Optimization of laser welding process parameters of stainless steel 316L using FEM, Kriging and NSGA-II

doi:10.1016/j.advengsoft.2016.06.006

Advances in Engineering Software

Volume 99, September 2016, Pages 147-160

https://doi.org/10.1016/j.advengsoft.2016.06.006 Get rights and content

Highlights

•
Multi-objective laser welding process parameters optimization approach is proposed.
•
The effects of process parameters on bead profile in light of Kriging are analyzed.
•
Experiment results show the efficiency of the proposed approach.

Abstract

Laser welding process parameters have significant effects on the welding bead profile and quality of the welding joint. This paper proposes an integration method of process parameters optimization using finite element method (FEM), Kriging metamodels and nondominated sorting genetic algorithm II (NSGA-II) in laser welding for stainless steel 316L. The process parameters in this study are laser power (LP), welding speed (WS) and laser focal position (LF). Firstly, a three-dimensional thermal finite element model is developed to obtain the simulated results of bead width (BW) and depth of penetration (DP). Then, Kriging metamodels are constructed to reflect the relationship between input process parameters and output responses. Finally, NSGA-II is used to search for multi-objective Pareto optimal solutions. In addition, the main effects and contribution rates of multiple process parameters on welding bead profile are analyzed. The results of verification experiments indicate that the optimal process parameters are effective and reliable for producing expected welding bead profile.

Introduction

Laser welding technology is widely used in the field of automotive, aerospace, shipbuilding, energy, electronics and medical industries. The advantages of laser welding include precise welding energy control, small heat-affected zone, low heat distortion, high welding speed and deep penetration [1]. In the laser welding process, welding process parameters (laser power, welding speed, laser focal position, design of welded joints) play decisive role on welding bead profile (bead width, depth of penetration and bead reinforcement). It is very important to determine process parameters that are highly relevant to impact welding bead profile. However the relationships between the process parameters and bead profile cannot be expressed explicitly, which makes it impractical to determine the optimal process parameters intuitively. Meanwhile, trial and error methods often lead to sub-optimal solution and to some extent may result in a tremendous waste of resources.

To grasp the relationships between the welding process parameters and the bead performance, polynomial response surface (PSR) methods, artificial neural networks (ANN), Radial basis function (RBF) have been widely studied [2], [3], [4]. Khan et al.. [5] developed mathematical models between parameters and weld characteristics in process parameters optimization for laser welding of stainless steels. Zhou et al. [6] optimized process parameters of galvanized steel in laser brazing using genetic algorithm (GA) and ensemble of metamodels (EMs). Although these optimization methods can obtain the desired process parameters, the required laser welding experiments is a time-consuming and costly work.

Finite element method (FEM), as a promising way to investigate welding process, has been widely used in computer simulation field. Shanmugam et al. [7], [8] predicted the weld bead geometry by FEM in laser spot welding of AISI 304 stainless steel sheet of thickness 2.5 mm. Han et al. [9] set a three-dimensional finite element model to analyze the temperature distribution weld bead shape in laser beam welding process. Recently, researchers combined process parameters optimization with FEM. Bag et al. [10] developed a three-dimensional heat-transfer model using FEM and coupled with GA for identification of uncertain input parameters for the gas tungsten arc welding process. Acherjee et al. [11] developed mathematical models which were based on simulation results of FEM to investigate the influence of process parameters on output responses. Acherjee et al. [12] used an FEM-RSM integrated approach to obtain optimal process parameters for simultaneous laser transmission welding of polycarbonates. Wang et al. [13] used ANN to establish the relationship between welding process parameters and welding bead profile based on FEM for laser penetration welding, and the model is optimized by GA. Mohammad al [14] predicted the weld performance using FEM and ANN and obtained the optimal welding parameters by multi-objective optimization in friction stir welding. Islam et al. [15] used PSR to study the relative influence of different parameters on welding distortion based on a three-dimensional finite element model and obtained optimal solution with the goal of minimizing the welding distortion using GA in arc welding.

To some extent, these methods could improve the efficiency of optimization and obtain optimal process parameters. However, PSR belongs to local modeling methods, which is only suitable for local optimization problems, while machine learning techniques (e.g. RBF and ANN) need a large number of training sampling points to ensure their accuracy [16], [17]. Kriging metamodel, as a global surrogate modeling technique, has been widely used in the field of structural optimization due to its capability of interpolating the sampling points and filtering noisy data [18], [19]. On the other hand, nondominated sorting genetic algorithm II (NSGA-II) is an efficient technique for multi-objective optimization problems. It makes use of fast non-dominated sorting approach, elitist strategy, and a crowded comparison operator to create Pareto optimal solutions [20]. In this paper, a three-dimensional thermal finite element model is developed to simulate the distribution of temperature field that can determine welding bead profile. Kriging metamodels are used to construct the relationship between input parameters and output response. Then, main effects and contribution rates of multi-parameters on bead profile are analyzed. NSGA-II is used to obtain the optimal solutions with desirability function. In addition, experiments verify the effectiveness of optimal solutions. The summary of Kriging metamodels and NSGA-II are provided in the “Appendix”.

The remaining sections of the paper are as follows. In Section 2, the proposed approach is introduced. Then, a thermal finite element model is developed in Section 3. In Section 4, Kriging metamodels are constructed and the main effects of multiple parameters on the bead profile are analyzed. The multi-objective optimization problem of laser welding process parameters is presented in Section 5, followed by a conclusion in Section 6.

Section snippets

Methodologies of process parameters optimization

In this section, a method combining Kriging metamodel and NSGA-II is proposed where Kriging metamodel is used to establish the relationships between the input welding process parameters and welding bead profiles; NSGA-II is used to facilitate design space exploration and global optimum search. The overall optimization process using FEM, Kriging and NSGA-II methods is depicted in the flowchart of Fig. 1. The details steps are as follows:

Step 1 Determine the laser welding process parameters

Finite element simulation

In this study, a three-dimensional thermal finite element model is developed to simulate the distribution of temperature field in welding process. Schematic diagram of laser welding process is shown in Fig. 2. Due to complex changes in the actual welding process, simplifying assumptions are made as follows [21], [22]:

(1)
The initial temperature of the weldment is 300 K.
(2)
The finite element model is heat conduction model, which the formation of keyhole is not considered. The thermal transfer of

Design of experiments

Three laser welding process parameters, the laser power (LP), welding speed (WS) and laser focal position (LF), are selected as input parameter variables. Two parameters of welding bead profile, the bead width (BW) and depth of penetration (DP) are selected as the output response.

The method of optimal Latin hypercube is adopted for design of experiments to obtain the relationship between input parameters (LP, WS and LF) and output response (BW and DP) [29]. The ranges of input parameter

Mathematical model of parameters optimization

In the study, the objective of parameters optimization is minimum BW and maximum DP. Therefore, it can be regarded as multi-objective optimization problem. The program is run in Matlab R2010b. The mathematic model of multi-objective problem can be developed as below: $\begin{matrix} Objective : Minimize BW (LP, WS, LF) \\ Maximize DP (LP, WS, LF) \\ Subject to : 2.0 \leq LP \leq 3.5, 2.5 \leq WS \leq 3.5, - 2 \leq LF \leq 0 \end{matrix}$

Since there are trade-offs among these two objectives, the optimization problem in Eq. (4) generally has a set of optimum solutions. These

Conclusions

In this study, an integrated methodology by combining FEM, Kriging metamodels and NSGA-II is proposed for process parameters optimization in laser welding for stainless steel 316L. In addition, the main effects and contribution rates of multiple process parameters on welding bead profile have been analyzed. It is obvious that the approach can effectively produce the expected welding bead profile and provide a reliable guidance for laser welding experiments. Following conclusions can be drawn

Acknowledgments

This research has been supported by the National Basic Research Program (973 Program) of China under grant no. 2014CB046703, the National Natural Science Foundation of China (NSFC) under grant no. 51505163, No. 51323009 and No. 51421062, and the Fundamental Research Funds for the Central Universities, HUST: grant no. 2014TS040. The authors also would like to thank the anonymous referees for their valuable comments.

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Optimization of laser welding process parameters of stainless steel 316L using FEM, Kriging and NSGA-II

Highlights

Abstract

Introduction

Section snippets

Methodologies of process parameters optimization

Finite element simulation

Design of experiments

Mathematical model of parameters optimization

Conclusions

Acknowledgments

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