Modelling and interaction analysis of the self-pierce riveting process using regression analysis and FEA


Self-pierce riveting (SPR) is a major joining method used in the automotive industry. However, there still lacks a fast and easy-to-use joint quality prediction tool available for the automotive engineers. In this study, the simple but effective regression analysis method was applied to quickly predict the SPR joint quality. Two regression models were developed for the prediction of the interlock and the minimum remaining bottom sheet thickness (Tmin). The prediction accuracy of the developed regression models was validated by comparing with the experimental results. Under the studied joint configurations, the mean absolute errors (MAE) of the interlock and Tmin were 0.047 mm and 0.053 mm, respectively, and the corresponding mean absolute percentage errors (MAPE) were 10.4% and 12.3%. With the developed models, the interaction effects between rivet and die parameters on the joint interlock and Tmin were also systematically analysed. The results revealed that the rivet and die parameters demonstrated significant influences on the interlock but not on the Tmin. These interaction effects were further examined by analysing the deformations of the rivet and substrate materials. Moreover, the die-to-rivet volume ratio (R) was found to be critical for the formation of interlock, and a larger interlock is more likely achieved when the R is close to 1.0.

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The authors would like to thank Dr. Matthias Wissling, Paul Bartig and their team members from Tucker GmbH for their supports during the laboratory tests.


This research is funded by Jaguar Land Rover Limited.

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Huan Zhao, Li Han, Yunpeng Liu and Xianping Liu worked together to conceive this research. Huan Zhao designed the experiments, analysed the data and completed the original draft. Li Han supervised the experiments and provided critical paper revisions. Yunpeng Liu supported with the FEA simulation model and manuscript revision. Xianping Liu is the project leader and participated in the paper revision. All authors read and approved the final manuscript.

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Correspondence to Xianping Liu.

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Zhao, H., Han, L., Liu, Y. et al. Modelling and interaction analysis of the self-pierce riveting process using regression analysis and FEA. Int J Adv Manuf Technol 113, 159–176 (2021).

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  • SPR
  • Multiple regression model
  • Interaction effect
  • Rivet length
  • Die geometry
  • Die-to-rivet volume ratio