Effects of toolpath on defect phenomena in the incremental forming of thin polycarbonate sheets

doi:10.21203/rs.3.rs-4124482/v1

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Effects of toolpath on defect phenomena in the incremental forming of thin polycarbonate sheets

https://doi.org/10.21203/rs.3.rs-4124482/v1

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published 27 Jun, 2024

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The incremental sheet forming has been largely investigating in the last two decades because of its versatility and cost-effectiveness which make this technology especially viable for manufacturing highly customized parts, as well as small and medium-sized batches. One of its main strengths is that it allows reaching greater formability, compared to conventional sheet forming processes; in contrast, defect phenomena like twisting and wrinkling occur frequently and strongly influence the geometric accuracy of the formed parts. All these aspects are dramatically accentuated when forming soft materials like thermoplastics. With these premises, the following research aims to investigate the effects of the toolpath strategy on the occurrence of failures and defects in the incremental sheet forming under very severe process conditions; thin polycarbonate sheets were formed to obtain cone frusta with a fixed wall angle, imposing four unidirectional helical trajectory-based toolpaths, one traditional and three stair strategies. The analysis of the forming force trends, the evaluation of the worked surface quality and the monitoring of the defectiveness highlight understanding the advantages of an appropriate toolpath strategy to improve the accuracy of the incremental sheet forming of thermoplastic parts.

Incremental sheet forming

Polycarbonate

Defectiveness

Forming forces

Surface quality

Thermoplastics are strongly used in the manufacturing industry [1] because of their good properties like light-weight, strength, corrosion resistance, price, etc. Typical parts made of them are manufactured with operations oriented to mass production both for the energy costs and the investments in equipment and tools; they provide for repetitive actions of heating, shaping, and cooling [2]. Furthermore, processes usually employed in sheet metal forming are frequently considered to manufacture thermoplastic sheet components with different shapes [3]; in these cases, the forming processes strongly depend on the material properties and the temperature [4].

Recently, the significant advances in the use of computers applied to manufacturing have augmented the interest in developing procedures with a higher level of flexibility: consider, for example, the incredible development of additive manufacturing technologies [5]. The incremental sheet forming (ISF) moves along the same lines: it is a relatively recent technology that guarantees high customization, thanks to the layered manufacturing principle typical of rapid prototyping, and cost-effectiveness, because it does not require dedicated equipment. In this process, which guarantees high levels of materials’ formability and the carrying out at room temperature, a forming tool controlled by a CNC machine describes a path and deforms progressively a clamped sheet; by doing so, it manufactures the final part geometry [6] starting from sheets of pure metals, alloys, polymers, and composites [7, 8].

ISF is an effective alternative to conventional technologies based on heating-shaping-cooling manufacturing operations. Thanks to its flexibility, this process is strongly oriented toward the production of batches with small and medium size; in addition, it allows reducing energy consumption, compared to conventional processes, so as shown by recent researches on polymer forming [9].

The firsts studies on the polymer ISF concerned polyvinylchloride (PVC) sheets [10], before being extended to other commercial polymers [11] and new materials like the biocompatible polycaprolactone (PCL) [4]. Once checked the feasibility of the process, significant researches were carried out to investigate the influence of the main process parameters on the formability limits of different polymers like polyamide (PA), polycarbonate (PC), polyethylene terephthalate (PET), PVC and polypropylene (PP) [12–15]. The way to better estimate the formability limits was investigated in [2, 16], while new solutions to improve the quality of the ISF polymer parts represents a very hot focus; consider, for example, a prior cold-rolling process of the sheets [17] or their self-heating as the effect of the feed rate and the spindle [18].

Failure and defect modes that interest ISF sheets represent another significant field of investigation, since they influence the materials’ formability and worsen the geometrical accuracy of ISF parts [4, 19]. When incrementally formed, polymer sheets can be affected by ductile fracture at the transition zone between the wall and the corner radius or tearing along the walls, as well as defects like wrinkling and twisting [10]; these ones are strictly connected, since wrinkles can be twisted around the axis of revolution in the direction of tool rotation. The twisting phenomenon is common for all the ISF materials, but it is particularly relevant for materials with soft behaviour like thermoplastics; consider, for example, that twist angles on axisymmetric components obtained by a unidirectional toolpath were equal to about 6° and 22° for aluminum alloy [20] and polycarbonate sheets [21], respectively. This defect is caused by an uncontrolled pivoting of the formed components around the clamping frame, because of the in-plane shear generated by the tangential forces that the forming tool exerts on the sheet; in addition, it is more probable for higher and more regular plane forces, which determine a combination of continued strain accumulation and asymmetric strain levels [22, 23] and, considering polymer sheets, higher normal forces can determine significant indentation that accentuates the phenomenon [24, 25].

A way to reduce this defectiveness is to choose a more suitable toolpath strategy. For example, a dramatic reduction of the twisting phenomenon was observed by adopting an alternate toolpath instead of a unidirectional one, so as verified in [6] and, for PC parts, in [21]; by doing so, the amount of twist produced in a layer was recovered in the successive one almost completely. Despite this, severe forming conditions in terms of sliding forces on thin thermoplastic sheets, characterized by low mechanical resistance, can induce significant instability and generate wrinkling, also using an alternate toolpath strategy [26].

Monitoring and measuring the ISF forming forces represents an efficient tool for the control of the process quality [27]; their reduction limits the risk of failures and defects on the ISF polymer sheets and on the tools, as well as can improve the surfaces’ quality of the components, and allows reducing or avoiding lubricants to lower friction and sticking of material to the tool. These aspects can also involve energy implications that are of relevant interest in a perspective of sustainable manufacturing, since they can determine a positive impact on the environment [28, 29].

According to what reported above, a way to reduce the defect phenomena on ISF polymer sheets provides for acting on toolpath strategies that lower the forming forces in the sheet plane, in line with previous authors’ numerical works [30, 31]. The single-point incremental forming (SPIF), i.e. the simplest variant of ISF that involves the use of a simple tool, a clamping frame, and the absence of dies, was used in this work to manufacture cone frusta with fixed wall angle starting from thin PC sheets; the forming process was carried out by setting typical ISF parameters [21] and four different unidirectional helical trajectory-based toolpath strategies. From the experimental campaign, some important features like the forming forces, the twist angle and the surface roughness were analyzed, as well as the deformation states, the failures and the defects were monitored, to investigate the influence of the selected toolpath strategies on the defectiveness of incrementally formed polymer parts.

The SPIF tests were carried out at room temperature on Makrolon PC sheets, supplied by Bayer, with a thickness t = 1.0 mm. It is an amorphous thermoplastic polymer also known as a “transparency metal” because of its relevant mechanical and physiochemical properties like toughness, stiffness, strength, heat and flame resistance, and dimensionally stability, among others [32]; its main applications are in the fields of communication, transport, medical apparatus, aerospace environment, and so on [33]. The main tensile properties of the PC sheets are: Young modulus E = 2.3 GPa; strain at failure ε_f = 60%; yield stress σ_y = 60 MPa. The engineering stress–strain curves (like the ones for parent sheets, 2 mm in thickness, reported in [17]) show linear and nonlinear elastic behavior, shear-band forming and post-yield behavior with necking and its propagation corresponding to strain softening, common to many amorphous thermoplastics [34].

A C.B. Ferrari high-speed four-axis vertical machining center, driving the forming tool (a hemispherical head stainless steel stylus with a diameter D = 10 mm) at a feed rate of 1000 mm/min, was used to deform the sheets.

The experimental campaign provided the manufacture of cone frusta with a fixed wall angle α = 60° (significantly lower than the maximum one, equal to 80°, measured through varying wall angle cone frusta tests in similar conditions [21]), height h = 35 mm, radius of the major base R = 35 mm and a square flange with a side L = 100 mm, corresponding to the internal area of a clamping frame acting as sheet blocking system. A CAD representation of a cone frustum and of the forming tool with the corresponding main geometrical features is reported in Fig. 1, while Fig. 2 shows the experimental setup during a SPIF test.

The cone frusta were manufactured by four unidirectional helical toolpath-based strategies (two repetitions for each case). Figure 3 and Fig. 4 report a not-to-scale schematization of, respectively, the three-dimensional view of some turns of the helixes and a quarter turn in the XY and YZ-plane views; the arrows show the toolpath directions.

The first strategy (Fig. 3a and Fig. 4a) was considered as a reference toolpath (ref_tp): it was based on a common helical toolpath with a step down (the vertical distance between two consecutive turns) equal to sd = 1 mm (the same for all the strategies considered in this work); the tool described 60 equally spaced points for each complete turn of the conical helix, covering the distance between two consecutive points by a segment.

The other three strategies (labelled as stairA_tp, stairB_tp and stairC_tp) had in common the description of a stair path providing for an alternation of an upward and a downward segment between two consecutive points of ref_tp; for all the cases, the ramp height of the upward segment along the Z-axis was rh = 1.5 mm (equal to about the elastic springback of the components along the Z-axis and measured in preliminary tests).

stairA_tp strategy (Fig. 3b and Fig. 4b) provided that, considering two consecutive points on the helix, the peak of the stair had the same (x,y) coordinates of the second point (the downward segment was placed along the Z-axis and had a length equal to rh; stairA_tp and ref_tp strategies overlap in the XY-plane, see Fig. 4b left).

For stairB_tp and stairC_tp strategies, the projection of one of the two stair segments on the XY-plane was radial (rs); in detail, it was centrifugal for stairB_tp and centripetal for stairC_tp and its length was equal to rs = rh = 1.5 mm (see Fig. 3c-d and Fig. 4c-d).

The tool/sheet interaction induces a localized and incremental deformation of the sheet, peculiar to this forming process; at the same time, it can determine failures and defects, whose occurrence was reduced by lubricating the sheets with mineral oil for cold forming [35]. Some tests were also carried out in dry conditions, to investigate the influence of the lubrication on the process by varying the toolpath strategy.

The occurrence and the growth of failures and defects were investigated as a function of the toolpath strategies; concerning this, the magnitude of the twisting phenomenon was evaluated by measuring the twist angle θ: it was the angle described by a cross, marked on the bottom (the side not in contact with the tool) of the plane sheets [26]. Moreover, the deformation states of the cone frusta were analyzed through cross section observations, carried out by a Hirox RX-100 digital microscope.

Information on the process was also collected monitoring the forming forces; concerning this, a Kistler 9257A piezoelectric dynamometer acquired at 2000 Hz two components of the forming forces, the vertical and one horizontal (F_Z and F_X, respectively, see the reference system in Fig. 1); subsequently, the data were filtered through a NI 9239 input module and the VBA 1.0 B software.

Finally, the quality of the worked surfaces was estimated by measuring their mean roughness (R_a). Ten measurements, according to ISO 4288 − 1996 standard relatively to the recommended cut-off values were conducted for each case, divided equally over the lateral walls along the circumferential and the meridional directions (see Fig. 1); they were performed by means of a Mitutoyo Surftest SJ-301 roughness tester, with differential inductance used as the detecting method and with Gaussian filter.

Before showing the results of the tests, Fig. 5 reports a histogram of the work time depending on the toolpath strategies. They are not the same, due to the different lengths; they pass from 367 s for ref_tp to 870 s for stairB_tp and stairC_tp.

All the tests under lubricated conditions were carried out without the occurrence of tearing, in line with the results of the formability tests described in [21]. At the same time, they all show twisting (see Fig. 6); it is promoted by the in-plane forces exerted in the same circumferential direction and magnified by the indentation that affects the transition zone between the minor base and the lateral wall of the formed PC sheets [25, 36, 37], where necking occurs (as the 30x microscope observation in Fig. 7 shows).

The histogram of Fig. 8 reports the mean values of the twist angles. It is evident that the stair path strategies guarantee a reduction of the twisting phenomenon, due to a non-continuous and reduced torque action of the tool around the Z-axis; the angle reduces from 29.4° (ref_tp) to 17.2° (stairB_tp), while it presents similar and intermediate values for the other two strategies (22.5° and 23.8° for stairA_tp and stairC_tp, respectively).

The considerations on the twisting reflect on the occurrence of wrinkles; the cone frusta obtained by stairB_tp (that guarantees the lowest twist angle) do not show wrinkles, differently from what observed for the other three strategies. Wrinkles are not particularly significant for stairA_tp and similar for the other two strategies (highly interested by the twisting) and affect the transition area between the minor base and the lateral wall (see Fig. 6).

Passing to the tests carried out in dry conditions, stairB_tp ones fail for a vertical quote of about z = 25 mm but without the occurrence of wrinkling; this translates into a reduced formability of the sheets compared to the lubricated conditions. On the other hand, the other ones suffer a very significant instability for which it is possible to affirm that the tests can be completely failed. This instability, caused by both severe loading conditions (because of the absence of lubrication) and significant thinning (as a result of high wall angles on thin sheets; see the wall thickness in Fig. 7, value in good agreement with the Cosine’s law of thickness distribution [38]), determines the formation of wrinkles along the lateral wall. Images from ref_tp and stairB_tp tests (the limit cases with respect to the magnitude of twisting) in dry conditions are reported in Fig. 9.

The interpretation of the forming forces furnishes further information on the carrying out of the ISF process. Figure 10a shows that the trend for ref_tp strategy is typical of SPIF cone frusta obtained by a common unidirectional helical toolpath with a step down [39]: the continuous and constant tool/sheet contact involves that F_Z follows the tensile behavior of the material; the first turns (about five) allow reaching yielding, then the polymer chains align themselves along the meridional direction and this induces anisotropy in the material. In detail, it experiences a significant increase of the tensile properties in the direction of chain alignment (with a consequent increase of the forming force) and a decrease normal to this direction (circumferential) [40]. This is a further cause of the significant twisting interesting ISF polymers. F_X shows a sinusoidal trend, with increasing amplitude as well as the vertical one. This component furnishes information on a combination of effects, i.e. the force for the flattening by the vertical displacement of the tool, the friction associated to the tool/sheet interaction and the action for the thrust on the cone walls [41].

Moreover, a more detailed analysis can provide information on the occurrence of wrinkles. Limiting the observation to one turn and considering the absence of geometrical singularities like ribs in the cone frusta, a nearly constant value of F_Z and the sinusoidal trend of F_X (corresponding to a component of a rotating vector with constant modulus, i.e. the in-plane force), reflect on the lack of wrinkles (Fig. 10b; before wrinkling, 11th turn) [26]. On the contrary, the presence of noise in the signal, as highlighted in Fig. 10c (after wrinkling, last turn), indicates the presence of wrinkles. These observations, possible to ref_tp thanks to the regularity of the force signals, were not for the stair path-based ones, characterized by an irregular trend of the forces.

To compare the four strategies and considering their different working times, a part of the toolpath was considered, corresponding to the 19th and the 20th turns (see Fig. 11; the figure also reports the average of F_Z and of the absolute values of F_X, labelled as F_Z,m and |F_X|_m respectively, for a quantitative comparison).

The fluctuation of the forces increases from the reference to the other three strategies, resulting similar for the last two ones; the stair paths guarantee less severe contact conditions on average, even if loading and unloading determine higher force peaks: in particular, differently from stairA_tp, both stairB_tp and stairC_tp allow reaching very low F_Z,m (about 230 N, compared to about 340 for ref_tp) and F_Z values (under 100 N), since these paths during the upward segment reduce considerably the pressure between the tool and the sheet (not only on the minor base but also on the lateral wall of the components) through a partial elastic recovery, and facilitate for the tool to cross the indentation (this is particularly true for the stairB_tp strategy, in light of the results in terms of twist angle). Despite this, any toolpath determines no-contact between the tool and the sheet because in any time F_Z goes to zero.

Concerning the tests in dry conditions (for the limit cases), the graph of the forces for ref_tp clearly highlights the occurrence of wrinkles with a significant irregularity of the vertical component, followed by an increase in the amplitude of the horizontal one (see Fig. 12a). For the stairB_tp, the irregularity of F_Z corresponds to the tearing of the sheet (see Fig. 12b; the test was stopped after it).

Finally, Fig. 13 reports the R_a values, measured with a cut-off of 0.8 mm. The roughness is slightly lower for ref_tp and along the circumferential direction (along the meridional direction, it is affected by the technological signatures that the forming tool leaves along its path). However, all the toolpath strategies in lubricated conditions guarantee very high surface quality, with roughness values typical of burnished surfaces. The roughness increases significantly for dry tests when using ref_tp, differently from stairB_tp for which lubrication conditions are quite irrelevant, due to the non-continuous tool/sheet contact that makes less severe the wear action of the tool in absence of lubricants.

This paper investigates the effects of the toolpath strategy on defect phenomena in the single-point incremental forming of thin polycarbonate sheets. They were worked to manufacture cone frusta with a fixed wall angle by using a reference and three stair-based unidirectional helical toolpath strategies; deformation states, surface quality, failures and defects were analyzed, as well as the forming forces were monitored.

First of all, the stair paths present higher length and, then, higher working times.

Under lubricated conditions, all the components do not experience tearing; despite this and due to the asymmetric nature of the unidirectional toolpaths and the soft nature of the polycarbonate, in all the cases the incremental formed sheets suffer from twisting, which reaches almost 30° when using the reference strategy. The worst cases also show wrinkles along the lateral wall of the cone frusta.

Twisting phenomenon can be reduced by using the stair toolpaths (in particular, the twist angle is about 17° for the one labelled stairB_tp), because of a discontinuous and lower torque action and a facilitated crossing of the indentation for the tool.

The above considerations are confirmed by the analysis of the forming forces that also represent a valid tool to monitor the control, since the correct interpretation of values and trends of the forces allows individuate failures and defects.

From the roughness measures, all the toolpath strategies guarantee high surface quality.

Finally, the tests on lubricated and dry conditions allow affirming that the best solution to form incrementally the polycarbonate sheets is choosing stairB_tp strategy. In fact, it guarantees reduced defectiveness in lubricated conditions and the sheets do not incur instabilities in dry conditions, though suffering a reduced formability; in addition the lubrication results quite irrelevant in terms of surface roughness.

These conclusions, added up FEM predictions of reduced energy consumption from a previous authors’ work on stair-based toolpath strategies, makes stairB_tp, and more generally an opportune choice of the toolpath strategy, a viable way on the improvement of ISF towards more efficiency and green manufacturing process.

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Author Contributions

All authors contributed to the study conception and design. Material preparation was performed by Antonio Formisano and Massimo Durante. Data collection and analysis were performed by Antonio Formisano, Luca Boccarusso and Dario De Fazio. The first draft of the manuscript was written by Antonio Formisano and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Effects of toolpath on defect phenomena in the incremental forming of thin polycarbonate sheets

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