Free surface formation of the weld pool (on top and bottom in the case of full-penetration welding) is described by the equation of equilibrium of the forces at the.
J. Phys. D: Appl. Phys. 33 (2000) 662–671. Printed in the UK
PII: S0022-3727(00)07708-1
Numerical simulation of weld pool geometry in laser beam welding W Sudnik†, D Radaj‡, S Breitschwerdt‡ and W Erofeew† † State University Tula, Lenin Avenue 92, 300600 Tula, Russia ‡ DaimlerChrysler AG, D-70546 Stuttgart, Germany Received 10 September 1999, in final form 13 January 2000 Abstract. A linear correlation between the depth and the length of the weld pool is found in
laser beam welding experiments with varied laser beam power and constant welding speed. On the other hand, the weld pool length changes only slightly with increased welding speed and constant laser beam power. The existing analytical and numerical models fail to explain these dependences. The observed effects are essentially conditioned by the fluid flow in the weld pool caused by the thermocapillary effect, by the friction forces of the metal vapour passing through the capillary and by the convexity of weld pool and fusion zone caused by thermal expansion of the weld pool and the joined workpieces. In order to predict the weld pool length more accurately the model developed by Sudnik et al in 1996 is enlarged by the heat transport produced by the recirculating flow in radial sections of the weld pool. Verification of the model for 16MnCr5 steel with sheet thicknesses of 2 and 6 mm shows that it is suitable for predicting the weld pool geometry and for analysing the thermodynamics of the process. In order to gain a better understanding of the structure of heat transport in the weld pool, the different modes of transport are compared in respect of their contribution to the depth-to-length ratio of the weld pool. A calculation of the weld pool length for welding speeds of 1–8 m min−1 with a laser beam power of 2.5 kW shows that the relative contributions of the transport modes are as follows. Approximately 50–90% of the weld pool length (increasing with welding speed) results from conductive and translatory heat transport (with the fusion zone convexity contributing approximately 20–30%). The remaining 50–10% of the weld pool length (decreasing with welding speed) result from convective heat transport. The model predicts the shoulder in the weld pool trough. It also explains the change in the weld pool length by the effect of the gap width, by the transition from through welding to penetration welding and by improvements in beam quality.
1. Introduction
The increasing use of laser beam welding poses new theoretical tasks with respect to process development, defect explanation and process control. The evaluation and calculation of the ratios of the geometric weld pool surface parameters (two-dimensional models) and weld pool depth parameters (three-dimensional models) provide an important means for quality control in laser beam welding. A linear correlation between the depth and length of the weld pool was found in laser beam welding tests with varied laser beam power and constant welding speed (Breitschwerdt 1996). The most simple manner of simulating the shape and size of the weld pool is based on the linear heat conduction model (Rosenthal 1941, Rykalin 1951), figure 1(a). SwiftHook and Gick (1973) described the temperature field in laser beam welding with a cylindrical heat source, figures 1(b) and 1(c). The revision of the heat conduction models by means of a Gauss-distributed surface heat source (Gratzke et al 1991), a plasma plume (Ducharme et al 1994) or a conical heat source (Lankalapalli et al 1996) did not bring the desired improvement in results. The purely experimental findings by Gavrilyuk et al (1983) and Breitschwerdt (1996) show that the real weld 0022-3727/00/060662+10$30.00
© 2000 IOP Publishing Ltd
pool geometry, figure 1(d), is not predicted by the existing analytical and numerical weld pool models of laser beam welding without consideration of the fluid flow in the weld pool. Three driving mechanisms of the fluid flow were analysed, the forces resulting from temperature-dependent surface tension (Anthony and Cline 1977, Mitkevich et al 1982, Beck 1996), the friction force of the metal vapour escaping from the capillary (Anisimov et al 1984, Arutjunjan et al 1986, Beck 1996) and the movement of the capillary relative to the work piece (Beck 1996, Kern et al 1998). Lambrakos et al (1993) and Williams et al (1993) presented a three-dimensional flow model, Kar and Mazumder (1995) developed a model for determining the flow velocities and the temperature distribution at the free surface of the weld pool and in the capillary. Beck (1996) showed that surface tension and vapour exhaust from the capillary essentially contribute to the kinetic energy in the weld pool. His numerical solutions indicate the formation of a shoulder in the weld pool under certain conditions. A self-consistent overall model of laser beam welding and the relevant computer program DB-LASIM for engineering applications was developed by Sudnik et al (1996). The fluid dynamical part of the model comprises the
Numerical simulation of weld pool geometry in laser beam welding
(a)
(b)
(c)
(d)
Figure 1. Longitudinal sections of weld pool geometry (shaded): line source in plate (a), cylindrical source in plate (b), cylindrical source in a semi-infinite solid (c) and the actual weld pool determined experimentally in austenitic steel of 4mm thickness (d).
flow driven by the capillary movement and the flow initiated by the gradient of surface tension in transverse sections, i.e. one and a half from a total of three essential mechanisms. Despite the large body of investigation referenced above, sufficiently accurate solutions for the length of the weld pool and for the shoulder in the pool shape have not yet been found. In order to predict the weld pool length sufficiently well, the original model (Sudnik et al 1996, 1998) is enlarged below by the heat transport caused by a recirculating flow in radial sections driven by the temperature-dependent surface tension and by the vapour friction at the capillary wall, and caused by the weld convexity resulting from thermal expansion in the high-temperature zone. Welding test results are presented which verify the model and demonstrate its applicability for predicting the weld pool geometry and for analysing the thermodynamic processes. The approximately linear correlation between the weld pool length and weld pool depth for a constant welding velocity found experimentally is explained theoretically. 2. Physical and numerical modelling
2.1. Experimental starting basis The experiments for determining the weld pool geometry in laser beam welding of 16MnCr5 low-alloy steel under argon were performed by Breitschwerdt (1996) using the Trumpf laser TLF6000 and TLF12000 as well as the Rofin Sinar laser DC025. The focusing capability of these lasers is variable within a beam quality number range of K = 0.23–0.70. The sheet thicknesses covered the range 2–10 mm. The laser beam power and the welding speed (that is the rate of traverse of the workpiece under the stationary laser beam) were varied. The geometry of the weld pool surface was detected by means of a CCD (charge coupled device) video camera with subsequent computer-aided image processing. The experimental data show a correlation between the length and depth of the weld pool for variations of laser beam power and welding speed. The weld pool depth is approximately linearly dependent on the weld pool length for varied power with constant speed. Increased power means larger length and depth. On the other hand, increased speed with constant power causes smaller depth with only a slight change in length. Considering ring welds, the weld pool length was increased by approximately 20% under identical process parameters when the end of the first run was remolten. A significant reduction in weld pool length occurred with gaps. Some of the experimental results are depicted in section 3.
2.2. Enlarged physical model Two hypotheses are available to explain the observed behaviour of the weld pool length: weld pool flow caused by thermocapillary forces and by vapour friction forces at the capillary wall on the one hand and convexity of the fusion zone caused by thermal expansion in the high-temperature area on the other hand. The flow alongside the weld pool is conditioned by the thermocapillary effect and the friction forces of the evaporating metal. Both phenomena produce fluid motion at the surface, from the vapour capillary to the weld pool boundary in radial directions. This flow reduces the cooling rate and elongates the weld pool. The correlation between the depth and length of the weld pool may be attributed mainly to the vapour friction forces at the capillary wall because the length of contact between the metal vapour and molten pool increases with a deepened vapour capillary. Another explanation for the increase in the surface length of the weld pool is in the change of shape of the welded joint during welding caused by thermal expansion. The increase in volume by thermal expansion of the metal in the weld pool reaches 8–12% in deep weld pools of beam welding processes and produces a significant convexity of the molten pool at the surface of the welded parts. The convex weld reinforcement cools mainly by heat conduction into the metal of the workpiece. The higher reinforcement has a longer cooling time under the assumption of identical reinforcement widths. This results in a larger weld pool length (equal to the cooling time multiplied by the welding speed). More heat has therefore to be allocated to the surface layer of the weld pool (and less heat to the inner region) in the original thermodynamic model which is designed without convexity. The opposite effects occur with a weld concavity caused by a joint gap. The second hypothesis is supported by the substantial reduction of the top-side weld pool extension in the case of a gap between the welded parts. The gap width has nearly no influence on the flow in the weld pool, but the convexity of the weld pool, is substantially reduced (concavity may result in the case of a large gap width). On the other hand, a larger full-penetration-welded sheet thickness is connected with an increase in the weld pool volume. This results in an increase of the weld pool length because the cooling time of the weld pool increases. 2.3. Original base model The basis of the model of laser beam welding proposed by Sudnik et al (1996, 1998) is the energy equation in Cartesian coordinates fixed to the laser beam axis (either the laser beam or the workpiece may move with welding 663
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speed vw ). Free surface formation of the weld pool (on top and bottom in the case of full-penetration welding) is described by the equation of equilibrium of the forces at the surface: surface pressure, gravity force and surface tension with the hydrodynamic pressure neglected. In the original model the fluid flow is restricted to a flow in horizontal sections driven by the moving capillary and to a recirculating flow in transverse sections driven by thermocapillary forces.
y u
u
c,x
2r
c
a)
σ σ
u σ
2.4.1. General approach. An examination of the experimental observations and of the published results of three-dimensional numerical solutions according to the Navier–Stokes equations (Fuhrich et al 1999) reveals that the fluid flow in the weld pool of laser beam welding has the character of a recirculating flow. The numerical analysis of the fluid flow presented below uses the semi-empirical method of assuming a simplified pattern of flow trajectories between plane sections and determining the flow velocities analytically on the basis of continuity considerations. In order to get acquainted with some details of the flow pattern generated under the assumption of axisymmetry, the Navier–Stokes equations were solved numerically for the stationary flow in an axisymmetric weld pool under the relevant driving forces, with the boundary shape and dimensions taken from an experimentally determined longitudinal section of a real weld pool. The results of the numerical solution just mentioned show recirculating flow patterns under the thermocapillary and vapour pressure forces acting on the weld pool. The recirculating flow comprises a major part of the weld pool. The rotary centre of the flow is shifted to the ‘cold edge’ of the weld pool in the case of thermocapillary flow, or to the ‘hot edge’ near the capillary in the case of flow induced by vapour friction. The centre is positioned in the upper, surface-adjacent part of the weld pool in both cases. The combined action of the two driving forces generates a common vortex in the upper part of the weld pool. The three-dimensional weld pool flow simulation by Fuhrich et al (1999) shows that the centre of recirculation and the point of maximum flow velocity is nearer to the capillary than to the solidification front. The coupled solution of the equations of energy conservation and surface deformation together with the Navier–Stokes equations is too time consuming for engineering purposes. Therefore, the simplified method below was developed to determine the local fluid flow velocities necessary for solving the energy equation. The fluid flow in the weld pool is described in a simplified manner by superposition of the flow velocity vectors of three independent flow fields, horizontal flow around the capillary, uEc , radial flow by the thermocapillary effect (Marangoni flow), uEσ , and radial flow by vapour friction, uEv , figure 2: (1)
2.4.2. Flow around the capillary. The flow around the capillary is described in the horizontal x–y plane based on the condition of mass conservation in radial sections with the sectional area dependent on the angle ϕ between the 664
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ϕ
x
2.4. Revised model of fluid flow in the weld pool
uE = uEc + uEσ + uEv .
v
u
c,y
z
r
s
l
r
2s
z
u
Section A - A
u r b)
y
x
u
c)
Figure 2. Weld pool flow patterns used in the numerical weld pool simulation: flow around the capillary (a), thermocapillary flow and flow resulting from vapour friction in the capillary (b) and radial sections (c); the radial flow divergence is not yet included.
capillary wall with radius rc and the weld pool outer boundary with radius rl (subscript l from ‘liquidus’), figure 2(a). Introducing the adhesion condition at the weld pool boundary and assuming a linear increase of the flow velocity uc directed perpendicular to the radial sections, this velocity results as 2rc r − rc 1− (2) uc = vw rl − r c rl − r c with the welding speed vw and the distance r from the axis of the capillary or laser beam. It can be seen from equation (2) that the adhesion condition, uc = 0, is met at the outer weld pool boundary, r = rl , and that the sectional maximum of the velocity, uc = 2vw rc /(rl −rc ), occurs at the capillary wall, r = rc . The maximum velocity depends on the angle ϕ, that is, rl = rl (ϕ). The overall maximum velocity occurs where the radius rl has a minimum, that is, in the heading part of the weld pool. The velocities are small behind the capillary and especially so in the rear part of the weld pool where they can be neglected. The equation of energy is solved in the Cartesian x–y coordinate system, the relevant velocity components,
Numerical simulation of weld pool geometry in laser beam welding
uEc = uEc,x + uEc,y , are derived with uc,x = uc sin ϕ
uc,y = uc cos ϕ
Kσ = (0 < ϕ < π ). (3)
2.4.3. Recirculating thermocapillary flow. The simplified modelling of the recirculating flow driven by the thermocapillary effect at the surface of the weld pool is based on an approximate description of the fast-moving boundary layer at the surface of the weld pool. The flow is considered between radially-diverging plane sections, figure 2(b) and (c). This description is combined with an estimate on the mean life time of the recirculating fluid. The thermocapillary forces act on the surface of the weld pool generating a boundary layer with shear stress τ at the surface. The theory of boundary layers offers a relation between the shear stress τ and the flow velocity u at the surface in the case of parallel flows (DebRoy and David 1995), r ρµu3 τ = 0.332 (4) r with the density ρ and the dynamic viscosity µ of the fluid, and with the coordinate r in flow direction. The relation above is applicable to radially-diverging flows by taking the radial reduction of flow velocity into account, which results from the radially-increasing perimeter of the weld pool. A recirculating flow channel between two neighbouring plane radial sections is considered. The mass flux (or better volume flux) in this channel must be constant (continuity condition). Using the maximum radial flow velocity uo at the capillary outlet (r = rc ) as the basis, the local radial velocity u at the distance r results from u = uo
rc . r
(5)
The combination of equations (4) and (5) gives the relation for the radially-diverging continuous flow, r ρµu3o rc3 . (6) τ = 0.332 r4 The thermocapillary surface shear stress assumed as constant is set equal to the following equivalent shear stress τeq of the boundary layer averaged over the ‘active radial length’ of this layer, lr = rl − rc , s Z rl 1 ρµu3o rc τ dr = 0.332 . (7) τeq = rl − rc rc rl2 Other similar choices as the basis of equivalence are also acceptable (especially the basis of identical shear force), but result in a more complicated formula without giving higher accuracy under engineering aspects (note that the constant surface shear stress resulting from the thermocapillary effect according to (10) is an assumption which may deviate substantially from the more complex reality). Equation (7) is used to determine the flow velocity uo at the weld pool surface at the capillary outlet from the equivalent shear stress τeq and a coefficient Kσ , the value of which depends on the considered weld pool section, 2 uσ uo = 3(τeq Kσ )1/3
(8)
9.07rl2 . ρµrc
(9)
The equivalent shear stress τeq is set equal to the shear stress τσ from the thermocapillary effect, assumed as constant, and as acting in the radial direction over the radial weld pool length, lr = rl − rc : τσ =
σl − σc rl − rc
(10)
with the surface tension at the liquid boundary, σl , and at the capillary outlet, σo . An estimate on the thickness s of the weld pool surface layer driven by surface forces was made by Vedenov and Gladush (1985). These authors defined a rotor of flow velocity at the surface describing the balanced action of a thermocapillary surface force and the viscosity force of the fluid. The variation of the rotor with velocity is described by the Helmholtz equation (Landau and Lifshitz 1968) which is similar to the equation of heat conduction. The depth of heat propagation from a heat source in the surface is given √ by z = ate , with the thermal diffusivity a and the elapsed time te . Similarly, the characteristic distance of surface force action from the centre of rotation is given by equation (12) below. The flow velocities in the weld pool are much larger than the welding speed. This produces the recirculating motion of the molten metal. Part of the metal participating in the recirculating flow solidifies and is substituted by newly molten metal. The time of action of the driving forces is set equal to the mean time of existence of the metal in the molten state, approximated by tm =
lw 2vw
(11)
with the weld pool length lw and the welding speed vw . The thickness s of the surface layer driven by surface forces is defined according to the heat flow analogy mentioned above, r √ µtm (12) s = νtm = ρ with the kinematic viscosity ν (dimension cm2 s−1 ). A parabolic distribution of the flow velocity according to figure 2(b) is assumed over the layer thickness s with the driving forces prolonged into the recirculating layer of thickness 2s with much smaller flow velocities. This distribution of velocities results from numerical simulations of plane thermocapillary flow within a rectangular domain, if the viscosity forces are sufficiently large relative to the thermocapillary forces. (Poleshaev et al 1987, Zehr 1991). It seems necessary to consider the boundary layer as turbulent in order to satisfy the above condition of a sufficiently high apparent viscosity. 2.4.4. Recirculating flow by vapour friction. The metal vapour passing through the capillary with high velocities (vv = 100–300 m s−1 with the maximum at the bottom according to Beck (1996)) exerts a frictional force on the 665
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molten metal at the capillary wall. The relevant shear stress τv results according to the Newton law applied on a linear decrease of the vapour velocity from a maximum value in the centre of the capillary to zero at the capillary wall: τv = µv
dvv vv = 2µv dr rc
(13)
with the cross sectional velocity vv of the metal vapour, the dynamic viscosity µv of the vapour and radius rc of the capillary. The flow velocity of the molten metal in the axial direction of the capillary resulting from vapour friction can be determined based on (4) with the assumption of a constant vapour flow velocity (and therefore shear stress) over the length of the capillary (the value vv ≈ 100 m s−1 seems to be appropriate according to Beck (1996) in the case of steels, the value vv ≈ 200 m s−1 was measured by Beyer (1995)). It is further assumed that the axial flow velocity is converted into a radial flow velocity at the capillary outlet without major loss, thus resulting in uv = uo = 3(τv2 Kv )1/3 Kv =
9.07lc ρµ
(14) (15)
with the capillary length lc , the radial flow velocity uo at the capillary outlet and the shear stress τv resulting from vapour friction in the capillary. The simplified pattern of the recirculating thermocapillary flow is also used in the case of the flow driven by vapour friction. This has the advantage that the numerical analysis can proceed from the superposed velocities at the capillary outlet, uo = uσ + uv . The thickness s of the boundary layer has to be introduced not only at the surface of the melting pool, but also at the capillary wall, figure 2(b). It was found by comparative numerical calculations that the details of the assumed pattern of recirculating flow are not very important in respect of the geometry of the weld pool provided that the chosen pattern has physical relevance in respect of the final aim of approximating the convective heat transport in the energy equation. 2.5. Numerical implementation The basic model of Sudnik et al (1996) was originally implemented for the decoupled problem, that is the differential equations of energy transport inclusive of fluid flow and of surface deformation were solved one after the other. Now the coupled problem is considered, that is the energy equation is solved for the body with convexity of the weld pool and the weld. The volume of the body is changed and the temperature dependency of the metal density ρ(T ) has to be taken into account. The distribution of enthalpy is correctly described by the redistribution of volume with consideration of the density change. The revised model of fluid flow in the weld pool is applied. The new algorithm is characterized by solving the equations of energy transport, surface deformation and weld pool flow iteratively in a coupled procedure. The calculation procedure, with precautions taken to achieve 666
convergence, is terminated by the accuracy condition, (lw,i − lw,i+1 )/ lw,i < ε, with the values of weld pool length after the last two iterations, lw,i and lw,i+1 , and the acceptable calculation error ε = 1x/ lw ≈ 0.8–1.6%, with applied mesh width 1x and weld pool length lw . 2.6. Thermophysical material parameters and beam quality The heat capacity and the thermal conductivity of the 16MnCr5 low-alloy steel (with 0.195%C, 0.21%Si, 0.83%Mn and 0.022%S) were measured in the temperature range up to 1250 ◦ C whereas the well known material parameters of pure iron can be applied above 1250 ◦ C. These and other thermophysical parameters are stored in the database as a table referring to nine temperatures, inclusive of the solidus temperature. The parameters such as the density and viscosity of the metal vapour in the capillary (ρv = 0.1 mg cm−3 , µv = 0.008 µN s cm−2 ) were adjusted by calibration of the model on the basis of the measured geometrical parameters of the weld pool. A negative surface tension gradient dσ/dT was assumed because of the low sulfur content. The surface tension σl = 12.8 mN cm−1 at the liquidus temperature Tl = 1514 ◦ C decreases linearly with dσ/dT = −0.004 mN cm−1 K−1 until the vaporization temperature Tv = 2860 ◦ C is reached. In accordance with the negative gradient, a surface fluid flow directed to the outside of the molten zone occurs, that is the circulating flow of the thermocapillary convection rotates from the area of low surface tension in the middle of the weld pool to areas of higher surface tension at the outside, as depicted in figure 2. The beam quality number K (beam propagation factor according to DIN EN ISO 11195) is determined from the measured focus diameter df of the laser beam according to K = 4λf/π df d with wave length λ, beam diameter d and focal length f . The measured focus diameter is used in the calculations. 2.7. Calibration and verification Two calibration coefficients are introduced in respect of the weld pool length and width. The first calibration coefficient modifies the viscosity in the surface layer of the weld pool. Numerical simulation results, both from the formulae mentioned above and from the more detailed modelling of Fuhrich et al (1999) based on the FIDAP program system, indicate that the flow velocities are extremely high in a very-thin surface layer. The laminar flow changes into turbulent flow with such parameters. The turbulent flow can be approximated as a laminar flow with formally increased viscosity (according to Boussinesq 1897). This approximation was applied to the fluid flow in weld pools by Choo and Szekeley (1994) and by Hong et al (1998). Therefore, the viscosity µ of the molten metal in the weld pool (µ ≈ 0.25 µN s cm−2 ) was increased by a calibration coefficient kµ . The value of this coefficient was derived from welding 16MnCr5 steel with the low penetration depth of 2 mm (dominant thermocapillary flow). The weld pool length and width determined by calculation and experiment were conforming for kµ ≈ 16.
Numerical simulation of weld pool geometry in laser beam welding Table 1. Maximum flow velocities resulting from flow around the
12
capillary uc , from surface tension uσ and from vapour friction forces uv in the simulation of laser beam welding of 16MnCr5 steel, sheet thickness t = 6 mm, focus diameter df = 0.2 mm, focal length lf = 200 mm, focus position zf = 0 mm and beam quality number K = 0.7. Laser power, Pl (kW)
Welding speed, vw (m min−1 )
uc (m min−1 )
uσ (m min−1 )
uv (m min−1 )
1.0 1.5 2.0 2.5 2.5 2.5 2.5 2.5
2 2 2 1 2 3 4 8
3.9 3.7 3.5 1.4 3.5 6.1 9.7 23.3
6.9 6.6 6.5 6.9 6.3 6.1 5.9 5.5
5.0 5.1 5.3 6.0 5.6 5.1 4.4 3.4
8
Maximum flow velocity
The second calibration coefficient, kv , modifies the value of viscosity of the metal vapour in the capillary initially assumed as µv = 0.008 µN s cm−2 . Its choice is based on the assumption that the influence of vapour friction on weld pool flow is strong only with a deep capillary. Therefore, the coefficient kv was derived from the measured length of the weld pool with a penetration depth of 6 mm. The calibration was performed using the experimental data of welding 16MnCr5 steel with a sheet thickness of 6 mm, applying welding speeds of 1–8 m min−1 and a laser beam focus diameter of 0.5 mm. The result was kv ≈ 2.5, the increase above kv = 1.0 being explained by a wavy capillary surface. The experimentally determined dependences of the weld pool length and weld pool depth on the laser beam power and welding speed were used for verification. The correspondence between the calculated and experimentally determined dependences was achieved after a calibration was performed. Parametrical studies are possible on the basis of the calibrated and verified model.
4
0
a)
1
2
3
Laser beam power,
4
5
P (K=0.23)
kW
6
l
b)
Figure 3. Comparison of calculation results with the mean of experimental results: weld pool length and depth dependence on the laser beam power (a) and the correlation between the depth and the length (b), lf = 200 mm, zf = 0 mm and K = 0.23.
The maximum flow velocities in the weld pool were calculated for several test welds on the basis of the calibrated and verified model, table 1. The velocity components resulting from the flow around the capillary, uc , from the surface tension gradient, uσ , and from the vapour friction, uv , are separately evaluated. They occur at different positions. At low welding speeds, the flow caused by the thermocapillary forces and the frictional forces is predominant. With increased welding speed, the flow around the capillary is more important. This corresponds to the findings of Beck (1996).
laser beam power between 2.0 and 5.5 kW with constant welding speed resulted in an acceptable correspondence between the calculated and measured weld pool geometrical parameters, that is, weld pool depth and weld pool length, figure 3(a), inclusive of their mutual relation, figure 3(b). The approximately linear relation between the weld pool depth and the weld pool length can be used as the basis for process and quality controls. The deviations from the smooth curve both in testing and in calculation are explained from instabilities in the weld pool flow. The accuracy of the model can be amended by a recalibration in the considered parameter range of application. The weld pool lengths for welds with zero gap width and finite gap width according to calculation and experiment are compared in figure 4. A finite gap width reduces the weld pool length substantially compared with zero gap width. The difference in length is explained by the difference in the cooling conditions: a convex weld surface with zero gap width against a concave weld surface with the considered gap width.
3.2. Varied laser beam power and gap width, low beam quality
3.3. Varied laser beam power and welding speed, higher beam quality
First, the Trumpf laser TLF12000 with a low beam quality (quality number K = 0.23) was used. Varying the
Second, the Trumpf laser TL6000 with a higher beam quality (K = 0.32) and the Rofin laser DC025, with definitely
3. Parametrical investigations
3.1. Calculation of flow velocities
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12
6
Gap width
W
8
4
0
W
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0.15 mm
2
1
2
3
4
Laser beam power,
5
P (K=0.23)
kW
0 0.5
6
l
1.0
Figure 4. Comparison of calculation results with the mean of experimental results: weld pool length and depth dependence on the laser beam power for zero gap width and finite gap width, lf = 200 mm, zf = 0 mm and K = 0.23.
1.5
2.0
Laser beam power,
a)
2.5 kW 3.0
Pl (K=0.7)
6
4
high beam quality (K = 0.7), were used to confirm the above results and to evaluate further dependences. The weld pool length and weld pool depth as a function of the laser beam power for a constant welding speed, are shown in figure 5(a) and result in the depth-to-length ratios according to figure 5(b). The linear relationship presented in figure 3(c) is confirmed, but the absolute values have changed because of the difference in the quality number of the laser beam. The weld pool length as a function of the welding speed, for a constant laser beam power, varies only slightly, lw = 5 ± 0.25 mm, figure 6. This weak dependence necessitates a numerical investigation of the physical mechanisms contributing to the weld pool length.
2
0 2
3
4
5
Weld pool length,
b)
mm
lW
Figure 5. Comparison of calculation results with the mean of experimental results: weld pool length and depth dependence on the laser beam power (a) and the correlation between the depth and the length (b), df = 0.2 mm, lf = 200 mm, zf = 0 mm and K = 0.7.
3.4. Contribution of weld convexity and fluid flow The dependence of the weld pool length on the welding speed was recalculated on the basis of heat conduction only and then on the basis of heat conduction, weld convexity and fluid flow, thus separating the influence of the different heat transport mechanisms. It can be seen from figure 6 that counteracting partial dependences sum up to the observed weak (that is, nearly constant) total dependency. The simulated longitudinal and cross sections of the weld pool with vapour capillary are shown in figure 7 for a special combination of the laser beam power and the welding speed, differentiating between the original heat conduction model without weld convexity, figure 7(a), the same model with weld convexity, figure 7(b), and the model with weld convexity and fluid flow, figure 7(c). The first model is characterized by vanishing temperature gradients in the thickness direction and by only 40% of the measured weld pool length. The second model reaches 66% with non-vanishing gradients. The third model agrees with the experimental findings both in respect of the weld pool shape (showing a ‘shoulder’ in the longitudinal section) and weld pool length. The contributions of the partial mechanisms that are dependent on the welding speed are depicted in figure 8 (see figure 6 for the referenced weld pool lengths). Considering a laser beam power of 2.5 kW and welding speeds increasing from 1 to 8 m min−1 , the contribution of heat conduction and translatory heat transport increases from 50 to 90% (inclusive 668
6
4
2
0 0
2
4 Welding speed,
6
m/min 8
vW
Figure 6. Comparison of calculation results with the mean of experimental results: weld pool length dependence on the welding speed; calculation with heat conduction (and translatory motion) and with weld convexity and fluid flow supplemented.
of weld convexity contributing 20–30%) and the contribution of convective heat transport decreases from 50 to 10%. The hypothesis of the dominating effect of heat conduction and translatory motion is confirmed by the fact that both the capillary depth and the vapour friction force diminish with increasing welding speed for a constant laser
Numerical simulation of weld pool geometry in laser beam welding
16 MnCr5 t = 6 mm Pl= 2.5 kW K = 0.7 vW=2 m/min
c
l
l,s
s
Heat conduction )
100 % 80 60
with convex surface
40
Heat conduction plus matter motion with plane surface
20 00
c l,s l
Fluid flow
2
4 6 m/min 8 Welding speed, vW
Figure 8. Portions of weld pool length resulting from heat conduction (and translatory motion), weld convexity and weld pool fluid flow. 16MnCr5 steel, t = 6 mm, Pl = 2.5 kW and K = 0.7.
s
plus convexity )
c l,s
l
s
plus fluid flow )
Figure 7. Change of the weld pool geometry (c, capillary; l,
liquidus boundary; s, solidus boundary) for calculation with heat conduction (and translatory motion) (a), with weld convexity supplemented (b) and with the weld pool fluid flow supplemented (c) in longitudinal section, cross section and top view. 16MnCr5 steel, t = 6 mm, Pl = 2.5 kW, K = 0.7 and vw = 2 m min−1 .
beam power. The flow velocities in the weld pool are correspondingly smaller. Additionally, the weld width decreases and narrows the region where the high flow velocities are observed. Simultaneously, the energy transport by translatory motion increases. The minor rise in the contribution of weld convexity results from the growth in translatory heat transport in this zone. 3.5. Transition from full-penetration welding to partial-penetration welding The results from experiment and calculation indicate that the weld pool length is dependent on whether fullpenetration welding or partial-penetration welding takes place. To demonstrate the peculiarities, a calculation of the weld pool length over the welding speed was performed, which included the transition from full-penetration welding to partial-penetration welding. The sheet thickness was
t = 2 mm, the laser beam power Pl = 4 kW and the beam quality number K = 0.32. A sheet thickness of t = 6 mm, full-penetration welded without a transition, was considered for comparison. The weld pool length as a function of the welding speed for the two sheet thicknesses is shown in figure 9(a) (and compared with experimental results). The weld pool length decreases continuously with increasing welding speed for t = 6 mm where no transition occurs. This corresponds to a decrease in the weld pool depth and in the flow velocity resulting from vapour friction in the capillary. The weld pool length increases slightly over the welding speed in fullpenetration welding of the 2 mm sheet metal. After the transition to partial-penetration welding at vw = 6 m min−1 the further decrease of the weld pool length is identical to that of the thicker sheet metal. The explanation of the behaviour in full-penetration welding is based on figure 9(b). The slight increase in the weld pool length results from the reduction in the capillary diameter at the bottom side which lowers the loss in beam energy and increases the energy transfer efficiency. The maximum values of efficiency and vapour velocity in the capillary occur at the transition point. Here, the vapour hitherto escaping from the bottom side, is forced by the closing bottom of the capillary to move upwards. The subsequent decrease in the vapour velocity causes a similar change in the weld pool length as observed with the thicker sheet metal. 4. Conclusions
The following conclusions are drawn from the results of the investigation. (1) An approximately linear coupling between the weld pool depth and the weld pool length is observed experimentally for a constant welding speed and varying laser beam power. A weak dependence between the weld pool depth and the weld pool length occurs with a constant laser beam power and varying welding speed. The latter result is in contradiction to the predictions made by simple heat conduction models. 669
W Sudnik et al
References
vW η
Welding speed,
Welding speed,
vW
Figure 9. The weld pool length dependence on the welding speed with transition from through welding to penetration welding (calculation and experimental results) (a); the capillary diameter at the top and the bottom and the process efficiency (calculation results) (b). 16MnCr5 steel, t = 2 mm and t = 6 mm, Pl = 4 kW, df = 0.6 mm, lf = 270 mm, zf = 0 mm and K = 0.32.
(2) A good correspondence between the results of calculation and experiment in respect of the weld pool length is achieved by supplementing the basic model of laser beam welding with the fluid flow in the molten pool resulting from vapour friction forces at the capillary wall and by the convexity of the weld pool surface resulting from the thermal expansion of the molten metal. After calibration and verification, the model is applicable to the prediction of the pool geometry and to the numerical process analysis. (3) The effect of the convexity of the molten pool surface on the elongation of the weld pool is demonstrated. Considering a laser beam power of 2.5 kW and welding speeds increasing from 1 to 8 m min−1 , the contribution of heat conduction and translatory heat transport increases form 50 to 90% (inclusive of weld convexity contributing 20–30%) and the contribution of convective heat transport decreases from 50 to 10%. (4) The model explains the effect of the gap width on the weld pool length sufficiently well, and also the transition from full-penetration welding to partial-penetration welding, as well as the effect of higher beam quality. 670
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