Recent Investigations on Incremental Sheet Forming: From Fundamentals to Industrial Application Technologies

Abstract

Incremental sheet forming (ISF) is a promising flexible forming process in fabricating low-batch or customized sheet metal parts, and has potentials in reduced process lead time and cost, and increased formability. In the plenary talk, recent investigations on ISF fundamentals and the technologies for ISF industrial application will be presented, which cover tool path algorithms, forming tool development, surface roughness and forming load predictions, new variants of ISF, deformation mechanism of different ISF variants, and several industrial application cases. Finally, an outlook about ISF will be made as well.

1 Introduction

ISF is one of the advanced flexible forming processes appropriate for small batch production of sheet metal parts. Research in the ISF field has been extended to different aspects in recent years, including forming limit, deformation mechanism, forming force, geometric accuracy, surface roughness, and tool path. Duflou et al. [1] found that the dimensional accuracy and formability for a range of materials can be improved through laser-assisted incremental forming process. Araghi et al. [2] proposed a new hybrid forming process by combining ISF and stretch forming, and indicated that noticeable reduction of cycle time and more uniform thickness distribution can be obtained. Silva et al. [3] proposed an analytical model of contact stress based on membrane analysis in the ISF process, by which the cracks were claimed to be caused by meridional tensile stress instead of in-plane shearing stress. Emmens et al. [4] presented an overview of deformation mechanisms that were suggested to explain the enhanced formability of the ISF process. Six mechanisms were suggested as follows: contact stress, bending under tension, shearing, cyclic straining, geometrical inability to grow, and hydrostatic stress. To obtain a better understanding of the shear effect, Lu et al. [5] developed an analytical model based on the analysis of stress state in ISF deformation and proposed an explicit relationship between stress state and forming parameters. Eyckens et al. [6] investigated the straining behavior in the ISF process based on Digital Image Correlation and numerical simulation. Experimental results demonstrated that the dominant mechanism for the cone with a low wall angle is through-thickness shearing, while bending for the cone with a large wall angle. Silva et al. [7] proposed a link between plastic flow, void coalescence and growth, ductile damage, crack opening modes, and fracture toughness in ISF, and proposed an analytical framework to estimate the location of the fracture loci in the principal strain space. Duflou et al. [8] investigated the effects of tool radius, sheet thickness, wall angle, and step depth on forming load, and indicated that the slope of the force curve can be used as a failure prediction indicator. Mulay et al. [9] studied the effects of feed rate, step depth, tool diameter, and sheet thickness on surface roughness, and found that the step depth and tool diameter have significant effects on the surface roughness. Li et al. [10] investigated dimensional accuracy of straight-wall cylinders in multi-stage incremental forming based on an experiment method and mathematic analysis. Besides, some advanced materials have been applied in this field, such as titanium alloy[11], polymers [12], and composite sheets [13].

Although there have been lots of researches targeting to reveal the deformation mechanism, there is a lack of new experimental researches output in recent years. This paper attempts to present systematic investigations of the current state of the art in the ISF process over the last 2 years explored by our team, with the target of throwing light on the future development that can take place using this manufacturing process.

2 Tool Path Algorithm

Different from linear interpolation of conventional tool path, a novel quadratic spiral tool path (QSTP) generation algorithm was proposed by Chang et al. [14]. The new tool path can be generated based on the quadratic interpolation of three neighboring contour lines as shown in Fig. 1, and the points on the tool path can be obtained through the calculation of Lagrange quadratic interpolation.

Fig. 1

Quadratic Lagrange interpolation based on three neighboring contour lines. (Color figure online)

For better understanding of the impact of QSTP, the thickness thinning and geometric accuracy were case-studied by forming typical parts with varied wall angles and compared with conventional spiral tool path (CSTP). Two different materials AA5052 and DC05 were used to evaluate the influences of sheet material properties. As shown in Fig. 2a, the results of two sheet materials indicate similar tendencies but with different deviations, and the part formed by QSTP has better geometric accuracy than that formed by CSTP. Thinning tendencies are similar in both parts and both materials, but better thickness distribution can be obtained in the part formed by QSTP as shown in Fig. 2b. Experimental results confirm that QSTP can improve geometric accuracy, and reduce severe thickness thinning for different sheet materials compared with CSTP.

Fig. 2

Experimental results for different sheet materials using QSTP and CSTP: (a) geometric deviation; (b) thickness thinning. (Color figure online)

3 Analytical Prediction Model

3.1 Analytical Model of Forming Force

In order to overcome the problems of the widely used empirical models for load prediction, other than the regression method by experimental results, the new analytical models to predict the forming force were developed by Chang et al. [15] based on the analytical calculations for the contact area and the through-thickness stress. As shown in Fig. 3, the contact area is an ellipsoid crown surface, and the updated models for calculating the contact area can be developed by sliding the tool configuration along meridional and circumferential directions.

Fig. 3

Schematic illustration of contact area. (Color figure online)

To calculate the through-thickness stress, the membrane approach was conducted as shown in Fig. 4. Along the directions of thickness, circumference, and meridian, the corresponding stress components were considered during membrane analysis. The stress components of a small element at the contact zone were analyzed for the solution of the through-thickness stress in the contact area. By multiplying the updated calculations of contact area with the through-thickness stress, the analytical force models of ISF can be represented by,=

$$ F = \sigma_{t} S = \frac{2}{\sqrt 3 }\frac{2t}{{r + 2.5t}}\overline{\sigma } \frac{\pi r}{2}(h_{1} + r(1 - \cos \alpha )\frac{{\alpha + \arccos \frac{r - hs}{r}}}{{\arccos \frac{{r - h_{1}^{{}} }}{r}}})\,\,\,\,\,\,\,\,\,\,\left( {1} \right) $$

Fig. 4

Membrane approach of ISF process: (a) Overview; (b) stress components; (c) meridional view; (d) circumferential view. (Color figure online)

A series of experiments of typical sheet metal parts with different geometries for different materials with varied process parameters including wall angle, step depth, tool radius, and sheet metal thickness in different typical ISF processes were used to validate the proposed analytical models. It can be seen from Fig. 5 that the predicted forces with different materials in different ISF processes are in good agreement with the measurements. It is concluded that the proposed analytical models are derived from the forming principle of ISF, have wider applicability than the empirical model, and can be used to calculate the forming force and force components along the axial, tangential, and radial directions for SPIF, MPISF, and IHF processes.

Fig. 5

Analytical predictions of forming force with varied process parameters in typical ISF processes. (Color figure online)

3.2 Analytical Model of Surface Roughness

In order to set up an analytical model to predict the surface roughness of the parts formed by ISF, a new mechanism about the evolution of surface roughness was assumed by Chang et al. [16] based on the forming principle of ISF as shown in Fig. 6. The “scallop” on the sheet surface is considered to be related to the uneven distribution of sheet thickness along the meridian direction, which considers elastic deflection and plastic deformation. The uneven distribution of sheet thickness under the tool head was calculated through the geometric relationship between the tool and the sheet as shown in Fig. 7. The surface roughness of the part surface can be calculated by the thickness difference of the “scallop”,

$$ Ra = 0.268Rz = 0.268(\frac{{t_{2} }}{{e^{{\frac{\sqrt 3 }{2}(\frac{1}{K}\overline{\sigma }^{B} )^{\frac{1}{n}} }} }} - t\cos \alpha )\,\,\,\,\,\,\,\,\left( {2} \right) $$

Fig. 6

Three steps of surface roughness evolution during incremental sheet forming. (Color figure online)

Fig. 7

Actual relationship between tool and sheet. (Color figure online)

A series of experiments for surface roughness of a conical part with varied process parameters for different materials have been conducted to validate the proposed models. As shown in Fig. 8, the predicted values of surface roughness are in good agreement with the measurements. The comparison between the calculated and measured results shows that the proposed analytical models maintain high prediction accuracy, which considered the effects of tool radius, wall angle, step depth, sheet thickness, and material properties. Besides, the new models are more accurate with wider applicability than the current geometry-based models, and can be used to calculate the surface roughness Ra and Rz under different process parameters and sheet materials.

Fig. 8

Variation of surface roughness under varied process parameters for different materials. (Color figure online)

3.3 Analytical Model of Twisting Angle

Revealing the twisting mechanism in ISF is of great importance for understanding the deformation mechanism and controlling the deformation stability. As shown in Fig. 9, the mechanism of the twisting phenomenon, proposed by Chang et al. [17], is that the uneven through-thickness stress distribution under the tool head leads to the uneven distribution of circumferential friction stress along the meridional direction, which generates a torque that causes the twisting of the elements on the sheet metal. The value of dσt/dɑ determines the direction of the torque and the direction of twisting.

Fig. 9

Schematic view of twisting phenomena: (a) 40° wall angle; (b) forward twisting; (c) 65° wall angle; (d) reverse twisting. (Color figure online)

An analytical model in predicting twisting angle was developed based on membrane analysis, which can be represented as

$$ \begin{gathered} \beta = \frac{{\sqrt 3 \mu_{\theta } \ln \cos \alpha }}{2}\frac{{d\sigma_{t} }}{d\alpha } \hfill \\ \hfill \\ = \frac{{2r_{t} t_{o} \mu_{\theta } \sin \alpha (\ln \cos \alpha + n) + 2.5nt_{0}^{2} \mu_{\theta } \sin (2\alpha )}}{{(r_{t} + 2.5t_{0} \cos \alpha )^{2} }}K(\frac{2}{\sqrt 3 }\ln \frac{1}{\cos \alpha })^{n} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {3} \right) \hfill \\ \end{gathered} $$

A series of experiments on the twisting angle of truncated pyramid parts with varied process parameters and different materials have been conducted to validate the analytical model. As shown in Fig. 10, for a specified part, a small wall angle causes positive twisting angle, while a large wall angle causes negative twisting angle. It is also found that the analytical value is in good agreement with the measured values for varied process parameters and different materials, with the average numerical measurement error of 15.6%.

Fig. 10

Variations of twisting angle for different process parameters and materials: (a) varied wall angles (AA5052); (b) varied wall angles (DC05); (c) varied tool radius (AA5052); (d) varied tool radius (DC05). (Color figure online)

4 New Variants of ISF

To improve the surface quality and formability of low-ductility metallic sheets, a novel three-sheet incremental forming (TSIF) process was proposed. As shown in Fig. 11, the idea of the TSIF process is to put a target sheet with lower ductility between the upper auxiliary (UA) sheet and lower auxiliary (LA) sheet, then the three sheets are fixed together and formed by the forming tool to a geometry. The existence of the UA sheet aims to avoid the direct contact between the tool and target sheet, and the LA sheet is prepared to provide the extra compressive stress to the target sheet and improve the stress state in the contact zone.

Fig. 11

Schematic of TSIF. (Color figure online)

For better understanding forming characteristic of TSIF, the surface quality and forming limit of the target sheet were investigated by experiments for different sheet materials and compared with the conventional single point incremental sheet forming (CISF) process. As shown in Fig. 12, experimental results demonstrate that the surface roughness can be significantly reduced by an average of 80% in the TSIF process compared with that by CISF. Ra of the part formed by TSIF always keeps at a small value with the variation of step depth, indicating that the effect of step depth on Ra of TSIF is obviously less sensitive than that of CISF. Results also prove that the forming limit and fracture strains of AA2024 and AA7075 sheets can be improved dramatically with the extra compressive stress from the LA sheet, which is helpful for low-ductility sheet metal component fabrication.

Fig. 12

Experimental results of different materials for CISF and TSIF: (a) surface roughness; (b) fracture strain. (Color figure online)

5 Process Window

5.1 Formability for ISF with High-Speed Tool Rotation

ISF with high-speed tool rotation is another promising alternative for forming low-ductility sheet metals. but high-speed friction between the tool and the deforming sheet metal might cause bad surface quality, and process parameters have contradictory effects on formability and surface quality. To solve this puzzle, the effects of four factors on forming temperature and surface quality were analyzed by Wang et al. [18] through orthogonal experiments for a truncated cone with a constant wall angle of AA2024-T. A process window for ISF with high-speed tool rotation was obtained to have a higher forming temperature for better formability with reasonable surface quality. Orthogonal analysis results on forming temperature show that rotating speed has the greatest influence, followed by step depth.

By collecting the experimental results of cutting (red point) and no cutting (blue point), Fig. 13 demonstrates the safe area (blue area) and the cutting area (orange area), which shows that the ranges of rotating speed and step depth can be used to define the process window to avoid cutting. Thus, the optimal area (green area) which can guarantee high forming temperature without cutting is provided in Fig. 13. Besides, the applicability of the process window proposed was verified by another truncated cone with varied wall angles using AA2024-T and AA5052-H32. Figure 14 shows the maximum wall angle with process parameters set within the optimal area, and the formability of two aluminum alloy sheets was improved.

Fig. 13

Process window. (Color figure online)

Fig. 14

Measured maximum wall angles of AA2024-T3 and AA5052-H32. (Color figure online)

5.2 Geometric Deviation

One of the key challenges for ISF is geometric accuracy, especially for complex sheet metal parts. A typical non-axisymmetric part of AA5052 with the stepped feature was studied by Dai et al. [19] through orthogonal experiments with 4 parameters in 4 levels to determine the optimal process parameters for better geometric accuracy.

Three-pass ISF was developed to form the stepped feature as shown in Fig. 15. An attempt was made to change the forming process sequence, in which the stepped flank is formed prior to the stepped plane, and later the stepped plane is formed in several passes. Experiments demonstrate that a larger angle is helpful in subsequently forming the upper sidewall and the stepped plane, respectively.

Fig. 15

Three-pass ISF of the stepped feature. (Color figure online)

To further improve the local geometric accuracy, the angle of the stepped flank and the height of the stepped plane need to be compensated in Multi-pass ISF. Based on the local geometric deviation and the deflection mode at the corner between the stepped plane and the stepped flank, the compensation scheme of the intermediate configuration in each pass is shown in Fig. 16. Based on the proposed methodology, the geometric accuracy of the non-axisymmetric part with the stepped feature has been obviously improved, particularly at the stepped feature as shown in Fig. 17.

Fig. 16

Compensation scheme of the intermediate configuration for each pass. (Color figure online)

Fig. 17

Sectional profile and the error of new multi-pass ISF with toolpath compensation. (Color figure online)

6 Outlook

A systematic review of the latest developments of the ISF process was conducted, and this provides a feasible direction for future research. The process fundamentals in terms of process window, analytical models, tool paths and new variants of ISF were systematically introduced. The new tool path and variants of ISF have the capability of extending the process window for industrial application and obtaining parts with some specific requirements. Analytical models developed based on membrane analysis have the ability to accurately predict the forming force, surface roughness, and twisting angle, and provide feasible solutions to better control the forming quality of parts formed by ISF. The investigations on the process window are significant for improving the formability and geometric accuracy of sheet metal for further industrial application. The application of ISF has increased significantly, which will provide directions for the development of flexible industrial systems based on ISF.