Abstract

In this paper we present a novel approach to monitoring the deformations of a steel plate’s surface during various types of laser processing, e.g., engraving, marking, cutting, bending, and welding. The measuring system is based on a laser triangulation principle, where the laser projector generates multiple lines simultaneously. This enables us to measure the shape of the surface with a high sampling rate (80 Hz with our camera) and high accuracy (±7 μm). The measurements of steel-plate deformations for plates of different thickness and with different illumination patterns are presented graphically and in an animation.

© 2004 Optical Society of America

1. Introduction

Surface-processing techniques that involve the use of lasers—for example, marking, engraving, cutting, cleaning, welding and forming—have become increasingly common as industrial processes over the past few years [1]. A common feature of all these techniques is the need for them to operate as close as possible to the optimal working point. However, this situation usually involves a compromise between the operation time for the process and the quality of the finished product. For example, increasing the average power of the laser and the traveling speed of the laser beam usually decreases the operating time; however, at a certain point the quality of the processed surface is no longer acceptable as a result of unwanted permanent deformations. These deformations, which are caused by various thermoplastic mechanisms, such as the temperature-gradient mechanism, the buckling mechanism or the upsetting mechanism [2–4], must be minimized for processes like engraving, marking, cutting, and cleaning. On the other hand, during laser-forming processes the deformation should generate the required shape with the minimum of deviations [5–8].

At present there is a lot of effort being put into investigating the fundamentals and possible applications of laser-forming processes. Indeed, many analytical and numerical models have already been proposed; however, these are mainly restricted to very simple laser-beam patterns and initial plate shapes [3,5,9]. Experimental measurements of the deformed surface have also been limited to some characteristic values, such as the bending angle or the radii of curvature [2,9,10]. Furthermore, these measurements are mainly performed after the process is complete, using a linear variable differential transformer (LVDT), a coordinate measuring machine (CMM), or techniques such as laser-point or line-triangulation. So far, only one group has published some preliminary experimental results from a full-field dynamic shape measurement during laser-based plate bending [11].

This paper presents a high-speed technique for a three-dimensional measurement of plate deformation during laser processing. The full-field absolute-distance measurement is performed on a single acquired image, where the illuminating laser-light pattern is composed of multiple light planes. The laser-light source was used because of its several advantages over ordinary light sources (such as halogen or xenon light sources). Firstly, the ambient light can be efficiently filtered out due to the monochromatic nature of the laser light. Secondly, the laser pattern can be held in tight focus over a long range. And thirdly, the heat dissipation of lasers (especially semiconductor diode lasers) is much less than with conventional projectors, which consequently reduces the measuring errors due to any thermal expansion of the apparatus [12].

In the following sections we describe the measuring system, the experimental procedure and the results. In the first set of experiments we focused on the type of beam-propagation paths that could be used as a reference for some proposed analytical or numerical models. We chose a simple beam-propagation path such as a standing beam, either as a point or a straight line. The second set of experiments was carried out to demonstrate the thin-plate bending effects that occur during the laser hole drilling. The deformations of the plate must be maintained within certain tolerances, and the presented measuring technique can be very useful for adjusting the process parameters accurately and quickly. In the last set of experiments we demonstrate the application of flattening a deformed plate. The deformation could be the result of mechanical loads or due to previous surface-processing techniques involving a laser, such as drilling, engraving, or cutting.

2. Experimental set-up

The experimental set-up for the laser surface processing is shown in Fig. 1. The main components are the processing laser with its XY scanning head, the shape-measuring apparatus and the personal computer. The experimental set-up is constructed in such a way that the specimen’s top side is laser processed, while the measurements are made simultaneously on the bottom side of the specimen. The problem of the very intense scattered light from the processing laser, which disables the shape measurement near this point [11], is effectively solved by using such a configuration.

The specimens are 0.1, 0.2 or 0.5 mm thick. The material is Ck 101 [13] with a yield stress of 1275 N/mm2, a tensile stress of ~1500 N/mm2 and an elongation of 6%.

 

Fig. 1. Experimental set-up.

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The processing laser is a diode-pumped Nd-YAG laser with a wavelength of 1064 nm. It can operate in either pulsed or continuous modes. The pulse duration varies from 50 to 600 ns and its maximum average output power is 8 W. Both the pulse duration and the maximum power are functions of the frequency and the electrical current that drives the diode. The XY galvo-type scanning head has an f-theta lens with a 160-mm focal length. It has a square scanning region with side lengths of 90 mm. The resolution along each axis is 1.5 μm, the maximum traveling speed of the beam is 90 m/sec, and the minimum traveling speed is 1.8 mm/sec. This laser system is primarily designed for marking or engraving applications, but the laser drilling of small-diameter holes and the cutting of thin plates can also be accommodated.

The shape-measuring apparatus is based on the multiple-line laser triangulation principle, similar to the one used in [14]. It consists of a laser projector and a camera. The laser projector (Lasiris SNF-533L, 20 mW, 670 nm) generates a light pattern of 33 equally inclined light planes that are directed toward the measured surface. The middle light plane has a higher intensity than the others. The camera (Basler 301f, 656×494 pix., 8 bit, 80 frames/sec, Fire Wire) records the illuminated surface from a different viewpoint, and consequently, the light pattern is distorted by the shape of the surface. To improve the image contrast an interference filter (10 nm FWHM, center at 670 nm) is placed between the lens and the camera’s CCD sensor.

The measuring apparatus is designed to operate in two modes: high-speed and real-time. In the high-speed mode the image sequence is acquired first, and the processing is done later. The maximum acquisition speed is limited to 80 Hz by the camera. In the real-time measuring mode all the processing is done after each image is acquired. The maximum measuring speed is, therefore, lower. However, it is still fairly high, approximately 5 Hz, when using a 1 GHz Celeron processor.

After the acquisition the image is transferred to the computer. The next step is to use the sub-pixel line-detection algorithm, which is based on the first-derivative zero-crossing of pixel values perpendicular to the lines. After this the image is reconstructed into three-dimensional coordinates and by knowing the exact relationship between the detected lines and the light planes, an absolute three-dimensional transformation can be performed. Finally, the measured points on the surface are triangulated and displayed in the interactive viewer. This viewer can be used for an interactive distance measurement, a surface approximation, or a surface comparison with the reference surface.

The measuring range of the apparatus is approximately 40×30 mm in the horizontal plane and approximately 10 mm in the vertical direction. The calibration is made in situ, simply by replacing the specimen with the reference sample: a groove-shaped plate, which is measured at various heights. The transformation parameters are then numerically optimized until the minimum deviation (the sum of the squared errors) between the measured points and the reference surface is found. The major advantage of this procedure is that all the transformation parameters can be determined in a single measuring step, i.e., the camera’s internal parameters (focal length, central point and distortion), the projector’s distortion and the projector’s position relative to the camera (rotation and translation). The accuracy of the calibrated apparatus in vertical direction is ±7 μm, which is calculated as a standard deviation between points of a measured and nominal reference surface.

This relatively high accuracy was achieved by employing some additional actions. In the case of a shiny surface, the specimens were given a removable white coating (HELLING gmbh, Standard-Check, medium nr. 3) on their bottom, i.e., measurable, surface. The influence of the speckle noise was further minimized by setting the aperture of the camera lens to its highest value (f/1.4). The remaining high-frequency noise – mostly due to speckles and surface roughness – was filtered out by applying a spatial average over a line length of approximately 1 mm during the line-detection phase. And finally, the calibration and measuring procedure were always performed after constant temperature conditions were achieved.

3. Results and discussion

To illustrate the basic mechanisms that cause the plate bending, experiments with a very simple beam-propagation path and a range of basic laser-processing parameters—light intensity, beam diameter, and illumination time—were performed first. For this reason, point illumination was chosen for the first set of experiments. The 0.1-mm-thick plate was clamped circularly (with a radius of 12.5 mm) and illuminated at its center, i.e., near cyclic-symmetrical loading conditions were achieved. The laser worked in continuous mode at maximum power and only the beam diameter and the illumination time were varied. The images in the first row of Fig. 2 show the growing deformation for a 200-μm laser-beam diameter and a 2-sec illumination time. For the images in the second row the beam diameter was changed to 1 mm, while the illumination time remained the same. The out-of-plane deformation of the plate relative to its initial state is expressed using color variation and magnified by a factor of 10. The most obvious difference between the two sets of measurements is that in the first case (the first row) the plate deflects away from the illumination source, and in the second case the plate deflects toward to the illumination source. However, after many experiments we observed that the direction of the deflection is associated with the initial deformation of the plate, and not with the beam width, which mainly affects the type of bending mechanism. We assume that in both cases the buckling mechanism was present. The next difference relates to the deformation amplitude: the more focused is the laser beam, the bigger is the deformation. We found that the permanent deformations were about twenty times smaller than the maximum deformation, which was mainly due to us using a high-strength steel plate.

 

Fig. 2. Plate deformation during laser-spot illumination. The beam diameter was 200 μm for the first row, and 1 mm for the second row. The illumination time was 2 sec in both cases. The vertical axes in the graphs are magnified 10 times. [Media 1]

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As a result of the rapidly growing number of published numerical simulations involving laser bending processes where the beam-propagation path is a straight line along the entire plate width, a second set of experiments was undertaken to look at plate deformation during such an illumination procedure. The 0.2-mm-thick, 25×40-mm plate was freely supported on its two shorter sides. The laser was operated in continuous mode, the beam diameter was 200 μm, and the beam-propagation speed was 1.8 mm/s. From Fig. 3 and from the movie clip the bending process can be clearly observed; it is also clear that quite complex thermo-mechanical effects are present. The most interesting of these are the phenomena at the start of the illumination. We can see, for example, that the deformation during the first scan has the opposite sign to the deformation during subsequent scans. In addition, the location of the current beam is clearly visible throughout the entire process because the position of the current beam is reflected in the point of maximum deformation. The plate was scanned four times, and the time between two consecutive scans was ~20 sec.

 

Fig. 3. Plate deformation during laser illumination with a linear beam-propagation path. The image shows the plate deformation during the third scan at the moment when the beam reaches ¾ of the plate width. The vertical axis is magnified 10 times. [Media 2]

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The next experiment shows the deformation effects during the laser drilling of a small-diameter hole into a 0.2-mm-thick plate. In this case the laser was operated in pulsed mode, and the frequency was varied from 50 kHz down to 442 Hz. The plates were clamped circularly, the same way as in the first set of experiments. The pulse duration also varied, depending on the variation in the frequency, which is related to the size of the heat-affected zone. As a consequence, the final deformation is closely related to the frequency. Figure 4 shows the deformed plates, where the hole was made using different frequencies. Color is used to represent the deformation amplitude. The maximum deformation was found to occur at 50 kHz; the minimum was at 442 Hz, which is below the detection limit of the apparatus.

 

Fig. 4. Plate deformation after laser drilling with various frequencies.

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The last set of experiments demonstrates the possibility of using the most sophisticated combination of laser-based processing and measuring techniques. Figure 5 illustrates the flattening process for a 0.2-mm-thick plate that was deformed during some previous laser-based drilling (the frequency was 20 kHz). The clamping used during the flattening was the same as used in the drilling experiments. The first image shows the deformed plate after the laser drilling. The convex-shaped deformation has maximum amplitude of 0.021 mm and a radius of ~3 mm. The flattening strategy involved encircling (i.e., drawing circles) around the peak at a radius of 4 mm. The laser was operated in CW mode at maximum power (8 W) and the beam diameter was 500 μm. For the flattening the plate was illuminated from the same side as during the drilling. The next three images show the progress of the flattening after each encircling step. The deformation is two times smaller after the first step. After the second encircling step the peak is no longer visible, but some negative (blue) deformation has occurred. After the third encircling the amount of this negative deformation has increased. We can conclude, therefore, that the plate was optimally flattened after the second encircling step.

 

Fig. 5. Laser-based flattening of a convex-shaped plate deformation.

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The proper shape-measuring apparatus plays an important role in the various stages of the laser-based flattening process: first, it locates the deformed features; second, it helps to select the proper beam-propagation path; and third, it helps us to observe the progress of the flattening—and tell us how well the process is going—in real time.

4. Conclusions

Our high-speed technique for three-dimensional measurements of plate deformation presented above is opening up new possibilities for monitoring and controlling various laser-processing techniques, e.g., laser forming, drilling, cutting, and engraving. The measuring apparatus is designed to operate in high-speed mode with subsequent image processing and a measuring speed of 80 Hz. Alternatively, we can operate in real-time mode, and the speed of the surface-deformation observation is 5 Hz. In both cases the accuracy is ±7 μm. The full-field absolute-distance measurement is performed on a single acquired image. The problem of very intense scattered light from the processing laser, which disables the shape measurement near this point, is effectively solved by using a configuration where the plate is measured from the opposite side relative to the processing laser. When this is not possible, due to, for example, hollow specimens without any convenient opening, there is still a front-side solution. But in this case a more powerful laser projector should be used together with the already included narrow-band interference filter, which is placed in front of the camera and is intended to transmit only the light that has the same wavelength as the projector emits.

In the first set of experiments we chose a simple beam-propagation path such as a standing beam, either as a point or a straight line. The second set of experiments was carried out to demonstrate the thin-plate bending effects during the laser hole drilling. The presented measuring technique is a very useful tool that can help to adjust the process parameters accurately and quickly in order to control the maximum allowable deformations. In the last set of experiments we demonstrated the application of flattening a plate that had been deformed by a previous laser drilling process.

Reference and links

1. V. Kovalenko and R. Zhuk, “Systemized approach in laser industrial systems design,” J. Mat. Processing Technol. 149 (1–3), 553–556 (2004). [CrossRef]  

2. K. G. Watkins, S.P. Edwardson, J. Magee, G. Dearden, and P. French, “Laser Forming of Aerospace Alloys,” Proceedings of the 2001 Aerospace Congress SAE Aerospace Manufacturing Technology Conference Seattle (2001).

3. M. Dove, J. Možina, and F. Kosel, “Optimizing the final deformation of a circular plate illuminated by a short laser pulse,” J. Phys. D: Appl. Phys. 32, 644–649 (1999). [CrossRef]  

4. L. Zhang and P. Michaleris, “Investigation of Lagrangian and Eulerian finite element methods for modeling the laser forming process,” Finite Elements in Analysis and Design 40(4), 383–405 (2004). [CrossRef]  

5. J. Bao and Y. L. Yao, “Analysis and Prediction of Edge Effects in Laser Bending,” ASME Trans. J. Manufacturing Sci. Eng. 123(1), 53–61 (2001). [CrossRef]  

6. Jitae Kim and S. J. Na, “Feedback control for 2D free curve laser forming,” Optics & Laser Technology In Press, Corrected Proof, Available online 26 April 2004.

7. G. Thomson and M. Pridham, “A feedback control system for laser forming,” Mechatronics 7(5), 429–441 (1997). [CrossRef]  

8. An. K. Kyrsanidi, Th. B. Kermanidis, and Sp. G. Pantelakis, “Numerical and experimental investigation of the laser forming process,” J. Mat. Processing Technol. 87(1–3), 281–290 (1999). [CrossRef]  

9. H.S. Hsieh and J. Lin, “Thermal-mechanical analysis on the transient deformation during pulsed laser forming,” International J. Machine Tools and Manufacture 44 (2–3), 191–199 (2004).

10. Z. Hu, R. Kovacevic, and M. Labudovic, “Experimental and numerical modeling of buckling instability of laser sheet forming,” International Journal of Machine Tools and Manufacture 42(13), 1427–1439 (2002).

11. M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003). [CrossRef]  

12. B. Curless, New Methods for Surface Reconstruction from Range Images (Stanford - Ph.D. Dissertation1997).

13. DIN 17222, “Kaltgewalzte Stahlbänder für Federen,” Deutsche Normen August 1997.

14. D. Bračun, M. Jezeršek, and J. Možina, “Apparatus for determining size and shape of a foot,” PCT patent nr. WO2004037085 (2004).

References

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  1. V. Kovalenko and R. Zhuk, “Systemized approach in laser industrial systems design,” J. Mat. Processing Technol. 149 (1–3), 553–556 (2004).
    [CrossRef]
  2. K. G. Watkins, S.P. Edwardson, J. Magee, G. Dearden, and P. French, “Laser Forming of Aerospace Alloys,” Proceedings of the 2001 Aerospace Congress SAE Aerospace Manufacturing Technology Conference Seattle (2001).
  3. M. Dove, J. Možina, and F. Kosel, “Optimizing the final deformation of a circular plate illuminated by a short laser pulse,” J. Phys. D: Appl. Phys. 32, 644–649 (1999).
    [CrossRef]
  4. L. Zhang and P. Michaleris, “Investigation of Lagrangian and Eulerian finite element methods for modeling the laser forming process,” Finite Elements in Analysis and Design 40(4), 383–405 (2004).
    [CrossRef]
  5. J. Bao and Y. L. Yao, “Analysis and Prediction of Edge Effects in Laser Bending,” ASME Trans. J. Manufacturing Sci. Eng. 123(1), 53–61 (2001).
    [CrossRef]
  6. Jitae Kim and S. J. Na, “Feedback control for 2D free curve laser forming,” Optics & Laser Technology In Press, Corrected Proof, Available online 26 April 2004.
  7. G. Thomson and M. Pridham, “A feedback control system for laser forming,” Mechatronics 7(5), 429–441 (1997).
    [CrossRef]
  8. An. K. Kyrsanidi, Th. B. Kermanidis, and Sp. G. Pantelakis, “Numerical and experimental investigation of the laser forming process,” J. Mat. Processing Technol. 87(1–3), 281–290 (1999).
    [CrossRef]
  9. H.S. Hsieh and J. Lin, “Thermal-mechanical analysis on the transient deformation during pulsed laser forming,” International J. Machine Tools and Manufacture  44 (2–3), 191–199 (2004).
  10. Z. Hu, R. Kovacevic, and M. Labudovic, “Experimental and numerical modeling of buckling instability of laser sheet forming,” International Journal of Machine Tools and Manufacture  42(13), 1427–1439 (2002).
  11. M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
    [CrossRef]
  12. B. Curless, New Methods for Surface Reconstruction from Range Images (Stanford - Ph.D. Dissertation1997).
  13. DIN 17222, “Kaltgewalzte Stahlbänder für Federen,” Deutsche Normen August 1997.
  14. D. Bračun, M. Jezeršek, and J. Možina, “Apparatus for determining size and shape of a foot,” PCT patent nr. WO2004037085 (2004).

2004 (3)

V. Kovalenko and R. Zhuk, “Systemized approach in laser industrial systems design,” J. Mat. Processing Technol. 149 (1–3), 553–556 (2004).
[CrossRef]

L. Zhang and P. Michaleris, “Investigation of Lagrangian and Eulerian finite element methods for modeling the laser forming process,” Finite Elements in Analysis and Design 40(4), 383–405 (2004).
[CrossRef]

H.S. Hsieh and J. Lin, “Thermal-mechanical analysis on the transient deformation during pulsed laser forming,” International J. Machine Tools and Manufacture  44 (2–3), 191–199 (2004).

2003 (1)

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

2002 (1)

Z. Hu, R. Kovacevic, and M. Labudovic, “Experimental and numerical modeling of buckling instability of laser sheet forming,” International Journal of Machine Tools and Manufacture  42(13), 1427–1439 (2002).

2001 (1)

J. Bao and Y. L. Yao, “Analysis and Prediction of Edge Effects in Laser Bending,” ASME Trans. J. Manufacturing Sci. Eng. 123(1), 53–61 (2001).
[CrossRef]

1999 (2)

M. Dove, J. Možina, and F. Kosel, “Optimizing the final deformation of a circular plate illuminated by a short laser pulse,” J. Phys. D: Appl. Phys. 32, 644–649 (1999).
[CrossRef]

An. K. Kyrsanidi, Th. B. Kermanidis, and Sp. G. Pantelakis, “Numerical and experimental investigation of the laser forming process,” J. Mat. Processing Technol. 87(1–3), 281–290 (1999).
[CrossRef]

1997 (1)

G. Thomson and M. Pridham, “A feedback control system for laser forming,” Mechatronics 7(5), 429–441 (1997).
[CrossRef]

Bao, J.

J. Bao and Y. L. Yao, “Analysis and Prediction of Edge Effects in Laser Bending,” ASME Trans. J. Manufacturing Sci. Eng. 123(1), 53–61 (2001).
[CrossRef]

Bracun, D.

D. Bračun, M. Jezeršek, and J. Možina, “Apparatus for determining size and shape of a foot,” PCT patent nr. WO2004037085 (2004).

Curless, B.

B. Curless, New Methods for Surface Reconstruction from Range Images (Stanford - Ph.D. Dissertation1997).

Dearden, G.

K. G. Watkins, S.P. Edwardson, J. Magee, G. Dearden, and P. French, “Laser Forming of Aerospace Alloys,” Proceedings of the 2001 Aerospace Congress SAE Aerospace Manufacturing Technology Conference Seattle (2001).

Dove, M.

M. Dove, J. Možina, and F. Kosel, “Optimizing the final deformation of a circular plate illuminated by a short laser pulse,” J. Phys. D: Appl. Phys. 32, 644–649 (1999).
[CrossRef]

Edwardson, S.P.

K. G. Watkins, S.P. Edwardson, J. Magee, G. Dearden, and P. French, “Laser Forming of Aerospace Alloys,” Proceedings of the 2001 Aerospace Congress SAE Aerospace Manufacturing Technology Conference Seattle (2001).

French, P.

K. G. Watkins, S.P. Edwardson, J. Magee, G. Dearden, and P. French, “Laser Forming of Aerospace Alloys,” Proceedings of the 2001 Aerospace Congress SAE Aerospace Manufacturing Technology Conference Seattle (2001).

Hand, D. P.

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

Hsieh, H.S.

H.S. Hsieh and J. Lin, “Thermal-mechanical analysis on the transient deformation during pulsed laser forming,” International J. Machine Tools and Manufacture  44 (2–3), 191–199 (2004).

Hu, Z.

Z. Hu, R. Kovacevic, and M. Labudovic, “Experimental and numerical modeling of buckling instability of laser sheet forming,” International Journal of Machine Tools and Manufacture  42(13), 1427–1439 (2002).

Jezeršek, M.

D. Bračun, M. Jezeršek, and J. Možina, “Apparatus for determining size and shape of a foot,” PCT patent nr. WO2004037085 (2004).

Jones, J. D. C.

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

Kermanidis, Th. B.

An. K. Kyrsanidi, Th. B. Kermanidis, and Sp. G. Pantelakis, “Numerical and experimental investigation of the laser forming process,” J. Mat. Processing Technol. 87(1–3), 281–290 (1999).
[CrossRef]

Kim, Jitae

Jitae Kim and S. J. Na, “Feedback control for 2D free curve laser forming,” Optics & Laser Technology In Press, Corrected Proof, Available online 26 April 2004.

Kosel, F.

M. Dove, J. Možina, and F. Kosel, “Optimizing the final deformation of a circular plate illuminated by a short laser pulse,” J. Phys. D: Appl. Phys. 32, 644–649 (1999).
[CrossRef]

Kovacevic, R.

Z. Hu, R. Kovacevic, and M. Labudovic, “Experimental and numerical modeling of buckling instability of laser sheet forming,” International Journal of Machine Tools and Manufacture  42(13), 1427–1439 (2002).

Kovalenko, V.

V. Kovalenko and R. Zhuk, “Systemized approach in laser industrial systems design,” J. Mat. Processing Technol. 149 (1–3), 553–556 (2004).
[CrossRef]

Kyrsanidi, An. K.

An. K. Kyrsanidi, Th. B. Kermanidis, and Sp. G. Pantelakis, “Numerical and experimental investigation of the laser forming process,” J. Mat. Processing Technol. 87(1–3), 281–290 (1999).
[CrossRef]

Labudovic, M.

Z. Hu, R. Kovacevic, and M. Labudovic, “Experimental and numerical modeling of buckling instability of laser sheet forming,” International Journal of Machine Tools and Manufacture  42(13), 1427–1439 (2002).

Lin, J.

H.S. Hsieh and J. Lin, “Thermal-mechanical analysis on the transient deformation during pulsed laser forming,” International J. Machine Tools and Manufacture  44 (2–3), 191–199 (2004).

Magee, J.

K. G. Watkins, S.P. Edwardson, J. Magee, G. Dearden, and P. French, “Laser Forming of Aerospace Alloys,” Proceedings of the 2001 Aerospace Congress SAE Aerospace Manufacturing Technology Conference Seattle (2001).

Michaleris, P.

L. Zhang and P. Michaleris, “Investigation of Lagrangian and Eulerian finite element methods for modeling the laser forming process,” Finite Elements in Analysis and Design 40(4), 383–405 (2004).
[CrossRef]

Moore, A. J.

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

Možina, J.

M. Dove, J. Možina, and F. Kosel, “Optimizing the final deformation of a circular plate illuminated by a short laser pulse,” J. Phys. D: Appl. Phys. 32, 644–649 (1999).
[CrossRef]

D. Bračun, M. Jezeršek, and J. Možina, “Apparatus for determining size and shape of a foot,” PCT patent nr. WO2004037085 (2004).

Na, S. J.

Jitae Kim and S. J. Na, “Feedback control for 2D free curve laser forming,” Optics & Laser Technology In Press, Corrected Proof, Available online 26 April 2004.

Pantelakis, Sp. G.

An. K. Kyrsanidi, Th. B. Kermanidis, and Sp. G. Pantelakis, “Numerical and experimental investigation of the laser forming process,” J. Mat. Processing Technol. 87(1–3), 281–290 (1999).
[CrossRef]

Pridham, M.

G. Thomson and M. Pridham, “A feedback control system for laser forming,” Mechatronics 7(5), 429–441 (1997).
[CrossRef]

Reeves, M.

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

Thomson, G.

G. Thomson and M. Pridham, “A feedback control system for laser forming,” Mechatronics 7(5), 429–441 (1997).
[CrossRef]

Watkins, K. G.

K. G. Watkins, S.P. Edwardson, J. Magee, G. Dearden, and P. French, “Laser Forming of Aerospace Alloys,” Proceedings of the 2001 Aerospace Congress SAE Aerospace Manufacturing Technology Conference Seattle (2001).

Yao, Y. L.

J. Bao and Y. L. Yao, “Analysis and Prediction of Edge Effects in Laser Bending,” ASME Trans. J. Manufacturing Sci. Eng. 123(1), 53–61 (2001).
[CrossRef]

Zhang, L.

L. Zhang and P. Michaleris, “Investigation of Lagrangian and Eulerian finite element methods for modeling the laser forming process,” Finite Elements in Analysis and Design 40(4), 383–405 (2004).
[CrossRef]

Zhuk, R.

V. Kovalenko and R. Zhuk, “Systemized approach in laser industrial systems design,” J. Mat. Processing Technol. 149 (1–3), 553–556 (2004).
[CrossRef]

ASME Trans. J. Manufacturing Sci. Eng. (1)

J. Bao and Y. L. Yao, “Analysis and Prediction of Edge Effects in Laser Bending,” ASME Trans. J. Manufacturing Sci. Eng. 123(1), 53–61 (2001).
[CrossRef]

Finite Elements in Analysis and Design (1)

L. Zhang and P. Michaleris, “Investigation of Lagrangian and Eulerian finite element methods for modeling the laser forming process,” Finite Elements in Analysis and Design 40(4), 383–405 (2004).
[CrossRef]

J. Mat. Processing Technol. (2)

V. Kovalenko and R. Zhuk, “Systemized approach in laser industrial systems design,” J. Mat. Processing Technol. 149 (1–3), 553–556 (2004).
[CrossRef]

An. K. Kyrsanidi, Th. B. Kermanidis, and Sp. G. Pantelakis, “Numerical and experimental investigation of the laser forming process,” J. Mat. Processing Technol. 87(1–3), 281–290 (1999).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

M. Dove, J. Možina, and F. Kosel, “Optimizing the final deformation of a circular plate illuminated by a short laser pulse,” J. Phys. D: Appl. Phys. 32, 644–649 (1999).
[CrossRef]

Mechatronics (1)

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Supplementary Material (2)

» Media 1: GIF (2740 KB)     
» Media 2: GIF (3335 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Experimental set-up.

Fig. 2.
Fig. 2.

Plate deformation during laser-spot illumination. The beam diameter was 200 μm for the first row, and 1 mm for the second row. The illumination time was 2 sec in both cases. The vertical axes in the graphs are magnified 10 times. [Media 1]

Fig. 3.
Fig. 3.

Plate deformation during laser illumination with a linear beam-propagation path. The image shows the plate deformation during the third scan at the moment when the beam reaches ¾ of the plate width. The vertical axis is magnified 10 times. [Media 2]

Fig. 4.
Fig. 4.

Plate deformation after laser drilling with various frequencies.

Fig. 5.
Fig. 5.

Laser-based flattening of a convex-shaped plate deformation.

Metrics