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A novel weld-pool-length monitoring method based on pixel analysis in plasma arc additive manufacturing

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Abstract

The real-time monitoring of the weld pool during deposition is important for automatic control in plasma arc additive manufacturing. To obtain a high deposition accuracy, it is essential to maintain a stable weld pool size. In this study, a novel passive visual method is proposed to measure the weld pool length. Using the proposed method, the image quality was improved by designing a special visual system that employed an endoscope and a camera. It also includes pixel brightness-based and gradient-based algorithms that can adaptively detect feature points at the boundary when the weld pool geometry changes. This algorithm can also be applied to materials with different solidification characteristics. Calibration was performed to measure the real weld pool length in world coordinates, and outlier rejection was performed to increase the accuracy of the algorithm. Additionally, tests were carried out on the intersection component, and the results showed that the proposed method performed well in tracking the changing weld pool length and was applicable to the real-time monitoring of different types of materials.

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Abbreviations

CDL:

Center detecting line

CNC:

Computer numerical control

ROI:

Region of interest

DL:

Detecting line

\(b\) :

Interval between two pixels when determining the gradient

\({b}_{\mathrm{c}}\) :

Bias of the CDL in the image coordinate

\({b}_{\mathrm{r}}\) :

Bias of the reference line in the world coordinate

\(B_{\text{a}}^n(k)\) :

Smoothed brightness

\({B}_{\mathrm{max}}\) :

Maximum global brightness of all iterations

\({B}^{n}(k)\) :

Discrete brightness function along the \({n}\text{th}\) DL

\({c}_{x}\),\({c}_{y}\) :

Displacement away from the axis

\(d\) :

Distance between each DL

\(\mathrm{d}x\),\(\mathrm{d}y\) :

DL axis increment based on the CDL

\({f}_{\mathrm{s}}(x)\) :

Smooth function

\({f}_{x}\),\({f}_{y}\) :

Focal length on the optic axis

\({G}_{\mathrm{min}}\) :

Minimum global gradient of all iterations

\({G}^{n}\left(k\right)\) :

Pixel gradient

\({G}_{\rm{a}}^{n}(k)\) :

Smoothed gradient

\(H\) :

3×3 Homography matrix

\(W\) :

Array sliding over \({B}_{\rm{a}}^{n}(k)\) and \({G}_{\rm{a}}^{n}(k)\)

\(j\) :

Index in W

\({k}_{\mathrm{c}}\) :

Bias of the CDL in the image coordinate

\({k}_{\mathrm{r}}\) :

Slope of the reference line in the world coordinate

\({L}_{\mathrm{d}}\) :

Distance used to define the points falling on DL

\({M}_{n}\) :

Number of pixels points in \({P}_{\mathrm{DL}}^{n}\)

\(n\) :

Index of the DLs

\(N\) :

Number of DLs on one side of the CDL

\(O,X,Y\) :

Origin and axis of the world coordinate

\(o,x,y\) :

Origin and axis of the image coordinate

\(P(x,y)\) :

Point within the ROI

\({P}_{\mathrm{c}1}\left({x}_{\mathrm{c}1},{y}_{\mathrm{c}1}\right)\) :

Starting point of the CDL

\({P}_{\mathrm{c}2}\left({x}_{\mathrm{c}2},{y}_{\mathrm{c}2}\right)\) :

Ending point of the CDL

\({P}_{\mathrm{DL}}^{n}\) :

Points falling on the nth DL

\({P}_{\mathrm{L}1}^{n}\),\({P}_{\mathrm{L}2}^{n}\) :

End points of the nth DL

\({P}_{\mathrm{L}},{P}_{\mathrm{L}1},{P}_{\mathrm{L}2}\) :

Molten length and its two portions

\({P}_{\mathrm{R}1}\left({x}_{\mathrm{R}1},{y}_{\mathrm{R}1}\right)\) :

Upper left corner point of the ROI

\({P}_{\mathrm{R}2}\left({x}_{\mathrm{R}2},{y}_{\mathrm{R}1}\right)\) :

Upper right corner point of the ROI

\({P}_{\mathrm{R}3}\left({x}_{\mathrm{R}2},{y}_{\mathrm{R}2}\right)\) :

Lower right corner point of the ROI

\({P}_{\mathrm{R}4}\left({x}_{\mathrm{R}1},{y}_{\mathrm{R}2}\right)\) :

Lower left corner point of the ROI

\({{\varvec{r}}}_{1}\), \({{\varvec{r}}}_{2}, \, {{\varvec{r}}}_{3}\) :

3×1 vectors of the rotation transformation

\(s\) :

Scale factor

\({\varvec{t}}\) :

3×1 vector of the translation transformation

\({w}_{\mathrm{d}}\) :

Width of \(W\)

\({X}_{\mathrm{m}}\),\({Y}_{\mathrm{m}}\) :

Mean coordinates of the remaining feature points

x n, \({y}_{{n}}\) :

Image coordinates of the detected feature points

X n, Y n :

World coordinates of the detected feature points

\({\mu }_{y}\) :

Mean of \({Y}_{n}\)

\({\sigma }_{y}\) :

Standard deviation of \({Y}_{n}\)

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Acknowledgments

The authors are grateful for the financial support provided by the China Scholarship Council and Basic and Applied Basic Research Foundation of Guangdong Province (Grant No. 2022A1515110733). The Cranfield University and the Ji Hua Laboratory are also gratefully acknowledged.

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Correspondence to Yong-Hua Shi.

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Zhang, BR., Shi, YH. A novel weld-pool-length monitoring method based on pixel analysis in plasma arc additive manufacturing. Adv. Manuf. 12, 335–348 (2024). https://doi.org/10.1007/s40436-023-00466-w

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  • DOI: https://doi.org/10.1007/s40436-023-00466-w

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