Abstract

In this paper, we introduce a method for dynamic and three-dimensional (3D) arc temperature measurement in non-axisymmetric arc plasma. Optical filters with narrow spectral bands are used to gain 696.5 nm line spectral information of a free-burning Argon (Ar) arc. A measuring system with a setup of mirrors allows a single camera chip to image multi-views of identical welding arc onto one monochromatic image. And based on the underlying characteristics of the arc plasma, we present a modified maximum likelihood expectation maximum (ML-EM) algorithm to reconstruct the emission coefficients from the line intensities. To verify the accuracy of our algorithm, two models of arc plasma have been established to simulate the reconstruction process. Simulation results demonstrated that the modified ML-EM can be utilized to improve the performance of 3D reconstruction compared to common ML-EM methods. To obtain the optimal scheme of the measuring system with limited view directions, the reconstruction quality with different directions is presented and discussed. In the experiment, asymmetric 3D plasma temperature distribution was determined at a direct current (DC) of 80 A and 100A. The results proved the feasibility of the 3D temperature measure method to characterize an asymmetric arc.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
    [Crossref]
  2. L. Wu, J. Cheon, D. Kiran, and S. J. Na, “CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models,” J. Mater. Process. Technol. 231, 221–238 (2016).
    [Crossref]
  3. X. Xiao, X. Hua, F. Li, and Y. Wu, “A modified Fowler–Milne method for monochromatic image analysis in multi-element arc plasma welding,” J. Mater. Process. Technol. 214(11), 2770–2776 (2014).
    [Crossref]
  4. L. O. Vilarinho and A. Scotti, “Proposal for a modified Fowler-Milne method to determine the temperature profile in TIG welding at low currents,” J. Braz. Soc. Mech. Sci. Eng. 26(1), 34–39 (2004).
    [Crossref]
  5. J. Hlina, J. Sonsky, J. Gruber, and Y. Cressault, “Fast tomographic measurements of temperature in an air plasma cutting torch,” J. Phys. D Appl. Phys. 49(10), 105202 (2016).
    [Crossref]
  6. G. N. Haddad and A. J. D. Farmer, “Temperature determinations in a free-burning arc. I. Experimental techniques and results in argon,” J. Phys. D Appl. Phys. 17(2), 139–151 (1984).
  7. M. F. Thornton, “Spectroscopic determination of temperature distributions for a TIG arc,” J. Phys. D Appl. Phys. 26(9), 1432–1438 (1993).
    [Crossref]
  8. S. Ma, H. Gao, S. Zheng, and L. Wu, “Spectroscopic measurement of temperatures in pulsed TIG welding arcs,” J. Phys. D Appl. Phys. 44(40), 405202 (2011).
    [Crossref]
  9. X. Xiao, X. Hua, and Y. Wu, “Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma,” Opt. Laser Technol. 66, 138–145 (2015).
    [Crossref]
  10. S. Ma, H. Gao, and L. Wu, “Modified Fowler-Milne method for the spectroscopic determination of thermal plasma temperature without the measurement of continuum radiation,” Rev. Sci. Instrum. 82(1), 013104 (2011).
    [Crossref] [PubMed]
  11. H. N. Olsen, “The electric arc as a light source for quantitative spectroscopy,” J. Quant. Spectrosc. Radiat. Transf. 3(4), 305–333 (1963).
    [Crossref]
  12. J. Yan, M. Gao, and X. Zeng, “Study on microstructure and mechanical properties of 304 stainless steel joints by TIG, laser and laserTIG hybrid welding,” Opt. Lasers Eng. 48(4), 512–517 (2010).
    [Crossref]
  13. M. B. Schwedersky, J. C. Dutra, R. H. G. E. Silva, U. Reisgen, and K. Willms, “Double-electrode process speeds GTAW,” Weld. J. 94(10), 64–67 (2015).
  14. T. Yang, H. Gao, S. Zhang, J. Shi, and L. Wu, “The study on plasma-Mig hybrid arc behaviour and droplet transfer for mild steel welding,” Rev. Adv. Mater. Sci. 33(5), 459–464 (2013).
  15. Y. Gao, Q. Yu, W. Jiang, and W. Xiong, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
    [Crossref]
  16. J. Hlína, F. Chvála, J. Šonský, and J. Gruber, “Multi-directional optical diagnostics of thermal plasma jets,” Meas. Sci. Technol. 19(19), 015407 (2007).
  17. G. Zhang, J. Xiong, H. Gao, and L. Wu, “Reconstruction of emission coefficients for a non-axisymmetric coupling arc by algebraic reconstruction technique,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 92–99 (2011).
    [Crossref]
  18. G. Zhang, J. Xiong, H. Gao, and L. Wu, “Effect of process parameters on temperature distribution in twin-electrode TIG coupling arc,” J. Quant. Spectrosc. Radiat. Transf. 113(15), 1938–1945 (2012).
    [Crossref]
  19. N. Kazufumi, K. Takashi, S. Kentaro, H. Yoshinori, and K. Kotaro, “Temperature measurement of asymmetrical pulsed TIG arc plasma by multidirectional monochromatic imaging method,” Weld. World 59(2), 283–293 (2015).
    [Crossref]
  20. K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
    [Crossref]
  21. K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).
  22. G. Wang, H. T. Tsui, Z. Hu, and F. Wu, “Camera calibration and 3D reconstruction from a single view based on scene constraints,” image. Vis. Comput. 23(3), 311–323 (2005).
    [Crossref]

2016 (3)

L. Wu, J. Cheon, D. Kiran, and S. J. Na, “CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models,” J. Mater. Process. Technol. 231, 221–238 (2016).
[Crossref]

J. Hlina, J. Sonsky, J. Gruber, and Y. Cressault, “Fast tomographic measurements of temperature in an air plasma cutting torch,” J. Phys. D Appl. Phys. 49(10), 105202 (2016).
[Crossref]

K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).

2015 (3)

N. Kazufumi, K. Takashi, S. Kentaro, H. Yoshinori, and K. Kotaro, “Temperature measurement of asymmetrical pulsed TIG arc plasma by multidirectional monochromatic imaging method,” Weld. World 59(2), 283–293 (2015).
[Crossref]

X. Xiao, X. Hua, and Y. Wu, “Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma,” Opt. Laser Technol. 66, 138–145 (2015).
[Crossref]

M. B. Schwedersky, J. C. Dutra, R. H. G. E. Silva, U. Reisgen, and K. Willms, “Double-electrode process speeds GTAW,” Weld. J. 94(10), 64–67 (2015).

2014 (1)

X. Xiao, X. Hua, F. Li, and Y. Wu, “A modified Fowler–Milne method for monochromatic image analysis in multi-element arc plasma welding,” J. Mater. Process. Technol. 214(11), 2770–2776 (2014).
[Crossref]

2013 (2)

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

T. Yang, H. Gao, S. Zhang, J. Shi, and L. Wu, “The study on plasma-Mig hybrid arc behaviour and droplet transfer for mild steel welding,” Rev. Adv. Mater. Sci. 33(5), 459–464 (2013).

2012 (1)

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Effect of process parameters on temperature distribution in twin-electrode TIG coupling arc,” J. Quant. Spectrosc. Radiat. Transf. 113(15), 1938–1945 (2012).
[Crossref]

2011 (3)

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Reconstruction of emission coefficients for a non-axisymmetric coupling arc by algebraic reconstruction technique,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 92–99 (2011).
[Crossref]

S. Ma, H. Gao, S. Zheng, and L. Wu, “Spectroscopic measurement of temperatures in pulsed TIG welding arcs,” J. Phys. D Appl. Phys. 44(40), 405202 (2011).
[Crossref]

S. Ma, H. Gao, and L. Wu, “Modified Fowler-Milne method for the spectroscopic determination of thermal plasma temperature without the measurement of continuum radiation,” Rev. Sci. Instrum. 82(1), 013104 (2011).
[Crossref] [PubMed]

2010 (2)

J. Yan, M. Gao, and X. Zeng, “Study on microstructure and mechanical properties of 304 stainless steel joints by TIG, laser and laserTIG hybrid welding,” Opt. Lasers Eng. 48(4), 512–517 (2010).
[Crossref]

Y. Gao, Q. Yu, W. Jiang, and W. Xiong, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

2009 (1)

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

2007 (1)

J. Hlína, F. Chvála, J. Šonský, and J. Gruber, “Multi-directional optical diagnostics of thermal plasma jets,” Meas. Sci. Technol. 19(19), 015407 (2007).

2005 (1)

G. Wang, H. T. Tsui, Z. Hu, and F. Wu, “Camera calibration and 3D reconstruction from a single view based on scene constraints,” image. Vis. Comput. 23(3), 311–323 (2005).
[Crossref]

2004 (1)

L. O. Vilarinho and A. Scotti, “Proposal for a modified Fowler-Milne method to determine the temperature profile in TIG welding at low currents,” J. Braz. Soc. Mech. Sci. Eng. 26(1), 34–39 (2004).
[Crossref]

1993 (1)

M. F. Thornton, “Spectroscopic determination of temperature distributions for a TIG arc,” J. Phys. D Appl. Phys. 26(9), 1432–1438 (1993).
[Crossref]

1984 (1)

G. N. Haddad and A. J. D. Farmer, “Temperature determinations in a free-burning arc. I. Experimental techniques and results in argon,” J. Phys. D Appl. Phys. 17(2), 139–151 (1984).

1963 (1)

H. N. Olsen, “The electric arc as a light source for quantitative spectroscopy,” J. Quant. Spectrosc. Radiat. Transf. 3(4), 305–333 (1963).
[Crossref]

Bachmann, B.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Bachmann, J. P.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Cheon, J.

L. Wu, J. Cheon, D. Kiran, and S. J. Na, “CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models,” J. Mater. Process. Technol. 231, 221–238 (2016).
[Crossref]

Chvála, F.

J. Hlína, F. Chvála, J. Šonský, and J. Gruber, “Multi-directional optical diagnostics of thermal plasma jets,” Meas. Sci. Technol. 19(19), 015407 (2007).

Cressault, Y.

J. Hlina, J. Sonsky, J. Gruber, and Y. Cressault, “Fast tomographic measurements of temperature in an air plasma cutting torch,” J. Phys. D Appl. Phys. 49(10), 105202 (2016).
[Crossref]

Dutra, J. C.

M. B. Schwedersky, J. C. Dutra, R. H. G. E. Silva, U. Reisgen, and K. Willms, “Double-electrode process speeds GTAW,” Weld. J. 94(10), 64–67 (2015).

Ekkert, K.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Farmer, A. J. D.

G. N. Haddad and A. J. D. Farmer, “Temperature determinations in a free-burning arc. I. Experimental techniques and results in argon,” J. Phys. D Appl. Phys. 17(2), 139–151 (1984).

Gao, H.

T. Yang, H. Gao, S. Zhang, J. Shi, and L. Wu, “The study on plasma-Mig hybrid arc behaviour and droplet transfer for mild steel welding,” Rev. Adv. Mater. Sci. 33(5), 459–464 (2013).

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Effect of process parameters on temperature distribution in twin-electrode TIG coupling arc,” J. Quant. Spectrosc. Radiat. Transf. 113(15), 1938–1945 (2012).
[Crossref]

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Reconstruction of emission coefficients for a non-axisymmetric coupling arc by algebraic reconstruction technique,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 92–99 (2011).
[Crossref]

S. Ma, H. Gao, and L. Wu, “Modified Fowler-Milne method for the spectroscopic determination of thermal plasma temperature without the measurement of continuum radiation,” Rev. Sci. Instrum. 82(1), 013104 (2011).
[Crossref] [PubMed]

S. Ma, H. Gao, S. Zheng, and L. Wu, “Spectroscopic measurement of temperatures in pulsed TIG welding arcs,” J. Phys. D Appl. Phys. 44(40), 405202 (2011).
[Crossref]

Gao, M.

J. Yan, M. Gao, and X. Zeng, “Study on microstructure and mechanical properties of 304 stainless steel joints by TIG, laser and laserTIG hybrid welding,” Opt. Lasers Eng. 48(4), 512–517 (2010).
[Crossref]

Gao, Y.

Y. Gao, Q. Yu, W. Jiang, and W. Xiong, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Gött, G.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Gruber, J.

J. Hlina, J. Sonsky, J. Gruber, and Y. Cressault, “Fast tomographic measurements of temperature in an air plasma cutting torch,” J. Phys. D Appl. Phys. 49(10), 105202 (2016).
[Crossref]

J. Hlína, F. Chvála, J. Šonský, and J. Gruber, “Multi-directional optical diagnostics of thermal plasma jets,” Meas. Sci. Technol. 19(19), 015407 (2007).

Haddad, G. N.

G. N. Haddad and A. J. D. Farmer, “Temperature determinations in a free-burning arc. I. Experimental techniques and results in argon,” J. Phys. D Appl. Phys. 17(2), 139–151 (1984).

Hlina, J.

J. Hlina, J. Sonsky, J. Gruber, and Y. Cressault, “Fast tomographic measurements of temperature in an air plasma cutting torch,” J. Phys. D Appl. Phys. 49(10), 105202 (2016).
[Crossref]

Hlína, J.

J. Hlína, F. Chvála, J. Šonský, and J. Gruber, “Multi-directional optical diagnostics of thermal plasma jets,” Meas. Sci. Technol. 19(19), 015407 (2007).

Hu, Z.

G. Wang, H. T. Tsui, Z. Hu, and F. Wu, “Camera calibration and 3D reconstruction from a single view based on scene constraints,” image. Vis. Comput. 23(3), 311–323 (2005).
[Crossref]

Hua, X.

X. Xiao, X. Hua, and Y. Wu, “Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma,” Opt. Laser Technol. 66, 138–145 (2015).
[Crossref]

X. Xiao, X. Hua, F. Li, and Y. Wu, “A modified Fowler–Milne method for monochromatic image analysis in multi-element arc plasma welding,” J. Mater. Process. Technol. 214(11), 2770–2776 (2014).
[Crossref]

Jiang, W.

Y. Gao, Q. Yu, W. Jiang, and W. Xiong, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Kazufumi, N.

N. Kazufumi, K. Takashi, S. Kentaro, H. Yoshinori, and K. Kotaro, “Temperature measurement of asymmetrical pulsed TIG arc plasma by multidirectional monochromatic imaging method,” Weld. World 59(2), 283–293 (2015).
[Crossref]

Kentaro, S.

N. Kazufumi, K. Takashi, S. Kentaro, H. Yoshinori, and K. Kotaro, “Temperature measurement of asymmetrical pulsed TIG arc plasma by multidirectional monochromatic imaging method,” Weld. World 59(2), 283–293 (2015).
[Crossref]

Kiran, D.

L. Wu, J. Cheon, D. Kiran, and S. J. Na, “CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models,” J. Mater. Process. Technol. 231, 221–238 (2016).
[Crossref]

Konishi, K.

K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).

Kotaro, K.

N. Kazufumi, K. Takashi, S. Kentaro, H. Yoshinori, and K. Kotaro, “Temperature measurement of asymmetrical pulsed TIG arc plasma by multidirectional monochromatic imaging method,” Weld. World 59(2), 283–293 (2015).
[Crossref]

Kozakov, R.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Li, F.

X. Xiao, X. Hua, F. Li, and Y. Wu, “A modified Fowler–Milne method for monochromatic image analysis in multi-element arc plasma welding,” J. Mater. Process. Technol. 214(11), 2770–2776 (2014).
[Crossref]

Lowke, J. J.

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Ma, S.

S. Ma, H. Gao, S. Zheng, and L. Wu, “Spectroscopic measurement of temperatures in pulsed TIG welding arcs,” J. Phys. D Appl. Phys. 44(40), 405202 (2011).
[Crossref]

S. Ma, H. Gao, and L. Wu, “Modified Fowler-Milne method for the spectroscopic determination of thermal plasma temperature without the measurement of continuum radiation,” Rev. Sci. Instrum. 82(1), 013104 (2011).
[Crossref] [PubMed]

Marques, J. L.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Murata, A.

K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).

Murata, T.

K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).

Murphy, A. B.

K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Na, S. J.

L. Wu, J. Cheon, D. Kiran, and S. J. Na, “CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models,” J. Mater. Process. Technol. 231, 221–238 (2016).
[Crossref]

Nakata, K.

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Olsen, H. N.

H. N. Olsen, “The electric arc as a light source for quantitative spectroscopy,” J. Quant. Spectrosc. Radiat. Transf. 3(4), 305–333 (1963).
[Crossref]

Reisgen, U.

M. B. Schwedersky, J. C. Dutra, R. H. G. E. Silva, U. Reisgen, and K. Willms, “Double-electrode process speeds GTAW,” Weld. J. 94(10), 64–67 (2015).

Schein, J.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Schöpp, H.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Schwedersky, M. B.

M. B. Schwedersky, J. C. Dutra, R. H. G. E. Silva, U. Reisgen, and K. Willms, “Double-electrode process speeds GTAW,” Weld. J. 94(10), 64–67 (2015).

Scotti, A.

L. O. Vilarinho and A. Scotti, “Proposal for a modified Fowler-Milne method to determine the temperature profile in TIG welding at low currents,” J. Braz. Soc. Mech. Sci. Eng. 26(1), 34–39 (2004).
[Crossref]

Shi, J.

T. Yang, H. Gao, S. Zhang, J. Shi, and L. Wu, “The study on plasma-Mig hybrid arc behaviour and droplet transfer for mild steel welding,” Rev. Adv. Mater. Sci. 33(5), 459–464 (2013).

Shigeta, M.

K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).

Silva, R. H. G. E.

M. B. Schwedersky, J. C. Dutra, R. H. G. E. Silva, U. Reisgen, and K. Willms, “Double-electrode process speeds GTAW,” Weld. J. 94(10), 64–67 (2015).

Sonsky, J.

J. Hlina, J. Sonsky, J. Gruber, and Y. Cressault, “Fast tomographic measurements of temperature in an air plasma cutting torch,” J. Phys. D Appl. Phys. 49(10), 105202 (2016).
[Crossref]

Šonský, J.

J. Hlína, F. Chvála, J. Šonský, and J. Gruber, “Multi-directional optical diagnostics of thermal plasma jets,” Meas. Sci. Technol. 19(19), 015407 (2007).

Suzuki, K.

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Takashi, K.

N. Kazufumi, K. Takashi, S. Kentaro, H. Yoshinori, and K. Kotaro, “Temperature measurement of asymmetrical pulsed TIG arc plasma by multidirectional monochromatic imaging method,” Weld. World 59(2), 283–293 (2015).
[Crossref]

Tanaka, M.

K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Tashiro, S.

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Thornton, M. F.

M. F. Thornton, “Spectroscopic determination of temperature distributions for a TIG arc,” J. Phys. D Appl. Phys. 26(9), 1432–1438 (1993).
[Crossref]

Tsui, H. T.

G. Wang, H. T. Tsui, Z. Hu, and F. Wu, “Camera calibration and 3D reconstruction from a single view based on scene constraints,” image. Vis. Comput. 23(3), 311–323 (2005).
[Crossref]

Uhrlandt, D.

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

Vilarinho, L. O.

L. O. Vilarinho and A. Scotti, “Proposal for a modified Fowler-Milne method to determine the temperature profile in TIG welding at low currents,” J. Braz. Soc. Mech. Sci. Eng. 26(1), 34–39 (2004).
[Crossref]

Wang, G.

G. Wang, H. T. Tsui, Z. Hu, and F. Wu, “Camera calibration and 3D reconstruction from a single view based on scene constraints,” image. Vis. Comput. 23(3), 311–323 (2005).
[Crossref]

Willms, K.

M. B. Schwedersky, J. C. Dutra, R. H. G. E. Silva, U. Reisgen, and K. Willms, “Double-electrode process speeds GTAW,” Weld. J. 94(10), 64–67 (2015).

Wu, F.

G. Wang, H. T. Tsui, Z. Hu, and F. Wu, “Camera calibration and 3D reconstruction from a single view based on scene constraints,” image. Vis. Comput. 23(3), 311–323 (2005).
[Crossref]

Wu, L.

L. Wu, J. Cheon, D. Kiran, and S. J. Na, “CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models,” J. Mater. Process. Technol. 231, 221–238 (2016).
[Crossref]

T. Yang, H. Gao, S. Zhang, J. Shi, and L. Wu, “The study on plasma-Mig hybrid arc behaviour and droplet transfer for mild steel welding,” Rev. Adv. Mater. Sci. 33(5), 459–464 (2013).

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Effect of process parameters on temperature distribution in twin-electrode TIG coupling arc,” J. Quant. Spectrosc. Radiat. Transf. 113(15), 1938–1945 (2012).
[Crossref]

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Reconstruction of emission coefficients for a non-axisymmetric coupling arc by algebraic reconstruction technique,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 92–99 (2011).
[Crossref]

S. Ma, H. Gao, and L. Wu, “Modified Fowler-Milne method for the spectroscopic determination of thermal plasma temperature without the measurement of continuum radiation,” Rev. Sci. Instrum. 82(1), 013104 (2011).
[Crossref] [PubMed]

S. Ma, H. Gao, S. Zheng, and L. Wu, “Spectroscopic measurement of temperatures in pulsed TIG welding arcs,” J. Phys. D Appl. Phys. 44(40), 405202 (2011).
[Crossref]

Wu, Y.

X. Xiao, X. Hua, and Y. Wu, “Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma,” Opt. Laser Technol. 66, 138–145 (2015).
[Crossref]

X. Xiao, X. Hua, F. Li, and Y. Wu, “A modified Fowler–Milne method for monochromatic image analysis in multi-element arc plasma welding,” J. Mater. Process. Technol. 214(11), 2770–2776 (2014).
[Crossref]

Xiao, X.

X. Xiao, X. Hua, and Y. Wu, “Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma,” Opt. Laser Technol. 66, 138–145 (2015).
[Crossref]

X. Xiao, X. Hua, F. Li, and Y. Wu, “A modified Fowler–Milne method for monochromatic image analysis in multi-element arc plasma welding,” J. Mater. Process. Technol. 214(11), 2770–2776 (2014).
[Crossref]

Xiong, J.

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Effect of process parameters on temperature distribution in twin-electrode TIG coupling arc,” J. Quant. Spectrosc. Radiat. Transf. 113(15), 1938–1945 (2012).
[Crossref]

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Reconstruction of emission coefficients for a non-axisymmetric coupling arc by algebraic reconstruction technique,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 92–99 (2011).
[Crossref]

Xiong, W.

Y. Gao, Q. Yu, W. Jiang, and W. Xiong, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Yamamoto, E.

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Yamamoto, K.

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Yamazaki, K.

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

Yan, J.

J. Yan, M. Gao, and X. Zeng, “Study on microstructure and mechanical properties of 304 stainless steel joints by TIG, laser and laserTIG hybrid welding,” Opt. Lasers Eng. 48(4), 512–517 (2010).
[Crossref]

Yang, T.

T. Yang, H. Gao, S. Zhang, J. Shi, and L. Wu, “The study on plasma-Mig hybrid arc behaviour and droplet transfer for mild steel welding,” Rev. Adv. Mater. Sci. 33(5), 459–464 (2013).

Yoshinori, H.

N. Kazufumi, K. Takashi, S. Kentaro, H. Yoshinori, and K. Kotaro, “Temperature measurement of asymmetrical pulsed TIG arc plasma by multidirectional monochromatic imaging method,” Weld. World 59(2), 283–293 (2015).
[Crossref]

Yu, Q.

Y. Gao, Q. Yu, W. Jiang, and W. Xiong, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Zeng, X.

J. Yan, M. Gao, and X. Zeng, “Study on microstructure and mechanical properties of 304 stainless steel joints by TIG, laser and laserTIG hybrid welding,” Opt. Lasers Eng. 48(4), 512–517 (2010).
[Crossref]

Zhang, G.

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Effect of process parameters on temperature distribution in twin-electrode TIG coupling arc,” J. Quant. Spectrosc. Radiat. Transf. 113(15), 1938–1945 (2012).
[Crossref]

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Reconstruction of emission coefficients for a non-axisymmetric coupling arc by algebraic reconstruction technique,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 92–99 (2011).
[Crossref]

Zhang, S.

T. Yang, H. Gao, S. Zhang, J. Shi, and L. Wu, “The study on plasma-Mig hybrid arc behaviour and droplet transfer for mild steel welding,” Rev. Adv. Mater. Sci. 33(5), 459–464 (2013).

Zheng, S.

S. Ma, H. Gao, S. Zheng, and L. Wu, “Spectroscopic measurement of temperatures in pulsed TIG welding arcs,” J. Phys. D Appl. Phys. 44(40), 405202 (2011).
[Crossref]

image. Vis. Comput. (1)

G. Wang, H. T. Tsui, Z. Hu, and F. Wu, “Camera calibration and 3D reconstruction from a single view based on scene constraints,” image. Vis. Comput. 23(3), 311–323 (2005).
[Crossref]

J. Braz. Soc. Mech. Sci. Eng. (1)

L. O. Vilarinho and A. Scotti, “Proposal for a modified Fowler-Milne method to determine the temperature profile in TIG welding at low currents,” J. Braz. Soc. Mech. Sci. Eng. 26(1), 34–39 (2004).
[Crossref]

J. Mater. Process. Technol. (2)

L. Wu, J. Cheon, D. Kiran, and S. J. Na, “CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models,” J. Mater. Process. Technol. 231, 221–238 (2016).
[Crossref]

X. Xiao, X. Hua, F. Li, and Y. Wu, “A modified Fowler–Milne method for monochromatic image analysis in multi-element arc plasma welding,” J. Mater. Process. Technol. 214(11), 2770–2776 (2014).
[Crossref]

J. Phys. D Appl. Phys. (5)

J. Hlina, J. Sonsky, J. Gruber, and Y. Cressault, “Fast tomographic measurements of temperature in an air plasma cutting torch,” J. Phys. D Appl. Phys. 49(10), 105202 (2016).
[Crossref]

G. N. Haddad and A. J. D. Farmer, “Temperature determinations in a free-burning arc. I. Experimental techniques and results in argon,” J. Phys. D Appl. Phys. 17(2), 139–151 (1984).

M. F. Thornton, “Spectroscopic determination of temperature distributions for a TIG arc,” J. Phys. D Appl. Phys. 26(9), 1432–1438 (1993).
[Crossref]

S. Ma, H. Gao, S. Zheng, and L. Wu, “Spectroscopic measurement of temperatures in pulsed TIG welding arcs,” J. Phys. D Appl. Phys. 44(40), 405202 (2011).
[Crossref]

B. Bachmann, R. Kozakov, G. Gött, K. Ekkert, J. P. Bachmann, J. L. Marques, H. Schöpp, D. Uhrlandt, and J. Schein, “High-speed three-dimensional plasma temperature determination of axially symmetric free-burning arcs,” J. Phys. D Appl. Phys. 46(12), 125203 (2013).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (3)

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Reconstruction of emission coefficients for a non-axisymmetric coupling arc by algebraic reconstruction technique,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 92–99 (2011).
[Crossref]

G. Zhang, J. Xiong, H. Gao, and L. Wu, “Effect of process parameters on temperature distribution in twin-electrode TIG coupling arc,” J. Quant. Spectrosc. Radiat. Transf. 113(15), 1938–1945 (2012).
[Crossref]

H. N. Olsen, “The electric arc as a light source for quantitative spectroscopy,” J. Quant. Spectrosc. Radiat. Transf. 3(4), 305–333 (1963).
[Crossref]

Meas. Sci. Technol. (1)

J. Hlína, F. Chvála, J. Šonský, and J. Gruber, “Multi-directional optical diagnostics of thermal plasma jets,” Meas. Sci. Technol. 19(19), 015407 (2007).

Opt. Laser Technol. (2)

Y. Gao, Q. Yu, W. Jiang, and W. Xiong, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

X. Xiao, X. Hua, and Y. Wu, “Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma,” Opt. Laser Technol. 66, 138–145 (2015).
[Crossref]

Opt. Lasers Eng. (1)

J. Yan, M. Gao, and X. Zeng, “Study on microstructure and mechanical properties of 304 stainless steel joints by TIG, laser and laserTIG hybrid welding,” Opt. Lasers Eng. 48(4), 512–517 (2010).
[Crossref]

Rev. Adv. Mater. Sci. (1)

T. Yang, H. Gao, S. Zhang, J. Shi, and L. Wu, “The study on plasma-Mig hybrid arc behaviour and droplet transfer for mild steel welding,” Rev. Adv. Mater. Sci. 33(5), 459–464 (2013).

Rev. Sci. Instrum. (1)

S. Ma, H. Gao, and L. Wu, “Modified Fowler-Milne method for the spectroscopic determination of thermal plasma temperature without the measurement of continuum radiation,” Rev. Sci. Instrum. 82(1), 013104 (2011).
[Crossref] [PubMed]

Weld. J. (1)

M. B. Schwedersky, J. C. Dutra, R. H. G. E. Silva, U. Reisgen, and K. Willms, “Double-electrode process speeds GTAW,” Weld. J. 94(10), 64–67 (2015).

Weld. World (3)

N. Kazufumi, K. Takashi, S. Kentaro, H. Yoshinori, and K. Kotaro, “Temperature measurement of asymmetrical pulsed TIG arc plasma by multidirectional monochromatic imaging method,” Weld. World 59(2), 283–293 (2015).
[Crossref]

K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata, E. Yamamoto, K. Yamazaki, K. Suzuki, A. B. Murphy, and J. J. Lowke, “Numerical simulation of diffusion of multiple metal vapours in a tig arc plasma for welding of stainless steel,” Weld. World 53(7–8), 166–170 (2009).
[Crossref]

K. Konishi, M. Shigeta, M. Tanaka, A. Murata, T. Murata, and A. B. Murphy, “Numerical study on thermal non-equilibrium of arc plasmas in TIG welding processes using a two-temperature model,” Weld. World 61(1), 1–11 (2016).

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Figures (18)

Fig. 1
Fig. 1 Scheme of 3D measurement.
Fig. 2
Fig. 2 (a)Welding arc. (b) emission coefficient distribution at the XY surface. (c)Objective reconstruction area.
Fig. 3
Fig. 3 Scheme of reconstruction process.
Fig. 4
Fig. 4 (a) The location of two sections. (b) Emission coefficient distribution model A (c) Emission coefficient distribution model B
Fig. 5
Fig. 5 Projections of an asymmetric arc at various directions.
Fig. 6
Fig. 6 Measured intensity distribution signal and smooth signal
Fig. 7
Fig. 7 (a) Result of common ML-EM for model A. (b) Result of modified ML-EM for model A. (c) Result of common ML-EM for model B. (d) Result of modified ML-EM for model B.
Fig. 8
Fig. 8 (a) Result of common ML-EM with projections of different SNR. (b) Result of modified ML-EM with projections of different SNR.
Fig. 9
Fig. 9 (a) Result of five-views. (b) Result of six-views. (c) Reconstruction error versus iteration times.
Fig. 10
Fig. 10 (a)Result of five-views. (b) Result of six-views. (c) Reconstruction error versus iteration times.
Fig. 11
Fig. 11 Scheme of captured projections.
Fig. 12
Fig. 12 Schematic of the measurement system.
Fig. 13
Fig. 13 Coordinate system of camera.
Fig. 14
Fig. 14 (a) Schematic of verification. (b) Verification of P3 acquisition channel.
Fig. 15
Fig. 15 Grayscale image captured by the CMOS.
Fig. 16
Fig. 16 (a) Five arc projections at 0°, 36°, 72°, 108°, and 144°. (b) Emission coefficient distribution of arc plasma.
Fig. 17
Fig. 17 (a)The relationship between normalized emission coefficients and temperature. (b)Measured temperature distribution of arc plasma.
Fig. 18
Fig. 18 (a)Temperature distribution of arc plasma at z = -1 and z = -4 mm surface. (b)Measured temperature distribution in previous research [19].

Equations (13)

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g( j )= i=0 M P i ( n ).
{ f j ( k ) =0,   g( j )<T f j ( k )* = f j ( k ) ,   g( j )>T ,
S= 1 40 ( 1 4 1 4 20 4 1 4 1 ).
f j ( k+1 ) = i=1 M w ij ×p( n ) i=1 N w ij × f j ( k )** i=1 M w ij × f j ( k )** .
SNR=10lg( Ps Pn ),
 E r ( k ) = | S j Rec( k ) S j Tru | | S j Tru | ,
P( d,α )= L( d,α ) f( x,y )ds ,
α i =arctan( l×| x i | k×f ),
β i =arctan( w×| y i | k×f ),
R 5 = d R cos36° + d R tan36° + d C ,
R i = R 5 ×cos( arctan l 2 x 5 2 + w 2 y 5 2 k×f ) cos( arctan l 2 x i 2 + w 2 y i 2 k×f )        (i=1,2,3,4).
ε= hc 4πλ g m A nm n j U j exp( E m kT ),
ε=K n j U j exp( E m kT ).

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