Numerical investigation of incremental forming process of AISI 304 stainless steel

Abstract

In recent years, sheet metal forming has gained great importance in the production process. To improve the quality of the manufactured products and reduce the production cost, incremental forming, particularly that adapted to small pieces, can be a good alternative. It is within this scope that the present study was carried out. This research work deals with the finite element simulation of the incremental forming process applied to achieve a trunk cone. It also examines the effects of the geometrical parameters of the tool and of the sheet on the forming force, stress distribution and thinning of the sheet. The obtained results show that the thinning of the sheet is more important in the case of the continuous tool path (about 0.2 mm), compared to that in the discontinuous one.

Introduction

The forming processes for sheet metal are one of the most important processes in the industrial sector. Among these processes, we may cite the single incremental forming which is a strategic process allowing to reduce the cost of producing small pieces or manufacturing prototype [1–3]. Indeed, this process consists in deforming the sheet metal with a hemispherical tool according to a predefined tool path [4]. It makes the forming sector more flexible, making it possible to produce pieces that cannot be realized by conventional processes, as it is the case of manufacturing single-use pieces used in the medical field [5]. In fact, the incremental forming process is characterized by its high flexibility, low tooling cost and its ability to realize complex shapes [6–10]. Although manufacturers use materials having higher formability to produce pieces by incremental forming (e.g. aluminium alloys) [1,11,12], many studies focused on the forming of other types of materials. For example, it is possible to deform Titanium sheets through lubrication to increase their formability [5]. Franzen et al. [4] evaluated the formability limit of PVC sheets as a function of different process parameters. The results they obtained show that the forming of PVC sheets is interesting for a high vertical increment. Conte et al. [13] studied the effect of cutting depth, inclination angle and process temperature on the forming of composite materials. Other studies focused on the hot forming of magnesium alloys [14]. They concluded that the forming forces decrease with the rise of the process temperature. Besides, the stainless steel AISI 304 can be used to manufacture prostheses because of its higher resistance to corrosion, lower oxidation and more reduced cost, compared to Titanium. Moreover, this type of steel has high formability due to its excellent mechanical properties. Chezhian et al. [4] applied the incremental forming process on a stainless steel sheet with a thickness of 0.6 mm to investigate its formability and measure its stress and thickness after forming. They showed that feed rate influences remarkably the forming force, the formability and the thinning of the used sheet. Several studies were conducted to evaluate the effect of certain parameters on the forces generated by the process [15,16]. Ambrogio et al. [17] revealed that the forming forces are proportional to the tool dimension, the vertical step, the sheet thickness and the forming wall angle. Other researches demonstrated that the adjustment of the rotation speed and the use of lubrications are efficient in the incremental forming process and allow reducing the forming force [12–22]. Some studies [14,15] examined the effect of the vertical increment, the tool diameter and the rotational speed on the forming force for AISI 304 stainless steel sheets. The results obtained in these works proved that the forming forces can be enhanced by increasing the tool diameter and the vertical increment and that they decrease with high rotational speeds. Concerning the thinning of the sheet, Jeswiet et al. [6] developed a new tool path and showed that the thickness of the formed sheet decreases at a small-cone angle. Hagan et al. [23] investigated the effect of vertical increment on the quality of formed surfaces. They concluded that the larger the vertical increment is, the more poor the surface quality will be. Ambrogio et al. [24] analysed the influence of the tool diameter and the depth of cut on the dimensional accuracy of the pieces obtained by incremental forming. Their results revealed that the error was minimal for the lowest possible diameter and vertical increment.

In order to reduce the number of experiments performed to develop and size the tools of this complex process, manufacturers still use more powerful numerical devices to simulate the forming operation and optimize the process parameters such as tool diameter and vertical step.

Nowadays, the most discussed topic in the incremental forming process is sheet thinning (how to achieve a uniform thickness of the piece to be manufactured after incremental forming).

This manuscript studies the effect of the incremental forming process parameters on the evolution of the forming force, stress distribution and blank thinning.

Modelling of the single-point incremental forming process (SPIF)

Incremental forming is a process of forming, by plastic deformation, sheet metal with small-sized tool. The newly-introduced forming processes are based on local plastic deformation of sheets and allow the production of complex-shaped pieces. The tool path was designed using the CAD/CAM software (discontinuous trajectory) and programmed (continuous) using Matlab.

Presentation of the final manufactured piece

In this study, the final shape of the piece obtained after simulation must be of trunk cone shape with precise dimensions, as shown in Figure 1.

Figure 1.

Dimensions of the piece to be manufactured.

Determination of the tool path

Generally, the geometry of the mechanical part produced by the incremental forming process depends on the used tool path. In this context, the main objective of the present work is to design the trajectory describing the geometry of the final product by applying mathematical equations and using CAD/CAM software.

Case of a continuous path

Theoretical study

The movement of tool forms a spiral path. The spiral is a curve drawn on a cone whose base is a circle, as shown in Figure 2.

Figure 2.

Cylindrical coordinate system and associated basis .

The path tool is the whole position occupied by point M. To represent that of the propeller in Cartesian coordinates, the parameters on which the path tool depends should be studied. These parameters are presented below:

Rotation angle of a point M on the trajectory (1) Vertical step expressed as a function of the height of the piece shape and the maximum inclination angle. (2) Radius of the piece to be manufactured given by the following expressions: (3) (4) (5)

The components X, Y and Z expressed on the Cartesian basis as follows: (6) (7) (8)

Tool path correction on the tool radius

The use of a continuous path (spiral) depends on the corrections made by Equations (7) and (8) applied to obtain the final shape of the piece to be manufactured. New parameters were used and programmed into the equation of the tool motion to obtain the new path. These parameters are defined in Figure 3.

Figure 3.

Geometry of required final shape.

Then, the new equations of X′ and Y′ after were applied: (9) (10)

With:

is the tool radius.

Figure 4(a) shows the tool path without correction and that obtained after correction using the new expressions of X and Y.

Figure 4.

Tool path: (a) continuous, (b): discontinuous.

Case of a discontinuous path (circular)

The tool path of the trunk cone part can be determined using the CAD/CAM software, as shown in Figure 4(b).

Mechanical characteristics of the sheet metal

In the simulation, each element was associated to its mechanical properties. The sheet is made of stainless steel AISI 304 L. Their mechanical properties are presented in Table 1.

Table 1.

Mechanical properties of stainless steel AISI 304 L.

	Density	Young’s modulus (MPa)	Tensile strength R _m (MPa)	Yield strength R _p0.2 (MPa)	Poisson's ratio	Elongation A (%)
Stainless steel AISI 304 L	7800	200,000	650	350	0.3	50

The applied law of strain hardening is Swift's law: with K = 1506 MPa, and n = 0.5842.

Geometrical model description

The geometrical model used to simulate the incremental forming process is presented in Figure 5. It includes the following elements:

Sheet metal: circular sheet metal having an external diameter of 50 mm and a thickness e = 1 mm.

Lower platen: rigid and circular shape with an external diameter D _m = 60 mm, an internal diameter d _m = 43 mm, a thickness of 10 mm and a roundness equal to 0.75 mm.

Top platen: rigid and circular shape with diameter d _s = 43 mm and thickness equal to 5 mm.

Tool: (rigid) Two hemispherical punches of diameter D = 10 mm and D = 6 mm. were used.

Figure 5.

Incremental forming device.

Loading conditions

The loading conditions of the developed model are defined by Figure 6. A clamping pressure applied (P _s) by the top platen on the sheet is about 70 MPa.

Figure 6.

Device loading conditions.

The imposed boundary conditions eliminated all degrees of freedom from the lower platen. It was assumed that the contact surface between the lower platen and the blank has a friction coefficient of 0.1. The sheet was blocked on the lower platen by moving the top platen in the direction . The friction coefficient of the contact between the top platen and the sheet was equal to 0.1. The tool was placed at the six degrees of freedom of the sheet/tool contact point. The coefficient of friction between the tool and the sheet was 0.1 [1,2].

Mesh generation

Mesh generation is a very important phase in the field of finite element calculation. Indeed, a high-quality mesh is essential to obtain an accurate and correct calculation result as it improves the convergence, the accuracy of the solution and, especially, the computation time. Good mesh quality can be obtained by the minimization of distorted features and the good resolution in regions presenting a strong gradient. A good mesh should also be sufficiently smooth. The mesh of the used sheet is linear hexahedral of type C3D8R (reduced integration). The latter contains 4500 elements and 9002 nodes and is refined until an element size of 160 µm at the contact region. The elements used in this mesh form a standard integration schema (Figure 7).

Figure 7.

Mesh of sheet metal.

Simulations used three parameters that are the tool size, the vertical step and the tool path. For the tool diameter and the tool path, they have two levels. The vertical step has three levels. Table 2 gives the different parameters of the process and their levels. For all the studied cases, the feed rate of the tool was set to 2000 mm min⁻¹. The total processing durations are around 9 min and 30 s for vertical steps of 0.1, 3 min and 10 s for vertical steps of 0.3 and 2 min for vertical steps of 0.5.

Table 2.

Process parameters and their levels.

Parameters	Levels
Tool diameter D (mm)	6, 10
Vertical steps (mm)	0.1, 0.3 and 0.5
Tool paths	Continuous and discontinuous

Results and discussions

The aim of the simulation is to identify and analyse the effect of the main parameters of the used tool geometry, vertical step and tool path strategy on the evolution of forming force and stress distribution and sheet thinning.

Evolution of forming forces

Effect of tool diameter

The curves presented in Figures 8 and 9 depict the evolution of the lateral forming force ( , ) supplied by the utilized tool as a function of the time relative to the discontinuous tool path respectively by a fixed vertical step and a variable tool diameter of D = 6 mm and D = 10 mm.

Figure 8.

Evolution of the lateral forces at different tool diameters with a step = 0.5 mm.

Figure 9.

Evolution of the lateral forces at different tool diameters with a step = 0.5 mm.

From the two figures, it can be observed that the value of maximum force obtained for a tool diameter of 10 mm attains a value of about 1565 N. However, for a tool diameter of 6 mm, the maximum force does not exceed 1184 N.

It is also clear that, in the case of trunk cone shape (axisymmetric part), the evolution of force is of the same order as that of (to the nearest sign). Therefore, it will be sufficient to present force along a single axis to highlight the influence of the tool parameters on the forming forces. The required incremental forming force depends on many parameters including tool size. Indeed, the tool diameter increase provokes an increase in the amplitude of forming force. This proportional relationship corresponds to the contact surface between the tool and sheet (increase of the contact surface between the tool and sheet). It is also evident that the forming force changes also as a function of the tool diameter variation.

Figure 10 shows the evolution of the incremental forming axial forces provided by a specific tool during forming at different tool diameters, with a fixed cutting depth . The variation of the vertical force is proportional to the tool size. This study confirms the work conducted by Duflou et al. [15].

Figure 10.

Evolution of the axial tool forces Fz at different tool diameters with a step = 0.5 mm.

This force reaches a maximum value of 3185 N at a tool diameter equal to 10 mm. However, at a diameter of 6 mm, its maximum value is almost equal to 2446 N.

Effect of vertical increment

One of the important forming process parameters is the vertical increment size. Several simulations were carried out to study the influence of vertical step on the forces provided by the tool.

Figures 11 and 12 describe the evolution of force components and obtained by the numerical simulation of a discontinuous path tool. The tool diameter was fixed to 6 mm as well as at a variable axial increment .

Figure 11.

Evolution of lateral forces at different vertical pitches with a tool diameter D = 6 mm.

Figure 12.

Evolution of axial forces at different vertical steps with D = 6 mm.

The maximum lateral force necessary to form the trunk cone with a vertical step size of 0.5 mm is approximately 1184 N greater than that obtained with a step size of 0.1 mm.

As demonstrated in Figure 12, the forming force increases with the rise of the vertical step size. In the case of a vertical step equal to 0.5 mm, the maximum axial force is quite large (2446 N), which shows that the force increase is proportional to the cutting depth. When the vertical step is very small, the tool penetrates less into the sheet, which explains the lower vertical force compared to that in a larger vertical step. Experimental results concerning the variations of the curves of the same gaits and obtained by Saidi et al. [25], Filice et al. [26] and Duflou et al. [17] confirm those provided in this study.

Effect of tool path

Figures 13 and 14 represent the evolution of forces and obtained by simulating two types of tool path: continuous (spiral) and discontinuous (circular). The lateral force of the discontinuous path attains a maximum value of 802 N which is inferior to that of the continuous path (about 1300 N).

Figure 13.

Evolution of lateral forces at different tool paths with D = 6 mm and .

Figure 14.

Evolution of axial forces at different tool paths with D = 6 mm and

The axial force corresponding to the spiral path (continuous) is more important than that of the discontinuous path. It admits a maximum value of about 1900 N, as shown in Figure 14. Indeed, the latter decreases and attains a value of 1200 N for the circular path (discontinuous). It can be also noticed that the axial forces exerted by the tool are more stable in the case of a continuous path, compared to force obtained using a discontinuous path. These results were confirmed by Abdelkader et al. [13].

Table 3 shows the maximum values corresponding to the maximum forces in the lateral (

and

) and axial

directions.

Table 3.

Distribution of the maximum forces at different tool diameters and vertical steps.

Path type	Material	Tool diameter D (mm)	Vertical steps (mm)	(N)	(N)	(N)
Discontinuous path	Stainless steel AISI 304L	10	0.5	1566	1576	3185
		6	0.5	1184	1140	2446
		6	0.3	993	983	1840
		6	0.1	802	798	1226
Continuous path		6	0.1	1300	1286	1868

Evolution of stress

This section focuses on the influences of the tool diameter, vertical step and tool path on the stress distribution after incremental forming. Figure 15 shows the profile chosen to determine the Von Mises stress distribution after sheet metal forming. The profile was applied along the longitudinal direction .

Figure 15.

Profile used to determine the stress distribution.

It is obvious that the variation of the tool diameter affects remarkably the stress distribution. Indeed, the stress increases with the decrease in tool diameter. It can be also seen, from Figure 15, that the increase in stress is proportional to the cutting depth increase. The maximum achieved stress value is more important at vertical step equal to 0.5 mm at a vertical step equal to 0.1 mm. Figure 16 shows the stress curves obtained at different tool diameters, vertical steps and tool paths.

Figure 16.

Von Mises stress distribution, (a): tool diameter, (b): vertical step, (c): tool path.

Figure 17 shows that the stress distribution can be divided into four main areas:

Area 1: It is the area of the clamping of the sheet. In area 1, the stress does not exceed the value of 200 MPa because the force applied by the sheet clamping device remains the same during all simulation tests. It is also noticed that the stress depends on the force of the sheet clamping. We may conclude that the reduction of the clamping force allows reducing the stress (risk of sliding).

Area 2: It represents the contact area between the die, the sheet and the tool: the tool exerts moderate forces on the sheet metal, which causes an increase in the contact stress (about 400 MPa). In fact, the smaller the diameter of the tool is, the more important the contact stress will be.

Area 3: It is the contact area between the tool and the sheet. In area 3, the stress reaches a maximum value of about 950 MPa. The main parameter that influences the stress distribution in this area is the stamping depth. In conclusion, although the increase in Von Mises stress rises level of plastic deformation, it causes the sheet thinning. In other words, the thicker the sheet is, the greater the Von Mises stress will be.

Area 4: In this area, the Von Mises stress remains constant during the incremental forming test at about 76 MPa because the tool penetrates the ends (at the edges) of the piece, but it does not move in this area.

Figure 17.

Distribution of mean stress at different areas of the piece.

Table 4 shows the stress values and the thickness of the sheet at the different above-described areas.

Table 4.

Distributions of Von Mises stress and the sheet thickness at different areas of mean stress distribution.

Area	Thickness (mm)		Stress (MPa)
	Max	Min	Max	Min
1	1	0.92	172	133
2	0.92	0.5	363	81
3	1	0.4	951	76
4	1	1	76	75.9

Based on the results presented in Table 3, the thinning phenomenon of the sheet (studied in the following sub-section) can be explained. Indeed, the maximum stress provides the minimum thickness.

Thinning of the sheet metal

The geometry of the final product is one of the most important parameters in the numerical simulation of incremental forming process. To guarantee the piece final geometry that is satisfactory and reliable from a practical point of view in domains where certain conditions (force, pressure, etc.) may cause the breaking of the piece, it is necessary to highlight the phenomenon of the sheet thinning. This phenomenon remains a topic widely studied by the research community.

In the conducted simulation, the piece thickness was determined from the normal distance between the inside and outside surface of the sheet metal over the entire section (Figure 18). Figure 19 shows its distribution and how the latter is affected by the tool diameter variation, the vertical step and the tool path.

Figure 18.

Characterization of the thinning areas.

Figure 19.

Evolution of the sheet thickness at different conditions.

Figure 19 exposes the relative evolution of the sheet thickness. Three parts can be distinguished: (AC), (CD) and (DB). The final product has an axisymmetric shape. It presents two identical parts (AC) and (DB) whose thickness is reduced equally. For this reason, the present study focuses only on two areas.

Area 1 (AC and DB): It is an active area corresponding to the contact surface with the tool. It presents a major reduction in thickness (major thinning). The important thinning is caused by the penetration of the tool, which makes the material move along the path. The thinning can be further explained by the increased strain and stress required to plasticate the material. The thickness decreases from its initial value e = 1 mm until reaching the minimum value equal to 0.4 mm for a discontinuous path (the thickness reduction is about 60%). For a continuous path, the thickness decreases by 0.27 mm, representing a reduction of about 70%. The large minimization in the thickness of the plate causes problems in the domains of use as it cannot be adapted to the forces and pressures. This problem of thinning involves the rupture of the piece when used.

Area 2 (CD): This area has no contact with the tool. Indeed, sheet thickness remains constant and equal to 1 mm (no thinning). No force is applied on this area because the tool moves to the sheet edges, but it does not touch the centre of the piece. Obviously, the thickness remains approximately constant due to the absence of stress (or insignificant stress). These results are comparable to those obtained by Filice et al. [27].

In conclusion, a discontinuous path gives lower sheet thinning, compared to a continuous path (the thickness of the discontinuous path is twice larger than that of the continuous path). It is, therefore, necessary to take this phenomenon into account in order to reduce the sheet thinning or make it almost uniform. It is assumed that the single-point incremental forming process (SPIF) enhances considerably the piece final quality (sheet thinning).

Because of this problem and in order to attain almost uniform thickness, in the performed simulations, the TPIF two-point incremental forming process was applied. The tools used in the two-point incremental forming process are shown in Figure 20.

Figure 20.

Device used in two-point incremental forming process TPIF.

From Figure 21, it can be noticed that the thickness remains constant in the centre of the sheet and decreases locally at the edges of the piece, resulting in the thinning problem.

Figure 21.

Sheet thinning: case of two-point incremental forming process TPIF.

It may be deduced that the thinning problem does not depend on the choice of the incremental forming process, but rather on a path that allows the tool to deform the centre of the piece.

Comparison of the theoretical profile (required) and the simulated profile

After simulations, the numerical profile was determined for the two continuous and discontinuous paths on the inside surface of the piece and compared to the theoretical (required) profile.

The results obtained by simulating numerically the incremental forming and varying the main applied parameters (tool diameter, vertical step, tool path), the simulated profiles at the different paths for a step equal to 0.1 mm and a tool diameter equal to 6 mm were obtained.

It is also clear that the discontinuous path provided the best final geometry of the trunk cone shape, as shown in Figure 22. The error between the required and simulated profile is in the centre of the final shape. Therefore, the continuous path allowed obtaining an unsatisfactory geometry because of the force applied by the tool.

Figure 22.

Comparison of theoretical (required) and simulated profile.

Figure 23 shows the final Trunk Cone shape at different views, obtained for a discontinuous path, for a cutting depth equal to 0.1 mm and a tool diameter equal to 6 mm.

Figure 23.

Final shape of the piece cone trunk.

Conclusions

In this work, numerical simulations based on the variation of some main parameters (tool diameter, depth of cut and tool path) were performed. The influence of these parameters on the force evolution, stress distribution and sheet thinning was also examined. The obtained results reveal that:

The tool diameter, the vertical step and the tool path affected significantly the evolution of forces and stress distribution.

The axial force was generated and, at some values, it stabilized along the path.

The vertical force was more stable in the case of a continuous trajectory.

In the case of a continuous path, the thickness decreased by 70%, compared to its initial value.

The decrease in tool diameter resulted in a stress increase.

The increase in stress was proportional to the axial increment.

Stress distribution presented the problem of sheet thinning. Indeed, an increase in stress led to a significant reduction in thickness.

The numerical simulation accounts for the tool path, vertical step and tool diameter on the final shape of the part.

The discontinuous path provided a better final geometry of the piece.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the author(s).

References

Kim

Park

Effect of process parameters on formability in incremental forming of sheet metal. J Mater Process Technol. 2002;130:42–46.

Park

J-J

Kim

Y-H.

Fundamental studies on the incremental sheet metal forming technique. J Mater Process Technol. 2003;140(1–3):447–453.

Liu

Daniel

et al. Simulation and experimental observations of effect of different contact interfaces on the incremental sheet forming process. Mater Manuf Processes. 2014;29(2):121–128.

Chezhian Babu

Senthil Kumar

VS.

Experimental studies on incremental forming of stainless steel AISI 304 sheets. Proc Inst Mech Eng, Part B: J Eng Manuf. 2012;226(7):1224–1229.

Ambrogio

De Napoli

Filice

et al. Application of incremental forming process for high customised medical product manufacturing. J Mater Process Technol. 2005;162:156–162.

Jeswiet

Micari

Hirt

et al. Asymmetric single point incremental forming of sheet metal. CIRP Ann. 2005;54(2):88–114.

Cao

et al. An efficient method for thickness prediction in multi-pass incremental sheet forming. The Int J Adv Manuf Technol. 2015;77(1–4):469–483.

Zhang

Xiao

Guo

et al. Warm negative incremental forming of magnesium alloy AZ31 sheet: new lubricating method. J Mater Process Technol. 2010;210(2):323–329.

Pandre

Morchhale

Kotkunde

et al. Processing of DP590 steel using single point incremental forming for automotive applications. Mater Manuf Processes. 2021;36(14):1658–1666.

10.

Şen

Taşdemir

Seçgin

. Investigation of formability of HC380LA material via the TPIF-RL incremental forming method. Ironmak Steelmak. 2020;47(10):1199–1205.

11.

Jeswiet

Young

Forming limit diagrams for single-point incremental forming of aluminium sheet. Proc Inst Mech Eng, Part B: J Eng Manuf. 2005;219(4):359–364.

12.

Jeswiet

Hagan

Szekeres

Forming parameters for incremental forming of aluminium alloy sheet metal. Proc Inst Mech Eng, Part B: J Eng Manuf. 2002;216(10):1367–1371.

13.

Abdelkader

Bahloul

Arfa

Numerical investigation of the influence of some parameters in SPIF process on the forming forces and thickness distributions of a bimetallic sheet CP-titanium/low-carbon steel compared to an individual layer. Procedia Manuf. 2020;47:1319–1327.

14.

Ambrogio

Duflou

Filice

et al. Some considerations on force trends in incremental forming of different materials, AIP Conference Proceedings, American Institute of Physics. 2007:193–198.

15.

Duflou

Tunckol

Szekeres

et al. Experimental study on force measurements for single point incremental forming. J Mater Process Technol. 2007;189(1–3):65–72.

16.

Jeswiet

Duflou

Szekeres

Forces in single point and two point incremental forming. Adv Mater Res, Trans Tech Publ. 2005:6–8;449–456.

17.

Ambrogio

Filice

Micari

A force measuring based strategy for failure prevention in incremental forming. J Mater Process Technol. 2006;177(1–3):413–416.

18.

Durante

Formisano

Langella

et al. The influence of tool rotation on an incremental forming process. J Mater Process Technol. 2009;209(9):4621–4626.

19.

Bagudanch

Centeno

Vallellano

et al. Forming force in single point incremental forming under different bending conditions. Procedia Eng. 2013;63:354–360.

20.

Palumbo

Brandizzi

Experimental investigations on the single point incremental forming of a titanium alloy component combining static heating with high tool rotation speed. Mater Des. 2012;40:43–51.

21.

Baharudin

Azpen

Sulaima

et al. Experimental investigation of forming forces in frictional stir incremental forming of aluminum alloy AA6061-T6. Metals. 2017;7(11):484.

22.

Hussain

Gao

Hayat

et al. Tool and lubrication for negative incremental forming of a commercially pure titanium sheet. J Mater Process Technol. 2008;203(1–3):193–201.

23.

Hagan

Jeswiet

Analysis of surface roughness for parts formed by computer numerical controlled incremental forming. Proc Inst Mech Eng, Part B: J Eng Manuf. 2004;218(10):1307–1312.

24.

Ambrogio

Costantino

De Napoli

et al. Influence of some relevant process parameters on the dimensional accuracy in incremental forming: a numerical and experimental investigation. J Mater Process Technol. 2004;153:501–507.

25.

Saidi

Boulila

Ayadi

et al. Experimental force measurements in single point incremental sheet forming SPIF. Mech Ind. 2015;16(4):410.

26.

Filice

Ambrogio

Micari

On-line control of single point incremental forming operations through punch force monitoring. CIRP Ann. 2006;55(1):245–248.

27.

Ambrogio

Filice

Gagliardi

et al. Three-dimensional FE simulation of single point incremental forming: experimental evidences and process design improving. VIII International Conference on Computational Plasticity (COMPLAS VIII). CIMNE, Barcelona, 2005.