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Material optimization: A case study using sheet metal-forming analysis
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
journal homepage: www.elsevier.com/locate/jmatprotec
Material optimization: A case study using sheet metal-forming analysis K. Hariharan ∗ , C. Balaji 1 Ashok Leyland Ltd., Chennai 600035, Tamilnadu, India
a r t i c l e
i n f o
a b s t r a c t
Article history:
This paper focuses on material optimization by reduction in raw material size for sheet
Received 10 October 2006
metal components. Panel roof, an automobile component is chosen for analysis. Using a
Received in revised form
commercial explicit solver, the sheet metal-forming process is analysed. To represent the
29 December 2007
actual tool profile in the analysis, computer-aided design (CAD) model of the tool geom-
Accepted 31 January 2008
etry is developed by scanning the die in coordinate measuring machine (CMM). Forming limit diagram (FLD) and percentage reduction in thickness are checked in the finite element analysis (FEA). Experimental verification of the optimized blank is done by circular
Keywords:
grid analysis technique. Difference in major strain varies from 2 to 10% and difference in
Forming limiting diagram
minor strain varies from 0 to 6%. Weight savings of about 1.57% is achieved in the current
Thinning
work.
Sheet metal forming
© 2008 Elsevier B.V. All rights reserved.
Circular grid analysis
1.
Introduction
The advent of simulation tools for sheet metal-forming analysis has enabled precise prediction of forming strains and other process parameters during sheet metal forming. Using finite element analysis (FEA), the sheet metal-forming process and the influence of various process parameters on formability can be studied. In the present work, the raw material size is optimized with the help of FEA analysis. Inputs required to simulate a sheet metal-forming process are computer-aided design (CAD) model of the forming tools (die, punch and binder), mechanical properties of the material used and other process parameters like binder load, lubrication, etc.
∗
2. CAD model development of forming tools The CAD model of the surface of the forming tools is required for simulating the forming process. CAD data of the forming tool surfaces is developed by reverse engineering the tools using coordinate measuring machine (CMM). The earliest coordinate measuring machine which came in early 1960s was a 3D device with a simple DRO displaying the XYZ position of the X Y Z machine. Bosch (1995) claims that the first CMM was developed in 1956 by Harry Ogden of Ferranti (now International Metrology Systems or IMS) from Dalkeith, Scotland. The probe is a link between CMM and work piece measured. The probe senses the location and transfer the information to
Corresponding author at: Ashok Leyland Ltd., Technical Centre, Vellivoyal Chavadi, Chennai 600103, Tamilnadu, India. Tel.: +91 44 25398165; fax: +91 44 25398003. E-mail addresses: [email protected] (K. Hariharan), [email protected] (C. Balaji). 1 Cab Panel Pres Shop, Hosur, Tamilnadu, India. Tel.: +91 4344 260001. 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.01.063
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
Table 1 – Material properties used for analysis Material property Yield strength Strain hardening exponent, n Strength coefficient, K Plastic anisotropy ratio, R¯ Young’s modulus Poisson’s ratio Density
Value 180 MPa 0.22 478 MPa 1.65 21000 MPa 0.3 7.8 × 0−6 kg/mm3
CMM. Campbell (1995) and Farago and Curtis (1994) discussed the functioning of probes in CMM. The probe sends the input to a computer as electrical impulses; the computer interprets and records them as specific points in space. A contact probe collects data by physically touching the work piece. Contact probes are classified as hard probes, touch trigger probes and analog scanning probes. Genest (1997) discussed that one of the limitations in touch probe is the force required to deflect the probe under contact. Park et al. (2006) have proposed compensation of systematic measurement error of touch probes owing to its spherical shape by calculating the exact contact point of the probe by estimating the force tensor acting on the probe. In the current work the CAD models are developed (refer Table 1: material properties used for analysis (Fig. 1)] using Wenzel CMM (model name: RAF 1625; measurement range: Xaxis, 4000 mm; Y-axis, 1600 mm; Z-axis, 2500 mm); Renishaw’s scanning probe (SP600) is used (scanning probing error: 20 m; repeatability: 10 m). The probe used is analog scanning probe and is useful for rapid data collection. The analog scanning probe maintains contact with the work piece continuously and gives analog data rather than point to point contact like other contact probes. Non-contact probes are useful for high-speed inspection as well as to scan soft surfaces. In Dusharme’s (2006) review on 3D inspection technologies, laser and visionbased non-contact probes are found to be common in the industry. The data collected from CMM is converted to CAD model with the assistance of a service provider. The CMM software can compile the coordinate data and give an IGES (standard graphic exchange format) output of the surfaces. While scanning complex surfaces, sensible variation in the curvature is one of the common problems encountered and is usually addressed by inbuilt algorithms in the commercially available software. Demand for deeper scansion of local curvature variation in the surface profile is defined by a threshold value in algorithm. Galetto and Vezzetti (2006)
325
have explained a methodology to describe the threshold value based on measurement system.
3.
Finite element analysis
The objective is to understand the formability of the ‘panel roof component’ (under study) for existing blank size and based on that optimize the blank dimensions for the component. This leads to savings in raw material consumption. Other than blank size and blank holding force all other changes towards the objective of blank size optimization are practically constrained. The component is pressed in a double action mechanical press. In the earlier work of the author, Hariharan et al. (2005), it is found that the binder (blank holder) load cannot be varied appreciably to optimize the blank size in the particular double action press. Hence the current work concentrates on blank size optimization for fixed binder load.
3.1.
Finite element mesh
The forming tools namely die, punch and binder are considered as rigid bodies whereas the blank as deformable. Deformable blank is described by thin-walled four-noded quadrilateral shell elements. Usually forming analysis is performed using Belytschko–Tsay shell elements, which are computationally less expensive. However, Belytschko–Tsay shell elements are less accurate and also prone to zero energy mode deformation called hourglassing modes (to suppress the hourglassing effects due to single-point integration, Hallquist (2006) have discussed in LSTC theory manual that hourglass viscosity stresses are added to the physical stresses at local element level). Hourglassing modes are physically impossible mathematical states which arise due to single-point integration. In the current work, fully integrated shell elements are used for better accuracy and also to avoid hourglassing. Besides, if the forming simulation is extended to spring back analysis, Maker and Zhu (2000) inferred that Belytschko–Tsay shell elements have more convergence trouble than fully integrated shell elements. Through thickness variation due to bending is captured using five integration points. The usage of triangular elements is minimized in meshing. However, some of the triangular shell elements and the degenerated quadrilateral shell elements are automatically sorted to C0 triangular shell elements. (According to Maker and Zhu (2000), C0 triangular shell elements due to Kennedy, Belytschko and
Fig. 1 – CAD model development of forming tools (from left: CMM, data generated from CMM and the CAD models developed from the CMM data).
326
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
Lin are more accurate and are computationally efficient). The thickness change option is used which captures the shell thickness change due to membrane straining. Adaptive meshing is used for deformable blank. Adaptive meshing interrupts the forming simulation at the specified adaptive frequency and evaluates the meshing for refinement. Angle of the neighbouring elements and curvature of the approaching tooling are used as criteria to refine the mesh. LSDYNA uses an h-adaptive fission process based on Belytschko, Wong and Plaskacz (1989).
3.2.
Contact and boundary condition
The deformable blank forms the slave side and the rigid tools form the master side interface in the contact definitions. Penalty function-based contact interfaces is used to enforce contact and sliding boundary condition between the sheet metal and tooling elements. The contact algorithm search the closest master segment/node for each slave node, computes orthogonal distance and if penetration exists, applies force proportional to penetration depth to master and slave nodes. The penalty formulation models a linear spring between the slave node and the master segment and the stiffness of the modelled spring is based on material constants, mass and area of master segment. Default penalty stiffness scale factor, 0.01 is used and no significant penetration is detected in the results. However, based on the results for significant penetrations, the stiffness scale factor should be corrected for each contact interface. The sheet thickness is considered by offsetting the nodes to half the sheet thickness and also the change in sheet thickness is captured while dealing with contact. The Coulomb friction model is imposed between the contact interfaces of the sheet and the tooling surfaces. In the model taken for analysis, a constant friction coefficient of 0.125 is used. Since the press is a double action pres, die is completely constrained; punch and binder are allowed for z-direction translation only. Tool velocities higher than the actual values are employed to reduce the computational expense due to extremely small time step (4 e−7). In the present work, velocity of punch is 5 m/s against the actual 0.5 m/s. According to Worswick (2000), numerical results showed only minor difference between simulation with accelerated and actual tool velocities. Taking advantage of the symmetry of the component only half of the model is simulated. The nodes in one edge of the half-blank are constrained in z-direction translation for symmetry consideration.
3.3.
Material model
Tools (die, punch and binder) are described using ‘rigid’ material model. Sheet metal blank is defined by ‘Transversely Anisotropic Elastic Plastic’ model of LSDYNA. This is the most commonly used material model for sheet metal-forming applications using LSDYNA. This particular material model uses Hill’s (1948) yield theory as denoted by the following equation: 2
2
2
2 Hill-48 = F(22 − 33 ) + G(33 − 11 ) + H(11 − 22 ) + 2L23 2 2 +2M31 + 2N12 =1
(1)
where 11 , 22 and 33 denote principal yield stresses; 11 , 12 , 23 and 31 denote shear stresses and G, H, L, M and N denote material constants. The material model captures only transverse anisotropy. Using transverse anisotropy and defining anisotropic hardening parameter ‘R’ as R = ε22 /ε23 the yield function can be simplified to the following equation:
2 2 11 + 22 −
2R 2R + 1 2 11 22 + 2 R+1 R + 1 12
1/2 (2)
Material properties used for analysis are detailed in Table 1.
3.4.
Criteria under consideration
Formability and maximum reduction in thickness are the criteria for sheet metal components. Formability is the ability to impart plausible geometry to the work piece and is the sole criterion from manufacturing perspective. Formability is measured using forming limit diagram (FLD). However, considering the functional aspect of the sheet metal component, the maximum reduction in thickness is specified for each application. For automotive components maximum thickness reduction of 15–20% is the accepted rule of thumb. With the advent of sophisticated numerical tools, it is possible to carry out the application specific analysis (like linear static analysis for strength) incorporating the effects of forming strain, stress, etc., thereby the thumb rule can be replaced by problem/application specific value.
3.4.1.
Forming limit diagram
As discussed in literature (Butuc et al. (2003)), Keeler and Backhofen (1964) and Goodwin (1968) introduced and developed the experimental method to obtain the forming limit diagram (FLD). As stated by Stoughton and Zhu (2004) in their review of concept of strain-based forming limit diagram, FLD is strictly strain path dependent which challenges its application in secondary forming processes (like restriking, flanging, etc.) where the strain path is independent of the first stage strain path and also for non-linear strain path-forming process like hydroforming, complex stamping, etc. The basis of theoretical prediction of FLD is from Marciniak and Kuczyniski, 1967 (M–K) theory. Their mathematical formulation for biaxial stretching is based on the concept of local heterogeneity represented by a long groove perpendicular to higher stress direction. The mathematical prediction of FLD is dependent on the yield criteria used. Antonio et al. (2003) used five different yield criteria for predicting FLD in simulation and observed good correlation with experimental results for IF grade steel when either Hill’s (1979) or Logan and Hosford’s criterion was used for 2036-T4 aluminium when Hill’s (1993) criterion was used and for AK steel when Logan and Hosford’s criterion was used. Butuc et al. (2003) observed successful correlation between experimental and theoretically predicted FLD for aluminium alloy when using Barlat’s yield function Yld96 and hardening law with Voce equation. The accuracy of the yield functions is based on the material constants in the function and is usually determined experimentally. Dariani and Azodi (2003) for six different materials have experimentally found optimum Hill’s
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
327
Fig. 2 – FLD of the component before optimization (top curve is the forming limit curve and the cluster of black boxes below indicate the principal strain states).
index for both left and right side of FLDs when using Hill’s non-quadratic yield criterion. Samuel (2004) used C.L. Chow’s orthotropic damage model to predict FLD in numerical simulation and found by comparing against experimental results that FLD prediction using orthotropic damage model is better. Chow et al. (2004) later developed a generalized mixed isotropic–kinematic hardening plastic model coupled with anisotropic damage criterion for sheet metal forming under non-proportional loading based on Hill’s anisotropy theory. As explained by Aghaie-Khafri and Mahmudi (2004), Jones–Gillisis (JG) theory for the mathematical analysis of FLD approximates plastic deformation in three phases namely homogeneous deformation, deformation localization under constant load followed by local necking. Aghaie-Khafri and Mahmudi (2004) calculated FLD (using JG theory) for alu-
minium alloys using Hosford Yield criterion with the Voce, the Tian–Zhang and the power-law constitutive equations and observed in experimental results that Voce and Tian–Zhang laws predict the limit strains for aluminium alloys better than power-law. Levy (2002) studied the enhancement in formability due to the bending and unbending effect of sheets over draw bead during forming and have proposed mathematical equation to account the increment in the formability effect due to draw bead. The experimental method of FLD generation is by measuring the major and minor strains at the onset of failure. Banabic et al. (2001) have discussed about different tests that are available for measuring FLD. The sheet metal surface is imprinted with circles, which after forming elongates into ellipses. The major and minor axes of the ellipse give the respective strain.
Fig. 3 – FLD of component after optimization.
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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
Fig. 4 – % reduction in thickness for the optimized blank size.
The diameter of the circle used decides the accuracy of the FLD captured. Circular grid analysis is widely used to generate FLD experimentally.
3.5.
Forming predictions
The result of the analysis is focused mainly on the FLD and the percentage reduction in thickness. FLD is taken as the primary tool to ensure that there is neither excess thinning nor wrinkles in the area of interest. It is preferable to have a uniform distribution of thinning. Analysis is performed for the existing non-optimized condition. FLD (refer Fig. 2) shows that all the plots (every plot is a principal strain state) are below the forming limit curve (the top curve in Fig. 2) and hence the component is considered safe.
3.5.1.
4. Experimental validation of FEA analysis by circular grid analysis Circular grid analysis is an effective experimental method to determine the FLD of sheet metal components wherein a circular pattern is etched over the surface of the work piece and the circles are deformed in different manners during forming. Buchar (1996) used circular grid analysis on a car body panel to compare formability of blanks for two different orientations to rolling direction. As discussed by Banabic et al. (2001), the diameter of the grid circles influences the measurement of
Material optimization
As explained earlier, FLD and percentage reduction in thickness are considered as criteria for optimization. From the simulation results, the area of material outside the trim line is calculated. Iterations are performed by reducing the size (length and breadth) of the sheet metal blank. For every reduced dimension the forming analysis is performed and the formability is checked. The iterations by reducing the size of the blank is carried out till the FLD shows failure due to excessive thinning. Among the iterations, minimum blank size with safe formability is chosen as the optimized blank size. FLD (refer Fig. 3) and percentage reduction in thickness (refer Fig. 4) distribution for the optimized blank predicted numerically are shown. In certain locations, due to compression, the material thickness increases, this potentially can lead to wrinkles. The increase in thickness is indicated by negative values (refer Fig. 4) for percentage reduction in thickness. The forming predictions are compared with experimental results. Circular grid analysis method is employed for experimental measurement of formability.
Fig. 5 – Synthetic screen for screen-printing grid circles.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
Fig. 6 – Screen-printing process (screen placed on the blank and the squeegee wipes the ink to form grid circles on the blank).
329
Fig. 8 – Mylar scale used to measure the surface strains. The vertical line in the centre corresponds to the circle diameter and a series of vertical lines (ranging from −20 to +20% strain) are marked on either sides of the central vertical line.
in this work considering the ease of availability of resources in terms of materials, labor and expertise. The accuracy of the process is related to the accuracy of the screen made. Drying of paint during the printing process may clog the semipermeable pores. Frequent washing of the screen is required to avoid the clogging of pores. Selection of ink is important as the ink should not be wiped off during forming. In this case, black paint is used for screen printing.
5. Comparison of experimental and numerical results
Fig. 7 – Enlarged view of grid circles (after forming).
strain. The important part of the process is imprinting grid circles on the metal surface.
4.1.
The blank samples are sheared to optimized size and marked with circles. Circles for strain measurement are marked only in the area where maximum deformation is observed in simulation. The grid marked blanks are formed (refer Fig. 7) and the strains at maximum deformation region are measured using a ‘Mylar scale’ (refer Fig. 8). The major and minor strains are measured at certain locations and are compared against the FEA results. The major and minor strains represent only the surface strains captured by the deformation of the grid circles.
Grid marking techniques
Grid marking is the process of printing circles of definite diameter in the area of interest in the sheet metal blank. The strains accompanying the plastic deformation process and hence the FLD can be studied from the deformation of the grid circles. Carasusan and Fernand (2003) discuss different methods for engraving the grid circles in the blank. Some of the methods are screen-printing, electrochemical method, photo-emulsion method and Laser etching method. Screen-printing method is one of the easy and cost effective methods for grid marking. In this method, a framed screen with a semi-permeable membrane (refer Fig. 5) is made from nylon or other synthetic materials. The screen is placed over the cleaned surface of the blank. Ink is poured on one side of the screen and wiped throughout (refer Fig. 6) the useful area using a rubber squeegee. On the removal of screen, grid circles are printed on the blank. Screen-printing method is used
Fig. 9 – Comparison of major strain between experiment and simulation.
330
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
Fig. 10 – Comparison of minor strain between experiment and simulation.
The thickness strain is calculated based on volume constancy principle from the surface strains. The major strain and minor strain are compared between experimental data and simulation (refer Figs. 9 and 10). Difference in major strain varies from 2 to 10% and difference in minor strain varies from 0 to 6%. The x coordinate in the graph represents a particular location in the plane of sheet. The FLD generated from experimental data (refer Fig. 11) for the optimized blank size shows that all the measured strain states (represented as dots) are below the forming limit curve (top curve) and hence indicates safe forming of component. The major and minor strain comparison indicates that the simulation under-predicts the strain values. In the case of minor strain, some of the strains are positive in nature against negative strains in same location in the simulation. The dif-
Fig. 12 – Weight reduction due to optimization.
ference could be due to the error (observation error) in using Mylar scale. Following bar graph (refer Fig. 12) compares the weight of the blank before and after optimization where blank weight before optimization is taken as 100%.
6.
Conclusions
By varying the sheet metal-forming parameters, the raw material consumption can be optimized leading to cost reduction. Under this study, weight of blank size for the component is reduced by 1.57%. The CAD model of the forming tools for analysis is scanned using a CMM. The optimization is carried out by predicting FLD and also conforming the allowable reduction in thickness. The tool used for numerical prediction is Hyperform–LSDYNA combination. The numerically predicted results are compared with experimental results.
Acknowledgements The authors acknowledge their thanks to Mr. Suresh who assisted in the conversion of CMM cloud point data to CAD surface models. The authors also acknowledge their sincere thanks to Dr. M. Sathya Prasad, Mr. K.K. Rama Rao, Mr. M.P. Sivakumar and Mr. Biradar Devedas for their support throughout the course of project.
references
Fig. 11 – FLD using experimental data.
Aghaie-Khafri, M., Mahmudi, R., 2004. Predicting of plastic instability and forming limit diagrams. Int. J. Mech. Sci. 46, 1289–1306. A.F. Avila, E.L.S. Vieira, 2003. Forming-limit diagram numerical predictions: yield criteria studies. Commun. Numer. Meth. Eng. 19, 223–232 (doi:10.1002/cnm.582). Banabic, D., Bunge, H.J., Pvhlandt, K., Tekkaya, A.E., 2001. Formability of Metallic Materials: Plastic Anisotropy,
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
Formability Testing Forming Limits. Springer Publication, pp. 194–198. Bosch, J.A., 1995. Evolution of measurement. In: Bosch, J.A. (Ed.), Coordinate Measuring Machines and Systems. Marcel Dekker, OH, pp. 23–24. Buchar, Z., 1996. Circular grid analysis applied to the production problems of the car body panel. J. Mater. Process. Technol. 60, 205–208. Butuc, M.C., Gracio, J.J., Barata da Rocha, A., 2003. A theoretical study on forming limit diagrams prediction. J. Mater. Process. Technol. 142, 714–724. Campbell, P.D.Q., 1995. An Introduction to Measuration and Calibration, 1st ed. Industrial Press Inc., New York, p. 109. Carasusan, E., Fernand, 2003. An Automated Procedure for Non-contact Strain Analysis of Sheet Metal Parts©. IEEE. Chow, C.L., Yang, X.J., 2004. A generalized mixed isotropic–kinematic hardening plastic model coupled with anisotropic damage for sheet metal forming. Int. J. Damage Mech. 13, 2004. Dariani, B.M., Azodi, H.D., 2003. Finding the optimum Hill index in the determination of the forming limit diagram, Proceedings of Institution of Mechanical Engineers, vol. 217, Part B: J. Eng. Manuf., pp. 1677–1683 (IMechE 2003). Dusharme, D., June 2006. 3D Inspection, Quality Digest Magazine. The article can be accessed in http://www.qualitydigest.com/june06/articles/01 article.shtml. Farago, F., Curtis, M., 1994. Handbook of Dimensional Measurement, 3rd ed. Industrial Press Inc., New York, pp. 329–332. Galetto, M., Vezzetti, E., 2006. Reverse engineering of free-form surfaces: a methodology for threshold definition in selective sampling. Int. J. Mach. Tools Manuf. 46, 1079–1086.
331
Genest, D.H., January 1997. The Right Probe System Adds Versatility to CMMs, Quality Digest Magazine. The article can be accessed in http://www.qualitydigest.com/jan97/probes.html. Hallquist, J. (Ed.), 2006. LSDYNA—Theory Manual. Livermore Software Technology Corporation. Hariharan, K., et al., 2005. Optimization of Blanks for Sheet Metal Forming, SAE 2005-26-313. Levy, B.S., October 2002. The Auto/Steel Partnership, “Enhanced Forming Limit Diagram-Project Team Research Report”, Enhanced Forming Limit Diagram Project Team, Southfield, MI. The report can be accessed in http://www.a-sp.org/publications.htm. Maker, B.N., Zhu, X., 2000. Input Parameters for Metal Forming Simulation Using LSDYNA, Livermore Software Technology Corporation. Marciniak, Z., Kuczyniski, K., 1967. Limit strains in the processes of stretch-forming sheet metal. Int. J. Mech. Sci. 9, 609–620. Park, J.-J., et al., 2006. Development of a coordinate measuring machine (CMM) touch probe using a multi-axis force sensor. Meas. Sci. Technol. 17, 2380–2386. Samuel, M., 2004. Numerical and experimental investigations of forming limit diagrams in metal sheets. J. Mater. Process. Technol. 153–154, 424–431. Stoughton, T.B., Zhu, X., 2004. Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD. Int. J. Plast. 20, 1463–1486. Worswick, M.J., 2000. Numerical simulation of sheet metal forming. In: Lenard, J.G. (Ed.), Metal Forming Science and Practice. Elsevier Science Ltd., pp. 136–152 (Chapter 8).
journal homepage: www.elsevier.com/locate/jmatprotec
Material optimization: A case study using sheet metal-forming analysis K. Hariharan ∗ , C. Balaji 1 Ashok Leyland Ltd., Chennai 600035, Tamilnadu, India
a r t i c l e
i n f o
a b s t r a c t
Article history:
This paper focuses on material optimization by reduction in raw material size for sheet
Received 10 October 2006
metal components. Panel roof, an automobile component is chosen for analysis. Using a
Received in revised form
commercial explicit solver, the sheet metal-forming process is analysed. To represent the
29 December 2007
actual tool profile in the analysis, computer-aided design (CAD) model of the tool geom-
Accepted 31 January 2008
etry is developed by scanning the die in coordinate measuring machine (CMM). Forming limit diagram (FLD) and percentage reduction in thickness are checked in the finite element analysis (FEA). Experimental verification of the optimized blank is done by circular
Keywords:
grid analysis technique. Difference in major strain varies from 2 to 10% and difference in
Forming limiting diagram
minor strain varies from 0 to 6%. Weight savings of about 1.57% is achieved in the current
Thinning
work.
Sheet metal forming
© 2008 Elsevier B.V. All rights reserved.
Circular grid analysis
1.
Introduction
The advent of simulation tools for sheet metal-forming analysis has enabled precise prediction of forming strains and other process parameters during sheet metal forming. Using finite element analysis (FEA), the sheet metal-forming process and the influence of various process parameters on formability can be studied. In the present work, the raw material size is optimized with the help of FEA analysis. Inputs required to simulate a sheet metal-forming process are computer-aided design (CAD) model of the forming tools (die, punch and binder), mechanical properties of the material used and other process parameters like binder load, lubrication, etc.
∗
2. CAD model development of forming tools The CAD model of the surface of the forming tools is required for simulating the forming process. CAD data of the forming tool surfaces is developed by reverse engineering the tools using coordinate measuring machine (CMM). The earliest coordinate measuring machine which came in early 1960s was a 3D device with a simple DRO displaying the XYZ position of the X Y Z machine. Bosch (1995) claims that the first CMM was developed in 1956 by Harry Ogden of Ferranti (now International Metrology Systems or IMS) from Dalkeith, Scotland. The probe is a link between CMM and work piece measured. The probe senses the location and transfer the information to
Corresponding author at: Ashok Leyland Ltd., Technical Centre, Vellivoyal Chavadi, Chennai 600103, Tamilnadu, India. Tel.: +91 44 25398165; fax: +91 44 25398003. E-mail addresses: [email protected] (K. Hariharan), [email protected] (C. Balaji). 1 Cab Panel Pres Shop, Hosur, Tamilnadu, India. Tel.: +91 4344 260001. 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.01.063
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 324–331
Table 1 – Material properties used for analysis Material property Yield strength Strain hardening exponent, n Strength coefficient, K Plastic anisotropy ratio, R¯ Young’s modulus Poisson’s ratio Density
Value 180 MPa 0.22 478 MPa 1.65 21000 MPa 0.3 7.8 × 0−6 kg/mm3
CMM. Campbell (1995) and Farago and Curtis (1994) discussed the functioning of probes in CMM. The probe sends the input to a computer as electrical impulses; the computer interprets and records them as specific points in space. A contact probe collects data by physically touching the work piece. Contact probes are classified as hard probes, touch trigger probes and analog scanning probes. Genest (1997) discussed that one of the limitations in touch probe is the force required to deflect the probe under contact. Park et al. (2006) have proposed compensation of systematic measurement error of touch probes owing to its spherical shape by calculating the exact contact point of the probe by estimating the force tensor acting on the probe. In the current work the CAD models are developed (refer Table 1: material properties used for analysis (Fig. 1)] using Wenzel CMM (model name: RAF 1625; measurement range: Xaxis, 4000 mm; Y-axis, 1600 mm; Z-axis, 2500 mm); Renishaw’s scanning probe (SP600) is used (scanning probing error: 20 m; repeatability: 10 m). The probe used is analog scanning probe and is useful for rapid data collection. The analog scanning probe maintains contact with the work piece continuously and gives analog data rather than point to point contact like other contact probes. Non-contact probes are useful for high-speed inspection as well as to scan soft surfaces. In Dusharme’s (2006) review on 3D inspection technologies, laser and visionbased non-contact probes are found to be common in the industry. The data collected from CMM is converted to CAD model with the assistance of a service provider. The CMM software can compile the coordinate data and give an IGES (standard graphic exchange format) output of the surfaces. While scanning complex surfaces, sensible variation in the curvature is one of the common problems encountered and is usually addressed by inbuilt algorithms in the commercially available software. Demand for deeper scansion of local curvature variation in the surface profile is defined by a threshold value in algorithm. Galetto and Vezzetti (2006)
325
have explained a methodology to describe the threshold value based on measurement system.
3.
Finite element analysis
The objective is to understand the formability of the ‘panel roof component’ (under study) for existing blank size and based on that optimize the blank dimensions for the component. This leads to savings in raw material consumption. Other than blank size and blank holding force all other changes towards the objective of blank size optimization are practically constrained. The component is pressed in a double action mechanical press. In the earlier work of the author, Hariharan et al. (2005), it is found that the binder (blank holder) load cannot be varied appreciably to optimize the blank size in the particular double action press. Hence the current work concentrates on blank size optimization for fixed binder load.
3.1.
Finite element mesh
The forming tools namely die, punch and binder are considered as rigid bodies whereas the blank as deformable. Deformable blank is described by thin-walled four-noded quadrilateral shell elements. Usually forming analysis is performed using Belytschko–Tsay shell elements, which are computationally less expensive. However, Belytschko–Tsay shell elements are less accurate and also prone to zero energy mode deformation called hourglassing modes (to suppress the hourglassing effects due to single-point integration, Hallquist (2006) have discussed in LSTC theory manual that hourglass viscosity stresses are added to the physical stresses at local element level). Hourglassing modes are physically impossible mathematical states which arise due to single-point integration. In the current work, fully integrated shell elements are used for better accuracy and also to avoid hourglassing. Besides, if the forming simulation is extended to spring back analysis, Maker and Zhu (2000) inferred that Belytschko–Tsay shell elements have more convergence trouble than fully integrated shell elements. Through thickness variation due to bending is captured using five integration points. The usage of triangular elements is minimized in meshing. However, some of the triangular shell elements and the degenerated quadrilateral shell elements are automatically sorted to C0 triangular shell elements. (According to Maker and Zhu (2000), C0 triangular shell elements due to Kennedy, Belytschko and
Fig. 1 – CAD model development of forming tools (from left: CMM, data generated from CMM and the CAD models developed from the CMM data).
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Lin are more accurate and are computationally efficient). The thickness change option is used which captures the shell thickness change due to membrane straining. Adaptive meshing is used for deformable blank. Adaptive meshing interrupts the forming simulation at the specified adaptive frequency and evaluates the meshing for refinement. Angle of the neighbouring elements and curvature of the approaching tooling are used as criteria to refine the mesh. LSDYNA uses an h-adaptive fission process based on Belytschko, Wong and Plaskacz (1989).
3.2.
Contact and boundary condition
The deformable blank forms the slave side and the rigid tools form the master side interface in the contact definitions. Penalty function-based contact interfaces is used to enforce contact and sliding boundary condition between the sheet metal and tooling elements. The contact algorithm search the closest master segment/node for each slave node, computes orthogonal distance and if penetration exists, applies force proportional to penetration depth to master and slave nodes. The penalty formulation models a linear spring between the slave node and the master segment and the stiffness of the modelled spring is based on material constants, mass and area of master segment. Default penalty stiffness scale factor, 0.01 is used and no significant penetration is detected in the results. However, based on the results for significant penetrations, the stiffness scale factor should be corrected for each contact interface. The sheet thickness is considered by offsetting the nodes to half the sheet thickness and also the change in sheet thickness is captured while dealing with contact. The Coulomb friction model is imposed between the contact interfaces of the sheet and the tooling surfaces. In the model taken for analysis, a constant friction coefficient of 0.125 is used. Since the press is a double action pres, die is completely constrained; punch and binder are allowed for z-direction translation only. Tool velocities higher than the actual values are employed to reduce the computational expense due to extremely small time step (4 e−7). In the present work, velocity of punch is 5 m/s against the actual 0.5 m/s. According to Worswick (2000), numerical results showed only minor difference between simulation with accelerated and actual tool velocities. Taking advantage of the symmetry of the component only half of the model is simulated. The nodes in one edge of the half-blank are constrained in z-direction translation for symmetry consideration.
3.3.
Material model
Tools (die, punch and binder) are described using ‘rigid’ material model. Sheet metal blank is defined by ‘Transversely Anisotropic Elastic Plastic’ model of LSDYNA. This is the most commonly used material model for sheet metal-forming applications using LSDYNA. This particular material model uses Hill’s (1948) yield theory as denoted by the following equation: 2
2
2
2 Hill-48 = F(22 − 33 ) + G(33 − 11 ) + H(11 − 22 ) + 2L23 2 2 +2M31 + 2N12 =1
(1)
where 11 , 22 and 33 denote principal yield stresses; 11 , 12 , 23 and 31 denote shear stresses and G, H, L, M and N denote material constants. The material model captures only transverse anisotropy. Using transverse anisotropy and defining anisotropic hardening parameter ‘R’ as R = ε22 /ε23 the yield function can be simplified to the following equation:
2 2 11 + 22 −
2R 2R + 1 2 11 22 + 2 R+1 R + 1 12
1/2 (2)
Material properties used for analysis are detailed in Table 1.
3.4.
Criteria under consideration
Formability and maximum reduction in thickness are the criteria for sheet metal components. Formability is the ability to impart plausible geometry to the work piece and is the sole criterion from manufacturing perspective. Formability is measured using forming limit diagram (FLD). However, considering the functional aspect of the sheet metal component, the maximum reduction in thickness is specified for each application. For automotive components maximum thickness reduction of 15–20% is the accepted rule of thumb. With the advent of sophisticated numerical tools, it is possible to carry out the application specific analysis (like linear static analysis for strength) incorporating the effects of forming strain, stress, etc., thereby the thumb rule can be replaced by problem/application specific value.
3.4.1.
Forming limit diagram
As discussed in literature (Butuc et al. (2003)), Keeler and Backhofen (1964) and Goodwin (1968) introduced and developed the experimental method to obtain the forming limit diagram (FLD). As stated by Stoughton and Zhu (2004) in their review of concept of strain-based forming limit diagram, FLD is strictly strain path dependent which challenges its application in secondary forming processes (like restriking, flanging, etc.) where the strain path is independent of the first stage strain path and also for non-linear strain path-forming process like hydroforming, complex stamping, etc. The basis of theoretical prediction of FLD is from Marciniak and Kuczyniski, 1967 (M–K) theory. Their mathematical formulation for biaxial stretching is based on the concept of local heterogeneity represented by a long groove perpendicular to higher stress direction. The mathematical prediction of FLD is dependent on the yield criteria used. Antonio et al. (2003) used five different yield criteria for predicting FLD in simulation and observed good correlation with experimental results for IF grade steel when either Hill’s (1979) or Logan and Hosford’s criterion was used for 2036-T4 aluminium when Hill’s (1993) criterion was used and for AK steel when Logan and Hosford’s criterion was used. Butuc et al. (2003) observed successful correlation between experimental and theoretically predicted FLD for aluminium alloy when using Barlat’s yield function Yld96 and hardening law with Voce equation. The accuracy of the yield functions is based on the material constants in the function and is usually determined experimentally. Dariani and Azodi (2003) for six different materials have experimentally found optimum Hill’s
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Fig. 2 – FLD of the component before optimization (top curve is the forming limit curve and the cluster of black boxes below indicate the principal strain states).
index for both left and right side of FLDs when using Hill’s non-quadratic yield criterion. Samuel (2004) used C.L. Chow’s orthotropic damage model to predict FLD in numerical simulation and found by comparing against experimental results that FLD prediction using orthotropic damage model is better. Chow et al. (2004) later developed a generalized mixed isotropic–kinematic hardening plastic model coupled with anisotropic damage criterion for sheet metal forming under non-proportional loading based on Hill’s anisotropy theory. As explained by Aghaie-Khafri and Mahmudi (2004), Jones–Gillisis (JG) theory for the mathematical analysis of FLD approximates plastic deformation in three phases namely homogeneous deformation, deformation localization under constant load followed by local necking. Aghaie-Khafri and Mahmudi (2004) calculated FLD (using JG theory) for alu-
minium alloys using Hosford Yield criterion with the Voce, the Tian–Zhang and the power-law constitutive equations and observed in experimental results that Voce and Tian–Zhang laws predict the limit strains for aluminium alloys better than power-law. Levy (2002) studied the enhancement in formability due to the bending and unbending effect of sheets over draw bead during forming and have proposed mathematical equation to account the increment in the formability effect due to draw bead. The experimental method of FLD generation is by measuring the major and minor strains at the onset of failure. Banabic et al. (2001) have discussed about different tests that are available for measuring FLD. The sheet metal surface is imprinted with circles, which after forming elongates into ellipses. The major and minor axes of the ellipse give the respective strain.
Fig. 3 – FLD of component after optimization.
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Fig. 4 – % reduction in thickness for the optimized blank size.
The diameter of the circle used decides the accuracy of the FLD captured. Circular grid analysis is widely used to generate FLD experimentally.
3.5.
Forming predictions
The result of the analysis is focused mainly on the FLD and the percentage reduction in thickness. FLD is taken as the primary tool to ensure that there is neither excess thinning nor wrinkles in the area of interest. It is preferable to have a uniform distribution of thinning. Analysis is performed for the existing non-optimized condition. FLD (refer Fig. 2) shows that all the plots (every plot is a principal strain state) are below the forming limit curve (the top curve in Fig. 2) and hence the component is considered safe.
3.5.1.
4. Experimental validation of FEA analysis by circular grid analysis Circular grid analysis is an effective experimental method to determine the FLD of sheet metal components wherein a circular pattern is etched over the surface of the work piece and the circles are deformed in different manners during forming. Buchar (1996) used circular grid analysis on a car body panel to compare formability of blanks for two different orientations to rolling direction. As discussed by Banabic et al. (2001), the diameter of the grid circles influences the measurement of
Material optimization
As explained earlier, FLD and percentage reduction in thickness are considered as criteria for optimization. From the simulation results, the area of material outside the trim line is calculated. Iterations are performed by reducing the size (length and breadth) of the sheet metal blank. For every reduced dimension the forming analysis is performed and the formability is checked. The iterations by reducing the size of the blank is carried out till the FLD shows failure due to excessive thinning. Among the iterations, minimum blank size with safe formability is chosen as the optimized blank size. FLD (refer Fig. 3) and percentage reduction in thickness (refer Fig. 4) distribution for the optimized blank predicted numerically are shown. In certain locations, due to compression, the material thickness increases, this potentially can lead to wrinkles. The increase in thickness is indicated by negative values (refer Fig. 4) for percentage reduction in thickness. The forming predictions are compared with experimental results. Circular grid analysis method is employed for experimental measurement of formability.
Fig. 5 – Synthetic screen for screen-printing grid circles.
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Fig. 6 – Screen-printing process (screen placed on the blank and the squeegee wipes the ink to form grid circles on the blank).
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Fig. 8 – Mylar scale used to measure the surface strains. The vertical line in the centre corresponds to the circle diameter and a series of vertical lines (ranging from −20 to +20% strain) are marked on either sides of the central vertical line.
in this work considering the ease of availability of resources in terms of materials, labor and expertise. The accuracy of the process is related to the accuracy of the screen made. Drying of paint during the printing process may clog the semipermeable pores. Frequent washing of the screen is required to avoid the clogging of pores. Selection of ink is important as the ink should not be wiped off during forming. In this case, black paint is used for screen printing.
5. Comparison of experimental and numerical results
Fig. 7 – Enlarged view of grid circles (after forming).
strain. The important part of the process is imprinting grid circles on the metal surface.
4.1.
The blank samples are sheared to optimized size and marked with circles. Circles for strain measurement are marked only in the area where maximum deformation is observed in simulation. The grid marked blanks are formed (refer Fig. 7) and the strains at maximum deformation region are measured using a ‘Mylar scale’ (refer Fig. 8). The major and minor strains are measured at certain locations and are compared against the FEA results. The major and minor strains represent only the surface strains captured by the deformation of the grid circles.
Grid marking techniques
Grid marking is the process of printing circles of definite diameter in the area of interest in the sheet metal blank. The strains accompanying the plastic deformation process and hence the FLD can be studied from the deformation of the grid circles. Carasusan and Fernand (2003) discuss different methods for engraving the grid circles in the blank. Some of the methods are screen-printing, electrochemical method, photo-emulsion method and Laser etching method. Screen-printing method is one of the easy and cost effective methods for grid marking. In this method, a framed screen with a semi-permeable membrane (refer Fig. 5) is made from nylon or other synthetic materials. The screen is placed over the cleaned surface of the blank. Ink is poured on one side of the screen and wiped throughout (refer Fig. 6) the useful area using a rubber squeegee. On the removal of screen, grid circles are printed on the blank. Screen-printing method is used
Fig. 9 – Comparison of major strain between experiment and simulation.
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Fig. 10 – Comparison of minor strain between experiment and simulation.
The thickness strain is calculated based on volume constancy principle from the surface strains. The major strain and minor strain are compared between experimental data and simulation (refer Figs. 9 and 10). Difference in major strain varies from 2 to 10% and difference in minor strain varies from 0 to 6%. The x coordinate in the graph represents a particular location in the plane of sheet. The FLD generated from experimental data (refer Fig. 11) for the optimized blank size shows that all the measured strain states (represented as dots) are below the forming limit curve (top curve) and hence indicates safe forming of component. The major and minor strain comparison indicates that the simulation under-predicts the strain values. In the case of minor strain, some of the strains are positive in nature against negative strains in same location in the simulation. The dif-
Fig. 12 – Weight reduction due to optimization.
ference could be due to the error (observation error) in using Mylar scale. Following bar graph (refer Fig. 12) compares the weight of the blank before and after optimization where blank weight before optimization is taken as 100%.
6.
Conclusions
By varying the sheet metal-forming parameters, the raw material consumption can be optimized leading to cost reduction. Under this study, weight of blank size for the component is reduced by 1.57%. The CAD model of the forming tools for analysis is scanned using a CMM. The optimization is carried out by predicting FLD and also conforming the allowable reduction in thickness. The tool used for numerical prediction is Hyperform–LSDYNA combination. The numerically predicted results are compared with experimental results.
Acknowledgements The authors acknowledge their thanks to Mr. Suresh who assisted in the conversion of CMM cloud point data to CAD surface models. The authors also acknowledge their sincere thanks to Dr. M. Sathya Prasad, Mr. K.K. Rama Rao, Mr. M.P. Sivakumar and Mr. Biradar Devedas for their support throughout the course of project.
references
Fig. 11 – FLD using experimental data.
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