Laser Beam Welding

To summarise it can be stated that the completeness of the reference data governs signifi-cantly the calibration behaviour of the heat source model. For the particular test cases pre-sented here, with the heat input as a degree of freedom, additional thermal information extracted from the thermal cycle is needed because it determines the heat input. If the heat input is known, the evaluation of the energy distribution parameters is dependent on the geometry of the weld pool. It was found that the fusion line in the cross section and the weld pool length at the top surface enables to identify the energy distribution parameters. Again, the neural network based optimisation algorithm adjusts and determines all three design variables simultaneously which is not a trivial task for a human operator.

In this context, it has to be mentioned that a double ellipsoidal heat source as it is widely used in welding simulation comprises 5 design variables. Of course, the single valued be-haviour of the objective functions presented in these test cases can not be assigned to the most general case directly. However, the general requirement to setup the objective func-tion on basis of temperature field characteristics that describe it uniquely is the same. As it could be shown for the three dimensional case at least the fusion line in the cross section, weld pool length and a single temperature value extracted during the cooling down phase is needed in order to reconstruct the entire three dimensional temperature field exactly. This result can be applied for the general case of a double ellipsoidal heat source in such a way that the likelihood of being able to reconstruct the three dimensional temperature field by neglecting the thermal cycle measurements is almost zero. The same, even though in an understated manner, holds for the weld pool length at the top surface since in determines the top shape of the molten pool. In other words a calibration of a weld thermal model only against the fusion line in the cross section does not necessarily yield the correct tempera-ture field since this information is clearly underdetermined. Furthermore, it corrupts the calibration behaviour of the heat source model since many optimal solutions may exist: It is argued in literature to solve this fact by evolutionary methods as genetic algorithms be-cause they account for the diversity of minimum values of the objective function. This fact should be further discussed by some authors who perform global calibrations of weld ther-mal models, i.e. Kumar [165].

pa-rameters are evenly distributed which confirms that the pattern of the global parameter space includes the relevant area of the global domain of parameters. This is necessary, because no initial set of model parameters is defined in order to guarantee an automated model calibration.

0 25 50 75 100 125 150

0 1000 2000 3000 4000 5000 6000

HeatinputpertimeinW

Number of randomly selected sets

q

q

Fig. 5.25 Random selection of values for net heat input during calibration

0 50 100 150

0 1 2 3 4

Energydistributionparametersinmm

Number of randomly selected sets

z

= z

r

r

Fig. 5.26 Random selection of energy distribution parameters during calibration

In Fig. 5.27 the simulated and experimental fusion line in the cross section is shown. As indicated the simulated fusion line agrees well with the experimental one. The overall devia-tion is below 5 %. Consequently, the model setup enables to reconstruct the real acdevia-tion of the laser in terms of the molten pool. This is furthermore tested by validation of the simu-lated and experimental thermal cycles at the top and bottom surface. The comparison be-tween of the thermal cycles is shown in Fig. 5.28 for the top surface and Fig. 5.29 for the bottom surface. The transversal distances to the welding centre line of the thermo couples of the experiment and simulation are listed in Table 5.2.

With respect to the thermo cycles it can be seen that the agreement between the simulation and the experiment is good. Nevertheless, the effect of latent heat due to the solid-state transformation is not considered by the analytical approach. This yields a deviation with respect to the experiment that is in a range of 5 %. Furthermore, the linearisation of the model may also effect the predicted net heat input as plotted in Fig. 4.68.

The corresponding geometry of the weld pool is shown in Fig. 5.30. Again, the comparison of the simulation result with the high speed record of the real weld pool exhibits a good correspondence.

-3 -2 -1 0 1 2 3

6 5 4 3 2 1 0

z- coordninate in mm

h- coordinate in mm

Simulation

Fig. 5.27 Comparison of calculated and experimental fusion line in the cross section for a superposi-tion of two heat sources, values in °C, PLaser = 8 kW, vWeld = 3.0 m min^-1, focus position f = -6 mm, material: S355J2+N

Table 5.2 Comparison of distances to the welding centre line (experiment versus simulation); meas-ures in mm, PLaser = 8 kW, vWeld = 3.0 m min-1, focus position f = -6 mm, material: S355J2

Thermo couple A B C D E F

Experiment 0.95+/-0.15

1.05+/-0.25

1.25+/-0.25

0.45+/-0.15

0.57+/-0.125

0.85+/-0.15 Simulation 1.2 1.3 1.45 0.4 0.55 1

0 2 4 6 8 10 12 14 16 18 20 0

200 400 600 800 1000 1200

A (Experiment) B (Experiment) C (Experiment) A (Simulation) B (Simulation) C (Simulation)

Temperaturein°C

Time in s

Fig. 5.28 Comparison of calculated and experimental thermal cycles at the top surface, PLaser = 8 kW, vWeld = 3.0 m min^-1, focus position f = -6 mm, material: S355J2+N

0 2 4 6 8 10 12 14 16 18 20

0 200 400 600 800 1000 1200

D (Experiment) E (Experiment) F (Experiment) D (Simulation) E (Simulation) F (Simulation)

Temperaturein°C

Time in s

Fig. 5.29 Comparison of calculated and experimental thermal cycles at the bottom surface, P La-ser = 8 kW, vWeld = 3.0 m min^-1, focus position f = -6 mm, material: S355J2+N

Experimental pool shape during welding

Experimental pool shape during welding

Simulated pool shape

20 400 770 1100 1500

Temperature in °C 2 mm

Fig. 5.30 Comparison of calculated and experimental geometry of the weld pool at the top surface for the superposition of two heat sources, PLaser = 8 kW, vWeld = 3.0 m min^-1, focus position f = -6 mm, material: S355J2+N