The mechanical analysis of flexible die drawing for spherical parts based on weight function

  • Xiang-dong JiaEmail author
  • Chang-cai Zhao


With the development of sheet metal forming technology and the increase in the application of spherical shell parts, flexible male die drawing technology has become one of the research hotspots because of its merits on strong applicability and ability to significantly increase the forming limit of the sheet. As a new type of flexible male die drawing process, solid granule medium forming (SGMF) has been rapidly developed in recent years. During the granule medium drawing process, there is a significant reduction in the thickness of the sheet metal in the female die in addition to the flange deformation. Thus, the stress state and the required forming force during the sheet metal forming process are very different from those during the conventional drawing. Taking the deformation process of the spherical shell parts as research object, the stress state of the spherical shell and the pressure of the granule medium were studied between the single drawing deformation and the single bulging deformation. On this basis, the stress model, pressure model, and required forming force model of the spherical shell parts in the granule medium drawing process were established with the drawing weight and bulging weight. Theoretical analysis, experiments, and FEM-DEM numerical simulations were employed to study the deformation of the spherical shell parts. The results show that the mechanical model based on the weight function theory can accurately reflect the stress state of the spherical shell parts during SGMF and can fully reveal the sheet metal deformation mechanism during SGMF. In addition, the theoretical analysis model established in this paper provides necessary theoretical support for the selection of equipment for SGMF process in practical application.


Flexible die drawing Granules medium Mechanical model Weight function FEM-DEM 


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The authors are very grateful to Master Jing Zhao, who provided language help for the authors to improve their paper significantly.

Funding information

The research is supported by the Natural Science Foundation of Jiangsu Higher Education Institutions of China (18KJB460020), and supported by the High-level (Higher education) Science Foundation of Nanjing Forestry University (GXL2018020) and the Youth Science and Technology Innovation Foundation of Nanjing Forestry University (CX2018027).


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mechanical and Electrical EngineeringNanjing Forestry UniversityNanjingChina
  2. 2.Key Laboratory of Advanced Forging and Stamping Technology and Science (Yanshan University)Ministry of Education of ChinaQinhuangdaoChina

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