# Multi-Pass Stamping Forming a Concave Ring
## 1 Introduction  
As a key part of an aero-engine, sheet metal casing parts are directly related to the overall performance of the aero-engine. The concave ring is an important and consumable part of the sheet metal casing parts. The shape and accuracy of the concave ring must remain stable during the operation of the aero-engine. Therefore, the processing technology of the concave ring must be efficient and highly precise. The widely used process for processing concave rings is spinning technology. The average processing efficiency of spinning the concave ring is 10 min per piece [1]. However, from years of practice and experience, the spinning forming concave ring has been found to have the disadvantages of high technical requirements, a low production efficiency and poor forming quality [2]. So the forming process of the concave ring needs to be improved. Based on the requirements of the forming quality and production efficiency of the concave ring in the production practice, this paper uses the stamping process to form the concave ring. As shown in Figure 1, the structure of the concave ring is complicated. Concave ring-forming needs to complete the inward bending and the outward bending of the ring part in a small space at the same time. According to the characteristics of the sheet metal stamping and bending process, the dimensional accuracy and geometric accuracy of the workpiece will inevitably change after bending [3, 4]--i.e., by locally thinning, springback, warping and twisting after bending. Therefore, to determine whether the bending part is suitable for bending, it is necessary to judge the geometric characteristics of the bending part in combination with the corresponding process limit value before bending. In the research of the sheet metal bending process, [PERSON] et al. [5] proposed a process model for V bending sheet metal. This model combines the analysis method and trial-and-error method to establish the relationship between the punch insertion depth and the corresponding unloading bending angle. [PERSON] et al. [6] established a complete theory and reliable mathematical model for flat strain plate bending to predict the springback, bendability or minimum bending ratio, strain and stress distribution, and maximumloads on punches and dies. A computer code called \"BEND\" was developed to simulate the air bending and die bending process of U-die, V-die and wiping die. [PERSON] [7] presented a springback test method in which the amount of springback of several metal sheets with different bending angles was obtained on a modular V bending die. [PERSON] et al. [8] presented numerical studies based on various yield criteria and compared the results with the experiments to show that the springback varies with the orientation of the anisotropic sheet in the U-die bending process. [PERSON] and [PERSON] [9] developed a nonlinear finite element program to predict the distribution of large plastic strains in 3D complex sheet metal forming parts at the design stage. This method is based on knowledge of 3D surfaces. The shape of the original blank was not fixed. [PERSON] and [PERSON] [10] have done a lot of research on the numerical analysis of the sheet metal forming process. The formability of sheet metal is introduced from the perspective of a numerical simulation. [PERSON] et al. [11] established a typical sheet metal bending model based on the large deformation algorithm of total elastic incremental plastic strain (TEIP). The springback prediction was carried out through numerical experiments. [PERSON] [12] proposed an effective and economical method for prototyping sheet metal workpieces while maintaining angular dimensional accuracy and without creating new molds. [PERSON] et al. [13] conducted a numerical study on the springback characteristics of the main process parameters. The updated lagrangian thermoelastoplastic finite element method (FEM) was applied to the U bending process of plane strain sheet metal.