A mechanical model of symmetrical three-roller setting round process: The static bending stage

The static bending deformation of three-roller setting round process is an elastic-plastic secondary indeterminate problem, and belongs to the plane bending deformation. This paper adopts a bilinear material model. In consideration of shifting of the tangent points between the pipe and the lower rollers, the static equilibrium conditions, the physical relationships of elastic-plastic deformation, the deformation compatibility conditions, and the constraint conditions are analyzed comprehensively. By applying the discrete method, a semi-circular pipe is meshed equably into N micro-pipe-wall elements with the same geometric parameters. Deformation characteristics of each micro-pipe-wall element are calculated, and then the deformation history responses of the whole pipe are resolved by applying the load increment method, based on the variable step size, and the experimental apparatus is further designed to verify the theoretical model. Finally, the effects of various process parameters on the upper roller load and bending curvature are studied. The results show that the static bending deformation can be assumed to be a pure bending process; the cross section of the pipe has two positive bending regions and two reverse bending regions; the upper roller diameter and the lower rollers spacing are the major factors for the upper roller load and the bending curvature; the dynamic roll bending process can be simplified into a static to-and-fro bending process.