Codification of scan path parameters and development of perimeter scan strategies for 3D bowl-shaped laser forming

Optics and Laser Technology 98 (2018) 121–133

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Codification of scan path parameters and development of perimeter scan strategies for 3D bowl-shaped laser forming A. Tavakoli a, H. Moslemi Naeini b,⇑, Amir H. Roohi c, M. Hoseinpour Gollo d, Sh. Imani Shahabad a a

Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, P.O.Box 14115/143, Tehran, Iran c Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran d Department of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), Lavizan, Tehran, Iran b

a r t i c l e

i n f o

Article history: Received 10 March 2017 Received in revised form 4 July 2017 Accepted 28 July 2017

Keywords: Bowl-shaped products Scan path parameters Linear combined scan path Hexagonal scan path

a b s t r a c t In the 3D laser forming process, developing an appropriate laser scan pattern for producing specimens with high quality and uniformity is critical. This study presents certain principles for developing scan paths. Seven scan path parameters are considered, including: (1) combined linear or curved path; (2) type of combined linear path; (3) order of scan sequences; (4) the position of the start point in each scan; (5) continuous or discontinuous scan path; (6) direction of scan path; and (7) angular arrangement of combined linear scan paths. Regarding these path parameters, ten combined linear scan patterns are presented. Numerical simulations show continuous hexagonal, scan pattern, scanning from outer to inner path, is the optimized. In addition, it is observed the position of the start point and the angular arrangement of scan paths is the most effective path parameters. Also, further experimentations show four sequences due to creat symmetric condition enhance the height of the bowl-shaped products and uniformity. Finally, the optimized hexagonal pattern was compared with the similar circular one. In the hexagonal scan path, distortion value and standard deviation rather to edge height of formed specimen is very low, and the edge height despite of decreasing length of scan path increases significantly compared to the circular scan path. As a result, four-sequence hexagonal scan pattern is proposed as the optimized perimeter scan path to produce bowl-shaped product. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Laser Forming (LF) is a thermal process, in which the forming conducts without physical contact between tool and workpiece. LF divides into 2D and 3D categories. The scan path in the 2D LF is a straight line, which the workpiece experiences a onedirection bending. On the other hand, in the 3D LF, scan pattern would be either curved or combined linear scan pattern based on the final shape of the intended product. LF process has been extensively investigated during recent years, and many records can be found in scientific literature. Guan et al. [1] studied the effect of material properties in the laser forming process. According to their results, thermal expansion coefficient is in direct proportion to bending angle. Also, an increase in thermal conductivity limits the amount of forming. Roohi et al. [2] performed an experimental study of the influences of process parameters in LF of Al6061-T6 sheets. Results show the scan ⇑ Corresponding author. E-mail address: [email protected] (H.M. Naeini). http://dx.doi.org/10.1016/j.optlastec.2017.07.046 0030-3992/Ó 2017 Elsevier Ltd. All rights reserved.

velocity and sheet thickness have a reverse relation with the bending angle. However, increase in laser power and number of scan passes increases the final sheet forming. Also, a randombased subtractive model was presented by Roohi et al. [3] to study the behavior of closed-cell metallic foams in LF. The relative density of the foam, metal foam sheet thickness, and mean cell sizes were specified as a more-to-less effective in the process. Maji et al. [4] investigated process parameters and pulsed laser parameters, such as pulse frequency and energy on the forming of stainless steel AISI 304. They proposed the optimized condition to achieve the maximum amount of forming. Shidid et al. [5] used an inert gas shielding to minimize the oxidation and improve the absorption of the laser beam on highly reflective Grade-2 Titanium sheet. They recommended coating in per pass in a multi-scan system to enhance bending angle. Kant and Joshi [6] investigated the multi-pass LF process. They showed that large bending angle could be generated on the difficult-to-form materials, such as Magnesium by implementing multi-pass laser forming process. 90-degree bending angle, using an external force-assisted laser forming was proposed by Roohi et al. [7]. Numerical results

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Table 1 Thermal and mechanical properties of stainless steel AISI 304 [18–23]. Temp. T (C)

Conductivity k (w/mk)

Yield stress

Expansion coefficient

ry (MPa)

a (l/°C)

Specific heat Cp (J/kgk)

Poisson ratio ʋ

Modulus of elasticity E (GPa)

20 100 200 205 300 315 400 427 500 538 600 650 800 815 1000 1150 1200 1300 1400

15 16.3 17.8 – 17.8 – 20.8 – 23.6 – 25 – 26.25 – – – – – –

240 – – 160 – – – 130 – – – 105 – 90 – 20 – – –

17.3 17.3 – – – 17.8 – – – 18.4 – 18.7 – – – – – – –

496 512 531 – 571 – 571 – 611 – 627 – 638 – – – – – –

0.29 0.29 0.29 – 0.31 – 0.318 – 0.318 – 0.326 – 0.326 – 0.339 – 0.342 0.388 0.388

193 191 186 – 180 – 173 – 165 – 155 – 133 – 100 – 57 20 10

showed that the one-third of the final forming magnitude is due to the addition of the mechanical force. On the other hand, there are some studies about the 3D laser forming process. Watkins et al. [8] proposed concentric circular scan paths based on the upper mechanism to produce bowl shapes. Dearden and Edwardson [9] presented development of two and three dimensional laser forming process for both micro and macro scale applications. They showed that concentric racetrack line irradiation could be an appropriate scan pattern to form saddle shapes. Chakraborty et al. [10] investigated the forming of bowl shapes using radial and circular scan pattern. An increase in the bending angle and thickness increment for both circular and radial patterns was observed with increasing laser power, and reducing the laser beam diameter and scan velocity. Yang et al. [11] presented a spider scan strategy for forming both circular and square sheets into dome-shaped products. Kim et al. [12] utilized geometrical information of the specimen to produce complex shapes, including pillow and saddle. They proposed laser scan patterns without using stress-strain equations. Yang et al. [13] studied the effect of process parameters on the formed specimen using different scan strategies. In their work, spider and radial scan pattern were implemented, respectively, to achieve dome-shaped and saddle-shaped products. Using a spider-type scan path to produce dome-shaped products from circular sheets was investigated by Imani Shahabad et al. [14]. The dome height rises was found with a decrease in the beam diameter and scan velocity, and an increase in laser power or number of passes. Also, Imani Shahabad et al. [15] conducted a full factorial design of experiments to obtain an equation for predicting dome height of sheet metals. Moreover, the effects of heat flux, and line energy is investigated. In this paper, seven scan path parameters are considered to specify the optimum laser scan strategy to produce bowl-shaped products. These parameters are as follows: (1) combined linear or curved path; (2) type of combined linear path; (3) order of scan sequences; (4) the position of the start point in each scan; (5) continuous or discontinuous scan path; (6) direction of scan path; and (7) angular arrangement of combined linear scan paths. In addition, three criteria (i.e. the average height of the edge nodes; edge distortion; and standard deviation) are implemented to compare the height and the symmetry of the products. Experimental and numerical results show the four-sequence hexagonal scan pattern as the optimized perimeter scan path to produce bowl-shaped product.

2. Numerical simulation Circular plates with the diameter of 50 mm and the thickness of 3 mm were modeled as the blank sheet in ABAQUS software. The temperature-dependent physical and mechanical properties of the stainless steel AISI 304 were attributed to the geometric model, as listed in Table 1. Boundary conditions, consisting mechanical and thermal, were applied [16]; the center point of the specimens was fixed to restrict its 6-dofs (three translational and three rotational movement). Convection follows Newton’s law, and the radiation heat transfer as follows:

q ¼ hc ðTs  TÞ

ð1Þ

q ¼ 5:67  108 eðT4 s  T4 Þ

ð2Þ 2

In the above equations, q is heat dissipation (W/m ), hc is the heat transfer coefficient (W/m2 °C), Ts is the sheet temperature (°C), T is the temperature of the environment (here assumed to be 25 °C), and e is surface emissivity. Moving heat flux (DFLUX subroutine) was used to define the continuous laser scan with the actual process parameters and the assumption of Gaussian thermal distribution of laser intensity [17]. C3D4T (4-node thermally coupled tetrahedron) element types were used. Optimum mesh sizes equal to 1 mm were selected based on the mesh study, which led to 54,928 elements in numerical simulations. In addition, concentric circular partitions with different radius were applied to reach a more uniform mesh structure of the specimen. 3. Experimental procedure Experimental tests were conducted using CO2 laser with the wavelength of 10.6 lm, model Bystronic 3015, with the maximum power of 3000 W, and nitrogen shielding-gas with the pressure of 0.1 bar (Fig. 1). The laser scan paths were sketched in AUTOCAD software and then, imported in a readable language format to the CNC laser apparatus. All of the stages in the experimental tests conducted continually without stop in order to diminish duration of the tests. On the other hand, they can be carried out with specific stop, and was graphite coated on the workpiece surface after each sequence for cooling and increasing the temperature gradient in order to increase the workpiece height, improve the uniformity and symmetry, as well. The optical scanner machine, model Range

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4. Development of perimeter scan strategies

Fig. 1. 3D laser forming process.

Vision 3D scanner Standard Plus, was utilized to measure the geometrical profile of the products. The measurement includes (a) Specification of the cloud points of the product and importing them in a CAD software; (b) creation of 40 diagonal sections on the product model; (c) determination of 21 nodes on each diagonal section; (d) Extraction of the height of nodes in each diagonal line; and (e) plotting the edge node displacements (measurement approach is reported, in detail, in [24]). The optical scanner apparatus has the accuracy of 0.03 mm with the actual working range of 133  100  100 mm, and the resolution of 1.3 Megapixel (i.e. the capability of determining 1.3 million points) in each shot. Circular AISI304 specimens with the diameter of 50 mm and 150 mm, and the thickness of 3 mm were cut using laser beam machining. A bolt-and-nut type fixture is developed to restrict the sheet movement through the experimentations (Fig. 2). That is, a nut is welded to the center point of the back layer of the sheets and then screwed to the bolt in the base plate of the fixture. Furthermore, the sheets were graphite coated, preliminary, to enhance the laser absorption coefficient (0.6) during the laser forming process. 3.1. Process parameters In order to make comparison between scan patterns, process parameters, including laser power, scan velocity, and beam diameter, are considered constant. The process parameters are optimized in a way that (a) the workpiece surface reaches its highest temperature below the melting point; (b) the sheet edge height reaches its highest value; and (c) the temperature gradient mechanism is activated in the process. To activate the temperature gradient mechanism, Fourier number should be less than the unity [25]. By considering the mentioned conditions and following the approach reported in [24], process input parameters are chosen as P = 600 W, v = 10 mm/s, and d = 3 mm (Note that P is laser power, v is scan velocity, and d is beam diameter). This makes the Fourier number equal to 0.123.

Fig. 2. A bolt-and-nut type fixture.

In general, two types of scan paths could be considered in order to produce bowl-shaped products; (1) curved path; and (2) combined linear path. The scan paths might be radial or perimeter. However, radial paths are studied in [24], this investigation is pursuing the optimum perimeter scan paths to produce bowl-shaped products. Indeed, the combined liner path type is the first path parameter which is investigated. One fundamental instance of the curved scan path is a concentric circular scan pattern. In Fig. 3, a part of the circular path between two points (here, A and B) could be considered as a different curved path through an eccentric circle (d is the distance between the center of the two circles). Thus, an arbitrary curved path could be used, instead of a concentric circular path; a curve as a part of an eccentric circle with a curve length of S, radius of R2 and the distance of d from the concentric point (see Fig. 3). In fact, a four-, six- or eight-sequence of curved path could be used instead of each circular scan path, which their radius and distance and the length of each curved path (s) could be calculated according to trigonometric Eqs. (3)-(5). Continuing this trend and increasing the value of d, the curved path transforms into a linear path in infinity. Thus, a new scan strategy called combined perimeter linear pattern is proposed. Combined perimeter linear pattern includes four, six or eight linear sections (Fig. 4) and therefore, could be as foursquare, hexagonal, octagonal, etc.

cos



p

a

2

¼

R21 þ d  R22 2dR1

2 D : BO2 O1 R2 : Unknown a ðThe Relevent factor to number of Concenteric Circle Sectors 4; 6; 8; 10; etcÞ; R1 : Radius of Concenteric Circle as a Fundamental Circular Laser Scan Path; d : Choosen Distance : Known Parameter

cos

  2 b R2 þ d  R21 ¼ 2 2 2dR2

D : BO2 O1 R2

b : Unknown

ð3Þ ð4Þ

b  R2 ¼ S S : Length of the Curved Eccentric Circle S : Unknown

ð5Þ

However, uniform and symmetric bowl-shaped products are not achieved using foursquare path. Octagonal, decagon or upper combined linear paths are closer to a circular scan path. As a result, the hexagonal perimeter scan pattern is chosen as combined linear paths to produce bowl-shaped products. 4.1. Combined linear scan patterns In order to produce bowl shaped products, three hexagonal perimeter sequences are considered, which the value of their sides are 13, 17, and 21 mm. Actually, for increasing uniformity of the products, the distance between inscribed concentric circles are assumed to be 4 mm, based on trial and error method. In order to make a more symmetric specimen with a higher edge displacement, according to the simulation tests among distinctive compounds of hexagons and the distances between them, mentioned configuration showed the appropriate result. Thus, perimeter scan path with three sequences of R1 = L1 = 21 mm, R2 = L2 = 17 mm, and R3 = L3 = 13 mm is chosen (i.e. the total length of the laser scan path in combined linear scan path is 306 mm). So far, five different parameters to determine the hexagonal scan patterns are identified: (1) order of scan sequences; (2) the position of the start point of each scan; (3) continuous or discontinuous scan path;

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Fig. 3. Schematic image of a centric circular scan path, eccentric circle and linear path.

Fig. 4. Combined linear patterns: (a) foursquare; (b) hexagonal; and (c) octagonal.

(4) direction of scan path; and (5) angular arrangement of combined linear scan paths in each sequence. According to these parameters ten different perimeter patterns are proposed (see Fig. 5). 4.1.1. Reference pattern of hexagonal scan path The reference case is shown in Fig. 5(a), which has the same angular position of the start points. The scan also starts from the outer hexagonal to the inner. That is, three steps of scanning are considered; as it’s shown, scan paths are continuous with CCW direction. The scan starts from point P1 on the hexagonal path with the side length of L1 = 21 mm, and consequent path continues from start points P2, and P3 with the lengths of L2 = 17 mm and L3 = 13 mm, respectively. Fig. 6(a) shows bowl-shaped products using this scan pattern. On the other hand, second strategy (Fig. 5(b)) is considered if the order of scan sequences reversed. In this scan pattern, scanning starts from the inner hexagon to the outer one. 4.1.2. The position of start points in each sequence The patterns shown in Fig. 5(c) and (d) study the effect of the scan start point position. The angular difference of 120° and 180° are considered between the consequent start points, respectively, in patterns (c) and (d). By applying this angular difference, laserinduced heating of the specimen does not start from one region of the sheet metal and thus, more symmetric thermal distribution occurs through the workpiece. Fig. 5(d) shows the CCW-directed scan pattern, which starts initially from point P1 on the hexagonal path with the side length of L1 = 21 mm. Then, the second hexagonal path with the side length of L2 = 17 mm is scanned from point P2 (with the angular difference of 180° compared to point P1).

Finally, perimeter path is scanned from the point P3 and the hexagonal side length of L3 = 13 mm. Fig. 6(b) illustrates the displacement contour of the bowl-shaped produced by this scan pattern. 4.1.3. Directed-base continuous/discontinuous scan path Fig. 5(e) illustrates a two half discontinuous path, each starts from the same point, but with a contra-direction. This pattern of scanning repeats in inner hexagonal paths. Fig. 5(f) determines the same strategy compared to the previous, applied to the hexagonal paths with different position of the start points and reverse scan direction in each scan sequences. The reversed direction in consequent pass is considered if it decreases the distortion and non-uniformity of the previous path. Fig. 5(h) specifies a discontinuous CCW-directed scan in a rotated-hexagonal paths, in which each scan part is exactly in front of the previous. The same strategy is utilized in Fig. 5(i), but the scan direction in every discontinuous part is opposite to the former (i.e. a continuous directional change of CCW to CW and CW to CCW occurs). 4.1.4. Angular arrangement of combined linear path Fig. 5(g) shows a 30° rotation of the hexagonal paths arrangement in a CCW direction. It’s obvious this rotation affects the scan start point, too. The hexagon rotation is applied to decrease the distortion observed due to the polygon vertices. Finally, Fig. 5(j) is achieved by applying an angular difference between sequential scan paths shown in Fig. 5(g). Fig. 2(c) determines the final bowlshaped products with this scan strategy. Fig. 6(c) specifies the bowl-shaped product using scan pattern shown in Fig. 5(j).

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Fig. 5. Combined linear scan patterns.

4.2. Comparison criterion In comparing the results derived from each perimeter scan path, three criteria consisting the average height of the edge nodes (X), the edge distortion (d), and the standard deviation (r) for determining uniformity of the final bowl are considered. These three

criteria are presented, in details, in [24]. Briefly, the average height of edge nodes measures the average height of 157 perimeter nodes in the numerical simulations, and of 80 nodes in the experimentations. On the other hand, the difference between the maximum and minimum value of the edge height, called edge distortion, calculates the asymmetry quantity of the product. Finally, the standard

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Fig. 6. Displacement contour of bowl specimen according to perimeter scan pattern; (a) combined scan lines with constant start point; (b) combined scan lines with different start point (180° angular difference); (c) combined scan lines with 30° rotated scan paths (d) CCW-directed circular scan path with different start points (180° angular difference).

Table 2 Numerical results due to hexagonal combined linear perimeter scan patterns. Type of scan path

X (mm)

hmax (mm)

hmin (mm)

d (mm)

r

Constant start point (a) Different start points; 180° angular difference (d) Different start points; 30°-rotated hexagonal paths (j)

0.250 0.248 0.245

0.294 0.283 0.265

0.214 0.216 0.225

0.080 0.067 0.040

0.0209 0.0189 0.0121

Fig. 7. Diagram of perimeter edge height in the three different scan paths (a), (d), and (j).

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deviation, which determines the uniformity of the products, evaluates the distribution of perimeter nodes of the sheet over the average value. 5. Results and discussion 5.1. Scan strategies – numerical approach In this part, according to five remained scan parameters of defined previously, 10 hexagonal perimeter linear scan patterns are presented. Initial investigations show that discontinuous scan path with/without angular difference of start points is not effective. In addition, sequential reversing scan direction does not give an efficient result. Finally, continuous CCW-directed scan pattern (scanning from the outer edge to the center of the sheet) enhances the process condition to the desired bowl-shaped process. As is

follows now, three scan pattern of (a), (d) and (j) are compared in order to present the best combined perimeter scan paths: Step 1 – Scan patterns (a) and (d) are compared in order to determine the effect of start point position. Results show (see Table 2 and Fig. 7) the average perimeter edge height using these scan patterns is almost the same. Edge distortion and standard deviation of the product (d) is approximately 17% and 10% lower than the pattern (a), respectively. Thus, using different start point (with 180° angular step) achieves more symmetric and uniform bowl-shaped product. Step 2 – Scan patterns of (d) and (j) are compared to specify the effect of the rotated hexagonal arrangement on the quality of the product. The comparison between the results presented in Table 2 and Fig. 7 shows the average height of edge nodes are the same. However, edge distortion and standard deviation of

Fig. 8. Schematic picture of perimeter scan pattern; (a) circular path; and (b) hexagonal path.

Table 3 Numerical results due to hexagonal pattern (d) and circular path. Type of scan path

X (mm)

hmax (mm)

hmin (mm)

d (mm)

r

L (mm)

CCW-directed scan path with 180° angular step of start points Different start points; 180° angular difference; 30°-rotated hexagonal paths (j)

0.164 0.245

0.178 0.265

0.149 0.225

0.029 0.040

0.0105 0.0121

320.44 306

Fig. 9. Diagram of perimeter edge height in the hexagonal pattern, and circular paths.

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the scan pattern (j), respectively, is lower by the factor of 41% and 36%, compared to scan pattern (d). In fact, uniformity and symmetry of the bowl-shaped product increases significantly using scan pattern (j). Thus, the optimized perimeter linear scan pattern is the hexagonal scan path with 180° angular step of the start point and 30°-rotated of the subsequent paths. Step 3 – As discussed before, combined linear scan path with different start points and 30°-rotated hexagonal paths (j) is introduced as the optimized linear scan pattern. Now, this scan pattern is compared with its corresponding concentric circle paths (Fig. 8(a)) to choose the best perimeter scan strategy. In fact, choosing combined linear/curved path is the last parameter, which would be investigated. Results show that, despite of decreasing the scan path length by the factor of 5%, the edge

height of the hexagonal path is 34% higher compared to the circular path (see Table 3 and Fig. 9). However, edge distortion and standard deviation, respectively, increases by the factor of 27% and 13% using hexagonal scan pattern. The displacement contour of the final bowl-shaped product using CCW-directed concentric circular scan lines is illustrated in Fig. 6(d). 5.2. Numerical validation Experimental tests are conducted on circular specimens with the diameter of 50 mm and the thickness of 3 mm. All the geometrical and process parameters are chosen the same as the numerical simulations. Fig. 10 shows two LF formed specimens using circular and hexagonal scan patterns. Results show a good agreement

Fig. 10. LF formed specimen using (a) circular pattern; and (b) hexagonal path.

Fig. 11. Diagonal section nodes vs. edge heights using (a) circular; and (b) hexagonal pattern. Table 4 The experimental results according to combined perimeter linear scan patterns. Type of scan path

X (mm)

hmax (mm)

hmin (mm)

d (mm)

r

L (mm)

Reference pattern (Fig. 12(a)) Path shown in Fig. 12(b) Path shown in Fig. 12(c)

1.256 0.627 1.514

1.363 0.673 1.619

1.163 0.593 1.433

0.2 0.08 0.186

0.0556 0.0146 0.048

918 918 1080

Fig. 12. Combined linear scan path; (a) type one with three sequences; (b) type two with three sequences; and (c) type one with 4 sequences.

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between experimentations and numerical data (Fig. 11(a) and (b)). The maximum difference of 7.9% and 7.2%, respectively, in the circular and hexagonal pattern is observed (see Table 4). 5.3. Scan strategies – experimental approach

Fig. 13. LF formed products using combined linear scan patterns; (a) type one with three sequences; (b) type two with three sequences; and (c) type one with four sequences.

In order to present a supplementary perimeter scan path, using the results from the numerical simulations, three hexagonal scan patterns are introduced (Fig. 12). Fig. 12(a) is the hexagonal scan path with 180° angular step of the start point and 30°-rotated of the subsequent paths, which determined as the optimized scan strategy in the previous sections. The similar strategy with the same overall length of scan path is shown in Fig. 12(b). However, the 30°-rotated of the subsequent path is not applied to the third inner hexagonal path. This scan pattern is to determine if two smaller inner hexagonal paths are located in front of the edge nodes of the outer hexagonal, the final products have lower distortion with higher edge height or not. Fig. 12(c) illustrates a scan pattern with four-sequence of hexagonal paths to determine the effect of increasing 15% of overall scan length, using four-sequence instead of three-sequence, on the bowl-shaped products. The side lengths of hexagonal path are L1 = 63 mm, L2 = 51 mm, L3 = 39 mm, and L4 = 27 mm. Also, the radial distance between

Fig. 14. Diagram of perimeter edge height; (a) type one with three sequences; (b) type two with three sequences; and (c) type one with four sequences.

Fig. 15. Perimeter scan path; (a) circular with four circle; (b) four rotated hexagonal sequences.

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Fig. 16. LF formed products using (a) circular scan path with four concentric circles; (b) four rotated hexagonal sequences scan pattern.

assumed base circles is 12 mm. Note that these set of experimentations are carried out on circular plates with the diameter of 150 mm and the sheet thickness of 3 mm. Regarding with these results, the average height by using scan pattern type one is two times greater than using scan pattern type two. Distortion and standard deviation of scan pattern type two is 2.5 and 3.8 times lower than scan pattern type one, respectively. Therefore, using scan pattern type one gives more appropriate edge height and using scan pattern type two gives more uniform and symmetric products. Generally, according to the high value of edge height in scan pattern type one and having a low amount of distortion and standard deviation rather to its edge height, this scan pattern is more appropriate scan path for producing bowl shapes. Furthermore, in a scan pattern with four sequences, by increasing 15% length of scan path, the average height increases 18%. In addition,

Table 5 Experimental results due to two circular and hexagonal four-sequence pattern. Type of scan path

X (mm)

hmax (mm)

hmin (mm)

d (mm)

r

L (mm)

Four circular sequence Four rotated hexagonal sequence

0.822 1.514

0.857 1.619

0.792 1.433

0.065 0.186

0.02 0.048

1130.97 1080

Fig. 17. Diagram of perimeter edge height using circular and hexagonal scan path with four sequences.

Fig. 18. Diagonal section nodes vs. edge heights using four- sequence circular and hexagonal scan pattern.

Table 6 Previous scan patterns for bowl products with experimental conditions and results. Height/bending angle (mm) or (degree)

Symmetry and uniformity

Total length of scan path

Process parameters

The size of specimen

Material

Type of laser machine

Cross Spider [11]

X = 3.5 mm

None reported

None reported

Nd:YAG laser

X = 0.5 mm

None reported

None reported

D = 50 mm T = 0.8 mm (Circular Sheet) D = 50 mm T = 0.625 mm (Circular Sheet)

Stainless (1Cr18Ni9Ti)

Two consecutive parallel orthogonal laser paths (Plaid with 1.875 mm distance) [26] Geometrical information strategy [12] Circular scan path [10]

P = 300 w V = 20 mm s d = 0.8 mm P = 100 w V = 10 mm s d = 0.3125 mm

None reported

None reported

a = 12°

None reported

AISI 304 Stainless Steel

An Yb fibre laser (YLR 2000, iPG make)

X = 0.606 mm

d = 0.08 mm

L = 1634 mm

Mild Steel

Full fermat’s spiral [28]

X = 0.6 mm

d = 0.08 mm

L = 3600 mm

Convergent non-cross pathwith 30° angular step [24] Four circular sequence

X = 0.38 mm

d = 0.03 mm

L = 432 mm

30 mm  30 mm T = 0.8 mm (Square Sheet) D = 50mm T = 1 mm (Circular Sheet) D = 280mm T = 12 mm (Circular Sheet) D = 150mm T = 2 mm (Circular Sheet) D = 150 mm T = 3 mm (Circular Sheet) D = 150 mm T = 3 mm (Circular Sheet) D = 150 mm T = 3 mm (Circular Sheet)

100WCW Ytterbium fiber laser

Spiral path [27]

P = 75 w V = 5 mm s d = 2 mm P = 800w V = 83.3 mm s d = 2 mm P = 2500w V = 18 mm s d = 5 mm P = 1500w V = 33.3 mm s d = 2 mm P = 600 w V = 10 mm s d = 3 mm P = 600 w V = 10 mm s d = 3 mm P = 600 w V = 10 mm s d = 3 mm

Mild Steel

a = 24.17°

Maximum Error with; 16 Patches: 0.226 mm 64 Patches:0.131 mm None reported

A flame torch integrated with a 2-axes CNCworkstation CO2 laser machine (Bystronic with 3 kW power) CO2 laser machine (Bystronic with 3 kW power) CO2 laser machine (Bystronic with 3 kW power) CO2 laser machine (Bystronic with 3 kW power)

L = 5089 mm

r = 0.01 X = 0.822 mm

d = 0.06 mm

L = 1130 mm

r = 0.02 Four rotated hexagonal sequence

X = 1.514 mm

d = 0.186 mm

r = 0.048

L = 1080 mm

Al 6061

AISI 304 Stainless Steel

AISI 304 Stainless Steel

AISI 304 Stainless Steel

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Type of scan path

131

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distortion and standard deviation decrease 7% and 14% respectively. Therefore, the best-combined linear scan path in the supplement scan path is the scan pattern with four sequences (see Figs. 13 and 14). In the final step, the four-sequence rotated hexagonal scan pattern presented as a most appropriate linear scan path is compared with the four concentric circular paths shown in Fig. 15(a). The LF formed specimen using these two scan patterns is illustrated in Fig. 16. The bowl-shaped product data is listed in Table 5. Also, the edge height diagram of the formed specimen is shown in Fig. 17. Experimental results show the average height of the linear hexagonal pattern is almost two times higher compared to circular pattern (Note that four-sequence hexagonal pattern has a 5% decreased length of scan path compared to circular pattern). However, the edge distortion and the standard deviation of hexagonal path increase by the factor of 2.8 and 2.4, respectively. Fig. 18 illustrates the diagram of the average height of 21 diagonal points in the bowl-shaped products. Recall that in the hexagonal scan pattern, the values of edge distortion and standard deviation is negligible compared to the edge height of the formed products. As a result, the most optimized linear scan strategy to produce bowlshaped is the four rotated hexagonal sequences as is presented in Fig. 15(b). Moreover, there is a general report about previous presented scan patterns in order to produce a bowl shape in Table 6. Consequently, by considering distinctive experimental conditions in each test, length of laser scan path, average heights, distortion and uniformity, it can be extracted that Four rotated hexagonal sequence is the most appropriate perimeter scan path and Convergent non-cross path with 30° angular step is the most appropriate radial scan path to produce a bowl-shaped production. 6. Conclusion In this manuscript, combined linear scan pattern to produce bowl-shaped products are introduced. Eccentric circular scan paths (with the radius of R2 (shown in Fig. 3) and the distance of d from the sheet center point), and as a consequent, polyhedron scan paths were utilized to produce bowl-shaped pieces. However, hexagonal scan paths, which shows a more symmetry results in the products, is chosen as a most appropriate polyhedron scan patterns: (1) Numerical results show the continuous hexagonal CCWdirected (in general, where the scan direction in consequent paths is constant) with 180° angular step of the start point and 30°-rotated of the subsequent paths is the most appropriate 3-path scan pattern to produce bowl-shaped products. On the other hand, a discontinuous path leads to a decrease in the edge height and an increase in the edge distortion and non-uniformity of the final shape. Reversing the scan direction in the consequent paths in both continuous/ discontinuous patterns provides no proper effect on the final result. Also, scanning from the inner hexagonal to the outer, decreases the bowl height of the products. (2) Numerical and experimental results show that (a) combined linear scan path compared with curved path (b) start point of the path; and (c) the angular arrangement of the hexagon are the most effective parameters among other path parameters. In fact, applying a 180° angular step of the start point decreases the edge distortion and standard deviation 17% and 10%, respectively. In addition, the edge distortion and standard deviation show a 41% and 36% decrease, respectively, when a 30°-rotated hexagon as subsequent paths is considered. The rotated-hexagon produces more uniformdistributed hexagon vertices through the sheet and it leads to a more symmetric final bowl shape.

(3) Experimental results show with increasing 15% of the total scan length (i.e. scan pattern with four hexagonal paths), the average bowl height increases 18%, and the edge distortion and standard deviation decrease 7% and 14%, respectively. (4) Finally, four concentric circular paths are compared with the four-sequence rotated hexagonal scan pattern presented, as a most appropriate perimeter linear scan path. The average height of the linear hexagonal pattern is almost two times higher compared to circular pattern. However, the edge distortion and the standard deviation of hexagonal path increase by the factor of 2.8 and 2.4, respectively. In addition, the values of edge distortion and standard deviation is negligible compared to the edge height of the formed products. Thus, the continuous hexagonal CCW-directed with 180° angular step of the start point and 30°-rotated of the subsequent paths is the most appropriate scan pattern to produce bowl-shaped products. Therefore, combined linear scan path is better scan strategy compared to curved scan path for producing bowl-shaped product by laser forming process.

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