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Improving the prediction accuracy of thermal finite element analysis for laser welding through an automated optimization method

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Abstract

This paper proposed an automated optimization method to improve the prediction accuracy of thermal finite element analysis for laser welding. The method used particle swarm optimization (PSO) to find the optimal heat source parameters with the minimum prediction error, and the PSO was improved with a boundary mutation strategy of attenuation reflection. To improve the optimization speed, the effects of model geometry and latent heat on the prediction accuracy and solution speed of thermal analysis were studied. The results showed that the reduced 3/50-length model could increase the solution speed with a speed-up of 137 times and had the same predicted results as the full model. The latent heat could increase the nonlinearity, and thus gave rise to a speed-down of 4 times in solution speed but a decrease of 6.06% in prediction error. Therefore, a reduced 3/50-length model considering the latent heat was used in the optimization. The parameter optimization was first performed in the thermal analysis using a welding speed of 2.4 m/min, and then the optimized optimal parameters were used at other 5 speeds. The results showed that the error function of the parameters was a multi-peak function. In addition, it could be seen that the maximum, minimum, and mean errors of the weld cross sections were 9.47%, 4.36%, and 6.81% respectively, while the errors using the trial and error method were 12.48%, 7.20%, and 9.98% respectively. This indicated that the proposed method had a speed-up of about 6 times and higher prediction accuracy.

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Availability of data and materials

All data generated or analyzed during the present study are included in this published article.

Code availability

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Abbreviations

[X min, X max]:

Position feasible region

[V min, V max]:

Speed feasible region

X i :

Particle position

V i :

Particle speed

n :

Particle number

d :

Particle dimension

λ :

Attenuation coefficient

\(\Delta\) :

Predicted error

w i :

Experimental upper/bottom/waist widths

l i :

Predicted upper/bottom/waist widths

\(p_{id}^{m}\) :

Individual extreme value

\(p_{gd}^{m}\) :

Global extreme value

ρ(T) :

Density

k(T) :

Thermal conductivity

\(C_{p}^{eqv} (T)\) :

Equivalent specific heat capacity

\(q_{0} (x,y,z)\) :

Heat source model

Q L :

Laser power

Q L 1 :

Laser power of the upper heat source

Q L 2 :

Laser power of the bottom heat source

λ :

Welding efficiency

r 0 :

Heat source radius

H :

Sheet thickness

h 1 :

Height of the upper heat source

h 2 :

Height of the bottom heat source

f 1 :

Radius coefficient

f 2 :

Decay index of heat flux in thickness direction

a :

Inclination angle of heat source

h c :

Equivalent heat transfer coefficient

\(\varphi_{i}\) :

Volume fraction of each phase

\(H_{i} \left( T \right)\) :

Enthalpy of each solid phase

\(\dot{{\varphi }_{1}}\) :

Austenite formation rate

\(\varphi_{eq}\) :

Equilibrium volume fraction of austenite

\(\tau\) :

Time required for equilibrium

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Funding

This research is funded by National Natural Science Foundation of China (52188102, 51905191), Postdoctoral Science Foundation of China (2021M691113, 2022T150235), Key Research and Development Project of Hubei Province (2021BAA195).

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Authors and Affiliations

  1. State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China

    Jiajun Xu & Youmin Rong

  2. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, China

    Jiajun Xu & Youmin Rong

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  1. Jiajun Xu
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Correspondence to Youmin Rong.

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Xu, J., Rong, Y. Improving the prediction accuracy of thermal finite element analysis for laser welding through an automated optimization method. Int J Adv Manuf Technol 123, 1657–1668 (2022). https://doi.org/10.1007/s00170-022-10268-2

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