高速脉冲GMAW焊接熔池动态行为的数值分析
|
摘要
为了优化高速脉冲熔化极气体保护焊(GMAW)焊接工艺,本文建立了三维高速脉冲GMAW焊接熔池流体流动和传热过程的瞬态数值模型,对高速脉冲GMAW焊接熔池动态行为进行了研究。
本文首先根据高速脉冲GMAW焊接热过程中伴随周期性熔滴过渡、熔池自由表面发生变形以及液面波动的特点,建立了变形熔池自由表面受迫振动及熔池自由表面波动模型,并在此基础上建立了适合于描述变形及波动熔池表面上方电弧空间内热流密度分布的新型热源模型,即热流密度在电弧空间内分布模型。然后从能量守恒定律、动量守恒定律和质量守恒定律的角度出发,建立了高速脉冲GMAW焊接热过程的控制微分方程组,并给出了相应的初始条件和边界条件,对控制方程组进行了离散化。最后用FORTRAN语言编制了相应的计算程序。
利用新建的变形熔池表面受迫振动及熔池自由表面波动模型、热流密度在电弧空间内分布模型和热过程数值模型,对焊接熔池的动态行为进行了数值分析。应用变形熔池表面受迫振动及熔池自由表面波动模型,模拟了熔滴过渡引起的熔池自由表面的波动,获得了不同时刻下熔池自由表面的准确形貌。在此基础上,建立了电弧热流密度分布在三维电弧空间中的分布模型。应用该热输入模型研究了高速脉冲GMAW焊接工件的温度场和流场随时间的变化。将应用新型热源模型条件下数值模拟结果与实验测得结果相比较,结果表明新型热源模型适合于高速脉冲GMAW焊接传热、传质过程的数值模拟。本文采用显热容法处理了高速脉冲GMAW焊接过程中的相变潜热问题。计算了不同焊接工艺参数(焊接电流、焊接速度)条件下高速脉冲GMAW焊接熔池的动态行为,得到不同焊接电流和焊接速度条件下熔池三维温度场、流场和形状随时间的瞬时演变规律。分析了不同焊接电流和焊接速度条件下熔池三维温度场、流场和形状的变化趋势,与实验结果吻合良好。
本文的工作能够为高速脉冲GMAW焊接工艺的工业化生产和焊接工艺参数的优化提供基础数据和理论指导。
In order to optimize the welding parameters, a 3D transient numerical model for the fluid flow and heat transfer in high-speed pulsed gas metal arc welding (GMAW) is established to investigate the dynamic behaviors of weld pool.
First, according to the features of periodical droplet transfer, deformation and fluctuations on weld pool free surface in high-speed pulsed GMAW, a forced vibration model and a wave fluctuation model on deformed weld pool free surfaces are established. On this basis, a new heat source model that can describe the heat flow density distribution in arc spaces above the deformed and fluctuated weld pool free surfaces is developed, which is called heat flow density distribution model in arc spaces. Second, the governing differential equations are derived as the energy conservation, momentum conservation and mass conservation, respectively. After that, corresponding initial conditions and boundary conditions are given and the governing equations are discretized. Finally, the calculating software written in FORTRAN is programmed.
The dynamic behaviors of weld pools are analyzed numerically by using forced vibration and wave fluctuation models on deformed weld pool free surface, heat flow density distribution model in arc spaces and numerical model of the thermal process. The vibration and wave fluctuation of the free surface of weld pools are simulated by the established models above, so accurate morphology of weld pool free surface at different time is obtained. Therefore, the heat flux distribution of arc in 3D space is grounded on the wave behaviors of deformed weld pool free surfaces. By utilizing the heat input model, the heat and fluid flow fields of high-speed pulsed GMAW workpiece are studied carefully with time changes. Comparison between predicted data and measured ones are performed, and the results show that the new established heat source model is suitable for the numerical simulation of heat and mass transfer in high-speed pulsed GMAW. Apparent heat capacity method is used to deal with the latent heat of phase transformation.
The dynamic behaviors of weld pools in different welding parameters such as welding current and welding speed are predicted, thus the transient developments of 3D heat field, fluid field and shape of weld pool with different welding parameters are obtained. The changing tendency of the 3D heat fields, fluid fields and shapes of weld pool with different welding parameters are analyzed and the predicted results show a good agreement with the experimental data.
This study could provide basic data and theoretical instruction for the industry application and optimization of welding parameters of high-speed pulsed GMAW.
本文首先根据高速脉冲GMAW焊接热过程中伴随周期性熔滴过渡、熔池自由表面发生变形以及液面波动的特点,建立了变形熔池自由表面受迫振动及熔池自由表面波动模型,并在此基础上建立了适合于描述变形及波动熔池表面上方电弧空间内热流密度分布的新型热源模型,即热流密度在电弧空间内分布模型。然后从能量守恒定律、动量守恒定律和质量守恒定律的角度出发,建立了高速脉冲GMAW焊接热过程的控制微分方程组,并给出了相应的初始条件和边界条件,对控制方程组进行了离散化。最后用FORTRAN语言编制了相应的计算程序。
利用新建的变形熔池表面受迫振动及熔池自由表面波动模型、热流密度在电弧空间内分布模型和热过程数值模型,对焊接熔池的动态行为进行了数值分析。应用变形熔池表面受迫振动及熔池自由表面波动模型,模拟了熔滴过渡引起的熔池自由表面的波动,获得了不同时刻下熔池自由表面的准确形貌。在此基础上,建立了电弧热流密度分布在三维电弧空间中的分布模型。应用该热输入模型研究了高速脉冲GMAW焊接工件的温度场和流场随时间的变化。将应用新型热源模型条件下数值模拟结果与实验测得结果相比较,结果表明新型热源模型适合于高速脉冲GMAW焊接传热、传质过程的数值模拟。本文采用显热容法处理了高速脉冲GMAW焊接过程中的相变潜热问题。计算了不同焊接工艺参数(焊接电流、焊接速度)条件下高速脉冲GMAW焊接熔池的动态行为,得到不同焊接电流和焊接速度条件下熔池三维温度场、流场和形状随时间的瞬时演变规律。分析了不同焊接电流和焊接速度条件下熔池三维温度场、流场和形状的变化趋势,与实验结果吻合良好。
本文的工作能够为高速脉冲GMAW焊接工艺的工业化生产和焊接工艺参数的优化提供基础数据和理论指导。
In order to optimize the welding parameters, a 3D transient numerical model for the fluid flow and heat transfer in high-speed pulsed gas metal arc welding (GMAW) is established to investigate the dynamic behaviors of weld pool.
First, according to the features of periodical droplet transfer, deformation and fluctuations on weld pool free surface in high-speed pulsed GMAW, a forced vibration model and a wave fluctuation model on deformed weld pool free surfaces are established. On this basis, a new heat source model that can describe the heat flow density distribution in arc spaces above the deformed and fluctuated weld pool free surfaces is developed, which is called heat flow density distribution model in arc spaces. Second, the governing differential equations are derived as the energy conservation, momentum conservation and mass conservation, respectively. After that, corresponding initial conditions and boundary conditions are given and the governing equations are discretized. Finally, the calculating software written in FORTRAN is programmed.
The dynamic behaviors of weld pools are analyzed numerically by using forced vibration and wave fluctuation models on deformed weld pool free surface, heat flow density distribution model in arc spaces and numerical model of the thermal process. The vibration and wave fluctuation of the free surface of weld pools are simulated by the established models above, so accurate morphology of weld pool free surface at different time is obtained. Therefore, the heat flux distribution of arc in 3D space is grounded on the wave behaviors of deformed weld pool free surfaces. By utilizing the heat input model, the heat and fluid flow fields of high-speed pulsed GMAW workpiece are studied carefully with time changes. Comparison between predicted data and measured ones are performed, and the results show that the new established heat source model is suitable for the numerical simulation of heat and mass transfer in high-speed pulsed GMAW. Apparent heat capacity method is used to deal with the latent heat of phase transformation.
The dynamic behaviors of weld pools in different welding parameters such as welding current and welding speed are predicted, thus the transient developments of 3D heat field, fluid field and shape of weld pool with different welding parameters are obtained. The changing tendency of the 3D heat fields, fluid fields and shapes of weld pool with different welding parameters are analyzed and the predicted results show a good agreement with the experimental data.
This study could provide basic data and theoretical instruction for the industry application and optimization of welding parameters of high-speed pulsed GMAW.
引文
[1]林尚扬,关桥.我国制造业焊接生产现状与发展战略研究[c].熔焊新技术及应用研讨会论文集,2003,1-26.
[2]R. Olsson. High-speed welding gives a competitive edge [J]. Welding Review International, 1995,14(80):128-131.
[3]黄鹏飞,殷树言,卢振洋,等.高速熔化极气体保护焊机研制[c].汽车焊接国际论坛论文集,2003,213-218.
[4]卢振洋,黄鹏飞,蒋观军,殷树言.高速熔化极气体保护焊机理及工艺研究现状[J].焊接,2006,3：16-20
[5]赵明,翟磊,孙永兴. GMAW三维瞬态焊接热过程的数值模拟[J].焊接,2008,10：28-31
[6]胥国祥,武传松,秦国梁,等.激光+GMAW复合热源焊焊缝成形的数值模拟[J].金属学报,2008,44(6)：641-646
[7]张明贤,武传松,李克海,张裕明.基于有限元分析对新型DE_GMAW焊缝尺寸预测[J].焊接学报,2007,28(2)：33-37
[8]王振民,薛家祥,赵朋成,黄石生.基于适体坐标系的TCGMAW熔池行为数值模拟[J].华南理工大学学报,2007,35(8)：22-26
[9]张建刚,孙俊生,张敏.基于数值模拟的GMAW焊接熔深控制模型[J].山东大学学报,2002,32(3)：232-235
[10]李超,沈灿铎,赵继勋,朱胜.焊接工艺对GMAW堆焊焊缝区温度场影响的数值模拟[J].装甲工程学院学报,2009,23(2)：84-87
[11]武传松,陈茂爱,李十凯GMAW焊接熔滴长大和脱离动态过程的数学分析[J].机械工程学报,2006,42(2)：76-81
[12]何建萍,华学明,吴义雄,焦馥杰. GMAW短路过波动态模型的建立[J].焊接学报,2006,27(9)：77-80
[13]孙俊生.GMAW焊接熔滴热焓量分布模型[J].山东工业大学学报,1998,28(3)：212-216
[14]卢振洋,黄鹏飞,张撼鹏,殷树言.薄板高速熔化极脉冲气体保护焊控制及实现[J].焊接学报,2006,27(2)：47-51
[15]T.C.Nguyen, D.C.Weckman, D.A.Johnson and H.W.Kerr. High speed fusion weld bead defects [J]. Science and Technology of Welding and Joining,2006, 11(6):618-633
[16]T.C.Nguyen, D.C.Weckman, D.A.Johnson and H.W.Kerr. The humping phenomenon during high speed gas metal arc welding [J]. Science and Technology of Welding and Joining,2005, 10(4):447-459
[17]莫春立,钱百年,国旭名等.焊接热源计算模式的研究进展,焊接学报,2001,22(3)：93-96
[18]吴甦,赵海燕,王煜,等.高能束焊接数值模拟中的新型热源模型[J].焊接学报,2004,25(1)：91-94
[19]Zacharia T, Eraslan A H, Aidun D K. Modeling of non-autogenous welding [J]. Welding Journal,1988,67(1):15-18
[20]J.Dimey, D.K.Aidun, G.Ahmadi. Numerical simulation of the effect of gravity on weld pool shape [J]. Welding Journal.1995,74(8):263-268
[21]郑炜.脉冲TIG焊接熔池流场与热场动态过程的数值模拟[J].焊接学报,1997,18(4)：227-231
[22]赵朋成.全熔透TIG焊接熔池形态瞬时行为的数值模拟[D].济南：山东大学博士论文,2003
[23]王怀刚.三维瞬态小孔等离子弧焊接温度场的数值模拟[D].济南：山东大学硕士论文,2005
[24]陶文铨.数值传热学[M].西安：西安交通大学出版社,2001
[25]Choo R T C. Mathematical modeling of heat and fluid flow phenomena in a Mutually coupled welding arc and weld Pool[D].Cambridge:MIT,1991
[26]Choo R T C, Szekely J. Vaporzation kinetics and surface temperature in a mutually coupled spot gas tungsten arc weld and weld Pool[J]. Welding Journal,1992,71(3):75-93
[27]Choo R T C, Szekely J, Westhoff R C. On the calculation of the free surface temperature of gas-tungsten-arc weld Pools from first Principles:Part Ⅰ modeling the welding arc [J]. Metallurgical Transaction B,1992,23(6):357-369
[28]Choo R T C, Szekely J, David S A. On the calculation of the free surface temperature of gas-tungsten-arc weld Pools from first Principles:Part Ⅱ Modeling the weld Pool and comparison with experiments [J]. Metallurgical Transaction B,1992,23(6):371-384
[29]闰凤洁.基于PHOENICS的三维瞬态TIG焊接熔池数值模拟[D].济南：山东大学硕士论文,2003
[30]赵衍华,林三宝,吴林.2014铝合金搅拌摩擦焊接过程塑性流变可视化[J].焊接学报,2005,26(6)：73-76
[31]赵衍华,林三宝,贺紫秋,等.2014铝合金搅拌摩擦焊接过程数值模拟[J].机械工程学报,2006,42(7)：92-97
[32]S.A.Tsirkas, P.Papanikos, Th.kermanidis. Numerical simulation of the laser welding process in butt-joint specimens[J]. Materials processing Technology,2003,134(1):59-69
[33]张明贤DE-GMAW焊接温度场与热变形的有限元分析[D].济南：山东大学硕士论文, 2006
[34]Zacharia T, Eraslan A H, D K Aidum et al. Three-dimensional transient model for arc welding process [J]. Metall Trans B,1989,20(10):654-659.
[35]Turner J S. Buoyancy Effects in Fluid [M]. Cambridge University Press:Cambridge, Dec 1979.
[36]武传松.焊接热过程与熔池形态[M].北京：机械工业出版社,2007,6：102-105
[37]Din-Yu Hsieh, S. P. Ho. Wave and stability in fluids. Singapore:World scientific publishing Co. Pte. Ltd.,1994
[38]黄德波.水波理论基础[M].哈尔滨：哈尔滨船舶工程学院出版社,1991,4：5-15
[39]赵德志,李焱.水工模型试验关于表面张力影响的波速论证[J].水利学报,2004(1)：3-5
[40]冼爱平,王连文.液态金属的物理性能[M].北京：科学出版社,2005,5：144-151
[41]朱峰,苗润才,苏兵等.激光衍射法测量表面张力和毛细波波速与温度的关系[J].光子学报,2009,38(11)：2927-2929
[42]Sun J S, Wu C S, Gao J Q. Effects of distribution model of droplets heat content on fluid flow in weldpool. Acta Metallurgica Sinica,1999,35(9):964-970
[43]Ronald F. Probstein. Physicochemical hydrodynamics:an introduction. New York:John Wiley & Sons, Inc.,1994,2nd edition.
[44]武传松.焊接热过程与熔池形态[M].北京：机械工业出版社,2007,2：22-24
[45]Zacharia T, David S A and Vitek J M. Effect of evaporation and temperature-dependent material properties on weld pool development [J]. Metall Trans B,1991,22(4):233-241.
[46]Choi M, Greif R and Salcudean M. A study of heat transfer during arc welding with applications to pure metals or alloys and low or high boiling temperature materials [J]. Numerical Heat Transfer,1987,11:477-489.
[47]Doormaal J P Van, Raithby G D. Enhancement of the SIMPLE method for predicting incompressible fluid flows [J]. Numer. Heat Transfer,1984,7:147-163.
[48]陶文铨.数值传热学[M].西安：西安交通大学出版社,1987.
[49]Lee S Y and Na S J. A numerical analysis of molten pool convection considering geometric parameters of cathode and anode [J]. Weld. J.,1997,76(11):484s-497s.
[50]Patankar S V, Spalding D B. A calculating procedure for heat, mass and momentum transfer in three-dimensional parabolic flows [J]. Int. J. Heat Mass Transfer,1972,15:1787-1806.
[51]赵明,武传松,陈茂爱.焊接热过程数值分析中相变潜热的三种解决方案[J].焊接学报,2006,27(9)：55-58
[52]Lancaster J F. The Physics of Welding. New York:Pergamon Press,1986:135
[53]Lin M L, Eagar T W. Pressures produced by Gas Tungsten Arcs. Metallurgical Transactions B, 17(3):601-607.
[54]武传松. L.Dorn.熔滴冲击力对MIG焊接熔池表面形状的影响[J].金属学报,1977,33(7)：774-780.
[55]Kim J-W, Na S-J. A study on the effect of contract tube-to-workpiece distance on weld pool shape in gas metal arc welding. Welding Journal,1995,74(5):141s-152s
[56]Zhao P.C., Wu C.S. and Y.M.Zhang. Numerical simulation of the dynamic characteristics of weld pool geometry with step-changes of welding parameters. Modeling and Simulation in Materials Science and Engineering,2004,12:765-780
[2]R. Olsson. High-speed welding gives a competitive edge [J]. Welding Review International, 1995,14(80):128-131.
[3]黄鹏飞,殷树言,卢振洋,等.高速熔化极气体保护焊机研制[c].汽车焊接国际论坛论文集,2003,213-218.
[4]卢振洋,黄鹏飞,蒋观军,殷树言.高速熔化极气体保护焊机理及工艺研究现状[J].焊接,2006,3：16-20
[5]赵明,翟磊,孙永兴. GMAW三维瞬态焊接热过程的数值模拟[J].焊接,2008,10：28-31
[6]胥国祥,武传松,秦国梁,等.激光+GMAW复合热源焊焊缝成形的数值模拟[J].金属学报,2008,44(6)：641-646
[7]张明贤,武传松,李克海,张裕明.基于有限元分析对新型DE_GMAW焊缝尺寸预测[J].焊接学报,2007,28(2)：33-37
[8]王振民,薛家祥,赵朋成,黄石生.基于适体坐标系的TCGMAW熔池行为数值模拟[J].华南理工大学学报,2007,35(8)：22-26
[9]张建刚,孙俊生,张敏.基于数值模拟的GMAW焊接熔深控制模型[J].山东大学学报,2002,32(3)：232-235
[10]李超,沈灿铎,赵继勋,朱胜.焊接工艺对GMAW堆焊焊缝区温度场影响的数值模拟[J].装甲工程学院学报,2009,23(2)：84-87
[11]武传松,陈茂爱,李十凯GMAW焊接熔滴长大和脱离动态过程的数学分析[J].机械工程学报,2006,42(2)：76-81
[12]何建萍,华学明,吴义雄,焦馥杰. GMAW短路过波动态模型的建立[J].焊接学报,2006,27(9)：77-80
[13]孙俊生.GMAW焊接熔滴热焓量分布模型[J].山东工业大学学报,1998,28(3)：212-216
[14]卢振洋,黄鹏飞,张撼鹏,殷树言.薄板高速熔化极脉冲气体保护焊控制及实现[J].焊接学报,2006,27(2)：47-51
[15]T.C.Nguyen, D.C.Weckman, D.A.Johnson and H.W.Kerr. High speed fusion weld bead defects [J]. Science and Technology of Welding and Joining,2006, 11(6):618-633
[16]T.C.Nguyen, D.C.Weckman, D.A.Johnson and H.W.Kerr. The humping phenomenon during high speed gas metal arc welding [J]. Science and Technology of Welding and Joining,2005, 10(4):447-459
[17]莫春立,钱百年,国旭名等.焊接热源计算模式的研究进展,焊接学报,2001,22(3)：93-96
[18]吴甦,赵海燕,王煜,等.高能束焊接数值模拟中的新型热源模型[J].焊接学报,2004,25(1)：91-94
[19]Zacharia T, Eraslan A H, Aidun D K. Modeling of non-autogenous welding [J]. Welding Journal,1988,67(1):15-18
[20]J.Dimey, D.K.Aidun, G.Ahmadi. Numerical simulation of the effect of gravity on weld pool shape [J]. Welding Journal.1995,74(8):263-268
[21]郑炜.脉冲TIG焊接熔池流场与热场动态过程的数值模拟[J].焊接学报,1997,18(4)：227-231
[22]赵朋成.全熔透TIG焊接熔池形态瞬时行为的数值模拟[D].济南：山东大学博士论文,2003
[23]王怀刚.三维瞬态小孔等离子弧焊接温度场的数值模拟[D].济南：山东大学硕士论文,2005
[24]陶文铨.数值传热学[M].西安：西安交通大学出版社,2001
[25]Choo R T C. Mathematical modeling of heat and fluid flow phenomena in a Mutually coupled welding arc and weld Pool[D].Cambridge:MIT,1991
[26]Choo R T C, Szekely J. Vaporzation kinetics and surface temperature in a mutually coupled spot gas tungsten arc weld and weld Pool[J]. Welding Journal,1992,71(3):75-93
[27]Choo R T C, Szekely J, Westhoff R C. On the calculation of the free surface temperature of gas-tungsten-arc weld Pools from first Principles:Part Ⅰ modeling the welding arc [J]. Metallurgical Transaction B,1992,23(6):357-369
[28]Choo R T C, Szekely J, David S A. On the calculation of the free surface temperature of gas-tungsten-arc weld Pools from first Principles:Part Ⅱ Modeling the weld Pool and comparison with experiments [J]. Metallurgical Transaction B,1992,23(6):371-384
[29]闰凤洁.基于PHOENICS的三维瞬态TIG焊接熔池数值模拟[D].济南：山东大学硕士论文,2003
[30]赵衍华,林三宝,吴林.2014铝合金搅拌摩擦焊接过程塑性流变可视化[J].焊接学报,2005,26(6)：73-76
[31]赵衍华,林三宝,贺紫秋,等.2014铝合金搅拌摩擦焊接过程数值模拟[J].机械工程学报,2006,42(7)：92-97
[32]S.A.Tsirkas, P.Papanikos, Th.kermanidis. Numerical simulation of the laser welding process in butt-joint specimens[J]. Materials processing Technology,2003,134(1):59-69
[33]张明贤DE-GMAW焊接温度场与热变形的有限元分析[D].济南：山东大学硕士论文, 2006
[34]Zacharia T, Eraslan A H, D K Aidum et al. Three-dimensional transient model for arc welding process [J]. Metall Trans B,1989,20(10):654-659.
[35]Turner J S. Buoyancy Effects in Fluid [M]. Cambridge University Press:Cambridge, Dec 1979.
[36]武传松.焊接热过程与熔池形态[M].北京：机械工业出版社,2007,6：102-105
[37]Din-Yu Hsieh, S. P. Ho. Wave and stability in fluids. Singapore:World scientific publishing Co. Pte. Ltd.,1994
[38]黄德波.水波理论基础[M].哈尔滨：哈尔滨船舶工程学院出版社,1991,4：5-15
[39]赵德志,李焱.水工模型试验关于表面张力影响的波速论证[J].水利学报,2004(1)：3-5
[40]冼爱平,王连文.液态金属的物理性能[M].北京：科学出版社,2005,5：144-151
[41]朱峰,苗润才,苏兵等.激光衍射法测量表面张力和毛细波波速与温度的关系[J].光子学报,2009,38(11)：2927-2929
[42]Sun J S, Wu C S, Gao J Q. Effects of distribution model of droplets heat content on fluid flow in weldpool. Acta Metallurgica Sinica,1999,35(9):964-970
[43]Ronald F. Probstein. Physicochemical hydrodynamics:an introduction. New York:John Wiley & Sons, Inc.,1994,2nd edition.
[44]武传松.焊接热过程与熔池形态[M].北京：机械工业出版社,2007,2：22-24
[45]Zacharia T, David S A and Vitek J M. Effect of evaporation and temperature-dependent material properties on weld pool development [J]. Metall Trans B,1991,22(4):233-241.
[46]Choi M, Greif R and Salcudean M. A study of heat transfer during arc welding with applications to pure metals or alloys and low or high boiling temperature materials [J]. Numerical Heat Transfer,1987,11:477-489.
[47]Doormaal J P Van, Raithby G D. Enhancement of the SIMPLE method for predicting incompressible fluid flows [J]. Numer. Heat Transfer,1984,7:147-163.
[48]陶文铨.数值传热学[M].西安：西安交通大学出版社,1987.
[49]Lee S Y and Na S J. A numerical analysis of molten pool convection considering geometric parameters of cathode and anode [J]. Weld. J.,1997,76(11):484s-497s.
[50]Patankar S V, Spalding D B. A calculating procedure for heat, mass and momentum transfer in three-dimensional parabolic flows [J]. Int. J. Heat Mass Transfer,1972,15:1787-1806.
[51]赵明,武传松,陈茂爱.焊接热过程数值分析中相变潜热的三种解决方案[J].焊接学报,2006,27(9)：55-58
[52]Lancaster J F. The Physics of Welding. New York:Pergamon Press,1986:135
[53]Lin M L, Eagar T W. Pressures produced by Gas Tungsten Arcs. Metallurgical Transactions B, 17(3):601-607.
[54]武传松. L.Dorn.熔滴冲击力对MIG焊接熔池表面形状的影响[J].金属学报,1977,33(7)：774-780.
[55]Kim J-W, Na S-J. A study on the effect of contract tube-to-workpiece distance on weld pool shape in gas metal arc welding. Welding Journal,1995,74(5):141s-152s
[56]Zhao P.C., Wu C.S. and Y.M.Zhang. Numerical simulation of the dynamic characteristics of weld pool geometry with step-changes of welding parameters. Modeling and Simulation in Materials Science and Engineering,2004,12:765-780