Vol. 21, No. 3 (2014) 191 CW Hablanian plot 1,2 Hablanian plot Vd/K, P/θtk V m/s d m K m 2 /s P W θ K t m k W/mK Hablanian plot Vd/K V K/d P/θtk P θtk

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190 : 574-8530 3-1 - 1 431-1202 1955 1 472-0017 7 Prediction of Penetration Depth Using Hablanian Plot Based on Laser Welding Results for Stainless Steel HEYA Manabu, TSUBOI Akihiko, SHAMOTO Hideyasu and TAGAWA Masao Received December 20, 2013 In order to experimentally investigate the prediction accuracy of a penetration depth, we have organized numerous welding results of stainless steels (SUS304) using Hablanian plot. The lasers used were three fiber lasers, one disk laser, four YAG lasers, and one laser diode. These welding data obtained from bead - on - plate welding tests by the laser job shop consisted of about 1,700 data points. The following results were derived from the observations: (1) Hablanian plot results could be fitted using third - degree polynomial fitting but not linear fitting. (2) In the lower range of two dimensionless parameters, the effect of heat conduction into the adjacent material became remarkable. (3) Welding properties expressed by Hablanian plot showed similar properties even under the different welding conditions (such as the type of laser oscillator, welding speed, and power density), except for the focal length of focusing lenses used. Hablanian plot results for the different focal lengths could be expressed by the corresponding third - degree polynomial fitting curves. (4) A penetration depth could be precisely calculated by using the third - degree polynomial fitting curve in comparison with the linear fitting curve. Key words : laser welding, Hablanian plot, dimensionless parameters, penetration depth, prediction, stainless steel 1. Zn Al Ti Ni Co 3 CW

Vol. 21, No. 3 (2014) 191 CW Hablanian plot 1,2 Hablanian plot Vd/K, P/θtk V m/s d m K m 2 /s P W θ K t m k W/mK Hablanian plot Vd/K V K/d P/θtk P θtk 3 Vd/K t P/θtk Vd/K P/θtk 3 P/θtk 100 2 P/θtk 100 P/θtk Vd/K CO 2 3 5 6 Hablanian plot Hablanian plot SUS304 Hablanian plot Hablanian plot 1,700 2. 2.1 Table 1 CW IPG YLR - 5000 5 kw YLR - 2000 2 kw YLR - 300 300 W Trumpf HLD 1001.5 1 kw YAG Trumpf HL353D 350 W HL1003D 1 kw HL4006D 4 kw HLD3504 3.5 kw LD Laserline LDF400-4000 3.6 kw 1,070 nm 1,030 nm YAG 1,064 nm LDF400-4000 967 nm 1,000 nm Table 1 Type of the lasers used and the welding conditions examined. Type of laser Core diameter of fibers μm Fiber laser IPG YLR - 5000 ϕ200 YLR - 2000 ϕ100 YLR - 300 ϕ9 Disk Laser Trumpf HLD1001.5 ϕ150 YAG laser Trumpf HL353D ϕ300 HL1003D ϕ300 HL4006D ϕ600 HLD3504 ϕ400 LD Laserline LDF400-4000 ϕ400 Focal length of Welding Output focusing lens mm speed power W Focal length of m/min collimate lens mm 250-5,000 0.5-30 125/250/375/500 125 100-2,000 0.5-20 125/250/375/500 125 10-300 0.5-20 100/200/300 100 50-1,000 0.5-30 100/150/200 100-350 0.5-10 100/150/200 100-1,000 0.5-10 100/150/200 500-4,000 0.5-30 100/150/200 500-3,500 0.5-30 100/150/200 1,000-3,600 1-5 100/150 100 Spot diameter μm 200/400/600/800 100/200/300/400 9/18/27 75/112.5/150 150/225/300 150/225/300 300/450/600 200/300/400 400/600

192 : 2.2 Table 1 1,700 SUS304 SUS304 7 16.2 W/m K 1,723 K 4.05 10 6 m 2 /s 1 d s µm d core µm f f mm f c mm ff ds = dcore fc 1 3. Fig. 1 5 kw 0.4 mm LD 3.6 kw 0.4 mm Fig. 1 LD Fig. 1 1 mm Hablanian plot Fig. 2 Hablanian plot Fig. 2 Fig. 1 5 kw 3.6 kw LD 0.4 mm P/θtk Vd/K P/θtk Vd/K Fig. 2 1 Hablanian plot P/θtk Vd/K 1 3 Fig. 2 1 mm Fig. 3 Hablanian plot + 3 Poly Line log P/θtk 1.7 log Vd/K 1.0 1 log P/θtk 1.2 log Vd/K 0 1 Hablanian plot 3,5 3 2 3 0.5 mm 0.5 mm Fig. 1 Typical welding results for a 5 - kw - fiber laser and a 3.6 - kw - LD. Fig. 2 Relation between welding bead shapes and Hablanian plot results for the welding data as shown in Fig. 1 with a spot diameter of 0.4 mm.

Vol. 21, No. 3 (2014) 193 Fig. 3 Hablanian plot results for all welding data. Fig. 4 Estimation of the slopes of the fitting curve for Hablanian plot results in the lower P/θtk and Vd/K ranges. 0.5 mm y = 7.103 + 10.38x 4.548x 2 + 0.7311x 3 y = 2.230 + 1.891x y = log Vd/K x = log P/θtk 4. 2 3 4.1 P/θtk Vd/K Hablanian plot 1 1,3 Fig. 4 a1 2 3 3.36 4 a0 a1=3.36 y 3.36 P/θtk Vd/K P/θtk Vd/ K 4 C P 1 Vd = itk S 1.096#10-4 K X -3.36 +C 4 3 20 kw 1.8 log P/θtk 1.7 log Vd/K 1.2 log P/θtk 1.2 log Vd/K 0 3 1.8 3.36 Hablanian plot 3 P/θtk Vd/K 1 4.2 Fig. 5 6 7 Fig. 3 YAG YAG Disk LD 3 4.3 Fig. 8 Fig. 3 Hablanian plot Fig. 8 a P/θtk Vd/K Fig. 8 b P/θtk Vd/K Fig. 8 f100 100 mm 3 Fig. 3 Fig. 8 a 100 mm 125, 150, 200 mm 250 mm 3 NA

194 : Fig. 5 Hablanian plot results for fiber lasers. Fig. 8 Hablanian plot results for the focal lengths of focusing lenses used in the a lower and b higher P/θtk and Vd/K ranges. Fig. 6 Hablanian plot results for YAG lasers. Fig. 9 Hablanian plot results for power density. Fig. 7 Hablanian plot results for various lasers. Fig. 8 b 150 mm 500 mm f = 150, 500 mm Fig. 8 a f300 10 300 W µm 1 mm Fig. 9 10 Fig. 3 Hablanian plot 5 10 5 W/cm 2 5 10 5 W/cm 2 1 10 6 W/cm 2 1 10 6 W/cm 2 5 10 6 W/cm 2 5 10 6 W/cm 2 1 10 7 W/cm 2 1 10 7 W/cm 2 5 10 7 W/cm 2 5 10 7 W/cm 2 1 10 8 W/cm 2 1 10 8 W/cm 2

Vol. 21, No. 3 (2014) 195 Fig. 10 Hablanian plot results for welding speed. Fig. 11 Prediction of a penetration depth using a polynomial - fitting and b linear - fitting curves. 2 m/min 2 m/min 5 m/min 6 m/min 10 m/min 15 m/min 20 m/min 25 m/min 30 m/min 3 Fig. 5 Fig. 6 Fig. 7 4.4 Fig. 11 Hablanian plot t cal t mea Fig. 11 a b Fig. 3 3 Polynomial Line t cal t mea Polynomial Line 5 6 t cal Fig. 11 P tcal = 10 -R1.173+0.3358a+0.1379a 2 +0.05342a 3 ik W 5 Fig. 12 Dependence of Vd/K on a prediction error using a polynomial - fitting and b linear - fitting curves. P tcal = 10 -R1.236+0.4608a ik W 6 a = log Vd/K Fig. 12 a b Polynomial Line Vd/K 0 log Vd/K 1 1 Fig. 3 Vd/K 3 1.50±17.7% 4.65±34.6% Hablanian plot Hablanian plot mm mm 3

196 : Fig. 8 3 5. Hablanian plot SUS304 Hablanian plot 3 1 YAG 4 LD 1 1,700 1 3 2 log P/θtk 1.7 log Vd/K 1.0 1 3 log P/θtk 1.2 log Vd/K 0 1 4 3 3 5 3 Hablanian plot Fig. 8 1 Hablanian, M.H. : A Correlation of Welding Variables, Proc. of 4 th Symp. Electron Beam Technology, 1962, 262. 2 Lowry, J.F., Fink, J.H. and Schumacher, B.W. : A Major Advance in High - Power Electron - Beam Welding in Air, J. Appl. Phys., 47, 1976, 95. 3 Locke, E.V., Hoag, E.D. and Helia, R.A. : Deep Penetration Welding with High - Power CO 2 Lasers, IEEE J. Quantum Electron., 8, 1972, 132. 4 Baardsen, E.L. and Schmatz, D.J. : High - Speed Welding of Sheet Steel with a Carbon Dioxide Laser, Proc. of IEEE Conf. Laser Eng. Appl., Washington D.C., May, 1971. 5 Metzbwer, E.A. : Penetration Depth in Laser Beam Welding, Welding Rerearch, 1993, 403 - s. 6 Quintino, L., Costa, A., Miranda, R. and Yapp, D. : Welding with High - Power Fiber Lasers A Preliminary Study, Material & Design, 28, 2007, 1231. 7 Washko, S.D. and Aggen, G. : Metals Handbook, ASM International, 1990, 841.

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