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An equivalent volumetric heat source model for thermal conduction of plate forming by inducted line heating

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Abstract

Efficient computation for thermal conduction is particularly important for analyzing the plate forming induced by induction line heating. Coupled magneto-thermal model is time-consuming while the existing alternative heat source models are mainly based on empirical assumptions. This paper introduces an equivalent volumetric heat source model to enable the rapid estimation of thermal conduction in plate forming for a linear inductor. First, the distribution features of induced heat sources were investigated with a local yet accurate coupling model. Second, according to these features, an equivalent volumetric heat source (EVHS) model was proposed. Third, the relationship between the proposed EVHS model and the heating parameters was determined. Finally, the proposed model was applied to perform the thermal conduction analysis for a large-scale plate. The results reveal that the proposed model can be used to considerably reduce the calculation time while maintaining the same level of engineering precision.

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The authors declare that the data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Lee K, Hwang B (2014) An approach to triangular induction heating in final precision forming of thick steel plates. J Mater Process Tech 214:1008–1017. https://doi.org/10.1016/j.jmatprotec.2013.11.002

    Article  Google Scholar 

  2. Wang J, Yi B, Zhang C, Zhou H, Shu Y (2019) Experiments of double curvature plate bending with induction heating and processing parameters investigation by computational analysis. Ocean Eng 192:106596. https://doi.org/10.1016/j.oceaneng.2019.106596

    Article  Google Scholar 

  3. Yi B, Zhou H, Wang J (2019) Study on typical out-of-plane bending deformation of hull plate by high frequency induction heating. In: Proceedings of the 29th international ocean and polar engineering conference, Honolulu, Hawaii, p 8

  4. Xiao Y, Han Y, Mk C, Wang L, Xu D (2022) Spatial matching relationship of dual heat sources in electromagnetic heating of pipes. Appl Therm Eng 202:117858. https://doi.org/10.1016/j.applthermaleng.2021.117858

    Article  Google Scholar 

  5. Luo Y, Ishiyama M, Murakawa H (2004) Study of temperature field and inherent strain produced by high frequency induction heating on flat plate (mechanics, strength and structural design). Trans JWRI 33:59–63

    Google Scholar 

  6. Bae K, Yang Y, Hyun C (2012) Analysis of triangle heating technique using high frequency induction heating in forming process of steel plate. Int J Precis Eng Manuf 13:539–545. https://doi.org/10.1007/s12541-012-0069-4

    Article  Google Scholar 

  7. Zhu Y, Luo Y (2018) A simplified heat source model for thick plate bending via high-frequency induction line heating. Ships Offshore Struc 14:1–10. https://doi.org/10.1080/17445302.2018.1475883

    Article  Google Scholar 

  8. Zhu Y, Luo Y, Ma N (2019) Relationship between equivalent surface heat source and induction heating parameters for analysis of thermal conduction in thick plate bending. Ships Offshore Struc 14:921–928. https://doi.org/10.1080/17445302.2019.1589762

    Article  Google Scholar 

  9. Dong H, Zhao Y, Yuan H, Hu X, Yang Z (2019) A simplified calculation method of heat source model for induction heating. Materials 12:2938. https://doi.org/10.3390/ma12182938

    Article  Google Scholar 

  10. Chang L, Zhao Y, Yuan H, Hu X, Yang Z, Zhang H (2020) Effect of plate curvature on heat source distribution in induction line heating for plate forming. Appl Sci 10:2304. https://doi.org/10.3390/app10072304

    Article  Google Scholar 

  11. Ueda K, Murakawa H, Rashwan AM, Neki I, Kamichika R, Ishiyama M, Ogawa J (1993) Development of computer-aided process planning system for plate bending by line-heating (report 3)—relation between heating condition and deformation. TRANS JWRI 22:145–156

    Google Scholar 

  12. Osawa N, Hashimoto K, Sawamura J, Kikuchi J, Deguchi Y, Yamaura T (2007) Development of heat input estimation technique for simulation of shell forming by line-heating. CMES-Comp Model Eng 20:43

    MATH  Google Scholar 

  13. Tango Y, Ishiyama M, Osawa N, Hashimoto K, Sawamura J (2010) Method of estimating temperature distribution history. US 9271336 B2, 2010

  14. Zhang X, Liu Y, Yang Y, Ji Z, Deng Y (2011) Technical parameter analysis of high-frequency induction heating applied to steel plate bending. J Ship Prod Des 27:99–110. https://doi.org/10.5957/jspd.2011.27.3.99

    Article  Google Scholar 

  15. Cheng DK (1989) Field and wave electromagnetics. Pearson education India, Beijing

  16. Guru BS, Hiziroglu HR (2004) Electromagnetic field theory fundamentals, 2nd edn. Cambridge University Press, Cambridge

    Book  Google Scholar 

  17. Ishimaru A (2017) Electromagnetic wave propagation, radiation, and scattering: from fundamentals to applications, 2nd edn. Wiley, Hoboken

    Book  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52001174), the Natural Science Foundation of Zhejiang Province (Grant No. LQ21E090005), and the Natural Science Foundation of Ningbo (Grant No. 202003N4090).

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Authors and Affiliations

  1. School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Ye Zhu & Zhuguo Li

  2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Ye Zhu, Ziliang Li, Meng Li, Aibing Ding & Yu Luo

Authors
  1. Ye Zhu
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  2. Ziliang Li
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  3. Meng Li
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  4. Aibing Ding
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  5. Yu Luo
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  6. Zhuguo Li
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Contributions

YZ did the methodology, investigation, and writing of original manuscript. ZL, ML, and AD did the conceptualization, methodology, editing, and supervision of the study. YL and ZL did the conceptualization, methodology, review, and supervision.

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Correspondence to Zhuguo Li.

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The authors declare that they have no known competitive economic interests or personal relationships that could affect the work reported in this paper.

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Technical Editor: Daniel Onofre de Almeida Cruz.

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Zhu, Y., Li, Z., Li, M. et al. An equivalent volumetric heat source model for thermal conduction of plate forming by inducted line heating. J Braz. Soc. Mech. Sci. Eng. 45, 412 (2023). https://doi.org/10.1007/s40430-023-04219-5

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