# Study on Penetration Sensing Method Based on Pool Oscillation and Arc Voltage during Pulsed GMAW
## 3 Results and Discussion
### Oscillation Characteristics of Weld Pool in P-GMAW
In this paper, Morlet wavelet was used as the square-integrable function of CWT, also known as the wavelet basis function, as shown in Equation (1):  
\[\psi_{a,b}(t)=\sqrt{a}exp\left(i2\pi f_{a}\frac{(t-b)}{a}\right)exp\left(-\frac {(t-b)^{2}}{2a^{2}}\right) \tag{1}\]  
In Equation (1), \(a\) is the scale vector; \(b\) is the translation parameter; \(f_{a}\) is the center frequency of the wavelet; The center frequency of the wavelet used in this paper is 0.796. The square of the number modulus of the signal wavelet transform system (\(\psi_{a,b}(t)\)) reflects the energy density distribution of the signal in the timescale plane. The energy of the signal is mainly concentrated around the wavelet ridge curve in the timescale plane, which can determine the instantaneous frequency of the signal. As for the Morlet continuous wavelet transform, the scale vector \(a\) at the wavelet ridge has a relationship with the signal frequency and sampling frequency [17], as shown in Equation (2):  
\[f=f_{a}*f_{s}/a \tag{2}\]  
In Equation (2), \(f_{s}\) is the sampling frequency of the signal: 10,000 Hz. Figure 11 is the contour diagram of continuous wavelet transform coefficient of P-GMAW weld pool oscillation signal with different penetration status. Figure 10: Height of reference point B on the pool surface as a function of time: (**a**) full penetration; (**b**) partial penetration. Figure 3:0 Oscillation mode of weld pool: (**a**) partial penetration; (**b**) full penetration. As shown in Figure 11a-c, there were two continuous wavelet ridges in the contour diagram of the transform coefficient of oscillation of the full penetration pool. The scale vectors were 200 and 100, respectively, and with the Equation (2), the corresponding oscillation frequencies of the weld pool were 40 Hz and 80 Hz, respectively. As indicated by paper [18]. The pool was a dynamic system excited by periodic signals under the impact of a fixed frequency, oscillating at the same or integer multiple of the pulse frequency (40 Hz). There were also two wavelet ridges with the same scale vector in the wavelets of the oscillating signals in the weld pool, but the wavelet ridge with the scale vector of 200 was inconsecutive as shown in Figure 11d. As for partial penetration, only one wavelet ridge curve with the scale vector of 100 occurred in the contour diagram of transform coefficient, as shown in Figure 11e-g, and the corresponding oscillation of the partly penetrated weld pool was 80 Hz. The corresponding wavelet skeleton at the wavelet ridge curves was the composition of the weld pool oscillation signal at this frequency [17]. Figure 12 shows the composition of the weld pool oscillation signal at 40 Hz and 80 Hz with different penetration status. Figure 3:1 The contour diagram of transform coefficient of weld pool oscillation with different penetration status. Full penetration: (**a**) V = 11 cm/min; (**b**) V = 13.75 cm/min; (**c**) V = 16.5 cm/min. Critical penetration: (**d**) V = 19.25 cm/min. Full penetration: (**e**) V = 24.75 cm/min; (**f**) V = 30.25 cm/min; (**g**) V = 35.75 cm/min. As shown in Figure 12, the amplitude of the component curve of the weld pool oscillation signal at 40 Hz and 80 Hz gradually decreased with the weld pool translated from full to partial penetration. The curves at 40 Hz fluctuated only in full and critical penetration. The oscillating signals of the full penetrated weld pool appeared low-frequency components (40 Hz) with large amplitude due to the lack of solid boundary constraint at the weld pool bottom, while the oscillating signals of the partly penetrated weld pools were only composed of high-frequency signals (80 Hz). As for critical penetration, the high-frequency component of the oscillation signal persisted, while the high-frequency component was not stable due to the variational boundary conditions. These results suggest that different penetration status significantly affected the oscillation motion of the weld pool under the same impact.