Spring back is one of the most significant phenomenon that affect the accurateness of the sheet metal parts. In order to obtain fixed tolerances for the formed parts it is highly recommended to use such process parameters/tool geometry that allow a considerably diminishing of the spring back amount. A Finite Element (FE) model is developed for the 2- D numerical simulation of sheet metal deep drawing process (Parametric Analysis) by using HYPERFORM with the appropriate material properties (anisotropic material) and simplifies boundary conditions

1. http://www.iaeme.com/ijmet/index.asp 9 editor@iaeme.com
International Journal of Mechanical Engineering and Technology (IJMET)
Volume 6, Issue 12, Dec 2015, pp. 09-17, Article ID: IJMET_06_12_002
Available online at
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=6&IType=12
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
SPRING BACK PREDICTION OF SHEET
METAL IN DEEP DRAWING PROCESS
Sachin S Chaudhari
PG Student
Navneet K Patil
Asso. Professor, Mechanical Engineering Department,
SSBT’S College of Engineering and Technology,
Bambhori, Jalgaon, Maharashtra, India
ABSTRACT
Spring back is one of the most significant phenomenon that affect the
accurateness of the sheet metal parts. In order to obtain fixed tolerances for
the formed parts it is highly recommended to use such process parameters/tool
geometry that allow a considerably diminishing of the spring back amount. A
Finite Element (FE) model is developed for the 2- D numerical simulation of
sheet metal deep drawing process (Parametric Analysis) by using
HYPERFORM with the appropriate material properties (anisotropic material)
and simplifies boundary conditions. In this paper the effects of diverse deep
drawing process parameters were determined by FEA study with the use of
Design of Experiments (Taguchi) Method and analysis of variance (ANOVA)
using Minitab software for CRDQ steel in order to reduce the amount of
spring back. Ultimately confirmation test shows improvement in spring back.
Improvement in spring back quality characteristics of weld joint.
Key words: Deep Drawing, HYPERFORM, Taguchi Method, Orthogonal
Array, S/N Ratio, ANOVA.
Cite this Article: Sachin S Chaudhari and Navneet K Patil. Spring Back
Prediction of Sheet Metal In Deep Drawing Process, International Journal of
Mechanical Engineering and Technology, 6(12), 2015, pp. 01-08.
http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=6&IType=12
1. INTRODUCTION
Quality is of essential importance in today’s manufacturing globe due to multifarious
working environment and conditions linked in make use of the sheet metal
components [1]. Certainly, the quality of a product can be defined as the level of
customer fulfillment during the service life of the product [2]. It is marked that,
appropriate selection of parameters influencing the quality requirements to be well
defined. Prevention of defects in controlled quality measurements ultimately ends up

2. Sachin S Chaudhari and Navneet K Patil
http://www.iaeme.com/ijmet/index.asp 10 editor@iaeme.com
with reduced trial and error, tryout methods. As the complexity of the part formed is
constantly increasing in the present era with the requirement of high quality and the
use of highly developed optimization methods demands for in depth investigation in
sheet metal forming. Throughout forming, the forces and the properties of the
workpiece material are of alarm to the design engineer. The properties of the sheet
being formed change and have an effect on the process parameters throughout
processing.
Traditionally, the majority metal forming techniques have been tested
experimentally using trial-and-error or experimental methods, which are costly and
time taking approaches, as dies, punches and blank holders require to be
manufactured. By making use of finite element analysis (FEA) the prediction of
punch force (Fp), the blank holder force (BHF), the thickness distribution through
sections of the sheet metal can be obtained. This can considerably reduce the
manufacture costs, for higher quality geyser tanks by reducing the lead time to
production and give engineers the ability to respond to market shortfall with larger
speeds. In doing this, the level of knowledge in how a variety of materials interact at
the contact surfaces is improved, and the data for dealing with particular materials are
also increased, which is another good outcome.
Deep drawing is one of the commonly used sheet metal forming process used in
industries for cup shaped parts produced at high rate [1][3]. By this process, the
components produced are being widely used in aerospace, automobile, home
appliances and many other applications [4] [5].The deep drawing process consists of
five linked activities. i.e., 1) pure radial drawing between the die and blank holder, 2)
sliding and bending over the die profile, 3) stretching between the die and the punch,
4) bending and sliding over the punch profile radius, 5) stretching and sliding over the
punch face [6]. It is necessary to find out an optimum process parameter levels
capable for producing desired product quality. Proper level selection of process
parameters leads to deficiency free products.
The Objective of the paper is to successfully simulate the deep drawing process
for prediction of spring back in displacement (mm). Numerical simulation with
optimization methods for improving design, quality and low cycle times have been
used extensively [7]. The optimal parameter settings for most even wall thickness
were found out using Taguchi’s signal to noise ratio(S/N Ratio) [6]. The use of finite
element analysis (FEA) simulations with Taguchi design of experiments (DOE)
method because experimental and analytical solution for spring back is very difficult
and time consuming and also for determination of the contribution of the vital process
parameters in the deep deformation response of drawing process namely temperature
of blank, die shoulder radius and punch nose velocity were studied. The Pareto anova
was carried out for observing the influence of process parameters for the deformation
of the deep drawing cup and their percentage contribution [8].
In the present study, Taguchi Technique of design of experiment was applied to
set up relationships between punch nose radius (Rp), die profile radius (Rd) and blank
holder force (BHF) in influencing spring back. In this given method, statistical
method approach based on Taguchi and ANOVA techniques had been used for
obtaining the influence of each parameter such as punch nose radius (Rp), die profile
radius (Rd) and blank holder force( BHF) on drawing of deep drawing cup.
Spring back is the amount of elastic deformation a material has to gone through
before it becomes permanently deformed, or formed. It is also the amount of elastic
tolerance, which is to a few extents present in every material, be it ductile, and

3. Spring Back Prediction of Sheet Metal In Deep Drawing Process
http://www.iaeme.com/ijmet/index.asp 11 editor@iaeme.com
annealed metal or hard steel. Spring back found much lower extent in ductile
materials than in hard metals, with depending on the Young’s modulus of elasticity of
a particular material. The spring back amount increases with increasing yield strength
or with the strain-hardening tendency of materials. The amount of spring back in the
material increases with both Cold working and heat treatment. With due comparison,
the spring back of low strength steel material will be smaller than that of high-strength
steel and spring back will be two or three times higher of aluminum [9].
Brief definition of elastic spring back is a dimensional change generated in
component, which occurs because of elastic recovery when tool is removed or
released. This phenomenon causes deviations in dimensions [10]. The focus in
forming simulation has now forwarded to the Finite Element Method (FEM) [11][12].
When the spring back calculation has proven to be trustworthy, the simulation results
were used for optimization of tool shape loop [13 Thinin]. The spring back calculation
has been done in widely available commercial forming simulation software packages.
However, for deep drawn product in industry, the accuracy in results has not reached
at desired level yet [13].
The successful simulation of the deep drawing process is mostly dependent on
successful modeling of the process for numerical analysis.
2. MODELLING OF SPRINGBACK
Spring back is affected by various factors punch nose radius (Rp), die profile radius
(Rd) and blank holder force (BHF) etc. Spring back effect is a major cause of concern
for sheet metal forming industries which leads to inaccuracies in the final shape of
product produced and eventually leads to problems in assembly. The problem being
taken for the paper is to study the effect of spring back phenomenon on CRDQ
material which is elastic plastic material, using various parameters and validate the
results using DOE and analysis of variance. The material used is CRDQ steel for
geyser tank. The material is used with thickness a, 1.5mm. The material properties are
shown in a table 1 and Stress Strain Curve for CRDQ steel is shown in a Figure1.
Table 1 Physical Properties of CRDQ Steel
Sr.No. Properties Values
1 Young’s modulus (E) 210 GPa
2 Posisson’s ratio (ν) 0.3
3 Tangent modulus (Et) 0.5 Gpa
4 Density (ρ) 7800 kg/m3
5 Yield Stress (σy) 186 Mpa
6 Ultimate tensile Sress (σt) 315 Mpa
7 Frictions coefficient (µ) 0.1
8 Strain hardening exponent (n) 0.22
9 Strain hardening parameter (K)MPa 549.03

4. Sachin S Chaudhari and Navneet K Patil
http://www.iaeme.com/ijmet/index.asp 12 editor@iaeme.com
Figure 1 Stress Strain Curve for CRDQ steel (Hyperform database)
2.1 Finite element model
Figure2 shows drawing a circular cup. All important dimensions are shown in Figure
3[14] of the die; punch, die, and blank holder are given in table 2.
Figure 2 Cylindrical cup
Table 2 Geometric Parameters
Blank size radius (BR) 125 mm
Blank thickness (t) 1.5 mm
Punch radius (PR) 60 mm
Punch nose radius (rp) 3-8 mm
Die radius (DR) 61.65 mm
Die shoulder radius (rd) 5-13 mm
Radial clearance (wc) 1.65 mm
Cup Height of the first draw (h) 75 mm

5. Spring Back Prediction of Sheet Metal In Deep Drawing Process
http://www.iaeme.com/ijmet/index.asp 13 editor@iaeme.com
Figure 3 Geometry of Drawing Dies Assembly
3. TAGUCHI DESIGN
In this paper the prediction of the spring back in deep drawing process using FEA
simulation process and DOE/Taguchi approach to study the effects of process
parameters such as between punch nose radius (Rp), die profile radius (Rd) and blank
holder force (BHF), these three factors were the most significant factors which
directly affects the amount of spring back in final product and hence in the present
investigation these three factors are consider. In the in essence the spring back in deep
drawn cup must be less as possible, i.e., the smaller values are preferred for the cup.
Taguchi design it is also called as an orthogonal array is a design of experiments
method of that requires only a fraction of combinations of full factorial. An
orthogonal array balanced the design such a way that factor levels are equally
weighted. Due to this, each and every factor can be evaluated separately of all the
other factors; due to this the effect of one factor does not affect the estimation of
another factor. [15]
L9 orthogonal array had used to conduct the only nine experiments under three
levels of each parameter as shown in table 4, and the experiments were conducted so
as to investigate the spring back variation on deep drawn cup using relevant ranges of
parameters are shown in table 3.
Table 3 Process Parameters and Their Levels
Process Parameter
Levels
1 2 3
Die Shoulder Radius (rd) mm 7 10 13
Punch Nose Radius (rp), mm 4.5 7.5 11.5
Blank Holding Force (BHF), kN 15 16.5 17

6. Sachin S Chaudhari and Navneet K Patil
http://www.iaeme.com/ijmet/index.asp 14 editor@iaeme.com
Table 4 Orthogonal Array (L9) Of Taguchi Method
Exp. No.
Process Parameters
Die shoulder radius (rd) Punch nose radius (RP) Blank holder force (BHF)
1 7 4.5 15
2 7 7.5 16.5
3 7 11.5 17
4 10 4.5 16.5
5 10 7.5 17
6 10 11.5 15
7 13 4.5 17
8 13 7.5 15
9 13 11.5 16.5
Taguchi approach is most powerful Design of experiments (DOE) tool for
optimization of engineering process in the tool the concept of Signal to Noise ratio
(S/N ratio) is used for improvement of quality through variability reduction and
improvement of measurement[16].There are many types of Signal to Noise ratios
(S/N ratio) available for study as follows.
Larger is better: It is choosing when the goal is to maximize the response.
Nominal is best: It is choosing when the goal is to target the response and you want
to base the S/N ratio on standard deviations only.
Nominal is best: It is choosing when the goal is to target the response and want to
base the S/N ratio on means and standard deviations (default).
Smaller is better: It is choosing when the goal is to minimize the response. [15]
In essence the spring back in deep drawn cup must be smaller, so for this work
Smaller is better S/N ratio type were selected. S/N ratio had determine for each and
every experiments and the experiments are carried out using FEA and the values of
spring back obtained from each experiments is listed in table 5.
4. ANOVA
The use of the ANOVA is to investigate which process parameters considerably affect
the quality characteristic. It is a statistical approach evaluated for percentage of
contributions (%) for variance by each input factor. In ANOVA collection of
statistical models is done and related procedures used to get the contributions of each
parameter on the output characteristic. In this paper ANOVA is used to clarify the
input parameters, i.e. Rd, Rp, and BHF that noticeably influence the spring back. The
information on weightage of each parameter on thickness distribution was get
furnishes. It is recommended by Taguchi that, a logarithmic transformation of mean
square deviation (S/N ratio) for the analysis of results. ANOVA approach separates
the overall variation from the average Signal to noise ratio (S/N ratio) into
contribution by each of the parameters and the errors. [16].
5. RESULT AND DISCUSSION
In this study, the spring back percentage in material CRDQ steel in deep drawing
process was explored by investigating the effects of different process parameters, such
as punch nose radius (Rp), die profile radius (Rd) and blank holder force (BHF). A
model was developed by HyperForm software package for prediction of spring back
in the material CRDQ steel in deep drawing process related to spring back

7. Spring Back Prediction of Sheet Metal In Deep Drawing Process
http://www.iaeme.com/ijmet/index.asp 15 editor@iaeme.com
phenomenon. The RADIOSS is used as the solver which gives the results. The
reading of spring back obtained was converted into signal to noise ratio.
The springback percentage was calculated from formula
% springback = [{deformed diameter of cup after forming} – {Design diameter
of cup} / Desgin diameter of cup] *100 [17].
This springback percentage was calculated for each of nine experiments as shown in
table no.5.
Table 5 % of spring back for Experiments
Exp. No % of Spring back (FEA)
1 1.11583
2 1.13667
3 1.30667
4 1.07750
5 1.15083
6 1.07667
7 1.23667
8 1.06250
9 1.18417
After this, Taguchi analysis was done by using minitab software and found out the
optimal level of the forming parameters as shown in table 6. The optimum levels of
the three process parameter given above, in order to obtain an less spring back
percentage in the cup is as shown in table 7 as die shoulder radius of 10 mm, punch
nose radius of 11.5 mm, and the blank holding force of 15 kN.
Table 6 Response Table for Signal to Noise Ratios
LEVEL A B C
1 -1.4626 -1.1485 -0.7067
2 -0.8367 - 0.9532 -1.0764
3 -1.2800 -1.4777 -1.7962
Delta 0.6259 0.5246 1.0895
Rank 2 3 1
Table 7 Optimum Condition
Process Parameters Level Description Level
Die shoulder radius, mm 10 2
Punch nose radius, mm 7.5 2
Blank holder force, kN 15 1
% Spring back 1.12416
As the optimum combination level is not in the one of the experimental runs
(according to Table 4) an extra confirmation run is required. That extra run was done
again by FEA simulation and found that the % of spring back as 1.12416 and this
value was compared with predicted Taguchi smaller is better S/N ratio value which is

8. Sachin S Chaudhari and Navneet K Patil
http://www.iaeme.com/ijmet/index.asp 16 editor@iaeme.com
-0.110399 with % of spring back as 1.01251, this shows that % of spring back given
by Taguchi and FEA analysis are about to same with having negligible error.
Finally the importance of the process parameters was estimated by the ANOVA
statistical approach. The results of ANOVA are calculated using minitab and shown
in a table 8. And main effect plot of s/n ratio shown in Figure 4. The blank holder
force (BHF) has most significant process parameter followed by die shoulder radius
(Rd) and punch nose radius (Rp) small significant parameter is influencing spring
back.
Figure 4 Main effect plot for S/N ratio.
Table 8 ANOVA Results
Source DF SS MS F % Contri.
A 2 0.6216 0.3108 0.82 21.51907
B 2 0.4217 0.2109 0.51 14.59877
C 2 1.842 0.1745 5.28 63.76792
Error 2 0.0033 0.114242
Total 8 100
6. CONCLUSION
Several conclusions can be obtained from the results of the study:
 The finite element simulation provides a satisfactory prediction of spring back
percentage results with Taguchi approach.
 The results from this work open the platform of determination of optimum blank
holder force for enhance quality products.
 Anova results reveal that blank holder force has most significant parameter 63.76%,
followed by die shoulder radius 21.51% and the punch nose radius (14.59%) has
lower effect on % of spring back.
REFERENCES
[1] Jeswiet J, Geiger M, Engel U, Kleiner M, Schikorra M, Duflou J, Neugebauer R,
Bariani P, Bruschi S, 2008, Metal forming progress since 2000, CIRP Journal of
Manufacturing Science and Technology, Vol. 1, No. 1, pp. 2-17.
[2] Jahanshahi A.A, Gasthi M.A.H, Mirdamadi S.A, Nawaser K, Khaksar S.M.S,
2011, Study the effects of customer service and product quality on customer
satisfaction and loyalty, International Journal of Humanities and Social Science,
Vol. 1 No. 7, pp.253-260.

9. Spring Back Prediction of Sheet Metal In Deep Drawing Process
http://www.iaeme.com/ijmet/index.asp 17 editor@iaeme.com
[3] Reddy A.C.S, Rajesham S. and Reddy P.R, 2014, Evaluation of limiting drawing
ratio (LDR) in deep drawing by rapid determination method, International
Journal of Current Engineering and Technology, Vol. 4, No. 2, pp. 757-762.
[4] Prof. Dr. Ing. Karl Roll, 2008, Simulation of sheet metal forming-necessary
developments in the future, Keynote paper NUMISHEET 2008 Vol A-1 pp. 59-
68.
[5] J. Sutherland and K. Gunter, A global perspective on the environmental
challenges facing the automotive industry: state-of-the-art and directions for the
future, International Journal of Vehicle Design, Vol. 35, Nos. 1/2, 2004 pp.86-
110.
[6] S. Raju, G. Ganesan, R. Karthikeyan, Influence of variables in deep drawing of
AA 6061 sheet, Trans. Nonferrous Met. Soc. China20 (2010) pp.1856-1862.
[7] L.F. Menezes and C. Teodosiu, Three-dimensional numerical simulation of the
deep-drawing process using solid fnite elements, Elsevier, Journal of material
processing technology 97(2000), 2000,pp 100 -106.
[8] G. Venkateswarlu, M. J. Davidson and G. R. N. Tagore, Influence of process
parameters on the cup drawing of aluminium 7075 sheet, International Journal of
Engineering, Science and Technology Vol. 2, No. 11, 2010, pp. 41-49.
[9] Suchy I. Handbook of die design. 2nd
ed. McGraw-Hill Publishing, 2006, pp353–
400
[10] M. L. Garcia-Romeu, J. Ciurana, I. Ferrer, spring back determination of sheet
metals in an air bending process based on an experimental work, journal of
materials processing technology 191(2007) pp.174- 177.
[11] Huang Y M, Chen T C 2005, Influence of Blank Profile on the V-Die Bending
Camber Process of Sheet Metal, International Journal of Advanced
Manufacturing Technology (25), pp.668-77.
[12] Li-Ping Lei, Sang-Moon Hwang, Beom-Soo Kang, FEA and design in Stainless
steels sheet metal forming & its experimental comparison, Journal of materials
processing techniques 110, 2001.
[13] H. Zein, M. El Sherbiny, M. Abd-Rabou, M. El shazly, Thinning and Spring
Back Prediction of Sheet Metal in The Deep Drawing Process, Elsevier, aterials
& Design,Volume53, January 2014, pp.797–808.
[14] Mohd Naeemil Mahmudi Bin Mahmud, Reducing Wrinkling and Tearing of
Deep Draw Part, M. Tech thesis, Universiti Malaysia Pahang, MAY 2012, page
no. 16.
[15] Minitab version 17 user manual.
[16] A. C. S. Reddy, S. Rajesham, P. R. Reddy, T. P. Kumar, J. Goverdhan, An
experimental study on effect of process parameters in deep drawing using
Taguchi technique, International Journal of Engineering, Science and Technology
Vol. 7, No.1, 2015, pp. 21-32.
[17] Dr. Waleed Khalid Jawad, Investigation of Contact Interface between the Punch
and Blank in Deep Drawing Process, International journal of Eng. & Technology,
Vol.25, No.3, 2007, pp. 370-382.
[18] Dr. R. Uday Kumar, Dr. P. Ravinder Reddy. Influence of Viscosity on Fluid
Pressure in Hydroforming Deep Drawing Process, International Journal of
Mechanical Engineering and Technology, 3(2), 2012, pp. 604 – 609.
[19] Dr.R.Uday Kumar, Mathematical Modeling and Evaluation of Radial Stresses in
Hydroforming Deep Drawing Process, International Journal of Mechanical
Engineering and Technology, 3(2), 2012, pp. 693 - 701.