Searching for chaos in fluctuations of a plasma induced during cw- laser welding

Abstract

Fluctuations of cold ( eV) and dense plasmas which burn above metallic surfaces during welding with a cw laser are registered in monochromatic radiation. The aim of the present work is to check whether low-dimensional deterministic chaos can be an explanation for the irregular, random-like oscillations of the surface plasma induced during laser welding. The standard procedures of nonlinear time series analysis like the embedding technique, noise reduction by projection on the local manifold, calculations of the correlation dimension using the G-P algorithm, and looking for the largest Lyapunov exponent are applied. After cleaning original time series from the noise, 3D phase portraits displaying more or less regular structures of attractors were reconstructed. The values of the estimated fractal dimensions of these attractors lay in the range , for various cleaning conditions. The plots of the average orbits' `divergence' calculated for the estimation of the largest Lyapunov exponent display behaviour which is typically observed in chaotic systems. The value of the largest Lyapunov exponent obtained from the slope of the orbits' divergence curves is for our welding conditions, about and the average `period' of the plasma oscillation is estimated to be s. This means that the system is highly unpredictable. These results indicate that fluctuations of laser induced plasmas represent deterministic chaos and a nonlinear dynamical system consisting of several ordinary differential equations can be used for modelling laser welding.

A 3D transient model of keyhole and melt pool dynamics in laser beam welding applied to the joining of zinc coated sheets

“…Both spectra include a band of peaks at lower frequencies, corresponding to melt pool oscillations. The peaks at about 3,000 Hz correspond to the oscillation of the keyhole [6,18,19]. The similar structure of the spectra shows that the simulations reflect a realistic keyhole dynamics although there is of course no perfect correspondence.…”

Plasma plume oscillations during welding of thin metal sheets with a CW CO2laser

“…It has already been shown [26] that the optical signals registered during laser welding have many features characteristic of deterministic chaos. This fact suggests the possibility of using methods of process stabilization known from the theory of chaos, for example by periodic change of one of the intrinsic parameters of the process [27].…”

Qualitative and Quantitative Analysis of Stochastic Processes Based on Measured Data, Ii: Applications to Experimental Data

“…However, comparison of analytical and experimental results is hindered by experimental di$culties involved in measurements of the physical quantities meaningfully related to process dynamics. The most common measurement is of #uctuations in the intensity of light emitted by the welding process at a certain wavelength [10,11]. The recorded signals are usually noisy, and severe "ltering has been suggested to make them suitable for analysis by methods of deterministic chaos [10].…”

“…The most common measurement is of #uctuations in the intensity of light emitted by the welding process at a certain wavelength [10,11]. The recorded signals are usually noisy, and severe "ltering has been suggested to make them suitable for analysis by methods of deterministic chaos [10]. Experimental analysis of welding dynamics is also motivated by the need for reliable monitoring of the process.…”