A three-dimensional model of multiple reflections for high-speed deep penetration laser welding based on an actual keyhole

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Abstract

Keyhole shapes are observed experimentally by two high-speed cameras from two perpendicular directions in high-speed laser welding of glass. From the obtained keyhole pictures, it can be seen that in high-speed deep penetration laser welding, the keyhole is not only seriously bent in the direction opposite to that of welding speed, but also elongated along the direction of the welding speed. Based on the so-obtained keyhole photograph, the keyhole profiles in both the symmetric plane and its perpendicular plane (i.e., the cross-section plane) are determined by the method of polynomial fitting. Then, under the assumption of elliptical cross-section of the keyhole at each keyhole depth, a 3D bending keyhole is reconstructed, the behavior of focused Gaussian laser beam in the keyhole is analyzed by tracing a ray of light using geometrical optics theory. Fresnel absorption and multiple reflections in the keyhole are systematically studied, and the laser intensities absorbed on the keyhole walls are calculated. In determining the distribution of laser intensity on the keyhole wall, the bending of the keyhole plays the dominant role, elongation of the keyhole plays just a minor role. Because of the bending of the keyhole, not all the keyhole wall can be irradiated directly by laser beam. The absorbed laser intensity cannot be uniformly distributed on the keyhole wall even after multiple reflections. The keyhole wall absorbs laser intensity mainly on the small area near the front keyhole wall. Recoil pressure plays a dominant role in forming a keyhole and keeping it open.

Introduction

Keyhole formation is the core for deep penetration laser welding. When a laser beam with high intensity irradiates the workpiece, part of molten material is vaporized strongly, which can lead to production of high recoil pressure. Then, a deep, narrow keyhole, which is filled with a partially ionized plume of vapor and ambient gas, is formed in the molten material by the recoil pressure.

As well known, keyhole plays a very important role in coupling laser energy to the material to be welded. With the help of keyhole, laser energy can penetrate deeply into the workpiece by means of two mechanisms such as Fresnel absorption on the keyhole wall and inverse Bremsstrahlung absorption in the partially ionized plume of vapor (usually called as the plume of plasma) in the keyhole. So keyhole formation can greatly increase both the coupling efficiency of laser energy and the depth of welds.

Concerning the beam absorption in the keyhole, considerable experimental and theoretical studies have been done. Several different experimental methods were used to observe the keyhole shapes. Arata's group [1] first observed the keyhole shapes in laser welding a kind of transparent material of soda-lime glass using direct photographing. Due to unsuitable workpiece material (the difference between the melting point and the vaporization point of soda-lime glass is too small to distinguish the keyhole from other high-temperature emission region) and unsuitable welding parameters (too low laser power and too low welding speed) used, the keyhole picture they obtained was unstable and unclear. They also used X-ray transmission imaging technique to observe keyholes in deep penetration laser welding of steel [2], but the contrast of the radiographs they obtained was too low to understand the mechanism of deep penetration laser welding. Succeeding Arata's work, Semak et al. [3], Mohanty et al. [4] and Miyamato et al. [5] did some experimental studies on the keyhole dynamics from the top view in laser welding using high-speed photography, and obtained the keyhole shapes on the workpiece surface. Matsunawa's group [6], [7], [8], [9], [10], [11] did a lot of experimental investigations on observing the dynamic keyhole shapes in deep penetration laser welding of metals by X-ray transmission imaging systems with high-speed video cameras. Unfortunately, most of the keyholes they obtained were not clear enough for quantitative study. The author of this paper [12] also observed the keyhole profile in the media-plane consisting of the welding speed in laser welding glass using direct high-speed photography, and obtained clear keyhole pictures.

Regarding Fresnel absorption and multiple reflections in the keyhole, a lot of simulation investigations have been done. Beck et al. [13] established a numerical model of Fresnel absorption by tracing ray in a symmetric keyhole. Kaplan [14] developed a model to calculate the asymmetric keyhole profile and asymmetric heat flow on the keyhole walls by considering Fresnel absorption and multiple reflections in the keyhole in a simplified way. Solana and Negro [15] established an axisymmetrical model to study the effect of multiple reflections in the keyhole with a free boundary. Fabbro and Chouf [16] used a ray-tracing procedure to determine the keyhole geometry by taking into account the multiple reflections inside the keyhole. Kern [17] and Müller [18] simulated in a presumed three-dimensional (3D) keyhole, the Fresnel absorption and multiple reflections, respectively. However, in Refs. [13], [14], [15], [16], [17], [18], the keyhole walls were supposed to be totally exposed to the laser beam. Unfortunately, this is not always the case in practical deep penetration laser welding, especially in high-speed laser welding. Due to the bending of the actual keyhole in the opposite direction of the welding speed, not all the keyhole walls can be irradiated directly by the laser beam [19]. The author [20] of this paper also calculated the laser intensity absorbed on the front and rear walls of an experimentally observed keyhole in the symmetrical plane along the moving direction. He found that on the rear wall of the keyhole, there were only some weak power densities distributed in some individual regions, most of the rear wall did not have any beam illumination.

We all knew that there are two kinds of keyhole distortions in practical deep penetration laser welding. One is the bending of the keyhole in the opposite direction of the welding speed, the other one is the elongation of the keyhole cross-section along the welding direction. Both of the above distortions are closely related to the welding speed. In order to make clear the relation between the above two distortions of the keyhole and the welding speed (in other words, the extent of the distortions at different welding speed), the author of this paper did some experimental studies [21] to observe the keyhole shapes during low- and media-speed deep penetration laser welding. He found that in low- and media-speed deep penetration laser welding, the main distortion of the keyhole is the bending of the keyhole in the opposite direction of the welding speed, the elongation of the keyhole cross-section from rotational symmetry along the welding direction is very little. In this case, the keyhole can be treated as a circle. Then, under the assumption of a circular cross-section at each depth of the keyhole, he [21] also developed a 3D model based on an actual bending keyhole to analyze the behavior of the laser beam in the keyhole by tracing a ray of light using geometrical optics theory. However, we do not know how large distortion of the keyhole cross-section will produce in high-speed deep penetration laser welding. Can it still be treated as rotational symmetry? How to describe reasonably the behavior of laser beam in an actual bending and elongating 3D keyhole? All of these questions, which need further study, have not been solved.

In this paper, the keyholes during high-speed deep penetration laser welding of glass are observed from two perpendicular directions using two high-speed cameras. Then, on the basis of measuring the position of the keyhole wall, the keyhole profiles both in the symmetrical plane along the moving direction and in its perpendicular plane are determined by means of polynomial fitting. In turn, under the assumption of elliptical section at each depth of the keyhole, a 3D keyhole is constructed. Finally, according to geometrical optics theory, Fresnel absorption and multiple reflections are analyzed by tracing a ray of Gaussian beam in this 3D keyhole, and the absorbed laser power distribution on the keyhole wall is calculated.

Section snippets

Direct observation of keyhole shapes

In order to observe the keyhole shapes simultaneously from different directions, the same experimental set-up of laser welding glass as that used in Ref. [21] is used, which is shown in Fig. 1. In this experimental set-up, camera 1 is used to take the photographs of the keyholes in the symmetrical section, and camera 2 to take the photographs of the keyholes in the cross-section. The exposure of both cameras is 1/1000 s, and in such a short period, both the laser beam and the keyhole can be

Mathematical model of multiple reflections in the 3D keyhole

Because the main composition of glass GG17 is SiO2, the ionization energy of which is very high, it is difficult to form plasma, and the vapor of the glass is transparent to the CO2 laser beam. Hence, the only beam absorption mechanism existed inside the keyhole is Fresnel absorption, which will be considered in our further calculation.

In order to simplify the study of the behaviors of laser beam in the keyhole, the following assumptions are made:

  • (1)

    The cross-section of the keyhole at each keyhole

Results and discussion

The laser beam used is of circular polarization. The reflectivity of the glass GG17 was measured experimentally, which is shown in Fig. 9.

The keyhole picture shown in Fig. 2 is taken as an example for the following calculation. The calculation conditions are listed here: laser beam power P=800 W; focal length of the lens F=100 mm; the radius of focal spot ω=0.2 mm. The polynomial fitting coefficients of the front, rear keyhole wall, the central line and the side wall of the keyhole (both x and z

Conclusions

  • (a)

    In deep penetration laser welding with high speed, not only the cross-section of the keyhole is no longer rotational symmetric, but the keyhole is also seriously bent in the direction opposite to that of the welding speed.

  • (b)

    Due to bending of the keyhole, not all the keyhole wall, both on the front and the rear keyhole wall, can be irradiated directly by the laser beam. The laser intensity absorbed on the whole keyhole wall cannot be uniformly distributed even after multiple reflections.

  • (c)

    Between

Acknowledgment

The research of this paper was supported by the State Scholarship Fund of China, so the author would like to express his heartfelt thanks to China Scholarship Council.

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