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Study on chaos in short circuit gas metal arc welding process
- 期刊名字:中国焊接
- 文件大小:212kb
- 论文作者:Lü Xiaoqing,Cao Biao
- 作者单位:College of Mechanical Engineering
- 更新时间:2020-09-15
- 下载次数:次
Study on chaos in short circuit gas metal are welding process77Study on chaos in short circuit gas metal arc welding processLi Xiaogang, Cao Biao, Zeng Min, Wang Zhenmin and Huang Shisheng青,曹彪,曾敏,王振民,黄石生Abstract Based on the chaos theory an idea is put forward to analyze the short circuit Gas Metal Arc Welding( GMAW-S)analyze the chaos of the GMAW-S process. The largest Lyapunoy exponents of some current time series are calculated, andresults indicate that chaos exists in the GMAW-S process. The research of the chaos in the GMAW-S process can be help to getnew knowledge of the process.Key words chaos, Lyapunov exponents short circuit gas metal arc welding0 Introductionnamic system. Especially the largest LE is the key pa-As one of the nonlinear science theories chaos has rameter. If the largest LE is greater than zero it meansen developed rapidly and has significant effect on that chaos exists in the process. For a physical processmodern science since 1970s. it covers almost all sciwith known mathematical mode, the largest le can betific domains such as physics mathematics, biology, obtained easily l]. But for a process with an unknownhemistry and economies and has been widely applied mathematical mode the largest LE can only be achievedin the control medicine and economics forecast fields. from time series of some parameter obtained through exHowever, in the welding field especially in the arc periments. Based on experimental time series, A. Wolfwelding field there is no related research and applica- et al developed the trajectory tracing method to calculatetion report. Therefore, it is a new challenge to carry out the largest LE. As to the GMAW, the short circuitthe researches into whether chaos exists in the GMAW-s process isvery complexand there is no certain matheprocess or not, what are the effects of the welding matical mode known to describe itTherefore, theprocess parameters on the chaos and whether it is possi- application of the trajectory tracing method to calculateble to use chaos control methods to improve the welding the largest LE from a concrete welding current time se-ries will be a practical way to determine whether there isThe chaos is a unique motion mode in nonlinear dy- chaos existing in the gmaw-S process or notnamical systems and it is a ubiquitous and complex phe-nomenon. Devany defined chaos as a process that( 1) 1 Model and algorithmis sensitively dependent on initial conditions.( ii ) isTo calculate the largest LE, the application of thetopologically transitive and( iii)has periodic points that trajectory tracing method is related to the phase spacereconstruction and the selection of algorithused to depict chaotic attractors the fractal dimensionand the Lyapunov exponents( LE ) The fractal dimen- 1. 1 Phase space reconstructsion gives an estimate of the system complexity whileThere are three primary methods for phase spacethe le gives an estimate of the level of chaos in the dyrecons中国煤化工 time delay method hasCNMHGThe work was supported by National Natural Science Foundation of China( no. 50375053 50575077)Li Xiaoqing Cao Biao, Zeng Min, Wang Zhenmin and Huang Shisheng College of Mechanical EnSouth China University of Technology, Guangzhou, 5106Xiaoding有落据 Mechanical engineering, Tongji University, Shanghai,2001078CHINA WELDING Vol 16 No. 2 June 2007been widely applied in attractor reconstruction. It seemsthat the time series of 1-D variable can only provide limited dynamical information. But according to refe[3 ], because it implies other variables dynamical trading the chaos attractors can be re-established by using200the time delays phase space reconstruction method. TI150phase space reconstructed from a single variable pre-rves the topological properties of the original attractor100so the topological properties can be calculated. Durintion of a chaotic time series, thechoice of the time delay T and the embedding dimensionm is critical for the calculation of the largest LE01002003004005006001. 2 Parameter and algorithmTime t/msThere are many methods to select the time delay tFig 1 Wave of GMAW-S currentand the embedding dimension m. In this paper, the revised false nearest neighbors( rFnn) method and themutual information( MI method are adopted, becausethey are not sensitive to noise. The RFNN method isused to select m, while the mi method is used to select5In 1997 the rfnn method is first established byCao overcoming many shortcomings of the false nearest2neighbors( FNN method such as subjective criterion[4!. Except for its inexplicit physical mechanism,theRFNN method is proved to be very practical by lots of1.5experiments. In 1986, Fraser applied firstly the inforhase space reconstruction and puward the MI method!!. This approach is best inFig 2 Curve of S2)except for the enormous computational costsWhen T is equal to 0. 0023 s, the curve of the re-2 Analysis of welding current based on chaos algo- lation between E, m), E m)and the embedding dirithmmension m is exhibited by Fig 3. It is found that when2.1 Numerical resultsm9, the E,(m) keeps almost invariable. ThereforeFig. 1 shows an experimental current wave in the the optimum embedding dimension m is equal to 10ave controlled GMAW-S process with low heat Chop- So, as to the current wave in Fig. 1, T=0.002 3 s andArc. The sampling time is 0. 000 I s and this droplet m=10 are the best selected parameters in phase spacetransfer process is unstablereconstruction. In addition, because E, (1)and E, (2)The calculation result of mutual information /(S, are ul1( see Fig.3, it is known that theQ) is showed by Fig. 2 where n is a multiple integer of proces中国煤化工[4sampling time. When n is equal to 23, Ks gets toCNMHGce withthe first minimum. So, 0. 002 3 s is chosen as the optimeters can re-appear chaos attractor in low dimensionmum delay timecases, but in high dimension cases this does not workFig 4 shows the phase space reconstruction diagramwhen T=0. 0023 s and m=10. Obviously coordinateStudy on chaos in short circuit gas metal are welding processin this figure has little significance. The phase diagramFig. 6 shows the plot of the largest LEversusInof voltage and current is exhibited by Fig. 5. Comparing (n). In order to understand better the variable of theig. 4 with Fig. 5 it is found that there are some simi- largest LE, the natural logarithm of n value is chosen asrarities in structuretransverse axis label. From this figure, it is known thatthe largest LE converges at 32. 254的mn2500200100006△5000.5-50051000Fig·3 Curve of e1,E2-mFig 6 Calculation of the largest LEThe largest LE is defined by the largest expandingnature of different directions during the long-term evolttion of the axes of an infinitesimal sphere of state and itdenotes an average value unit time over long-term evolu-tion from the result of the largest le, it denotes thatthe largest le obtained is much larger than common attractor such as Lorenz attractor( 1. 497). That is be-Fig. 4struction diagram of current seriescause during the droplet short circuit transfer processthe current varies far faster than the lorenz attractor iunit time. Besides, as to some process with periodicrules evenbig variable in unit time itnot chaos and the largest LE will be equal to zero. Thismeans that the largest LE is decided by the stability of10welding process. The stabler the welding process is thesmaller the largest LE will beThe noise does have an influence on the calculation中国煤化工50050100150200250to the calculation of theCNMHGthat chaos informatioCurrent //Amay be lost when filter is used. For example, filter isFig 5 Phase diagram of voltage and currentexpected to distort the shapes eliminate small scalestructure and scramble phases. Therefore in this paper, the filter is not applied to the largest LE calculaCHINA WELDING Vol 16 No. 2 June 2007fer, T=0. 0023 s and m =10 are chosen as the opti-3 The significance of the chaos in the GMaw-s mum parameters by the MI method and the renn methprocessod respectively. The result of the largest LE 32. 25)The arc welding process is unstable and the short based on the A. Wolf theory proves primarily that chaoscircuit transfer process is especiallyal, such as the exists in the GMaw-s process.heterogeneous droplet transfer perispatter, etc. Though it is widely used in metal industry Referencesfor its high economy and efficiency the serious spatter 1 1 Ramasubramanian K, Sriram M S. A comparative study ofand bad bead formation problems will era oncomputation of Lyapunov spectra with different algorithysica D,2000J391/2)72-86The reveal of the chaos in the GMAW-S process[2] Wolf A, Swift J B, Swinney H L, et al. Determining Lypunov exponents from a time series. Physica D, 1985, 16will promote to make a better understanding of the drollet transfer and to establish more accurate models from [3 Takens F. Detecting strange attractors in turbulence. Lec-the chaos view. To make progress in the study of chaosture Notes in Mathematics. 1981, 898: 366-381in the gmaW-s process such as the influences of pa[4] Cao L Y. Practical method for determining the minimumrameters on chaos and the chaos control methods, it willembedding dimension of a scalar time series, Physica Dbe possible to solve the above problems in weldi199710(1/2):3-50process[5] Fraser A M, Swinney H L. Independent coordinates forstrange attractors from mutual information. Physical Re-4 Conclusionsview A198633(2)134-1140From a concrete current time series of droplet trans-中国煤化工CNMHG
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