In this paper, a novel multi-ring blank holder technique is developed. The blank holding force (BHF) provided by each ring can be independently and effectively applied on all radial regions. The principles and advantages of the multi-ring technique are first explained and analyzed by theoretical derivation, stress analysis, and forming simulation. The results indicate that the distribution of the blank holder force per unit area (FUA) applied by the new blank holder technique is more reasonable than using the conventional single blank holder, and can better suppress the wrinkles. Finally, the effectiveness of the multi-ring blank holder technique is proven by a deep drawing experiment of the 08Al plate. It is verified that due to the reasonable FUA distribution, the use of the blank holder technique can suppress the wrinkles on the flange very well.
Research Article
Research on deep drawing with multi-ring blank holder technique
https://doi.org/10.21203/rs.3.rs-1410243/v1
This work is licensed under a CC BY 4.0 License
You are reading this latest preprint version
Blank holder force
multi-ring
wrinkling
deep drawing
forming
Blank holding force (BHF) is an important variable to suppress defects during deep drawing, such as wrinkling because of insufficient BHF, or cracking caused by excessive BHF [1]. This is because the material flow of sheet metal is controlled by the values and distributions of the BHF [2]. Normally, BHF should be varied with the forming part, metal properties, and forming conditions to control the metal flow in the deep drawing.
In the past few decades, some theories and processes related to BHF control were developed. Many types of research were focused on the applications of the BHF. Hardt [3] proposed a constant BHF system to suppress wrinkling and prevent tearing. Maslennikov [4] developed a unique method that used the rubber ring placed in the container as a pressure medium to produce forming deformation of the sheet metal. Kergen [5] and Cao [6] realized variable BHF control to enhance the drawing limit, for common axisymmetric drawn cup and conical cup, respectively. Also, some new power systems were used in the application of BHF, such as the digressive gas springs system designed by Gunnarsson [7], the electromagnetic attractive force technique, and the electromagnetic repulsive force technique developed by Seo [8] and Lai [9], respectively.
Meanwhile, numerous scholars were concerned about the distribution of BHF on sheet metal. The technique of multipoint blank holder was proposed by Siegert [10] for drawn box, in which BHF applied on corners was different from that applied on the straight flanges to control the material flow. Hassan [11] divided the blank holder into two layers, each of which was also divided into several segments. Every upper segment and base segment can be moved relatively to apply BHF with an appropriate value for increase the metal forming limit. Murata [12] studied the segmented blank holder for rectangular boxes by applying different BHF on the corners and straight areas. Manabe [13] further divided the corners of the blank holder into more independent blocks to control the distribution of BHF more reasonably. Based on the multi-point blank holder method, Li [14] adopted the flexible blank holder method, which greatly improved the forming quality of thin metal plates. Then, Qu [15] combined the drawing pad with the segmented blank holder method to further improve the drawing accuracy and quality.
The above-mentioned multi-point or segmental blank holder method realized the application of different BHF at different flange areas as required. Compared with the single blank bolder, the segmental blank holder effectively controlled the flow speed of the sheet material and significantly improved the holding effect.
In fact, the blank holders mentioned above were divided into several blocks along the circumferential direction to control the circumferential distribution ratio of the BHF, which were used to solve the problem that deformed flange regions cannot be held effectively due to the different circumferential thickness distribution of metal plate. However, for the axisymmetric forming part, the uniform thickness distribution along the circumferential direction is slighter than that along the radial direction. The above segmental blank holder along circumferential direction cannot solve the problem of failing to apply proper BHF on the different radial areas.
In this research, a multi-ring blank holder technique for the axisymmetric drawn cup is investigated. The effectiveness of the new technique has been verified through theoretical analysis, numerical simulation and experimental research.
2.1 Necessity and concept of dividing blank holder into multi-ring
During the forming process, BHF is applied to the flange area of the metal plate to increase the radial tensile stress of the metal plate to increase the forming height and to reduce the circumferential compressive stress as much as possible to suppress wrinkles [16].
Theoretically, due to restricted material flow and reduced outer diameter, when the BHF is absent, the outer thickness of the flange would increase far greater than the inner flange. But in fact, using the conventional single blank holder, most of the BHF is forced in a narrow range of flange edge since the blank holder is a whole block. This will cause wrinkles to appear far away from the flange edge in the critical state of metal instability when BHF applied on the flange edge is sufficient to suppress wrinkling. This distribution of BHF increases the risk of drawing defects. Figure 1 and Fig. 2 show the simulated drawn cup and experimental results that the wrinkles appear somewhere inside because of the lack of effective holding.
For this reason, the multi-ring blank holder technique was designed here, and it was expected that appropriate BHF can be effectively applied on every radial flange position. The schematic diagram of the new blank holder can be understood from Fig. 3, where the blank holder is divided into several segments along the radial direction. Based on this configuration, the unreasonable distribution of BHF caused by the uneven metal thicknesses along the flange radial regions can be overcome. It is possible to enhance the forming quality using the new blank holder technique.
2.2 Theoretical basis for the feasibility of using multi-ring blank holder
Generally, the wrinkle height on the flange can be expressed by the following formula:
(1)where 
, 
, ρ is the particle radial coordinate of the flange, r0 is the opening radius of die, ym is the maximum value of wrinkle height (MWH), Rw is the radius of metal plate, φ is polar angle and φ0 is the angle of one wrinkle.
It can be seen from Eq. (1) that wrinkle height is monotonically increasing from the die opening to the plate edge along the radial direction, and the maximum value ym is at the outer edge of the plate (ρ = Rw). However, as mentioned above, BHF applied using the conventional method will be acted in a very small range of flange edge since the large thickness here. That is, the blank holder force per unit area (FUA) on the periphery region of the flange is much larger than the inner position, which is unreasonable and the forming effect will not good. If FUA on the flange periphery is sufficient to suppress wrinkles, then the MWH may appear some internal points due to lack of sufficient FUA. Under this critical state, the mathematical expression of wrinkle height can be improved as:
(2)where 
, 
, Rc is the radial coordinate of MHW point, and λ is the ratio between wrinkle height on flange edge and ym.
In this case, a simplified wrinkle curve along the radial direction can be seen in Fig. 4, which consists of two lines with slopes k1 and k2. And according to the point where BHF is applied, the total BHF can be divided into two parts: F1 applied on flange edge, and F2 applied on critical point Rc.
According to the radial wrinkle curve shown in Fig. 4, it can be seen that the wrinkle cannot be suppressed using the single blank holder. As shown in Fig. 5, in order to overcome the deficiency, a deep drawing setup using the multi-ring blank holder shown in Fig. 3 was designed.
Based on this structure of the new blank holder, the FUA applied on different regions can be independent and different. If the value of F2 applied on critical point Rc is suitable, the wrinkles at point Rc shown in Fig. 4 can be suppressed. At this time, the radial wrinkle curve can be improved as shown in Fig. 6, in which the curve has the same MHW between point Rc and point Rw.
Correspondingly, the mathematical wrinkling curve using the new blank holder technique is expressed as Eq. (3).
(3)From the above analysis, it can be predicted that since all deformation areas can be effectively suppressed by independent and different FUA, the effect of the new technique will be better.
3.1 Stress analysis of FUA on the metal plate
To evaluate the effectiveness of the multi-ring blank holder technique, the initial distribution of FUA on metal plate was studied. Because the main purpose is to verify the holding effect of dividing BHF into two main parts, F1 and F2, the FE model including two rings was established, as shown in Fig. 7.
The diameters of the metal plate and the value of BHF were 220 mm and 4 kN respectively. The diameter of the delimitation circle between the two rings was set to 160 mm and 180 mm, respectively, to study its influence on the FUA distribution. Based on theoretical analysis, it can be known that the outer region of the flange requires a larger FUA than the inner region to suppress wrinkles. Therefore, the BHF on the outer ring should be greater than the BHF on the inner ring.
Figure 8 shows the FUA distribution values along a defined path on a plate when the diameter of the delimitation circle is 160 mm, and the BHF ratios of the outer ring and the inner ring are 1, 2, 3, and 5, respectively. Figure 9 is the results when the delimitation circle is 180 mm. Figure 10a and Fig. 10b are the normal stress contour plot when the BHF ratio is 5, and the delimitation circle diameter is 160 mm and 180 mm, respectively. It can be seen that the diameter has a great influence on the FUA distribution.
By comparing the two figures, it can be seen that when the delimitation circle moves outward, FUA applied on the flange peripheral regions will increase significantly. The BHF ratio of the outer ring and the inner ring has a great impact on the distribution of FUA on the plate. So, if the ratio of BHF and diameter of the delimitation circle are appropriate, it is feasible to specify the FUA distribution and improve the forming effect. Also, the slope critical point of the curve is determined by the circle diameter, and has nothing to do with the ratio of F1 and F2. Therefore, the position of the delimitation circle has a direct influence on the holding effect, and should be determined by the coordinate value of Rc.
3.2 Forming simulation
To investigate the effectiveness of the multi-ring blank holder technique, the deep drawing of metal plate was simulated using DYNAFORM software. The yield and harden rules were Barlat-Lian and Hollomon, respectively. The Belytschko-Lin-Tsay shell element was used to mesh the metal plate [17]. The rigid deep drawing tools element is composed of a die, a punch and a blank holder. As mentioned earlier, the diameter of the delimitation circle is very important. In order to reduce this risk, the blank holder was composed of three independent rings instead of two. The frictional model was used for all the contact pair surfaces. Figure 11 shows the finite element model, which has been initially positioned.
Figure 12a shows the thickness distribution of the drawn cup using the single blank holder when BHF was 3550 N and the drawing height was 25 mm. Figure 12b shows the result at the same height using the new blank holder when BHF was 1600 N. Compared with the single blank holder, the reduction in the thickness of the drawn cup using the multi-ring blank holder is smaller, this is because the new technique can suppress wrinkles with a smaller BHF. Correspondingly, the maximum tensile stress of the sheet using the new method is 591 MPa, which is also less than the 602 MPa using the single blank holder, as shown in Fig. 14. All the above results indicate that the new method will obtain a better forming effect and a larger forming height.
As shown in Fig. 14, to further verify the superiority of the new blank holder technique, the same 4 kN BHF and 30 mm drawing height were used in the forming simulation. As illustrated in Fig. 14a, when using the single blank holder, the wrinkles on the flange are very serious. In addition, there has almost no wrinkle on the flange using the new blank holder at the same height and using the same BHF, as shown in Fig. 14b.
Comparative analysis results show that since the FUA distribution applied by the multi-ring blank holder technique is more reasonable, a smaller BHF can be used to suppress wrinkles. That is, the effective holding can be achieved by using the multi-ring blank holder with the same or a smaller BHF.
The experimental device used to verify the effectiveness of the designed blank holder technique is shown in Fig. 15. The forming experiments were conducted using the single blank holder and the multi-ring blank holder respectively. The metal plate 08Al with thickness of 1 mm and diameter of 220 mm were selected for the deep drawing. The BHF on every different holding ring is provided by each independent hydraulic cylinder.
Figure 16 shows the 08Al drawn cups when the BHF was 3.2 kN. As shown in Fig. 16a, when the single blank holder is used and drawing height was about 22 mm, the wrinkling on the flange was obvious. As presented in Fig. 16b, the wrinkles are obviously suppressed by the multi-ring blank holder with a ratio of 1:3:2.
It can be seen from the deep drawing experiment, because the FUA distribution is more reasonable, using the multi-ring blank holder technique can effectively improve the deformability of metal plates.
The main function of the blank holder and BHF is to increase the radial tensile stress, reduce the circumferential compressive stress on the flange, and suppress the forming defects. Therefore, the BHF applied on the flange should be sufficient to obtain a sufficiently large FUA away from the edge of the metal plate using the conventional blank holder. However, an oversized BHF will increase the tendency of cracking.
Superiorly, the deformed plate in different radial flange regions can be suppressed well by using the multi-ring blank holder technique. This is because every holding ring can independently and effectively apply BHF on the plate. Therefore, when using the multi-ring blank holder, the wrinkles can be suppressed and the drawing height can be increased since a more reasonable FUA distribution.
Taken together, the conclusions are as follows:
-
A novel multi-ring blank holder technique was developed, in which the blank holder was divided into several rings. Because every holding ring can act on the plate independently and effectively, the BHF applied by each ring can also be independent.
-
The thorough comprehensive studies of the key topics that are covered: theoretical analysis and stress analysis. The effectiveness of the multi-ring blank holder technique has been verified to work as expected by forming simulation and experiment.
-
The simulated and experimented results show that the holding effect can be improved using the multi-ring technique. The forming effective using the new blank holder technique is much better than using the single blank holder since a more reasonable FUA distributed along the radial direction can be applied.
- -Ethical Approval: Not applicable.
- -Consent to Participate: All authors agree to be signed in the manuscript.
- -Consent to Publish: Manuscript is approved by all authors for publication.
- -Authors Contributions: HS Zhang contributed significantly to analysis and manuscript preparation, SJ Qin and LY Meng performed the experiment and contributed to the conception of the study.
- -Funding: The work is supported by the National Natural Science Foundation of China (No. 51675466) and the Natural Science Foundation of Hebei Province of China (No. E2021203043). The work is also supported by the Science and Technology Research and Development Program of Qinhuangdao city (No. 202004A005).
- -Competing Interests: No conflict of interest exits in the submission of this manuscript.
- -Availability of data and materials: The data sets supporting the results of this article are included within the article.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
- El-Sebaie MG, Mellor PB (1972) Plastic instability conditions in the deep drawing of a circular blank of sheet metal. Int J Mech Sci 14:535–542
- Obermeyer EJ, Majlessi SA (1998) A review of recent advances in the application of blank-holder force towards improving the forming limits of sheet metal parts. J Mater Process Technol 75(1/3):222–234
- Hardt DE, Lee CGY (1986) Real-Time control of sheet stability during stamping, Proceedings of the 13th North American Manufacturing Research Conference, Society of Manufacturing Engineers, Dearborn, MI, pp. 315–322
- Maslennikov NA (1957) Russian developed punchless drawing. Metal- work Prod 16:1417–1420
- Kergen R, Jodogne P (1992) Computerized Control of the Blank Holder Pressure on Deep Drawing Process. SAE paper No.920433, Warrendale, PA
- Cao J, Boyce MC (1997) A predictive tool for delaying wrinkling and tearing failures in sheet metal forming. ASME J Eng Mater Technol 119:354–365
- Gunnarsson L, Asnafi N, Schedin E (1998) In-process control of blank holder force in axi-symmetric deep drawing with degressive gas springs. J Mater Process Technol 73(1/3):89–96
- Seo YR (2008) Electromagnetic blank restrainer in sheet metal forming processes. Int J Mech Sci 50(4):743–751
- Lai ZP, Cao QL, Zhang B, Han XT, Zhou ZY, Xiong Q, Zhang X, Chen Q, Li L (2015) Radial Lorentz force augmented deep drawing for large drawing ratio using a novel dual-coil electromagnetic forming system. J Mater Process Technol 222:13–20
- Siegert K, Doege E (1993) CNC hydraulic multipoint blankholder system for sheet metal forming presses. CIRP Ann-manuf Technol 42(1):319–322
- Hassan MA, Suenaga R, Takakura N, Yamaguchi K (2005) A novel process on friction aided deep drawing using tapered blank holder divided into four segments. J Mater Process Technol 159(3):418–425
- Murata A, Matsui M (1994) Effects of control of local blank holding forces on deep drawability of square shell. Proceedings of the 18th biennial congress IDDRG. International Deep Drawing Research Group Working Group, Lisbon, Portugal, 207–216
- Manabe K, Yang M, Teramae T et al (1996) Development of a square-drawing simulator with cellularly divided blank holder control system. Proceedings of the 19th biennial congress IDDRG, International Deep Drawing Research Group Working Group, Eger, Hungary, 101–108
- Li MZ, Cai ZY, Liu CG (2007) Flexible manufacturing of sheet metal parts based on digitized-die. Robot Cim-int Manuf 23(1):107–115
- Qu E, Li M, Li R (2019) Investigation of forming accuracy in multipoint forming with composite elastic pads. Int J Adv Manuf Technol 05:4401–4413
- Qin SJ, Xiong BQ, Lu H, Zhang TT (2012) Critical blank-holder force in axisymmetric deep drawing. T Nonferr Metal Soc 22(S2):239–246
- Morovvati MR, Mollaei-Dariani B, Asadian-Ardakani MH (2010) A theoretical, numerical, and experimental investigation of plastic wrinkling of circular two-layer sheet metal in the deep drawing. J Mater Process Technol 210(13):1738–1747