Evaluation of surface roughness and wall thickness in the incremental stamping process with variation in the degrees of freedom of the contact tool

In this study, the performance of a rotating semi-spherical tool (with two degrees of freedom) is compared with another rigid semi-spherical tool, both with a diameter of 8.0 mm. The stamping is performed on AA1100 aluminium blanks with a thickness of 0.8 mm, using a helical strategy and single point incremental friction. Our results show that the rigid tool presents the best working conditions for the AA1100 aluminium sheets because it generates less roughness in the stamped parts, when compared with the rotating tool (~54% lower in the final average of the R a roughness). The scanning electron microscopy image reveals the presence of adhesion both on the contact tip of the rotational tool and on the rigid tool, showing that the adhesive wear mechanism is predominant in the single point incremental forming process and influences the final roughness of the stamping cones.

the conformation limit of a material (maximum angle of the wall) based on the law of sines, according to Eq. (1): where ) is the initial plate thickness, " is the fracture depth, is the radius of the generatrix and " is the thickness in the fracture region, as shown in Error! Reference source not found.. Despite several previous studies being related to incremental stamping, the analysis of the influence of the degrees of freedom of the contact tool on the surface roughness and wall thickness has not yet been evaluated for AA1100 aluminium sheets. The purpose of this work is to employ two tools (rigid and rotating) with different degrees of freedom in the ISF process to investigate their influence on the variation of the roughness and thickness of AA1100 aluminium sheets. Additionally, the adhesion at the tip of the tools is analysed to verify its influence on the finishing of the parts.

MATERIALS AND METHODS
The sheet material used in the incremental stamping was characterised via optical emission spectroscopy as an AA1100 aluminium alloy. The chemical composition of the main elements of this alloy can be seen in Table 1. When comparing the results with other authors [0, 0], it is observed that the yield limit is close to the presented resistance limit.

Fig. 2. Behaviour of stress (MPa) versus strain (mm/mm)
For the tests of the SPIF process, rigid and rotating tools (with two degrees of freedom) were used in the 0.8 mm-thick aluminium sheets. The tools (rotating and rigid) were built using the AISI 4140 material by the conventional machining process, both with an 8.0 mm diameter working region. Posteriorly, the thermal treatment of beneficiation was carried out (tempering followed by quenched in both tools). In the tempering, the austenitisation temperature was 855 °C and the material was cooled in oil. To relieve tension, the material was subjected to quenching for 2 h at 200 °C. Error! Reference source not found. shows both tools. (c) Expanded view of the rotating tool with two degrees of freedom From the compound movement of the contact between the tool and plate, the rotating tool has two degrees of freedom. One degree of freedom is due to the circular translation movement. In addition to this, it can act, nominally, with a second degree of freedom around its own axis ("z" axis), because as the tool is free in the spindle and has two bearings, the rotation movement of the rotate shaft does not influence in the rotation movement of the metal rod, if it occurs.
Incremental stamping was performed with a computer numerical control machining centre (Travis model M-800). The process parameters are shown in Table 2. Solid petroleum jelly was used as a lubricant due to its better performance [0] compared to other lubricants. To obtain the maximum angle of the wall, tests were carried out in the SPIF process with a single pass in a truncated cone in the AA1100 alloy (Error! Reference source not found.). In addition to the tests on the truncated cone, three straight cones were stamped with each tool for analysis of the roughness and thickness. The single-factor analysis of variance (ANOVA) was used to test the hypothesis.
The surface roughness was evaluated on the inside of the cones, using the roughness parameters (Ra and Scanning electron microscopy (SEM) together with energy dispersion X-ray spectroscopy (EDS) was carried out to investigate the surface morphology and its chemical composition using a JEOL model JSM-IT300 with IT 300 software and an OXFORD/X-MaxN detector with Aztec software.   The tests made it possible to verify that the rotating tool with two degrees of freedom showed a greater

Experiments with straight cone geometry
After determining the maximum angle of the wall with the truncated cone test, an attempt was made to stamp a straight cone with the largest possible wall angle. The tests started with the largest angle of the wall found in the truncated cone test, with less than a 3º margin. Figure 6 shows the results of the stamped cones.
The tests were interrupted when the fracture occurred (indicated by the red arrows in ).

Fig. 6. Straight cones with fixed wall angle of (a) 75º, (b) 70º and (c) 65º
Under the conditions proposed for the tests, it was not possible to stamp the straight cone with the maximum angle of the wall found in the truncated cone test, as shown in Fig. 6. According to [0], a straight cone with a fixed inclination has a lower deformation limit in relation to the truncated cone, as the instantaneous inclination varies according to its depth (Fig. 7).
"F" is the forming force and "N" is the instantaneous position of the tool during the process. As shown in Fig. 7(a), the resulting force "FSinθ" acts only on the LN segment, which represents a small part of the MN segment. In contrast, in Fig. 7(b), the entire MN segment is under the action of the "FSinθ" force, which weakens the segment, contributing to the fracture of the piece [0].  aluminium plates. In the parts stamped with the rotating tool with two degrees of freedom ( Fig. 8(a)), a matte appearance is observed. Unlike the stamped part with a rigid tool ( Fig. 8(b)), where a mirrored surface was observed. The average roughness values (Ra and Rq) obtained in the tests for both tools can be seen in Table 4.  Table 4 shows the average of the results measured for the Ra and Rq roughness on the inner surface of the cones. Figure 9 presents the average of the measured roughness.  The rigid tool provided lower values of roughness (Ra and Rq) in the stamped parts, when compared to the rotating tool with two degrees of freedom (Fig. 9). Although the tools have the same apparent contact area, due to the identical diameter and the use of the same incremental stamping parameters, it is believed that the working condition imposed on the tool/plate interface was different for each tool. This explains the slight variation in roughness, since, in the tests performed, the rotation on the machine's spindle was zero (zero rpm), which made it possible for both tools to move freely in the spindle (spindle). As the rotary tool with two degrees of freedom has free rotation provided by the bearings, it is subject to friction by rolling with possible translation sliding, which influences the real contact area between the tool/plate tribological pair. In turn, the rigid tool is only subject to sliding friction in the actual contact area at the tool/plate

Roughness and thickness of the parts
The greater roughness on the internal surface of the cone occurred due to the friction in the contact located between the tool and the plate, and, due to the combined action of rolling and sliding friction, the roughness increased according to the freedom of rotation of the tool tip.
The F test for ANOVA (Table 5) showed that statistically the arithmetic means of the values obtained in the Ra (µm) experiments are equal, since the value obtained for the F factor was below the F-critical value.
where T . is the minimum final thickness of the plate, T ) is the initial thickness of the plate and φ is the angle of inclination of the wall. According to Eq. (2), with an initial thickness of 0.8 mm and a wall angle of 60º, the final thickness of the plate would be 0.41 mm. However, the final thickness obtained in the experiments was ~0.5 mm, i.e., the thickness of the plate did not follow the behaviour predicted by the law of sines; however, the experimental result obtained was close to that calculated, presenting a variation of ~23%. According to [0], the sine law is an approximate model for calculating the minimum wall thickness, as it only considers the angle of the wall, disregarding other important parameters that influence the thickness of the plate, such as the vertical increment and the tool radius.

SEM analysis
The wear mechanisms in the tools were investigated by surface morphology and variations in chemical composition, based on SEM analyses. The SEM analysis of the contact surfaces of the rotating tools with two degrees of freedom and rigid is shown in Fig. 11. Tool wear is influenced by the friction that occurs between the tool and the plate, in accordance with As the rigid tool works only with the sliding movement, the adhesion was located only in the centre of the contact tip ( Fig. 11(a)).
The rotating tool with two degrees of freedom showed two well-defined regions of adhesion, one along its perimeter and the other in the centre of its tip ( Fig. 11(b)). The angular adhesion located on the perimeter of this tool was caused by the rolling movement, because when the tool rolls over the surface, this is the region that is in contact. In contrast, the central adhesion was caused by the sliding movement, because a) b) when the rotating tool slides over the surface, the central region is in contact, with adhesion occurring at that point.
Therefore, during the deformation of the aluminium sheet from the ISF process, the contact friction between the tool and the sheet, caused the removal of aluminium particles, which can slide and roll under the tool. These fragments are pressed during stamping and adhere to the surface of the tool, leading to the adhesion mechanism. As the tool advances, the adhesion points can rub against the contact surface, which generates the grooves on the surface of the plates [0, [33], 0].
The presence of the internal bearings in the tool with two degrees of freedom should, in theory, decrease this adhesive effect in comparison to the rigid tool; however, the combination of rolling friction accompanied by sliding altered the characteristics of the tribological system contributing to the elimination of the lubricating film in the contact point and favouring adhesion by chemical affinity in the rotating tool.
In addition, the characteristic of the test with the free rotation of the tools contributed to the imprisonment of aluminium particles between the tool and the plate, damaging the surface of the tool, such behaviour can be found in the work carried out in [0].

CONCLUSIONS
In this study, a new type of rotating tool geometry was used at the ISF. The effects of varying degrees of freedom of the contact tool on the surface roughness and wall thickness of AA1100 aluminium plates were investigated. Two types of tools (rigid and rotating with two degrees of freedom) were used to stamp the 0.8 mm-thick aluminium sheets with straight cone geometry using the SPIF method.
The choice of tool used in the incremental stamping, influenced the final quality of the desired parameters of the AA1100 aluminium sheets. The tool with two degrees of freedom improved the formability of aluminium AA1100, allowing greater depths of stamping, but did not show improvement in surface roughness, as it contributed negatively to the quality of the internal finish of the parts compared to the results obtained with the rigid tool.
Adhesive wear was predominant in the SPIF process, influencing the final roughness of the printed cones. The greater location of adhesion points on the rotating tool contributed to the increase in the final roughness of the parts stamped with this tool, due to the friction of these points with the aluminium plate.
The friction conditions (rolling or sliding) influenced the location of the aluminium adhesion on the tools. In the condition of rolling friction, the adhesion was located in the perimeter adjacent to the contact tip of the tool and in the sliding friction the adhesion was located in the centre.