INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD 382 481, 08-10 DECEMBER, 2011 1 Influence of Lubrication and Draw Bead in Hemispherical Cup Forming G. M. Bramhakshatriya *12, S. K. Sharma #1, B. C. Patel $1 # Associate professor, Mechanical Department, semsharma@gmail.com $ Assistant Professor, Mechanical Department, bcpatel_77@yahoo.co.in * Research Scholar, Mechanical Department, girishvarde@gmail.com 1 S. V. M Institute of Technology College Campus, College Campus, Old NH. No. 8, Bharuch Abstract--Sheet metal forming processes widely used to fabricate different types of metal products in many industry like appliance, aerospace, automobile etc. The quality of sheet metal parts are maintained through material flow in die cavity. The material flow can be restrained by using draw beads in sheet metal forming. In this present study the circular draw bead is used its optimize position by using FE based HYPERFORM software. The obtained results are validating by literature results. Furthermore the influences of different lubrication conditions by using different lubricants like castor oil, soybean oil, tapping oil are also observed. In simulation, a hemispherical cup is considered and analyzes thickness and plastic strain distribution. Forming Limit Diagrams were used to determine the safe limit of the sheet metal operation. The results demonstrate excellent agreements between the numerical method and experiment. Index Terms-- Draw bead, Lubricant, Sheet metal forming, Thickness distribution, plastic strain. I I. INTRODUCTION n sheet metal forming processes, the quality of sheet metal part is secured by the material flow into the die cavity. Generally the restraining force required to control the material flow is provided by either the blank holder or drawbeads, for prediction and prevention of flange and sidewall wrinkling, tearing and galling. The blank holder creates restraining force by friction between sheet and the tooling. When a high restraining force is required, higher binder pressure must be applied to increase the frictional resistance force, which may cause excessive wear due to direct contact in the tooling. Hence to reduce blank holder force, a mechanism known as drawbeads provided. The draw bead consists of a small groove on the die surface / binder surface matched by protrusion on the binder surface / die surface as shown in Fig 1. After the binder closure, the sheet metal is drawn over the drawbead and is subjected to a bending and a subsequent unbending around the entry groove shoulder, bead and at the exit groove shoulder. These bending and unbending deformations together with the frictional force account for the draw bead restraining force. And use proper lubrication between contact areas which reduce frictional resistance force. Fig.1. Location of draw bead on press tool II. LITERATURE REVIEW Many efforts have been focused on the study of the drawbead. These include study of steady state experiments conducted by Nine [1],[2] who used simplified geometry to investigate the various parameters affecting the restraining forces in the bead. Wang [3] proposed a mathematical model of the drawbead forces for calculating the force required to draw sheet metal past a drawbead of constant cross section. Levy [4] had improved Wang and Nine s study on draw beads in 1983. A theoretical model based on virtual work principle was proposed by Chen [5] to calculate the restraining force produced by the drawbead located on a stamping die surface. Samuel [6] devised a numerical model to determine the pull force, shear force and bending moment required to form sheet metal subjected to plane strain. A simple and very effective algorithm has been outlined and demonstrated for the optimal drawbead design problem for deep drawing cups without ears by V.Vahdat et.al [7] in 2006. Numerical design optimization of drawbead position and experimental validation of cup drawing process had been determined by N. Mohamed Sheriff, M. Mohamed Ismail [8]. Analysis of Influence of Draw Bead Location and Profile in Hemispherical Cup forming carried out by A. Murali G et al. [9]. The work reported in this paper concentrates on numerical analyses by using different lubricants like static co-efficient µ=0.14 castor oil (µ=0.61), soybean oil (µ=0.05), tapping oil (µ=0.125) with circular drawbead and without
2 INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN TECHNOLOGY, NUiCONE 2011 draw bead on the die surface and their effect on the strain and thickness distribution over the formed cup. Numerical investigations are carried out using HYPERFORM to observe strain and thickness distribution. The obtained results are compared with available literature results for validation. III. NUMERICAL MODELING Drawbead radius Shoulder radius 6.5mm 6.5mm Modeling was done with PRO-E and analysis was carried out using HYPERFORM, a commercially available explicit FEA code. The punch and die were modeled using shell elements and have been assigned with RIGID MATERIAL MODEL [10]with surface mesh option. The diameter of punch was 100mm and diameter of die was 102.2mm with entry radius 6.5mm. The blank of 174mm diameter was assigned with HILLORTHITROPIC TABULATED model [10] and shell element with uniform thickness of 1.02mm. The material considered for this study was cold rolled steel and its properties are given in Table 1. TABLE 1 MECHANICAL PROPERTIES OF MATERIAL Material Cold rolled steel Young s modulus,gpa 210 Mass Density, kg/m3 7800 Poisson s ratio 0.28 Yield stress, MPa 280 A. NUMERICAL SIMULATION: In numerical simulation, contact is necessary between the sliding bodies for the metal forming process. In this Study DOUBLE ACTION DRAW title algorithm was used for the contact between the punch, die, blank holder and blank. The blank was treated as master surface and others were treated as slave surfaces. By using different lubricants between the contacts were taken as static co-efficient µ=0.14, tapping oil (µ=0.125), soybean oil(µ=0.05), castor oil(µ=0.61). An artificial velocity of 5m/sec was given to the punch in z direction downwards with stroke distance of 40mm. The binder force was set as 8.5 tons towards negative z direction. The flow of material on the drawbead during forming process is controlled by stress-strain curve provided in HYPERFORM. Numerical simulations were carried out for the given conditions and results were obtained. The circular drawbeads were modeled on the die surface with the dimensions given in Table 2. The profile of drawbeads given in HYPERFORM is shown in Fig.2. A uniform gap of 0.2mm was maintained between blank, blank holder and die surface using AUTOPOSITION command. Fig. 2. Profiles of Circular drawbead B. NUMERICAL RESULTS: Numerical simulations were conducted in two phases namely, with different lubrication, hemispherical cup forming without drawbead and with circular drawbead at optimized position similar to the experiments, which data taken from literature results. Post processor of HYPERFORM was utilized to obtain the thickness distribution, strain distribution, on the formed blank and the observations are given in Table 3,4. The thickness of drawn cup was noted at locations in the direction starting from the centre of the cup to the edge as shown in Fig 3. The numerical results of thickness variation for all cases are shown in Fig 4 and Fig 6. Fig. 3. Thickness measurement locations on cup surface TABLE 2 DIMENSION OF CIRCULAR DRAW BEAD Height 3.5mm
INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD 382 481, 08-10 DECEMBER, 2011 3 (c) (c) (d) Fig. 4 Thickness distributions (numerical without draw bead) µ=0.14 µ=0.125 (c) µ=0.05 (d) µ=0.61 (d) Fig. 6 Thickness distributions (numerical-circular draw bead) µ=0.14 µ=0.125 (c) µ=0.05 (d) µ=0.61 Fig. 5 Thickness distributions (numerical without draw bead) For µ=0.61 Fig-7 Thickness distributions (numerical-circular draw bead) for µ=0.14
4 INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN TECHNOLOGY, NUiCONE 2011 Table 3 THICKNESS DISTRIBUTION Without Draw bead With Circular Draw bead No exp µ=0.14 µ=0.125 µ=0.05 µ=0.61 exp. µ=0.14 µ=0.125 µ=0.05 µ=0.61 1 0.810 0.923 0.925 0.933 0.989 0.785 0.915 0.925 0.933 0.970 2 0.810 0.900 0.903 0.917 0.966 0.793 0.897 0.900 0.918 0.966 3 0.801 0.890 0.895 0.922 0.930 0.780 0.891 0.899 0.919 0.948 4 0.786 0.898 0.898 0.941 0.891 0.777 0.895 0.901 0.938 0.926 5 0.787 0.915 0.906 0.969 0.802 0.764 0.916 0.913 0.958 0.892 6 0.802 0.935 0.924 0.980 0.562 0.780 0.935 0.941 0.979 0.790 7 0.820 0.949 0.944 0.981 0.292 0.840 0.948 0.956 0.983 0.519 8 0.825 0.949 0.951 0.982 0.147 0.853 0.940 0.955 0.976 0.150 9 0.835 0.933 0.950 0.972 0.046 0.832 0.836 0.957 0.939 0.046 10 0.853 0.871 0.900 0.943 0.658 0.854 0.850 0.955 0.876 0.658 11 0.886 0.922 0.904 0.961 0.721 0.863 0.940 0.912 0.947 0.722 12 0.866 0.955 0.906 0.921 0.857 0.882 0.990 0.852 1.022 0.853 13 0.895 0.989 0.981 1.030 0.860 0.901 1.034 0.992 1.012 0.908 14 0.935 1.035 1.024 1.054 1.011 1.028 1.077 1.029 1.081 0.952 15 1.030 1.076 1.075 1.088 1.020 1.031 1.079 1.082 1.091 1.020 Table 4 PLASTIC STRAIN DISTRIBUTION Without Draw bead With circular Draw bead No. µ=0.14 µ=0.125 µ=0.05 µ=0.61 µ=0.14 µ=0.125 µ=0.05 µ=0.61 1 0.113 0.111 0.101 0.035 0.123 0.111 0.101 0.057 2 0.142 0.138 0.120 0.062 0.145 0.142 0.120 0.062 3 0.157 0.150 0.116 0.109 0.156 0.145 0.120 0.086 4 0.152 0.150 0.103 0.164 0.154 0.146 0.102 0.114 5 0.141 0.145 0.088 0.294 0.136 0.137 0.095 0.163 6 0.131 0.130 0.101 0.740 0.134 0.116 0.104 0.313 7 0.145 0.122 0.136 1.528 0.166 0.120 0.142 0.837 8 0.185 0.143 0.164 2.417 0.207 0.140 0.183 2.391 9 0.238 0.193 0.214 3.889 0.373 0.178 0.277 3.867 10 0.352 0.290 0.289 0.535 0.391 0.221 0.394 0.535 11 0.338 0.322 0.324 0.427 0.332 0.305 0.361 0.426 12 0.351 0.366 0.410 0.213 0.316 0.434 0.326 0.219 13 0.346 0.329 0.350 0.215 0.289 0.324 0.348 0.146 14 0.294 0.307 0.321 0.011 0.236 0.293 0.277 0.087 15 0.243 0.237 0.258 0.000 0.209 0.221 0.244 0.000 IV. RESULTS AND DISCUSSION To obtain the effect of lubricants in sheet metal forming few results are obtained without the presence of drawbeads and thickness was measured at different locations. Circular drawbead was introduced at optimized locations at die blank holder interface and analysis was carried out for different lubricants. A. THICKNESS DISTRIBUTION: The details of the thickness measured at 15 locations for different lubricants are given in Table 3 for experimental[9] and numerical studies. The thickness comparison graph for numerical values and experimental readings are shown in Fig. 6 respectively. Both the curve show thinning is more in the middle region where stretching taking place, gradually thickness increases towards the bottom portion. Due to compressive strain the flange portion has the maximum thickness, which is even thicker than original sheet thickness. From the Table 4 it is observed that there is a deviation between experimental and numerical findings for different lubrication condition which shows good agreement between them. when lubrication condition means co-efficient of friction was change, we can see the effect on the thickness distribution. Introduction of circular drawbeads reduces the
INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD 382 481, 08-10 DECEMBER, 2011 5 thickness in the side and bottom portion of the cup but there is no considerable change in the flange area. Since the circular drawbead controls more material, the flange portion is thicker than other two cases. We can see from table-3 the cup was failure, when we are using castor oil (µ=0.61) and in other three condition cup formation is safer. Fig.9. Strain comparision graph without draw bead with circular draw bead The strain distribution patterns obtained during cup formation with different lubrications condition without and the presence of circular drawbead shows that the strain distribution is constant over cup wall region where as in the neck region the strain value increases and near flange region it comes down. This curve pattern is true for different cases. Forming limit diagram (FLD) is a good representation of the stretchability of the sheet metal being drawn shown in Fig.10 for circular draw bead(µ=0.14) Fig.8 Thickness comparision graph without draw bead with circular draw bead B. STRAIN DISTRIBUTION: The numerical simulation of distribution of plastic strain during cup formation without and with circular drawbeads is shown in Fig. 5 for without draw bead(µ=0.61) and in Fig.7 for circular draw bead(µ=0.14)the plastic strain values are measured from numerical outcomes and presented in Table 4. The same values are plotted in a graph for better comparison in Fig.9. Fig. 10 Forming Limit Diagram for circular draw bead (µ=0.14) V. CONCLUSION Circular drawbead profile and different lubrication conditions have been used to identify the thickness and strain
6 INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN TECHNOLOGY, NUiCONE 2011 distribution pattern in hemispherical cup forming using finite element analysis and experimental analysis [9]. For this purpose PRO-E and HYPERFORM have been used. The parameters such as thickness and strain values were measured using circular grid pattern method and these details were used to validate the numerical findings. Based on the study the following remarks were drawn: 1) Drawbead locations are crucial to their effectiveness and proper selection of lubrication condition also necessary between the punch, die, blank holder and blank surface for reducing the tool wear. 2) On comparison of different lubrication conditions, when the value of co-efficient of friction is increased, thickness reduction is more for both without and with circular drawbead. 3) Simulations show that the friction influence the stress development in the cup formation. 4) Flange area thickening is more in the case of circular drawbead which is not desirable since the flange portion is generally trimmed off as a waste. VI. REFERENCES [1] H.D.Nine, New drawbead concepts for sheetmetal forming, J.Appl. Metal Working, 2(3), 1982,pp 185-192. [2] H.D.Nine, The applicability of Coulomb s friction law to drawbeads in sheetmetal forming, J.Appl.Metal Working, 2(3), 1982, pp 200-210. [3] N.M.Wang,, A mathematical model of drawbead forces in sheet metal forming, J.Appl.Metal Working, 2(3), 1982, pp 193-199. [4] B.S.Levy, Development of predictive model for drawbead restraining forces utilizing work of Nine and Wang, J.Appl.Metal Working, 3(1), 1983, pp 38-44. [5] Chen and Tszeng, An analysis of drawbead restraining force in stamping process, International Journal of Machine Tools and Manufacturing, (38),1998, pp 827-842. [6] M.Samuel, Influence of drawbead geometry on sheet metal forming, journal of Material Processing and Technology, (122), 2002, pp 94-103. [7] Vahid Vahdat, Sridhar Santhanam and Young W. Chun, A Numerical investigation on the use of drawbeads to minimize ear formation in deep drawing, Journal of Material Processing Technology, ( 176), 2006, pp 70-76. [8]Numerical design optimization of drawbead position and experimental validation of cup drawing by N. Mohamed Sheriff, M. Mohamed Ismail, journal of materials processing technology 2 0 6 ( 2 0 0 8 ) 83-91 [9]Analysis of Influence of Draw Bead Location and Profile in He,mispherical Cup by A. Murali G., B. Gopal M. and C. Rajadurai A, IACSIT International Journal of Engineering and Technology, Vol.2, No.4, August 2010 [8] PRO-E, Application Manual. [9] HYPERFORM, User Manual. [10] Donaldson, Tool Design, Tata McGraw Hill Publication, New Delhi, 1976.