the surface curvature, surface warp is extremely slight or nonexistent. Hemming recoil decreases from the center to the edge for the convex surfaces and increases for the concave surfaces. The interaction effect (s • XL) between the surface curvature and the location along the bending line has the most significant influence on hemming recoil. The R2 value of the regression model for recoil is relatively low, which indicates that recoil has a larger variance and is not easy to accurately predict. Radial Springback Radial springback is the curvature change of the entire sheet after unloading. The bending process (from a flat sheet to a curved sheet) contributes
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Journal of Manufacturing Processes Vol. 2/No. 4 2000
and solutions, 14th biennial congress IDDRG, April 21-23, 1986. 2. H. Sunaga and A. Makinouchi, “Elastic-Plastic FE Simulation of Sheet Metal Bending Process for Auto Body Panels,” Advanced Technology of Plasticity (v3, 1990), pp1525-1530. 3. N. Iwata, M. Matsui, N. Nakagawa, and S. Ikura, “Improvements in Finite-Element Simulation for Stamping and Application to the Forming of Laser-Welded Blanks,” Journal of Materials Processing Technology (v50, no. 1-4, 1995), pp335-347. 4. H. Hao, S. Cheng, G. Zhang, X. Wu, and C.F.J. Wu, “Design of Experiment on Flat Surface-Straight Edge Hemming,” Technical Report (Ann Arbor, MI: Dept. of Mechanical Engg. and Applied Mechanics, Univ. of Michigan, 1998). 5. G. Zhang, H. Hao, X. Wu, and S.J. Hu, “Design and Analysis of Experiments on Curved Surface-Straight Edge Hemming,” Technical Report (Ann Arbor, MI: Dept. of Mechanical Engg. and Applied Mechanics, Univ. of Michigan, 1999). 6. A. Muderrisoglu, M. Murata, M. Ahmetoglu, G. Kinzel, and T. Altan, “Bending, Flanging and Hemming of Aluminum Sheet—An Experimental Study,” Journal of Materials Processing Technology (v59, no. 1-2, 1996), pp10-17. 7. M. Hamada and C.F.J. Wu, Factorial Experiments: Planning, Analysis and Parameter Design Optimization (New York: John Wiley and Sons, Inc., 1998). 8. Y. Umehara, “Technologies for the More Precise Press-Forming of Automobile Parts,” Journal of Materials Processing Technology (v22, n3, Sept. 1990), pp239-256.
greatly to the radial springback. From the regression model, several factors have relatively significant effects on the radial springback, such as flange length, sheet metal thickness, surface contour radius, and convex/concave surface. Hemming Loads The pre-hem and final hem loads were considered as output responses in the experimental design. However, they could also be considered as input factors because the variations of the hemming forces will affect the other responses, such as recoil. However, because of the limitation of the experimental equipment, the load levels cannot be programmed. The hemming loads predicted by the regression models are quite close to the values used in industry under similar conditions.
Conclusions In this paper, the experimental results on the curved surface-straight edge hemming process have been presented. The experiments were conducted based on a fractional factorial design method. Through the regression analysis, the output hemming quality indices, such as creepage/growing, recoil, and radial springback, as well as hemming loads, can be expressed as functions of the input geometrical and process factors. The regression models obtained have relatively high R2 values. Curved-surface hemming has not been studied before. The results obtained from this study will benefit the automobile industry for hemming process design and die design. The regression models can provide information about the significance of the selected input factors and predict output responses under certain circumstances. However, more research work using an analytical modeling approach should be done in the future to study the mechanism of the curved hemming process in order for it to be applicable to manufacturing industry in large.
Authors’ Biographies Guohua Zhang is a PhD candidate at the University of Michigan, Ann Arbor. She obtained her BS and MS at Tsinghua University, Beijing, China. Her research interests are in sheet metal forming, solid mechanics, finite element analysis, and manufacturing process optimization. Hongqi Hao, research associate in the Dept. of Mechanical Engineering at Wayne State University (Detroit, MI), received his BS, MS, and PhD in the field of materials science and engineering from Xi’an Jiaotong University in 1982, 1987, and 1994, respectively. His research interests are metal forming, powder metallurgy, and fatigue and fracture. Dr. Xin Wu received his PhD in 1991 and his MS in 1989, both from the University of Michigan, and an MS in 1981 from Beijing University of Science and Technology. He is currently an assistant professor at Wayne State University. His research and teaching interests include thermomechanical processing and manufacturing of materials, metal forming, autobody stamping and subassembly, and mechanical behavior of materials at room and high temperatures. Dr. S. Jack Hu is currently an associate professor in the Dept. of Mechanical Engineering and Applied Mechanics at the University of Michigan. He received his BS from Tianjing University, China, and his MS and PhD from the University of Michigan. His areas of research are assembly and joining, manufacturing systems, and statistical methods. Kris Harper is currently a project engineer working in Research & New Product Development at Lamb Technicon Body and Assembly Systems. He graduated from GMI Engineering & Management Institute (Flint, MI) in 1998, receiving his bachelor of science degree in mechanical engineering, specializing in machine design. Most recently, he has focused on the design of automated equipment to perform sheet metal forming operations such as hemming and flanging, and on research into the parameters affecting the hemming and flanging processes.
Acknowledgment The authors of this paper gratefully acknowledge the financial support provided by the Advanced Technology Program through the Auto Body Consortium and equipment provided by Lamb Technicon.
William Faitel is the manager of Research and Technology at Lamb Technicon Body and Assembly Systems. He graduated from the University of Michigan with a bachelor of science degree in mechanical engineering in 1983. He also received an MBA from Michigan State University in 1993. He has been involved with both autobody welding and assembly and powertrain machining systems applications and developments. Mr. Faitel currently has nine patents, with additional patents pending.
References 1. Y. Hishida and Y. Sato, “Analysis of Hemming Processes by the FEM for Improving Hemming Quality,” Nissan Motor, Sheet metal requirements
246
An Experimental Investigation of Curved Surface-Straight Edge Hemming Guohua Zhang, Hongqi Hao, Xin Wu, and S. Jack Hu, Dept. of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, Michigan, USA Kris Harper and William Faitel, Lamb Technicon Body Assembly Systems, Detroit, Michigan, USA
Abstract
ing, pre-hemming, and final hemming, as illustrated in Figure 1. As the last stage of forming operations, hemming will directly influence product quality. Some of the dimensional inaccuracy introduced during the hemming process, such as creepage/growing (Figure 2), could cause problems in the assembly stage and influ-
In this paper, an experimental investigation of the curved surface-straight edge hemming process is presented. Because hemming is the last stage of automotive panel forming operations, it directly influences the product surface, fitting, and joining qualities. Dimensional accuracy and precision in shape are two major concerns of hemmed parts, and these concerns are usually influenced by a large number of material, geometrical, and process factors. Planned experiments have been carried out according to a fractional factorial design method. Through regression analysis of the experimental results, the hemming quality indices, such as creepage, recoil, and radial springback, as well as hemming loads, can be expressed as a weighted sum of the input variable effects. In addition, the magnitude of each effect can be ranked from the most to the least significant. Using this information, hemming design guidelines can be developed for the optimization of hemming processes.
Outer Panel
Inner Panel
180⬚
90⬚ Flanging
Pre-hemming
Final hemming
Figure 1 Three Stages Considered in the Hemming Process
Keywords: Hemming, Design of Experiment (DOE), Sheet Metal Forming, Creepage, Recoil
Introduction Hemming is a mechanical joining method that is typically used to connect two sheet metal components, such as the inner and outer panels of automobile doors or deck lids. It is also used to create a smooth edge on a sheet metal component by folding the edge of the sheet metal onto itself for appearance and safety considerations. Hemming is widely used in the automobile industry. The appearance of a car depends greatly on the hemmed edges of its external panels, such as doors, hood, and truck lid. Hemming usually consists of pre-hemming and final hemming operations conducted on a preflanged part. However, from the analysis point of view, the deformation of the workpiece is accumulated starting from the flanging operation. Therefore, in this paper, the hemming operation will be considered as three successive processes: flang-
Reference position
Creepage
Growing Creepage: Inward movement of panel edge Growing: Outward movement of panel edge The creepage/growing is measured relative to the reference position, which is defined as the flange line after 90° flanging.
This paper is an original work and has not been previously published except in the Transactions of NAMRI/SME, Vol. XXVIII, 2000.
Figure 2 Creepage and Growing
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Journal of Manufacturing Processes Vol. 2/No. 4 2000
Base plane Warp
Recoil (a) Inappropriate clearance
Recoil: Downward deflection of hemmed surface Warp: Upward deflection of hemmed surface
Level mismatch
Figure 4 Hemming Recoil and Warp Rear door Front door Blank (after springback) Radial springback (⌬R = R1 - R0)
(b) Level-mismatch
Figure 3 Typical Fitting Defects Hemming die
ence fitting quality. Figure 3 shows examples of inappropriate clearance and level-mismatch; these are typical cases of fitting defects that significantly impair the appearance of the vehicle. Creepage/growing introduced in the hemming process is considered the root source of the nonuniform clearance. In the levelmismatch case, dimensional inaccuracy in hemming is one of the major sources. The hemming process is performed under less restraint than most stamping processes, and the outer panel is liable to develop surface defects, which will damage the surface quality. One of the typical surface defects caused by the hemming operation is recoil/warp (Figure 4). Other defects such as wrinkling and splitting may cause failure of hemming. Sheet metal springback is a complex problem, which can lead to other defects, such as recoil/warp. One type of springback that will be discussed in this paper, namely radial springback, is shown in Figure 5. Because hemming is usually the final forming operation, the defects incurred during the process cannot be eliminated in the subsequent operations and may permanently undermine the product quality. Currently, hemming process control is experience-oriented, and die design is based on trial and error. Therefore, understanding the hemming process from the mechanistic point of view, developing predictive modeling capability, and realizing process optimization are important goals in the quest for better design and quality. For analysis purposes, hemming can be classified into four categories according to the geometry: flat surface-straight edge hemming, flat surface-curved
R0
R1
Figure 5 Radial Springback Table 1 Hemming Classification According to Surface and Edge Curvatures
EDGE
Straight
Straight
Concave
RCS
RCE
Concave
SURFACE
Concvex
Convex
edge hemming, curved surface-straight edge hemming, and curved surface-curved edge hemming, as shown in Table 1. For flat surface-straight edge hemming, some researchers1-3 used various finite element (FE) codes to simulate this process under the plane strain condition and compared the predictions with their experimental results. Hao et al.4 conducted a sys-
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Journal of Manufacturing Processes Vol. 2/No. 4 2000
n
Flanging
Surface contour radius (Rs)
A
Sheet A
C
n
B
Sheet
B (a)
(b)
Final hemming
Pre-hemming
Surface contour radius (Rs) B
B
D
D A
Convex
A
Concave
X Y (c)
Figure 7 Definition of Convex and Concave Surfaces
(d)
Figure 6 Experiment Setup and Hemming Process: Flanging, Pre-Hemming, and Final Hemming
Flange die corner radius Rd Pre-hemmer D
tematic experimental study on flat surface-straight edge hemming on AKDQ steel using the orthogonal array design method. These experiments were simulated using a general-purpose finite element code— ABAQUS/Standard.5 The numerical results are quite consistent with the experimental measurements. Muderrisoglu et al.6 conducted an experimental study on flat surface-curved edge hemming using aluminum alloy 1050. They investigated the relationships between the hemming load, springback, bottom deflection, and some input geometry and process factors. Very little information is available in the literature for curved surface-straight edge hemming. This paper presents the results obtained from curved surface-straight edge hemming experiments using the fractional factorial design (FFD).7 Design of experiments (DOE) is employed to obtain the most representative sampling points in the experimental region and provide a systematic approach to analyze the results. The material used in the experiments is AKDQ steel. Its major properties are: Young’s modulus E = 200 GPa, Yield strength Y = 180 MPa, Strength coefficient K = 527 MPa, strain-hardening coefficient n = 0.22, and normal anisotropy coefficient r = 1.6.
Pre-hemmer face angle
Flange die A
Sheet metal thickness (t) L
Flange length
Figure 8 Illustration of Some Design Variables
working surfaces of the hemming dies (A, B, C, and D) are concentric, with the radial difference being equal to the thickness of the sheet metal. According to the curvature of the sheet, the different dies with the corresponding curvature were combined to conduct the flanging, pre-hemming, and final hemming processes. Convex and concave surfaces are defined for consistency according to the outer surface normal of a hemmed part, as shown in Figure 7. Six critical geometric or process variables are selected as the input factors in the experimental design. They are: pre-hemmer face angle (), flange length (L), sheet metal thickness (t), flange die corner radius (Rd) (Figure 8), surface curvature (s: convex or concave surface), and
Experimental Design The experimental setup for the curved surfacestraight edge hemming is shown in Figure 6. The
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Table 2 DOE Design Matrix
Distance from center
L
Rd
t
Levels convex (-1)
127 mm
30°
6.0 mm
0.5 mm
0.76 mm
(+1) concave Run No.
254 mm
60°
12.0 mm 2.0 mm
0.91 mm
⫺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
Edge
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
x
Center
Rs
Factor
s
5
4
3
2
1
Figure 9 Measurement Points Along Bending Line Table 3 Linear Regression Results
Responses Creepage/ Growing (mm)
surface contour radius (Rs) (Figure 7). The response variables are creepage/growing (Figure 2), hemming recoil (Figure 4), radial springback (Figure 5), prehem, and final hem loads. Surface warp is so small under the experimental conditions that it could not be measured with sufficient accuracy. Because there are six factors, a 16-run 26-2 fractional factorial design was employed, which is listed in Table 2, with three replicates for each run.
R2
Regression Model Y = ( −0.650 + 0.36κ s − 0.152 L − 0.128θ
0.9464
−0.0845Rs − 0.0792t ) + (0.42κ s + 0.209θ ⋅ Rd ) ⋅ X L + (0.126κ s + 0.103θ ⋅ Rd ) ⋅ X q
Hemming Y = (0.183 + 0.0523κ s + 0.0242θ ⋅ L + 0.0138Rd recoil −0.0267θ ⋅ κ s ) + (0.0249 + 0.0868κ s − 0.0207 Rs ⋅ κ s (mm)
0.8525
Radial Y = 6.95 − 3.00 L − 2.71t − 2.70 Rs ⋅ L springback −2.68κ s − 2.20θ ⋅ L − 1.97 Rd ⋅ t (⌬R = R1 ⫺ R0) −1.27θ ⋅ R + 1.19 R − 1.16θ ⋅ κ − 0.768θ d d s (mm)
0.9257
Fx = −56.0 + 17.2 Rs + 11.4 L + 8.93Rs ⋅ κ s
0.9169
+0.0159 Rd + 0.0115θ ⋅ L) ⋅ X L + (0.0342 + 0.0539 κ s ) ⋅ X q
Pre-hem load (N/mm)
Results For curved-surface hemming, creepage/growing and recoil are functions of the locations along the bending line. Radial springback can be represented by the curvature change before and after springback, as shown in Figure 5. Because the sheet surface is symmetric about the central line (Figure 9), only half of the part should be considered. Five equally spaced points are chosen along the bending line, from point 1 at the center to point 5 at the edge, as the measurement points for the output responses. To obtain the relationship between the responses (creepage/growing and recoil) and the locations along the bending line, the location (x-coordinate of
Final hem load (N/mm)
+7.89 L ⋅ t − 6.74 κ s − 5.43θ ⋅ L Fy = 72.5 − 25.7θ − 20.1L + 15.5θ ⋅ L
0.8822
+11.3t − 6.36 Rs Fy = 143 − 22.5 Rs + 13.8t + 9.27 L + 7.17θ
0.9453
+6.43Rs ⋅ L − 6.33θ ⋅ L
the five points) is added into the design matrix as the seventh factor. Thus, the original design matrix, Table 2, is expanded five times by including a seventh factor—location, which has five levels. Radial springback is not a function of location, and the radius change can be obtained from the five measurement points. By using regression analysis, the output variables can be expressed as the weighted sum of the select-
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tors. Residual analysis is not presented in this paper, but it was conducted on all the regression models and the results are very supportive.
ed individual effects. The output response Y can be expressed as follows: Y = ΣWi X i
(1)
Discussion
where Xi represents the individual input effects and Wi is the corresponding weight coefficient. Xi includes main effects, two-factor, and three-factor interaction effects. Because a high-degree polynomial model will lack prediction power and be difficult to interpret, the regression models used for creepage/growing and recoil are quadratic models in regard to location; that is, only location linear effect (XL) and quadratic effect (Xq) are included in the regression models. The regression models for the mean values of creepage/growing, recoil, and radial springback are listed in Table 3. Because the maximum values of the pre-hem load and final hem load are very useful for the hemming machine design, the regression models for pre-hem and final hem loads are also included in the table. In the experiment, four load sensors were used to record the load information. An LVDT (linear voltage differential transducer) was used to record the hemmer displacement information. Because the pre-hemmer has a face angle, the two components of pre-hem load Fx and Fy (refer to Figure 6d for the coordinate system) are equally important. For the final hemming, only the vertical component Fy is important. In Table 3, the single symbols, such as s, L, , and so on, represent the main effects of the input factors. XL and Xq represent the location linear effect and quadratic effect, respectively. Two-factor and three-factor interaction effects are denoted by a multiplication of the individual factors. To make the different input factors comparable, all the input effects are normalized and orthogonalized to each other prior to the regression analysis. Thus, the weight coefficient of any effect in the regression model is independent of the other effects. R2 is the correlation coefficient of the regression model. For example, the creepage/growing can be predicted by Eq. (2), whose R2 = 0.9464; that means, 94.64% of the total variation in creepage/growing can be explained by this linear regression model. For all the regression models obtained, the R2 values are very high. This is a proof that the linear regression models can capture most of the characteristics of the relationships between the responses and input fac-
Creepage/Growing From the experimental results, along the bending line from the center to the edge, creepage increases for the convex surfaces and growing increases for the concave surfaces. This is because the surface curvature makes the contact between the flanged part and the hemming dies nonconcurrent. For the convex surface, the pre-hemmer makes contact with the edges first and then with the center. Therefore, there is more creepage at the edge than at the center. The concave surface is just the opposite. From the regression models, the interaction effect (s • XL) between the surface curvature and the location along the bending line has the most significant influence on creepage/growing. This agrees very well with the physical results. Hemming Recoil During the experiments, it was found that the recoil always appears near the bending line and in the gap region between the inner and outer panels. This is caused by the material work hardening around the bending corner and the springback after final hemming. However, surface warp is caused by the horizontal pushing effect and the reverse bending. Therefore, recoil and warp do not necessarily appear together. In these curved surface hemming cases, because of the geometry constraints from the surface curvature, surface warp is extremely slight or nonexistent. Hemming recoil decreases from the center to the edge for the convex surfaces and increases for the concave surfaces. The interaction effect (s • XL) between the surface curvature and the location along the bending line has the most significant influence on hemming recoil. The R2 value of the regression model for recoil is relatively low, which indicates that recoil has a larger variance and is not easy to accurately predict. Radial Springback Radial springback is the curvature change of the entire sheet after unloading. The bending process (from a flat sheet to a curved sheet) contributes
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and solutions, 14th biennial congress IDDRG, April 21-23, 1986. 2. H. Sunaga and A. Makinouchi, “Elastic-Plastic FE Simulation of Sheet Metal Bending Process for Auto Body Panels,” Advanced Technology of Plasticity (v3, 1990), pp1525-1530. 3. N. Iwata, M. Matsui, N. Nakagawa, and S. Ikura, “Improvements in Finite-Element Simulation for Stamping and Application to the Forming of Laser-Welded Blanks,” Journal of Materials Processing Technology (v50, no. 1-4, 1995), pp335-347. 4. H. Hao, S. Cheng, G. Zhang, X. Wu, and C.F.J. Wu, “Design of Experiment on Flat Surface-Straight Edge Hemming,” Technical Report (Ann Arbor, MI: Dept. of Mechanical Engg. and Applied Mechanics, Univ. of Michigan, 1998). 5. G. Zhang, H. Hao, X. Wu, and S.J. Hu, “Design and Analysis of Experiments on Curved Surface-Straight Edge Hemming,” Technical Report (Ann Arbor, MI: Dept. of Mechanical Engg. and Applied Mechanics, Univ. of Michigan, 1999). 6. A. Muderrisoglu, M. Murata, M. Ahmetoglu, G. Kinzel, and T. Altan, “Bending, Flanging and Hemming of Aluminum Sheet—An Experimental Study,” Journal of Materials Processing Technology (v59, no. 1-2, 1996), pp10-17. 7. M. Hamada and C.F.J. Wu, Factorial Experiments: Planning, Analysis and Parameter Design Optimization (New York: John Wiley and Sons, Inc., 1998). 8. Y. Umehara, “Technologies for the More Precise Press-Forming of Automobile Parts,” Journal of Materials Processing Technology (v22, n3, Sept. 1990), pp239-256.
greatly to the radial springback. From the regression model, several factors have relatively significant effects on the radial springback, such as flange length, sheet metal thickness, surface contour radius, and convex/concave surface. Hemming Loads The pre-hem and final hem loads were considered as output responses in the experimental design. However, they could also be considered as input factors because the variations of the hemming forces will affect the other responses, such as recoil. However, because of the limitation of the experimental equipment, the load levels cannot be programmed. The hemming loads predicted by the regression models are quite close to the values used in industry under similar conditions.
Conclusions In this paper, the experimental results on the curved surface-straight edge hemming process have been presented. The experiments were conducted based on a fractional factorial design method. Through the regression analysis, the output hemming quality indices, such as creepage/growing, recoil, and radial springback, as well as hemming loads, can be expressed as functions of the input geometrical and process factors. The regression models obtained have relatively high R2 values. Curved-surface hemming has not been studied before. The results obtained from this study will benefit the automobile industry for hemming process design and die design. The regression models can provide information about the significance of the selected input factors and predict output responses under certain circumstances. However, more research work using an analytical modeling approach should be done in the future to study the mechanism of the curved hemming process in order for it to be applicable to manufacturing industry in large.
Authors’ Biographies Guohua Zhang is a PhD candidate at the University of Michigan, Ann Arbor. She obtained her BS and MS at Tsinghua University, Beijing, China. Her research interests are in sheet metal forming, solid mechanics, finite element analysis, and manufacturing process optimization. Hongqi Hao, research associate in the Dept. of Mechanical Engineering at Wayne State University (Detroit, MI), received his BS, MS, and PhD in the field of materials science and engineering from Xi’an Jiaotong University in 1982, 1987, and 1994, respectively. His research interests are metal forming, powder metallurgy, and fatigue and fracture. Dr. Xin Wu received his PhD in 1991 and his MS in 1989, both from the University of Michigan, and an MS in 1981 from Beijing University of Science and Technology. He is currently an assistant professor at Wayne State University. His research and teaching interests include thermomechanical processing and manufacturing of materials, metal forming, autobody stamping and subassembly, and mechanical behavior of materials at room and high temperatures. Dr. S. Jack Hu is currently an associate professor in the Dept. of Mechanical Engineering and Applied Mechanics at the University of Michigan. He received his BS from Tianjing University, China, and his MS and PhD from the University of Michigan. His areas of research are assembly and joining, manufacturing systems, and statistical methods. Kris Harper is currently a project engineer working in Research & New Product Development at Lamb Technicon Body and Assembly Systems. He graduated from GMI Engineering & Management Institute (Flint, MI) in 1998, receiving his bachelor of science degree in mechanical engineering, specializing in machine design. Most recently, he has focused on the design of automated equipment to perform sheet metal forming operations such as hemming and flanging, and on research into the parameters affecting the hemming and flanging processes.
Acknowledgment The authors of this paper gratefully acknowledge the financial support provided by the Advanced Technology Program through the Auto Body Consortium and equipment provided by Lamb Technicon.
William Faitel is the manager of Research and Technology at Lamb Technicon Body and Assembly Systems. He graduated from the University of Michigan with a bachelor of science degree in mechanical engineering in 1983. He also received an MBA from Michigan State University in 1993. He has been involved with both autobody welding and assembly and powertrain machining systems applications and developments. Mr. Faitel currently has nine patents, with additional patents pending.
References 1. Y. Hishida and Y. Sato, “Analysis of Hemming Processes by the FEM for Improving Hemming Quality,” Nissan Motor, Sheet metal requirements
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