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Shape optimization of square weld nut in projection welding

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Abstract

This study provides an optimal shape of square nut for better projection welding performance. Both experimental design method and electrical-thermal-mechanical finite element analysis (FEA) are used to investigate the effects of nut shape parameters on the height decrease of nut leg, called setdown. The relationship between the setdown and weld strength is then analyzed. Also, welding time to reach 50% of setdown tset is introduced as another objective function for better welding performance. The optimal nut shape parameters are determined to maximize the setdown, and minimize the tset at the same time via Taguchi method. The difference of setdown values between experiments and FEA is within 12%, which verify the reliability of the FE model. The gap between DIN928 standard for nut leg geometry and the optimized nut leg shape is less than 0.2 mm. The differences of setdown and tset values for two nut shapes are 6% and 9%, respectively.

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Data and materials availability

The authors confirm that the data supporting the findings of this study are available within the article.

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Funding

This work was supported by the Sogang University research fund (No. 201919049.01) and the Carbon Industrial Cluster Development Program (No. 10083609) funded by the Ministry of Trade, Industry, & Energy (MOTIE, Korea).

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Authors and Affiliations

Authors

Contributions

Giyeol Han: conceptualization, methodology, finite element analysis, writing—review and editing

Sangun Ha: experiments, data curation

Karuppasamy Pandian Marimuthu: investigation

Siva Prasad Murugan: experiments

Yeongdo Park: project administration

Hyungyil Lee: supervision

Corresponding author

Correspondence to Hyungyil Lee.

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Appendices

Appendix 1. Welding conditions for Taguchi method

FE analyses are performed by modeling square nut in accordance with the DIN928 standard [20]. The pressing force f = 5 kN is applied as per the standard. A robust weld strength can be ensured only when the nugget is sufficiently formed on both the nut and steel sheet. Each experiment requires cross-sectional cutting of the nut-steel contact area to explore the nugget formation. This process is constrained by time and cost limitations. To address this problem, we perform several FE analyses to evaluate the depth of fusion into sheet under different current intensity (Fig. 14). At low electrode current densities, i.e., I = 5 and 7 kA, the nugget was formed only on the surface of the sheet, failing to penetrate the sheet, reducing the weld strength. This analysis is consistent with the results of most studies on nut projection welding with I = 10 kA or higher. Therefore, FE analyses are performed with a fixed current of I = 10 kA in this study.

Fig. 14
figure 14

Cross-sectioned nugget shape for current I = (a) 5 kA, (b) 7 kA, (c) 10 kA

Appendix 2. Effect of noise factor on S and t set

Tables 11 and 12 show FEA results of S and tset, respectively, for various conditions according to Table 1. Zero values of tset for run #1 in Table 11 indicate that the projection collapse by pressing force exceeds 50% without current flow. To analyze the effect of noise factor, level average analyses are performed by following the equation as shown in Table 13. The level average value \( {\overline{u}}_i \) is calculated as follows

$$ {\overline{u}}_i=\frac{{\sum \limits}_j^n{\overline{z}}_j}{n} $$
(A1)

where \( {\overline{z}}_j \) is the mean value of either tset or S for each jth noise factor combination. i means the level of each noise factor and n is the total number of simulations for each level. The zero value of delta for each noise factor demonstrates negligible effect of noise factors E, F, and G on S and tset. This is because heat losses due to convection and conduction can be ignored since nut projection welding is performed within few milliseconds of the welding process, which is identical to that of resistance welding.

Table 11 Values of setdown S according to various levels of design variables (in %)
Table 12 Values of tset according to various levels of design variables (in ms)
Table 13 Level average analysis results for noise factors

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Han, G., Ha, S., Marimuthu, K.P. et al. Shape optimization of square weld nut in projection welding. Int J Adv Manuf Technol 113, 1915–1928 (2021). https://doi.org/10.1007/s00170-021-06771-7

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