Sheet Metal 2023 Materials Research Forum LLC

Materials Research Proceedings 25 (2023) 53-60 https://doi.org/10.21741/9781644902417-7

Experimental investigation on thinning and forming force acting on

multi-stage single point incremental forming
Nikhil Bari1, a and Shailendra Kumar1, b*
1
Department of Mechanical Engineering, Sardar Vallabhbhai National Institute of Technology,
Surat, India
a
nikhilbari1665@gmail.com , b*skbudhwar@med.svnit.ac.in

Keywords: Incremental Sheet Forming, Predictive Models, Optimization

Abstract. This paper describes a study of thinning and forming force in multi-stage single point
incremental forming. Four process parameters namely pitch, tool diameter, blank thickness and
initial draw angle are considered to study their influence on maximum thinning and peak forming
force. Experiments are designed using face-centered composite design (CCD). Experimental
results are analyzed using analysis of variance (ANOVA). It is found that initial draw angle is the
most influencing parameter for maximum thinning, while peak forming force is most influenced
by blank thickness. Maximum thinning decreases with decrease in initial draw angle and increase
in blank thickness. Peak forming force decreases with decrease in blank thickness. Moreover,
predictive models are developed for maximum thinning and peak forming force. Also,
optimization of parameters is carried out to minimize thinning and forming force. The
confirmation tests are performed to validate predictive model and optimization results.
Introduction
Multi-stage single point incremental forming (MSPIF) is one of the efficient ways to resolve the
limitations like steeper wall angle and un-uniform thickness distribution over SPIF. In MSPIF,
deformation zone is expanded to larger areas therefore higher formability and uniform thickness
distribution is observed. To achieve a more uniform thickness distribution and more formability,
a MSPIF with accurate tool path is important [1]. Nowadays, MSPIF process is used in industries
to overcome the limitations of SPIF process. Some researchers have investigated the applications
like composite spherical pressure vessel mold, Carnio facial implants [2], bottom surface of the
wing in ground (WIG) ship [3] etc. Consequently, MSPIF also has some limitations like high
surface roughness, forming time, thinning, power consumption etc. [4].
Researchers have worked on thickness distribution and forming force in MSPIF process. Nirala
and Agrawal [5] developed a thinning determination model and verified it with finite element
analysis (FEA) and experimental results. Gheysarian et al. [6] investigated the influence of
parameters on maximum thinning and found that diameter of tool has most significant effect on
maximum thinning. An et al. [7] investigated the effect of process parameters on MSPIF process
using 4 stage and concluded that reduction in pitch, tool diameter and feed rate results in better
thickness distribution. Few researchers have studied the forming force acting in MSPIF. Ghafoor
et al. [8] investigated the effect of different toolpath strategies on forming force and they reported
that varying wall angle constant depth toolpath requires minimum forming force. Gandla et al. [9]
studied the effect of number of passes on forming force acting in MSPIF and they reported that
resultant forming force decreases with increase in number of passes. Aerens et al. [10]
experimentally studied the influence of blank thickness, tool size, wall angle, and pitch on X, Y
and Z components of forming forces and they also generated the predictive model for PFF.
Researchers [11, 12] have observed excessive thinning in parts made by MSPIF process. Few
researchers studied forming forces in SPIF process to determine power consumption and tool life
of the process, but limited literature [13, 14] is available on studying the forming force in MSPIF
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of
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Sheet Metal 2023 Materials Research Forum LLC
Materials Research Proceedings 25 (2023) 53-60 https://doi.org/10.21741/9781644902417-7

process. Further efforts should be made to investigate influence of process parameters on sheet
thinning and forming force in MSPIF. Present study aims to study the influence of process
parameters on maximum thinning and peak forming force acting in MSPIF process, to develop
prediction models for the responses, and to optimize the sets of process parameters for minimum
thinning and peak forming fore.
Experimental plan
Sheet of aluminum alloy 1050 is taken for the present study. High speed, high chromium steel of
grade M2 material is used to fabricate the tool. EP-90 hydraulic oil is used as a lubricant to
minimize friction and wear. The varying wall angle - constant depth multi-stage tool path
technique is employed to produces good thickness distribution as compared to other strategies. In
all test runs 110×110×35 mm square pyramid is formed using 4 stage tool path strategy. The
starting draw angle is used as one of process parameters, and the wall angle is changed by 50
degrees at each stage. As illustrated in Fig. 1, with a middle level of initial draw angle, 400, 450,
500, and 550 degree wall angles are formed in first to fourth stages respectively. Toolpath for the
operation are extracted using CATIA and MATLAB software [4].

Fig. 1. (a) Truncated pyramid with varying wall angle (b) holding fixture
For the present study, four process parameters are considered namely pitch, tool diameter, blank
thickness, and initial draw angle. Each parameter has three levels as given in Tab. 1. All process
parameters and their levels are selected as per available setup, literature review, and trial
experiments. The experiments are performed according to centered composite design i.e. CCD of
response surface methodology (RSM). Overall 30 experiments (24 non-center + 6 center point)
are designed.
Table 1. Parameters and their levels
Levels
Process parameters
-1 0 +1
Pitch [mm] 0.25 0.50 0.75
Tool diameter [mm] 8 10 12
Blank thickness [mm] 0.70 0.95 1.20
Initial draw angle [0] 35 40 45
Siemens controlled 3 axis milling machine (M/s Batliboi, India) is used to perform all the
experiments. The holding fixture is designed and assembled on the machine bed as shown in Fig.
1(b). Maximum thinning (%) is computed using Eq. 1,
𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚
Maximum thinning (%) = 1 − × 100. (1)
𝑡𝑡i

Where, 𝑡𝑡i = Initial blank thickness, 𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 = Minimum observed thickness. 𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 is measured
using digital micrometer (make MITUTOYO, Japan) whose accuracy is 0.001mm and
repeatability of 95%. To measure thickness at corner of part, the parts are cut into two halves. Peak

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Materials Research Proceedings 25 (2023) 53-60 https://doi.org/10.21741/9781644902417-7

forming force (PFF) readings are taken from milling tool dynamometer (M/s Syscon Instruments,
India). Dynamometer readings are converted to Newton (N) by multiplying 9.806 to the ‘Kgf’
reading.
Results and discussion
Total test runs and the respective values of responses are given in Tab. 2. The maximum thinning
is ranging from 50.30% to 71.00%, whereas, PFF ranges from 567.76N to 2441.24N. Significant
process parameters for the responses are determined by performing analysis of variance (ANOVA)
on experimental data. Selected confidence interval is 95% therefore terms having p-value is less
than 0.05 are considered as significant terms.
Table 2. Test run design and response values
S.N. Pitch Tool Blank Initial Max. PPF S.R. Pitch Tool Blank Initial Max. PPF
dia. thickness draw thinning dia. thickness draw thinning
angle angle
1 0.75 8 0.70 45 71.00 724.70 16 0.75 8 0.70 35 55.80 636.42
2 0.25 8 1.20 45 65.70 1862.52 17 0.50 10 1.20 40 60.20 1999.85
3 0.75 8 1.20 35 52.70 1911.57 18 0.50 10 0.95 40 62.80 1323.04
4 0.50 10 0.95 40 68.20 1323.04 19 0.25 10 0.95 40 63.80 1234.76
5 0.25 8 0.70 35 55.20 567.76 20 0.50 10 0.95 40 62.80 1323.04
6 0.50 10 0.95 40 62.80 1323.14 21 0.75 12 0.70 35 54.70 812.98
7 0.50 10 0.95 40 62.80 1323.04 22 0.75 12 0.70 45 68.90 840.32
8 0.25 12 1.20 45 66.00 2078.32 23 0.25 8 1.20 35 50.30 1656.54
9 0.50 12 0.95 40 62.20 1479.98 24 0.75 8 1.20 45 65.40 2097.94
10 0.25 12 1.20 35 51.00 1941.12 25 0.75 10 0.95 40 61.40 1460.36
11 0.25 8 0.70 45 70.50 620.11 26 0.50 10 0.95 40 62.80 1323.04
12 0.50 10 0.95 35 57.90 1260.65 27 0.50 10 0.95 40 62.80 1323.04
13 0.25 12 0.70 45 68.50 790.61 28 0.50 10 0.70 40 62.90 744.32
14 0.75 12 1.20 45 64.60 2441.24 29 0.25 12 0.70 35 59.20 685.47
15 0.50 8 0.95 40 62.20 1264.19 30 0.75 12 1.20 35 52.70 2264.69

The ANOVA for maximum thinning is given in Tab. 3. The R2 value for the model is 0.9551,
adjusted R2 and predicted R2 values are 0.9131, 0.8250 respectively, these values are close to 1.
The p-value of lack of fit is 0.8662 which is greater than 0.05 hence the lack of fit is not significant.
The model is significant which is satisfying the basic requirements of the ANOVA model. The
adequacy of the model is 16.842 which is greater than 4 hence the model is selected to examine
the design space. From the ANOVA, blank thickness and initial draw angle are found significant
because the p-value of these terms is less than 0.05. Moreover, no interaction term is found
significant.
Main effect of significant process parameter is shown in Fig. 2. It is noted that maximum
thinning of MSPIF parts decreases with increase in blank thickness (Fig. 2a). It is due to increase
in stiffness of blank with increase in blank thickness. Similar results for SPIF was reported by
Oleksik et al. [12]. Initial draw angle is also significant process parameter. As initial draw angle
increases, maximum thinning also increases as shown in Fig. 2b. This is due to increase in initial
draw angle, stretching in upcoming stages increases which increases the maximum thinning.
The ANOVA for PFF is given in Tab. 4. R2, adjusted R2, and predicted R2 values of the models
are 0.9989, 0.9980, and 0.9924. adjusted R2, and predicted R2 is in reasonable agreement with each
other because the difference is less than 0.2. Adequate precision is 108.028 implies acceptable
model. Overall p-value of the model is less than 0.05 means model is significant. Similarly, all
process parameters and interaction effect of pitch-blank thickness (AC), tool diameter-blank
thickness (BC), and blank thickness-initial draw angle (CD) are found significant since their p-
value is less than 0.05.

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Sheet Metal 2023 Materials Research Forum LLC
Materials Research Proceedings 25 (2023) 53-60 https://doi.org/10.21741/9781644902417-7

Table 3. ANOVA for maximum thinning

Sum of Mean
Source DoF F-value p-value Remark
Squares Square
Model 887.9 14 63.42 22.78 < 0.0001 significant
A-Pitch 0.5 1 0.5 0.1796 0.6777
B-Tool diameter 0.0556 1 0.0556 0.02 0.8895
C-Blank thickness 80.64 1 80.64 28.97 < 0.0001 significant
D-Initial draw angle 756.09 1 756.09 271.57 < 0.0001 significant
AB 3.06 1 3.06 1.1 0.3109
AC 1.82 1 1.82 0.6546 0.4311
AD 0.0625 1 0.0625 0.0224 0.8829
BC 0.1225 1 0.1225 0.044 0.8367
BD 4.2 1 4.2 1.51 0.2382
CD 0.0625 1 0.0625 0.0224 0.8829
Residual 41.76 15 2.78
Total 929.66 29

Fig. 2. Main effect plot for maximum thinning

The main effect graph for PFF is depicted in Fig. 3. From Fig. 3 (a) it is observed that PFF
slightly increases with increase in pitch value. This is due to the fact that a large pitch deforms
more material and consumes a larger amount of deforming energy. Similar results are reported for
by Liu et al. [13] and Sisodia et al. [14] for SPIF process. As tool diameter increases, PFF increases
marginally as shown in Fig 3 (b). The increasing trend is observed due to increase contact area
between sheet and tool tip, hence more material is pushed and more force is required. Aerense et
al. [10]; Kumar and Gulati [15] observed the same trend. It is observed that increase in blank
thickness, PFF increases substantially as seen in Fig. 3 (c). The upward trend is observed because
as blank thickness increases, stiffness of the blank increases and requires more energy to deform
and hence PFF increases. It is also noted that PFF slightly increases with increase in initial draw
angle (Fig. 3 (d)).

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Sheet Metal 2023 Materials Research Forum LLC
Materials Research Proceedings 25 (2023) 53-60 https://doi.org/10.21741/9781644902417-7

Table 4. ANOVA for peak forming force

Source Sum of DoF Mean F-value p-value Remarks
Squares Square
Model 8.33E+06 14 5.95E+05 1013.35 < 0.0001 significant
A-Pitch 1.71E+05 1 1.71E+05 290.81 < 0.0001 significant
B-Tool diameter 2.21E+05 1 2.21E+05 375.87 < 0.0001 significant
C-Blank thickness 7.78E+06 1 7.78E+06 13246.01 < 0.0001 significant
D-Initial draw angle 58579.49 1 58579.49 99.78 < 0.0001 significant
AB 2500.2 1 2500.2 4.26 0.0568
AC 42689.76 1 42689.76 72.72 < 0.0001 significant
AD 30.61 1 30.61 0.0521 0.8225
BC 23748.35 1 23748.35 40.45 < 0.0001 significant
BD 470.33 1 470.33 0.8011 0.3849
CD 11717.85 1 11717.85 19.96 0.0005 significant
Residual 8806.08 15 587.07
Total 8.34E+06 29

Fig. 3. Main effect plot for PFF

From ANOVA, three interactions are also found significant for PFF. The interactive effect of
process parameters is studied through 3-D response surface graph while other process parameters
are kept at middle level. The combined surface plot for pitch and blank thickness is depicted in
Fig. 4 (a). The PFF rapidly increases with increase in both pitch and blank thickness. At 0.75mm
pitch and 1.2mm blank thickness, maximum PFF value is observed. The contour lines of the
response are parallel to each other and also parallel to the axis of pitch which reveals that blank

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Materials Research Proceedings 25 (2023) 53-60 https://doi.org/10.21741/9781644902417-7

thickness has major influence than pitch. The response plot for interaction of tool diameter and
blank thickness is shown in Fig. 4 (b). It is observed that combined increase in blank thickness and
tool diameter, increases the PFF. Blank thickness has major effect than tool diameter. At 0.95mm
blank thickness, PFF increased by 16.22% (1257.21N to 1461.16N) with increase in tool diameter.
With simultaneous increase in initial draw angle and blank thickness, the value of PFF increases
rapidly (Fig. 4c). The response lines are nearly parallel to the axis of initial draw angle which infers
that blank thickness has more influence than initial draw angle. At 0.95mm blank thickness, there
is 9.27% (1241.81N to 1361.61N) increase in PFF. The present experimental study reveals that
most influencing process parameter is blank thickness subsequently, tool diameter, pitch and initial
draw angle.

Fig. 4. Response surface graph for PFF

Predictive models
Quadratic model is best fitted for the present experimental data. The predictive models in terms of
process parameters for maximum thinning and PFF are given in Eq. 2 and Eq. 3 respectively.
Predictive models are generated to determine the value of responses at certain values of each
process parameter. For better results, the values of process parameters must be bounded by original
range. Predicted R2 value for maximum thinning and PFF is 0.8250 and 0.9924 respectively which
are closed to 1 hence the models are accepted.

Maximum thinning [%] = 17.903+18.9222×(A)+8.658×(B)+43.544×(C)-2.303×(D)-

0.875×(A)(B)+5.400×(A)(C)-0.050×(A)(D)+0.175×(B)(C)-0.051×(B)(D)+0.050×(C)(D)-
13.968×(A2)-0.318×(B2)-30.768×(C2 )+0.051×(D2). (2)

PFF [N] = -1163.860 -713.685×(A) -166.391×(B) -379.694×(C) +91.129×(D)+25.001×(A)(B)

+826.460×(A)(C)-1.106×(A)(D) +77.052×(B)(C) -0.542×(B)(D)+21.649×(C)(D)+112.361×(A2)
+7.886×(B2)+504.777×(C2 )-1.171×(D2). (3)

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Materials Research Proceedings 25 (2023) 53-60 https://doi.org/10.21741/9781644902417-7

Optimization
Optimization is carried to get minimum thinning and PFF. The desirability approach is selected
for the study. The desirability function is bounded by 1 and 0, where 1 is acceptable and 0 is
unacceptable response. The optimum levels of pitch, tool diameter, blank thickness and initial
draw angle is determined, which also satisfies the required criteria as given in Tab. 5.
Table 5. Criteria for optimization
S.N. Parameters Criteria Lower bound Upper bound Optimum value
1 Pitch [mm] Within range 0.25 0.75 0.25
2 Tool diameter [mm] Within range 8 12 8
3 Blank thickness [mm] Within range 0.700 1.200 0.854
4 Initial draw angle [0] Within range 35 45 35
5 Max. Thinning [%] Within range 50.30 71.00 55.78
6 PFF [N] Within range 567.76 2441.24 877.08
The desirability value of maximum thinning and PFF is 0.735 and 0.835 respectively. Also, the
average desirability of responses is 0.783, which is close to 1, and hence acceptable.
Confirmation tests
The confirmation tests are performed to validate predictive models and optimization results. The
results of confirmation tests are given in Tab. 6.
Table 6. Results of confirmation tests
Results of predictive model
S.N. Parameters Responses
A B C D Max. Thinning PFF
Predicted Actual Deviation Predicted Actual Deviation
1 0.65 10 0.91 37 70.34 68.77 2.24% 1640.95 1580.04 3.71%
2 0.40 9 0.79 42 69.64 65.87 5.42% 1290.34 1327.25 2.86%
Results of optimized values
1 0.25 8 0.854 35 55.78 54.83 2.80% 877.08 858.38 2.13%
2 0.25 8 0.854 35 55.78 54.98 1.43% 877.08 861.27 1.80%
The results of confirmation tests are within 10% of acceptable range therefore predictive models
and optimization results are valid.
Conclusion
The present paper describes the experimental study on maximum thinning and peak forming force
acting on multi-stage single point incremental forming process. It is observed that initial draw
angle is the most influencing factor for maximum thinning followed by blank thickness. Maximum
thinning decreases with decrease in initial draw angle and increase in blank thickness. While, blank
thickness is the most influencing parameter for peak forming force followed by tool diameter,
pitch, and initial draw angle. It reduces with decreasing all four process parameters. Also predictive
models of second order (quadratic) are developed to predict maximum thinning and peak forming
force. Optimization of parameters has been carried out to get minimum thinning and forming force
and same are verified using confirmation tests.
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Materials Research Proceedings 25 (2023) 53-60 https://doi.org/10.21741/9781644902417-7

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