*3.2. Oscillation of Weld Pool*

High speed photograph pictures showed that the liquid waves in S-GMA welding were triggered primarily by the electric explosion, not by the change in the arc pressure during the arc period [15]. The relationship curves the height of the reference point on the weld pool surface with time were obtained by using the method described in Section 2.3, as shown in Figure 10.

**Figure 10.** Oscillation signal extracted by high speed photograph-image analysis system.

The period of droplet transfer cycles fluctuated randomly within a range, and the oscillation curve of weld pool is a time-varying signal, which causes the oscillation frequency of weld pool change within a range. The Fast Fourier Transform Algorithm (FFT) could not extract the characteristics of weld pool oscillation. The Continuous Wavelet Transform (CWT) can analyze time-varying signals in time domain and frequency domain simultaneously. In this paper, Morlet continuous wavelet transform was applied to weld pool oscillation signals at different wire feeding speeds. Morlet wavelet base function is shown in Equation (7):

$$\psi\_{a,b}(t) = \sqrt{a} \exp\left(ia\iota\_0 \frac{\left(t-b\right)}{a}\right) \exp\left(-\frac{\left(t-b\right)^2}{2a^2}\right) \tag{7}$$

In the continuous wavelet transform, the scale vector *a* is associated with the central frequency and the support interval of the basis function, and the frequency of weld pool oscillation and its corresponding time frequency resolution can be obtained at any time. For a particular scale vector, the signal frequency allowed by the wavelet transform should be close to the corresponding frequency of the scale vector. Therefore, the continuous wavelet transform can clearly reflect the variation of oscillation frequency with time. In this experiment, wavelet transform is carried out on the acquired signal of melt pool oscillation, and the center frequency ω<sup>0</sup> of base function was three. The oscillation frequency range of traditional GMAW weld pool is below 300 Hz [16]. The scale vector *a* selected in this experiment was between 50 and 700, and the corresponding oscillation frequency identification range was 40–600 Hz. *b* is the duration of signal acquisition. The contour diagram of transform coefficient of signal reflects the energy density distribution of the signal in the time-scale plane. The energy of the signal is mainly concentrated around the wavelet-ridge-cure in the time-scale plane, from which the instantaneous frequency of the signal can be determined. Signal sampling frequency (ƒSampling frequency) was equal with the fps of high-speed photography, and the corresponding relationship between the oscillation frequency of weld pool (ƒOscillation frequency) and the scale vector *a* of wavelet-ridge-cure is as Equation (8):

$$f\_{\text{Ocillation frequency}} = \frac{f\_{\text{Sampling frequency}}a\_0}{a} \tag{8}$$

Figure 10 is the contour diagram of continuous wavelet transform coefficient of weld pool oscillation signal of traditional S-GMAW process under different wire feeding speeds:

It can be seen from Figure 11 that the oscillation of weld pool of S-GMAW had significant periodicity. The relationship curve of the oscillation frequency with different wire-feed speeds is shown in Figure 12. When the wire feeding speed was 2.4 m/min, the weld pool volume was small, resulting high oscillation frequency of the weld pool. With the increase of wire feeding speed, the volume of weld pool increases, the propagation time of travelling wave on the surface of weld pool increased, and the oscillation frequency decreased.

**Figure 11.** The contour diagram of transform coefficient of weld pool oscillation: (**a**) 2.4 m/min; (**b**) 2.7 m/min; (**c**) 3.0 m/min; and (**d**) 3.3 m/min.

**Figure 12.** The oscillation frequency of weld pools with different wire-feed speeds.

Different waveforms and penetration states of weld pool led to different oscillation frequencies. Figure 13 shows the contour curves of the oscillation wavelet transform coefficients of the fusion and partial weld pools of three waveforms, and Table 4 shows the oscillation frequency statistics.

**Figure 13.** The contour curves of the oscillation wavelet transform coefficients of the fully and partly penetrated weld pools: (**a**) conventional process; (**b**) LSC; and (**c**) Cold Arc.


**Table 4.** The oscillation frequency statistics.

As can be seen from Figure 13, there was a significant difference in the oscillation frequency between the partly and fully penetrated weld pools. These pictures at both sides of Figure 13 are the contour diagram of the distribution of oscillation wavelet coefficients of partly and fully penetrated weld pool using different waveforms. Only one frequency occurred during the oscillation process of partly penetrated weld pool, while there were two characteristic frequencies on the oscillation spectrum of the fully penetrated weld pool. The difference between high frequency and low frequency was generally about 40 Hz, which indicated that there were two oscillation periods of different frequencies in the weld pool. Zacksenhouse [17] established a pool analysis model based on the stretch film theory and studied the oscillation frequency of the full penetration pool. In the full penetration pool, the vibration frequency is obviously lower than that of the partial penetration pool, and the amplitude of the oscillation of the fully penetrated weld pool is relatively larger than that of the partly penetrated weld pool due to the disappearance of the bottom constraint, which was consistent with the Figure 9.

In order to explain the two oscillation frequencies of the full penetration pool, the metal flow process in the pool should be considered, as shown in Figure 14. With the impact of electric explosion, the liquid weld pool flowed radially symmetrically with the arc axis. In the full penetration pool, axial flow occurred for the bottom of the weld pool was no longer supported by any solid material. The liquid in the middle of the weld pool can move vertically, while the liquid in the periphery of the weld pool was supported by the solid material and forced to flow laterally. It led to the fact that although the weld pool was in the state of full penetration, the traveling wave propagation process was still similar to that of non-molten penetration at the periphery of the weld pool. During travelling S-GMAW welding process, the penetration position was relatively small compared with the length of the weld pool, and most of the weld pool metal was still supported by solid metal at the bottom of the weld pool, the oscillation behavior was similar to partial penetration. Therefore, the full penetration pool had two characteristic oscillation frequencies: High frequency and low frequency.

**Figure 14.** Oscillation mode of weld pool: (**a**) partial penetration; (**b**) full penetration.

The characteristics of the pool oscillation of three waveforms were different. As shown in Figure 13, No stable wavelet-ridge-cure occurred in the contour curves of the oscillation wavelet transform coefficients of Cold Arc, so the weld pools of Cold Arc had no stable oscillation frequency. The Cold Arc process reduced the current at the end of short-circuit stage, which greatly reduces the impact of electric explosion on the pool. At the same wire feeding speed, the weld pool oscillation frequency of LSC was slightly lower than that of conventional process, which was related to the size of weld

pool and the electric explosive impact force at the end of short circuit, and the surface tension of weld pool was one of the factors that caused the difference of the frequency. Different waveforms led to different surface temperature of the weld pool, resulting in different surface tension of the weld pool. The surface tension of the weld pool metal is also one of the important factors affecting the oscillation frequency of the weld pool.
