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Flexible manufacturing of sheet metal parts based on digitized-die
ARTICLE IN PRESS
Robotics and Computer-Integrated Manufacturing 23 (2007) 107–115 www.elsevier.com/locate/rcim
Flexible manufacturing of sheet metal parts based on digitized-die Ming-Zhe Li, Zhong-Yi Cai, Chun-Guo Liu Roll Forging Research Institute, Jilin University (Nanling Campus), 5988 Renmin Street, Changchun 130025, PR China Received 13 November 2004; received in revised form 29 August 2005; accepted 29 September 2005
Abstract Digitized-die forming (DDF) is a flexible manufacturing technology through which a variety of three-dimensional sheet metal parts can be produced in a DDF system. It eliminates the need to design and produce the conventional die. The central component of DDF system is a pair of matrices of punches, the punches are controlled by computer and the desired shape of die is constructed by changing the heights of punches. Based on the flexibility of DDF, new forming processes are designed that cannot be realized in conventional stamping. In varying deformation path DDF, a sheet part is manufactured along an optimal forming path, and large deformation can be achieved for the material with poor formability. In sectional DDF, a sheet part is formed section by section, and this technique makes it possible to manufacture large-size parts in a small DDF press. A closed-loop forming system was built by combining DDF with rapid 3D-shape measurement system. It is used to compensate for material springback and improve dimensional accuracy of the formed part. And a DDF system with multi-point blankholder control system was developed to control the material flow, thereby to prevent sheet parts from wrinkling and tearing. The DDF integrated system is described, and the detailed forming procedures are explained in the paper. Typical examples are presented showing the applicability of the DDF technology. r 2006 Elsevier Ltd. All rights reserved. Keywords: Sheet metal; Digitized-die; Flexible forming; Multi-point forming; Process control; Forming system
1. Introduction Sheet metal forming is one of the most widely used manufacturing processes to plastically deform materials into desired shapes. This conventional process involves a matched monolithic die set that forms a cavity into which the sheet is displaced. Such dies are manufactured by machining or casting a solid block with a specific surface. They are designed only to manufacture a specific shape, and different shape parts will require different dies. Such dies are costly, bulky, require much set-up time at the forming press prior to commencement of manufacturing and utilize large amounts of storage space when not in a production mode. The idea of a forming die of variable shape has always been attractive as a means of reducing die design costs, since it would permit the design iterations to be rapid and nearly cost free. Refs. [1–7] are representative of previous Corresponding author.
E-mail address: [email protected] (Z.-Y. Cai). 0736-5845/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2005.09.005
research involving flexible discrete die. Iwasaki, Shiota and Taura [1] developed a triple-row-press to form simple three-dimensional (3D) sheet metal parts. Hardt, Boyce and Walczky [2–5] explored the mechanical design and shape control algorithms of discrete die tooling, the developmental technology known as reconfigurable tooling for flexible fabrication (RTFF). The reconfigurable tool they developed replaced multiple dies employed in stretchforming sheet metal aircraft components. Li and coworkers [6–16] have made a series of progress on the method so-called ‘‘multi-point forming (MPF) for sheet metal’’ [6,7]. ‘‘Digitized-die forming (DDF)’’ concept is derived from MPF. A DDF process of sheet metal is illustrated in Fig. 1. The conventional stamping dies are replaced by a pair of matrices of punches with hemispheric ends. By controlling the height of each punch, the matrix of punches is approximated to a continuous working surface of die. With digitized-die, the forming process of sheet metal parts of any arbitrary shape that can be contained in the working area can be accomplished. Based on the flexibility of DDF,
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Fig. 1. Schematic illustration of digitized-die forming (DDF) process of sheet metal.
Technical data of DDF press
Computer control system
Desired part geometry Materials data
CAD/CAE/CAM software system DDF press
Data for forming procedure selection
Final product
Shape feedback system
Data for forming simulation
Fig. 2. Schematic of DDF integrated system.
new forming procedures such as varying deformation path forming, sectional forming and closed-loop forming were developed, and new forming approaches can be used to avoid forming defects, compensate for the shape error due to springback and ensure high-precision of manufactured parts. In the sections below, a review of the relevant research topics are discussed, followed by the recent research results obtained in the Dieless Forming Technology Developing Center at Jilin University.
2.2. CAD/CAE/CAM software The general structure of the CAD/CAE/CAM software is shown as Fig. 3. The software system receives input data of the desired part, then generates the controlling data and sends to control system to perform a DDF process. The detailed explanations of the software are given below. The major functions of CAD software include:
2. DDF-integrated system
2.1. Structure and working process of DDF system A typical DDF-integrated system is composed of three parts—A DDF press, a CAD/CAE/CAM software and a computer control system (as shown in Fig. 2). If a shape feedback system is involved, a closed-loop DDF can be realized and more accurate forming results will be achieved. The digitized-die installed in the DDF press is the central component of the system. It is composed of a pair of matrices of punches, and sheet metal is formed by the enveloping surfaces of punch matrices. The CAD/CAE/ CAM software is for the design of the 3D shape of digitized-die, the numerical simulation of DDF process and the determination of DDF process parameters; whilst the computer control system commands the DDF press to establish the working surface of digitized-die based on the information generated by CAD, then controls the press to form the sheet metal part.
CAD model of desired part representation. The objective shape of the desired part is modeled by NURBS, based on the initial geometry data of the desired part. Sheet metal blank design. Sheet metal blank for a desired part is computed by a three-node membrane finite element based on the assumptions that the strains in the final shape are evenly distributed [9,10]. Forming direction optimization. This module selects the optimum forming direction to form sheet metal blank in order to obtain a part with smallest and evenly distributed deformation. Process planning and design. This part of CAD software includes technological parameters of DDF process determination, auxiliary surface for desired shape design, blankholder force design and suitable elastic cushion (thickness, material) selection, etc. These functions are realized by incorporating CAE with a special expert system and through an iterative way. Digitized die design and working surface calculation. It is necessary to compensate for springback and elastic cushion deformation by changing the objective shape of digitized-die surface. The amount of shape change is provided by FEM simulation. And the working surface
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CAD
CAM
CAD model of desired part representation
Digitized die shape design
Punch height adjusting path scheduling
Sheet metal blank design
Working surface calculation
Constructing process of virtual digitized die display
Decision of process parameters
Virtual DDF process display
Optimization of forming direction
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DDF Process planning and design
DDF process checking
CAE Suitable parameters selection DDF process FE simulation
DDF feasibility analysis
Process parameters
Controlling data for digitized die
Control system interface Fig. 3. Structure of CAD/CAE/CAM software for DDF.
is determined based on the calculation of the contact points between the punch and objective surface. CAE software comprises three parts:
Parameters selection and modification. The major function of this part is to select the parameters involved in FEM simulation and modify them in order to achieve desirable deformation and improve dimensional accuracy. DDF process simulation. This part involves a large deformation finite element analysis software. It was developed based on updated Lagrangian formulation and elastic–plastic material model [8,11,12]. The software conduct the numerical simulation to predict the defects that may occur in the DDF process. DDF feasibility analysis. The function of this part is to analyze the feasibility of DDF process on the basis of simulation results. If forming defects occur, return to CAD software and revise the DDF process.
Fig. 4. Sheet metal part formed by digitized-die (28 20 2 punches).
CAM software covers the following functions: 2.3. Application examples
Punch adjusting path design. Design an optimum punch-adjusting path so that the desired working surface can be constructed rapidly. Virtual digitized-die constructing. Display the constructing process of digitized-die virtually to check the contact points, punch distance of travel, etc. DDF process checking. Display and check the designed DDF process using virtual reality technique.
A large number of sheet metal parts with different shapes and different sizes have been formed through the flexible manufacturing technology of DDF. Figs. 4 and 5 present sheet metal parts manufactured by two DDF systems, the digitized-die in the first system is comprised by 28 20 punches and that in the second 16 12 punches. Figs. 4a and 5a show two pictures of virtual digitized-die and sheet
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part displayed by CAD/CAE/CAM software, Figs. 4b and 5b are the real digitized-dies constructed by control system of DDF press and Figs. 4c and 5c are the final sheet metal parts. 3. Special DDF modes and control Digitized-die can be used like conventional monolithic die to form sheet metal. The process of this forming mode is shown as Fig. 1 and the application examples are given in Figs. 4 and 5. Moreover, based on the flexibility of DDF, new forming modes can be designed that cannot be realized in conventional stamping. 3.1. Varying deformation path forming 3.1.1. Concept of varying path DDF (VP-DDF) Fig. 6 presents a so-called process of ‘‘varying path DDF (VP-DDF)’’. Comparing with Fig. 1, it can be found that in normal DDF mode the shape of digitized-die is not varied during the forming process after it is constructed, and the fixed shape of digitized-die determines an unchanged deformation path from a flat sheet blank to the final 3D part. While in VP-DDF mode, the shape of the digitized-die is varied continuously during the forming process and all punches are kept in contact with the sheet over all the process. With the change of shape of the
Fig. 5. Sheet metal part formed by digitized-die (16 12 2 punches).
digitized-die, the deforming path of the sheet metal changes accordingly. By controlling each punch in real-time, a sheet part can be manufactured along a prescribed forming path. Due to the good contact state between digitized-dies and the deformed sheet metal in VP-DDF, the deforming load applied by dies is distributed throughout the sheet, and the out-of-plane deformation of the sheet is restrained; Therefore, large deformation without forming defects can be obtained under this forming mode, if the forming path is designed properly. 3.1.2. Forming path design A method to design optimum forming path based on the ‘‘ideal forming’’ theory was suggested by the authors [8] and improved in Refs. [9] and [14]. Here, a simpler strategy based on the geometry of the initial blank and the desired part is employed. The initial blank of a 3D part is calculated from following iterative scheme [9,10]: X rþ1 ¼ X r þ DX r ; DX r ¼ ½r2 FðX r Þ1 rT FðX r Þ;
(1)
where X ¼ ðX 1 Y 1 X 2 Y 2 X N Y N ÞT is the nodal coordinates vector of three-node finite elements in the initial blank, r is iteration times and FðXÞ an objective functional set-up based on the assumptions that the strains in the final shape are evenly distributed: ( ) NL NE X 1 X 2 2 FðXÞ ¼ ðLl rl Lm Þ þ P ðDe re Def Þ , (2) 2 l¼1 e¼1 and re ¼ hef =he , rl ¼ Llf =Lmf , Ll and Llf are the length of the lth edge in the and final configuration, P initial P L L respectively, Lm ¼ ð N L Þ=N Lmf ¼ ð N L, l¼1 l l¼1 Llf Þ=N L ; NL is the total number of elemental edges in FE model, N E is the total number of the finite elements; P is penalty parameter. he and De are the thickness and area of the element e in the initial configuration, hef and Def are the thickness and area of the element e in the final configuration. From the geometry of the initial blank and the desired part, intermediate shapes at a series of specific time: t0,t1, y, ti, y, tf are interpolated (as shown in Fig. 7). Thus, the forming path from initial blank to desired part is described finally by a series of intermediate shape: S0, S1, y,Si, y, Sf. For computing the position of each punch at each specific time and to control the movements of punches instantaneously, a VP-DDF process will be performed.
Fig. 6. Schematic illustration of varying path digitized-die forming (VP-DDF).
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3.1.3. Multi-step DDF—an approximate VP-DDF Varying deformation path forming can be performed gradually in a multi-step way, which is approximate to VPDDF. This mode is implemented more easily in practice. Fig. 8 presents an illustration of multi-step DDF. A forming process is completed through many forming steps, and the final deformation of the part is accumulated by a series of small deformations in each step. Because of the small deformation of the sheet, the forming defects such as wrinkling, tearing and dimpling can be avoided completely. Fig. 9 shows the technological process of multi-step DDF. Forming experiments were carried out to check the validity of varying deformation path DDF to increase the formability of the metal sheet. The shape of the desired part is saddle surface, material pure aluminum (L2Y2). In Fig. 10 a comparison of the maximum deformations obtained by eight-tep DDF and that of normal DDF (single-step DDF) is shown. Failure is defined as visible wrinkling or dimpling of the part that is a clear deviation
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from the desired shape. It is, thus, obvious that the formability of sheet metal when deformed along a varying path is enhanced evidently comparing with that deformed by normal DDF. 3.2. Sectional forming By changing the shape of digitized-die, a sheet part can be formed in a section-by-section way, the so-called ‘‘sectional forming’’. With this technique, large size parts of sheet metal can be manufactured in a small DDF press. In Fig. 11, a sheet blank is divided into six sections and formed by six steps. Four major regions are included in sheet metal—formed region, forming region, undeformed region and transition region. Transition regions are the overlapping area between the formed sections in previous steps and the forming section in the current step. It plays a very important role in the sectional DDF process. The shape of digitized-die in transition region is the key factor to affect the geometry of the final product in
tf 8.0 Multi-step DDF Final part
Sf
Normal DDF
7.0
ti
Si+1 Si
ti-1
Curvature (m-1)
ti+1
Si-1
5.0
4.0
3.0
t1 t0
6.0
S1 1.0
S0
Initial blank
Fig. 7. Forming path described by a series of intermediate shape.
1.5
2.0 Thickness (mm)
Loop over each forming step Forming path design
3.0
Fig. 10. Comparison of maximum deformations of two DDF modes.
Fig. 8. Schematic illustration of multi-step DDF.
Objective shape input
2.5
Working surface design for each step
Digitized die shape constructing
Fig. 9. Process of multi-step DDF.
DDF
Final part
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sectional DDF. The following functional is suggested to decide the geometry of the transition region [13]: C¼
(
2 2 X 2 2 2 X 2 2 X X q kx1 q kx2 þ w2 qxi qxj qxi qxj Rt i¼1 j¼1 i¼1 j¼1 ) 2 X 2 X q2 kx1 x2 þw3 dx dy qxi qxj i¼1 j¼1 Z X 2 X 2 þ p1 ðkxi xj kfxi xj Þ2 dG Z Z
w1
Gft i¼1 j¼1
Z þ p2
2 X 2 X
Gtu i¼1 j¼1
ðkxi xj kuxi xj Þ2 dG,
ð3Þ
where F is the surface function of transition region; kx1 , kx2 and kx1 x2 are the curvature and twist curvature of transition surface, respectively; kf and ku curvatures or twist curvatures of the formed and undeformed regions, respectively; Gft and Gtu the boundaries between formed and transition regions as well as transition and undeformed regions, respectively; w1, w2 and w3 are weighting factors, p1 and p2 are penalty parameters and Rt is the area of transition region.
By minimizing the objective functional Eq. (3), the numerical solution of the curvatures of transition region surface can be determined. Then, combining with the conditions on boundary Gft and Gtu , the surface of transition region F can be calculated [13]. Fig. 12 shows the technological process of sectional DDF. By this mode, large size sheet metal parts have been manufactured in a small DDF press. Fig. 13 shows two parts formed in a press with working area of 140 mm 140 mm. The areas of the sampling parts with saddle shape are 3 3 times more than the working area, whilst the length of the part of twist shape is over seven times more than that of the forming area, and its twist degree is over 4001. 3.3. Closed-loop forming A closed-loop forming process is realized by integrating the DDF system with a shape feedback system. The shape feedback system consists of a rapid 3D-shape measurement system and the associated software. With a closed-loop control algorithm which uses the working surface of digitized-die as control parameters and the shape errors of the formed parts as feedback parameters, it is possible to compensate for material springback and other process uncertainties, so that the part with high dimensional accuracy can be achieved [15]. Closed-loop forming is an iterative process. On the basis of the previous forming cycle, the measured shape of a formed part is compared with the objective shape of the desired part to generate the shape errors, and shape errors are processed by associated software to correct the working surface and design a new digitized-die shape. Then, the part is formed again by correcting the working surface to obtain a new shape with smaller error. The forming cycles continue until the part shape coincided with the desired shape. Hardt and his co-workers [3,4] devised a mathematical procedure called the ‘‘deformation transfer function’’ to
Fig. 11. Sketch of sectional DDF.
Fig. 13. Parts formed by sectional DDF.
Loop over each forming section Objective shape input
Sectional forming process design
Transition region design for each section
Digitized die shape constructing
Fig. 12. Process of sectional DDF.
DDF
Final part
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predict correctly the die shape. Two initial die shapes are chosen that are slightly different from each other, a part is made on each die and the part shapes are measured. The deformation transfer function is then calculated from the known shapes, and the die shape required to produce the desired part is computed. A new approach to determine the corrected working surface from the measured shape errors is adopted in closed-loop DDF. For a digitized die comprised of m n punches on each side, the surface of a deformed sheet metal can be expressed as a function of the heights of all punches pi ði ¼ 1; 2; . . . ; m nÞ:
cycles the desired part with allowable shape error can be achieved. Closed-loop DDF mode has been used to the digital forming of titanium prosthesis for the repair of skull defects. To repair the skulls damaged in accidents or by disease, cranial titanium prostheses are used in neurosurgery operations. The CAD model of the region of skull to be repaired was reconstructed from X-ray CT image. Fig. 15 presents a flat blank and final shape of titanium prosthesis.
Sðx; yÞ ¼ f ðp1 ; p2 ; . . . ; pmn Þ.
Table 1 Shape error variation of a spherical shape part in closed-loop DDF process
(4)
If surface Sðx; yÞ is represented by m n discrete points, Eq. (4) is then written by the following equation:
Forming cycle
Maximum z-coordinate error (mm)
Root-mean-square error (mm)
1 2 3 4 5
4.215 2.509 0.924 0.687 0.250
1.316 0.742 0.262 0.201 0.120
(5)
S ¼ FðPÞ, T
where S ¼ fS 1 S 2 S mn g is an m n array of the z-coordinates of discrete sampling points; it represents the shape of the formed part. P ¼ f p1 p2 pmn gT is an m n array of the heights of punches; it represents the working surface of digitized die corresponding to surface S, F ¼ fF 1 F 2 F mn gT and Si ¼ F i ðp1 ; p2 ; . . . ; pmn Þ. A new working surface can be computed by following a correcting procedure based on the shape error of the formed part: Pðkþ1Þ ¼ PðkÞ þ C ðkÞ DS ðkÞ ,
Table 2 Shape error variation of a cylindrical shape part in closed-loop DDF process Forming cycle
Maximum z-coordinate error (mm)
Root-mean-square error (mm)
1 2 3 4 5
2.219 1.721 1.253 0.850 0.174
1.072 0.808 0.589 0.361 0.130
(6)
where k is the number of the correcting cycle, PðkÞ and DS ðkÞ are the shape of the working surface and shape error of the formed part after k-correcting iteration, respectively; Pðkþ1Þ is the working surface for next iteration; C ðkÞ ¼ r1 F ðkÞ is a correcting matrix, and the element in rF can be calculate approximately based on the results of the last two iterations. Fig. 14 shows the technological process of closed-loop DDF. Closed-loop DDF experiments were performed, the objective shapes are a spherical surface (R ¼ 300 mm) and a cylindrical surface (R ¼ 150 mm), the digitized die includes 10 10 punches, the initial blanks are square sheets of 140 mm 140 mm, with thickness 3.0 mm. The material of sheets is aluminum L2Y2. Tables 1 and 2 list the shape errors of the spherical and cylindrical parts during closed-loop DDF. It can be seen from the experiment results that the shape errors are reduced rapidly in closed-loop DDF process. After four to five forming
Fig. 15. Application example of closed-loop DDF.
Correct working surface calculation
Objective shape input
Digitized die shape constructing
DDF
Part shape measurement
Shape error calculation
Fig. 14. Process of closed-loop DDF.
No Shape error < emax?
Yes Final part
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3.4. DDF with multi-point blankholder During the forming of a complex 3D part of thin sheet metal, the in-plane compressive stresses created often lead to failure by wrinkling. In conventional stamping, the wrinkling defect is suppressed by a blankholder. In DDF, wrinkling can be eliminated in the same way. A DDF press with multi-point blankholder was developed to manufacture complex sheet metal parts. A schematic of DDF of sheet metal with blankholder is shown as Fig. 16. The upper and lower multi-point blankholders are comprised of several individual segments driven by hydraulic cylinders and placed around the digitized-die (as shown in Fig. 17). Each segment is individually controllable with its own proportional or servo valve. The multi-point blankholder, as described above, makes it possible to bring in a specific blankholder pressure (BHP) to certain areas of the flange of blank, and change these forces in such a way that the desired friction force and, in turn, the desired material flow is achieved. The optimal
Fig. 16. DDF of sheet metal with blankholder.
Fig. 17. Digitized-die and multi-point blankholder.
Objective shape input
Forming process simulation
BHP can be obtained based on the forming process simulation. Fig. 18 shows the technological process of DDF with blankholder, and Fig. 19 presents two thin sheet parts formed by this forming mode. It can be seen that DDF with an adjustable blankholder is an effective means to form 3D parts without failure of wrinkling and tearing.
4. Concluding remarks DDF is a flexible manufacturing method of sheet metal products. Because reconfigurable discrete dies are used, DDF system eliminates the need to design and produce the forming dies, and permits the design of the forming tools to be rapid and nearly cost-free when making new parts. It will result in a simpler, more agile and lower-cost production environment for the manufacturing of sheet metal products. DDF is most suitable for the forming of various shelllike parts. Varying deformation path DDF improves the forming ability of sheet metal and avoids defects in manufactured parts. Sectional DDF leads to a realization of forming large size parts on a small press. Closed-loop DDF is used to compensate for material springback and improve dimensional accuracy. An adjustable blankholder in DDF controls, and restrains the material flow by changing the blankholder pressure and ensures a successful thin sheet product. This technique will be very useful in the manufacturing of complex sheet metal parts such as automobile panels. Several DDF systems have been developed, and they have been applied to different sheet-forming processes, including the forming of the skin of high-speed train head, the forming of ship hull plate and, most recently, the digital forming of titanium prosthesis for cranioplasty.
Fig. 19. Application examples of DDF with blankholder.
BHP design
Digitized die shape constructing
BHP control
Fig. 18. Process of DDF with blankholder.
DDF
Final part
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Acknowledgements The work reported here was supported by the National Science Foundation (50275063) and Project 985—Automotive Engineering of Jilin University of China. References [1] Iwasaki Y, Shiota H, Taura Y. Development of a triple-row-press. Mitsubishi Heavy Industries, Technical review, 1977. [2] Hardt DE, Olsen BA, Allison BT, Pasch K. Sheet metal forming with discrete die surfaces. Proceedings of ninth NAMRC. 1981. p. 140–4. [3] Hardt DE, Webb RD. Sheet metal die forming using closed loop shape control. Ann CIRP 1982;31(1):165–9. [4] Hardt DE, Boyce MC, Ousterhout KB, et al. A CAD driven flexible forming system for three dimensional sheet metal parts. Michigan USA: Sheet Metal Stamping Symposium; 1993. p. 69–76. [5] Walczyk DF, Hardt DE. Design and analysis of reconfigurable discrete dies for sheet metal forming. J Manuf Syst 1998;17:436–54. [6] Li MZ, Nakamura K, Watanabe S, et al. Study of the basic principles (1st Report: research on multi-point forming for sheet metal). Proceedings of the Japanese spring conference for technology of plasticity. 1992. 519–22. [7] Li MZ, Nakamura K, et al. Harmful phenomena in multi-point forming (3rd report: research on multi- point forming for sheet
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metal). Proceedings of the 43rd Japanese joint conference for technology of plasticity. 1992. 425–8. Cai ZY. Numerical simulation of the forming process and study on the optimum path for multi-point forming of sheet metal. PhD thesis, Jilin University, 2000 [in Chinese]. Cai ZY, Li MZ. Multi-point forming of three-dimensional sheet metal and the control of the forming process. Int J Pressure Vessel Piping 2002;79(4):289–96. Cai ZY Li MZ, Cui XJ. Numerical method for the prediction of net shaped blank in the multi-point forming of sheet metal. Chin J Mech Eng 2002;15(4):314–8. Cai ZY, Li MZ, Fu WZ. Finite element analysis of the process of multi-point forming for sheet metal. Chin J Comput Mech 2002; 19(3):270–5 [in Chinese]. Cai ZY, Li MZ. Finite element simulation of multi-point sheet forming process based on implicit scheme. J Mater Process Technol 2005;161(3):449–55. Cai ZY, Li MZ, Yan QG. The theory and application of multi-point flexible forming for sheet metal. J Appl Sci 2002;20(2):202–6 [in Chinese]. Cai ZY, Li MZ, Feng ZH. Theory and method of optimum path forming for sheet metal. Chin J Aeronaut 2001;14(2):118–22. Liu CG, Li MZ, Cai ZY. Research on multi-point closed-loop forming of 3D sheet metal parts. Chin Mech Eng 2000 [in Chinese]. Sui Z, Li MZ, Cai ZY. General design and key technologies research on the control system for multi-point forming. J Jilin Univ (Eng Technol Ed) 2002 [in Chinese].
Robotics and Computer-Integrated Manufacturing 23 (2007) 107–115 www.elsevier.com/locate/rcim
Flexible manufacturing of sheet metal parts based on digitized-die Ming-Zhe Li, Zhong-Yi Cai, Chun-Guo Liu Roll Forging Research Institute, Jilin University (Nanling Campus), 5988 Renmin Street, Changchun 130025, PR China Received 13 November 2004; received in revised form 29 August 2005; accepted 29 September 2005
Abstract Digitized-die forming (DDF) is a flexible manufacturing technology through which a variety of three-dimensional sheet metal parts can be produced in a DDF system. It eliminates the need to design and produce the conventional die. The central component of DDF system is a pair of matrices of punches, the punches are controlled by computer and the desired shape of die is constructed by changing the heights of punches. Based on the flexibility of DDF, new forming processes are designed that cannot be realized in conventional stamping. In varying deformation path DDF, a sheet part is manufactured along an optimal forming path, and large deformation can be achieved for the material with poor formability. In sectional DDF, a sheet part is formed section by section, and this technique makes it possible to manufacture large-size parts in a small DDF press. A closed-loop forming system was built by combining DDF with rapid 3D-shape measurement system. It is used to compensate for material springback and improve dimensional accuracy of the formed part. And a DDF system with multi-point blankholder control system was developed to control the material flow, thereby to prevent sheet parts from wrinkling and tearing. The DDF integrated system is described, and the detailed forming procedures are explained in the paper. Typical examples are presented showing the applicability of the DDF technology. r 2006 Elsevier Ltd. All rights reserved. Keywords: Sheet metal; Digitized-die; Flexible forming; Multi-point forming; Process control; Forming system
1. Introduction Sheet metal forming is one of the most widely used manufacturing processes to plastically deform materials into desired shapes. This conventional process involves a matched monolithic die set that forms a cavity into which the sheet is displaced. Such dies are manufactured by machining or casting a solid block with a specific surface. They are designed only to manufacture a specific shape, and different shape parts will require different dies. Such dies are costly, bulky, require much set-up time at the forming press prior to commencement of manufacturing and utilize large amounts of storage space when not in a production mode. The idea of a forming die of variable shape has always been attractive as a means of reducing die design costs, since it would permit the design iterations to be rapid and nearly cost free. Refs. [1–7] are representative of previous Corresponding author.
E-mail address: [email protected] (Z.-Y. Cai). 0736-5845/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2005.09.005
research involving flexible discrete die. Iwasaki, Shiota and Taura [1] developed a triple-row-press to form simple three-dimensional (3D) sheet metal parts. Hardt, Boyce and Walczky [2–5] explored the mechanical design and shape control algorithms of discrete die tooling, the developmental technology known as reconfigurable tooling for flexible fabrication (RTFF). The reconfigurable tool they developed replaced multiple dies employed in stretchforming sheet metal aircraft components. Li and coworkers [6–16] have made a series of progress on the method so-called ‘‘multi-point forming (MPF) for sheet metal’’ [6,7]. ‘‘Digitized-die forming (DDF)’’ concept is derived from MPF. A DDF process of sheet metal is illustrated in Fig. 1. The conventional stamping dies are replaced by a pair of matrices of punches with hemispheric ends. By controlling the height of each punch, the matrix of punches is approximated to a continuous working surface of die. With digitized-die, the forming process of sheet metal parts of any arbitrary shape that can be contained in the working area can be accomplished. Based on the flexibility of DDF,
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Fig. 1. Schematic illustration of digitized-die forming (DDF) process of sheet metal.
Technical data of DDF press
Computer control system
Desired part geometry Materials data
CAD/CAE/CAM software system DDF press
Data for forming procedure selection
Final product
Shape feedback system
Data for forming simulation
Fig. 2. Schematic of DDF integrated system.
new forming procedures such as varying deformation path forming, sectional forming and closed-loop forming were developed, and new forming approaches can be used to avoid forming defects, compensate for the shape error due to springback and ensure high-precision of manufactured parts. In the sections below, a review of the relevant research topics are discussed, followed by the recent research results obtained in the Dieless Forming Technology Developing Center at Jilin University.
2.2. CAD/CAE/CAM software The general structure of the CAD/CAE/CAM software is shown as Fig. 3. The software system receives input data of the desired part, then generates the controlling data and sends to control system to perform a DDF process. The detailed explanations of the software are given below. The major functions of CAD software include:
2. DDF-integrated system
2.1. Structure and working process of DDF system A typical DDF-integrated system is composed of three parts—A DDF press, a CAD/CAE/CAM software and a computer control system (as shown in Fig. 2). If a shape feedback system is involved, a closed-loop DDF can be realized and more accurate forming results will be achieved. The digitized-die installed in the DDF press is the central component of the system. It is composed of a pair of matrices of punches, and sheet metal is formed by the enveloping surfaces of punch matrices. The CAD/CAE/ CAM software is for the design of the 3D shape of digitized-die, the numerical simulation of DDF process and the determination of DDF process parameters; whilst the computer control system commands the DDF press to establish the working surface of digitized-die based on the information generated by CAD, then controls the press to form the sheet metal part.
CAD model of desired part representation. The objective shape of the desired part is modeled by NURBS, based on the initial geometry data of the desired part. Sheet metal blank design. Sheet metal blank for a desired part is computed by a three-node membrane finite element based on the assumptions that the strains in the final shape are evenly distributed [9,10]. Forming direction optimization. This module selects the optimum forming direction to form sheet metal blank in order to obtain a part with smallest and evenly distributed deformation. Process planning and design. This part of CAD software includes technological parameters of DDF process determination, auxiliary surface for desired shape design, blankholder force design and suitable elastic cushion (thickness, material) selection, etc. These functions are realized by incorporating CAE with a special expert system and through an iterative way. Digitized die design and working surface calculation. It is necessary to compensate for springback and elastic cushion deformation by changing the objective shape of digitized-die surface. The amount of shape change is provided by FEM simulation. And the working surface
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CAD
CAM
CAD model of desired part representation
Digitized die shape design
Punch height adjusting path scheduling
Sheet metal blank design
Working surface calculation
Constructing process of virtual digitized die display
Decision of process parameters
Virtual DDF process display
Optimization of forming direction
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DDF Process planning and design
DDF process checking
CAE Suitable parameters selection DDF process FE simulation
DDF feasibility analysis
Process parameters
Controlling data for digitized die
Control system interface Fig. 3. Structure of CAD/CAE/CAM software for DDF.
is determined based on the calculation of the contact points between the punch and objective surface. CAE software comprises three parts:
Parameters selection and modification. The major function of this part is to select the parameters involved in FEM simulation and modify them in order to achieve desirable deformation and improve dimensional accuracy. DDF process simulation. This part involves a large deformation finite element analysis software. It was developed based on updated Lagrangian formulation and elastic–plastic material model [8,11,12]. The software conduct the numerical simulation to predict the defects that may occur in the DDF process. DDF feasibility analysis. The function of this part is to analyze the feasibility of DDF process on the basis of simulation results. If forming defects occur, return to CAD software and revise the DDF process.
Fig. 4. Sheet metal part formed by digitized-die (28 20 2 punches).
CAM software covers the following functions: 2.3. Application examples
Punch adjusting path design. Design an optimum punch-adjusting path so that the desired working surface can be constructed rapidly. Virtual digitized-die constructing. Display the constructing process of digitized-die virtually to check the contact points, punch distance of travel, etc. DDF process checking. Display and check the designed DDF process using virtual reality technique.
A large number of sheet metal parts with different shapes and different sizes have been formed through the flexible manufacturing technology of DDF. Figs. 4 and 5 present sheet metal parts manufactured by two DDF systems, the digitized-die in the first system is comprised by 28 20 punches and that in the second 16 12 punches. Figs. 4a and 5a show two pictures of virtual digitized-die and sheet
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part displayed by CAD/CAE/CAM software, Figs. 4b and 5b are the real digitized-dies constructed by control system of DDF press and Figs. 4c and 5c are the final sheet metal parts. 3. Special DDF modes and control Digitized-die can be used like conventional monolithic die to form sheet metal. The process of this forming mode is shown as Fig. 1 and the application examples are given in Figs. 4 and 5. Moreover, based on the flexibility of DDF, new forming modes can be designed that cannot be realized in conventional stamping. 3.1. Varying deformation path forming 3.1.1. Concept of varying path DDF (VP-DDF) Fig. 6 presents a so-called process of ‘‘varying path DDF (VP-DDF)’’. Comparing with Fig. 1, it can be found that in normal DDF mode the shape of digitized-die is not varied during the forming process after it is constructed, and the fixed shape of digitized-die determines an unchanged deformation path from a flat sheet blank to the final 3D part. While in VP-DDF mode, the shape of the digitized-die is varied continuously during the forming process and all punches are kept in contact with the sheet over all the process. With the change of shape of the
Fig. 5. Sheet metal part formed by digitized-die (16 12 2 punches).
digitized-die, the deforming path of the sheet metal changes accordingly. By controlling each punch in real-time, a sheet part can be manufactured along a prescribed forming path. Due to the good contact state between digitized-dies and the deformed sheet metal in VP-DDF, the deforming load applied by dies is distributed throughout the sheet, and the out-of-plane deformation of the sheet is restrained; Therefore, large deformation without forming defects can be obtained under this forming mode, if the forming path is designed properly. 3.1.2. Forming path design A method to design optimum forming path based on the ‘‘ideal forming’’ theory was suggested by the authors [8] and improved in Refs. [9] and [14]. Here, a simpler strategy based on the geometry of the initial blank and the desired part is employed. The initial blank of a 3D part is calculated from following iterative scheme [9,10]: X rþ1 ¼ X r þ DX r ; DX r ¼ ½r2 FðX r Þ1 rT FðX r Þ;
(1)
where X ¼ ðX 1 Y 1 X 2 Y 2 X N Y N ÞT is the nodal coordinates vector of three-node finite elements in the initial blank, r is iteration times and FðXÞ an objective functional set-up based on the assumptions that the strains in the final shape are evenly distributed: ( ) NL NE X 1 X 2 2 FðXÞ ¼ ðLl rl Lm Þ þ P ðDe re Def Þ , (2) 2 l¼1 e¼1 and re ¼ hef =he , rl ¼ Llf =Lmf , Ll and Llf are the length of the lth edge in the and final configuration, P initial P L L respectively, Lm ¼ ð N L Þ=N Lmf ¼ ð N L, l¼1 l l¼1 Llf Þ=N L ; NL is the total number of elemental edges in FE model, N E is the total number of the finite elements; P is penalty parameter. he and De are the thickness and area of the element e in the initial configuration, hef and Def are the thickness and area of the element e in the final configuration. From the geometry of the initial blank and the desired part, intermediate shapes at a series of specific time: t0,t1, y, ti, y, tf are interpolated (as shown in Fig. 7). Thus, the forming path from initial blank to desired part is described finally by a series of intermediate shape: S0, S1, y,Si, y, Sf. For computing the position of each punch at each specific time and to control the movements of punches instantaneously, a VP-DDF process will be performed.
Fig. 6. Schematic illustration of varying path digitized-die forming (VP-DDF).
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3.1.3. Multi-step DDF—an approximate VP-DDF Varying deformation path forming can be performed gradually in a multi-step way, which is approximate to VPDDF. This mode is implemented more easily in practice. Fig. 8 presents an illustration of multi-step DDF. A forming process is completed through many forming steps, and the final deformation of the part is accumulated by a series of small deformations in each step. Because of the small deformation of the sheet, the forming defects such as wrinkling, tearing and dimpling can be avoided completely. Fig. 9 shows the technological process of multi-step DDF. Forming experiments were carried out to check the validity of varying deformation path DDF to increase the formability of the metal sheet. The shape of the desired part is saddle surface, material pure aluminum (L2Y2). In Fig. 10 a comparison of the maximum deformations obtained by eight-tep DDF and that of normal DDF (single-step DDF) is shown. Failure is defined as visible wrinkling or dimpling of the part that is a clear deviation
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from the desired shape. It is, thus, obvious that the formability of sheet metal when deformed along a varying path is enhanced evidently comparing with that deformed by normal DDF. 3.2. Sectional forming By changing the shape of digitized-die, a sheet part can be formed in a section-by-section way, the so-called ‘‘sectional forming’’. With this technique, large size parts of sheet metal can be manufactured in a small DDF press. In Fig. 11, a sheet blank is divided into six sections and formed by six steps. Four major regions are included in sheet metal—formed region, forming region, undeformed region and transition region. Transition regions are the overlapping area between the formed sections in previous steps and the forming section in the current step. It plays a very important role in the sectional DDF process. The shape of digitized-die in transition region is the key factor to affect the geometry of the final product in
tf 8.0 Multi-step DDF Final part
Sf
Normal DDF
7.0
ti
Si+1 Si
ti-1
Curvature (m-1)
ti+1
Si-1
5.0
4.0
3.0
t1 t0
6.0
S1 1.0
S0
Initial blank
Fig. 7. Forming path described by a series of intermediate shape.
1.5
2.0 Thickness (mm)
Loop over each forming step Forming path design
3.0
Fig. 10. Comparison of maximum deformations of two DDF modes.
Fig. 8. Schematic illustration of multi-step DDF.
Objective shape input
2.5
Working surface design for each step
Digitized die shape constructing
Fig. 9. Process of multi-step DDF.
DDF
Final part
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sectional DDF. The following functional is suggested to decide the geometry of the transition region [13]: C¼
(
2 2 X 2 2 2 X 2 2 X X q kx1 q kx2 þ w2 qxi qxj qxi qxj Rt i¼1 j¼1 i¼1 j¼1 ) 2 X 2 X q2 kx1 x2 þw3 dx dy qxi qxj i¼1 j¼1 Z X 2 X 2 þ p1 ðkxi xj kfxi xj Þ2 dG Z Z
w1
Gft i¼1 j¼1
Z þ p2
2 X 2 X
Gtu i¼1 j¼1
ðkxi xj kuxi xj Þ2 dG,
ð3Þ
where F is the surface function of transition region; kx1 , kx2 and kx1 x2 are the curvature and twist curvature of transition surface, respectively; kf and ku curvatures or twist curvatures of the formed and undeformed regions, respectively; Gft and Gtu the boundaries between formed and transition regions as well as transition and undeformed regions, respectively; w1, w2 and w3 are weighting factors, p1 and p2 are penalty parameters and Rt is the area of transition region.
By minimizing the objective functional Eq. (3), the numerical solution of the curvatures of transition region surface can be determined. Then, combining with the conditions on boundary Gft and Gtu , the surface of transition region F can be calculated [13]. Fig. 12 shows the technological process of sectional DDF. By this mode, large size sheet metal parts have been manufactured in a small DDF press. Fig. 13 shows two parts formed in a press with working area of 140 mm 140 mm. The areas of the sampling parts with saddle shape are 3 3 times more than the working area, whilst the length of the part of twist shape is over seven times more than that of the forming area, and its twist degree is over 4001. 3.3. Closed-loop forming A closed-loop forming process is realized by integrating the DDF system with a shape feedback system. The shape feedback system consists of a rapid 3D-shape measurement system and the associated software. With a closed-loop control algorithm which uses the working surface of digitized-die as control parameters and the shape errors of the formed parts as feedback parameters, it is possible to compensate for material springback and other process uncertainties, so that the part with high dimensional accuracy can be achieved [15]. Closed-loop forming is an iterative process. On the basis of the previous forming cycle, the measured shape of a formed part is compared with the objective shape of the desired part to generate the shape errors, and shape errors are processed by associated software to correct the working surface and design a new digitized-die shape. Then, the part is formed again by correcting the working surface to obtain a new shape with smaller error. The forming cycles continue until the part shape coincided with the desired shape. Hardt and his co-workers [3,4] devised a mathematical procedure called the ‘‘deformation transfer function’’ to
Fig. 11. Sketch of sectional DDF.
Fig. 13. Parts formed by sectional DDF.
Loop over each forming section Objective shape input
Sectional forming process design
Transition region design for each section
Digitized die shape constructing
Fig. 12. Process of sectional DDF.
DDF
Final part
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predict correctly the die shape. Two initial die shapes are chosen that are slightly different from each other, a part is made on each die and the part shapes are measured. The deformation transfer function is then calculated from the known shapes, and the die shape required to produce the desired part is computed. A new approach to determine the corrected working surface from the measured shape errors is adopted in closed-loop DDF. For a digitized die comprised of m n punches on each side, the surface of a deformed sheet metal can be expressed as a function of the heights of all punches pi ði ¼ 1; 2; . . . ; m nÞ:
cycles the desired part with allowable shape error can be achieved. Closed-loop DDF mode has been used to the digital forming of titanium prosthesis for the repair of skull defects. To repair the skulls damaged in accidents or by disease, cranial titanium prostheses are used in neurosurgery operations. The CAD model of the region of skull to be repaired was reconstructed from X-ray CT image. Fig. 15 presents a flat blank and final shape of titanium prosthesis.
Sðx; yÞ ¼ f ðp1 ; p2 ; . . . ; pmn Þ.
Table 1 Shape error variation of a spherical shape part in closed-loop DDF process
(4)
If surface Sðx; yÞ is represented by m n discrete points, Eq. (4) is then written by the following equation:
Forming cycle
Maximum z-coordinate error (mm)
Root-mean-square error (mm)
1 2 3 4 5
4.215 2.509 0.924 0.687 0.250
1.316 0.742 0.262 0.201 0.120
(5)
S ¼ FðPÞ, T
where S ¼ fS 1 S 2 S mn g is an m n array of the z-coordinates of discrete sampling points; it represents the shape of the formed part. P ¼ f p1 p2 pmn gT is an m n array of the heights of punches; it represents the working surface of digitized die corresponding to surface S, F ¼ fF 1 F 2 F mn gT and Si ¼ F i ðp1 ; p2 ; . . . ; pmn Þ. A new working surface can be computed by following a correcting procedure based on the shape error of the formed part: Pðkþ1Þ ¼ PðkÞ þ C ðkÞ DS ðkÞ ,
Table 2 Shape error variation of a cylindrical shape part in closed-loop DDF process Forming cycle
Maximum z-coordinate error (mm)
Root-mean-square error (mm)
1 2 3 4 5
2.219 1.721 1.253 0.850 0.174
1.072 0.808 0.589 0.361 0.130
(6)
where k is the number of the correcting cycle, PðkÞ and DS ðkÞ are the shape of the working surface and shape error of the formed part after k-correcting iteration, respectively; Pðkþ1Þ is the working surface for next iteration; C ðkÞ ¼ r1 F ðkÞ is a correcting matrix, and the element in rF can be calculate approximately based on the results of the last two iterations. Fig. 14 shows the technological process of closed-loop DDF. Closed-loop DDF experiments were performed, the objective shapes are a spherical surface (R ¼ 300 mm) and a cylindrical surface (R ¼ 150 mm), the digitized die includes 10 10 punches, the initial blanks are square sheets of 140 mm 140 mm, with thickness 3.0 mm. The material of sheets is aluminum L2Y2. Tables 1 and 2 list the shape errors of the spherical and cylindrical parts during closed-loop DDF. It can be seen from the experiment results that the shape errors are reduced rapidly in closed-loop DDF process. After four to five forming
Fig. 15. Application example of closed-loop DDF.
Correct working surface calculation
Objective shape input
Digitized die shape constructing
DDF
Part shape measurement
Shape error calculation
Fig. 14. Process of closed-loop DDF.
No Shape error < emax?
Yes Final part
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3.4. DDF with multi-point blankholder During the forming of a complex 3D part of thin sheet metal, the in-plane compressive stresses created often lead to failure by wrinkling. In conventional stamping, the wrinkling defect is suppressed by a blankholder. In DDF, wrinkling can be eliminated in the same way. A DDF press with multi-point blankholder was developed to manufacture complex sheet metal parts. A schematic of DDF of sheet metal with blankholder is shown as Fig. 16. The upper and lower multi-point blankholders are comprised of several individual segments driven by hydraulic cylinders and placed around the digitized-die (as shown in Fig. 17). Each segment is individually controllable with its own proportional or servo valve. The multi-point blankholder, as described above, makes it possible to bring in a specific blankholder pressure (BHP) to certain areas of the flange of blank, and change these forces in such a way that the desired friction force and, in turn, the desired material flow is achieved. The optimal
Fig. 16. DDF of sheet metal with blankholder.
Fig. 17. Digitized-die and multi-point blankholder.
Objective shape input
Forming process simulation
BHP can be obtained based on the forming process simulation. Fig. 18 shows the technological process of DDF with blankholder, and Fig. 19 presents two thin sheet parts formed by this forming mode. It can be seen that DDF with an adjustable blankholder is an effective means to form 3D parts without failure of wrinkling and tearing.
4. Concluding remarks DDF is a flexible manufacturing method of sheet metal products. Because reconfigurable discrete dies are used, DDF system eliminates the need to design and produce the forming dies, and permits the design of the forming tools to be rapid and nearly cost-free when making new parts. It will result in a simpler, more agile and lower-cost production environment for the manufacturing of sheet metal products. DDF is most suitable for the forming of various shelllike parts. Varying deformation path DDF improves the forming ability of sheet metal and avoids defects in manufactured parts. Sectional DDF leads to a realization of forming large size parts on a small press. Closed-loop DDF is used to compensate for material springback and improve dimensional accuracy. An adjustable blankholder in DDF controls, and restrains the material flow by changing the blankholder pressure and ensures a successful thin sheet product. This technique will be very useful in the manufacturing of complex sheet metal parts such as automobile panels. Several DDF systems have been developed, and they have been applied to different sheet-forming processes, including the forming of the skin of high-speed train head, the forming of ship hull plate and, most recently, the digital forming of titanium prosthesis for cranioplasty.
Fig. 19. Application examples of DDF with blankholder.
BHP design
Digitized die shape constructing
BHP control
Fig. 18. Process of DDF with blankholder.
DDF
Final part
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Acknowledgements The work reported here was supported by the National Science Foundation (50275063) and Project 985—Automotive Engineering of Jilin University of China. References [1] Iwasaki Y, Shiota H, Taura Y. Development of a triple-row-press. Mitsubishi Heavy Industries, Technical review, 1977. [2] Hardt DE, Olsen BA, Allison BT, Pasch K. Sheet metal forming with discrete die surfaces. Proceedings of ninth NAMRC. 1981. p. 140–4. [3] Hardt DE, Webb RD. Sheet metal die forming using closed loop shape control. Ann CIRP 1982;31(1):165–9. [4] Hardt DE, Boyce MC, Ousterhout KB, et al. A CAD driven flexible forming system for three dimensional sheet metal parts. Michigan USA: Sheet Metal Stamping Symposium; 1993. p. 69–76. [5] Walczyk DF, Hardt DE. Design and analysis of reconfigurable discrete dies for sheet metal forming. J Manuf Syst 1998;17:436–54. [6] Li MZ, Nakamura K, Watanabe S, et al. Study of the basic principles (1st Report: research on multi-point forming for sheet metal). Proceedings of the Japanese spring conference for technology of plasticity. 1992. 519–22. [7] Li MZ, Nakamura K, et al. Harmful phenomena in multi-point forming (3rd report: research on multi- point forming for sheet
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