Thin-walled tube bending processes may produce a wrinkling phenomenon if the process parameters are inappropriate, especially for tubes with large diameter and thin wall thickness. How to predict this phenomenon rapidly and accurately is one of the urgent key problems to be solved for the development of this process at present. In this paper, a wrinkling wave function is proposed and a simplified wrinkling prediction model to predict the minimum bending radius for tubes is established based on thin-shell theory, forming theory, the energy principle and wave function. The minimum bending radius calculated according to the method established is in agreement with data reported in the literature. Furthermore, effects of parameters on the minimum bending radius are also analyzed: (1) the influence of bending angle on the minimum bending radius is negligibly small; (2) the effect of geometrical dimensions and material properties of tubes on the minimum bending radius is significantly large; (3) the minimum bending radius becomes larger with the original radius and strength coefficient of tubes increasing, whereas with the wall thickness and strain hardening exponent decreasing. The results are helpful to the design and optimization of the relevant processes in practice.

A blade with a damper platform, with excellent anti-vibration characteristics and high efficiency, has become one of the most important new types of blade being developed in the aeronautical engine. However, the blade is complicated in shape, and the material used for its manufacture is difficult to deform. Therefore, it is important to undertake research on the blade-oriented precision forging process using threedimensional finite element method (3D FEM) method numerical simulation for the practice and the development of the process. However, up to now, literature on such research has been scant. In this paper, based on the rigid–viscoplastic principle, three-dimensional finite element simulation is reported for the isothermal precision forging of the blade using the penalty function, and eight-node hexahedral isoparameteric elements for discretizing the deforming workpiece and triangular elements for discretizing the die cavity. The method of contracting from the boundary to the interior, proposed by the authors, is used for remeshing a distorted mesh system, and the method of modifying the position of nodes touching the die according to its original normal, also proposed by the authors, is used to avoid the "dead lock" problem due to the normal uncontinuity of scatted die meshes, to enable the simulation to be successful. Friction is considered for the die-workpiece interface boundary condition, and an arc is considered for the tenon-body joint, and a damper platform-body joint on the blade die cavity, respectively, which make it possible for the simulation to approach the practical forging process of a blade with a damper platform. 3D FEM simulation results have been obtained for the initial and deformed configurations, the deformed meshes of typical cross-sections, the distribution of effective strain at the final stage, load–displacement curves, in this way the deformation law of the forging of a blade with a damper platform being revealed. The achievements of this research serve as a significant guide to the optimization of design for the relevant process and dies. The method used is also of general significance to the forging processes of other type of blades and other complicated massive deformation processes.© 2002 Elsevier Science B.V. All rights reserved.

Based on the rigid-plastic finite element method (FEM) principle, a three-dimensional (3D) rigid-plastic FE simulation system named TB S-3D (tube bending simulation by 3D FEM) for the NC bending process of thin-walled tube has been developed. and a reasonable FEM model has been established. By the use of this FE simulation system. an NC bending process of thin-walled tube has been simulated. and deformed meshes under difierent bending stages, the stress distribution along the bending direction, and the relationship between the maximal wall thickness changing ratio and the bending angle have been obtained. Some forming laws of NC tube bending obtained are as follows:(1) the NC bending process make tube elongate to some extent;(2)the characteristic of the stress distribution is that the outer area is undergoing tensile stress, the inner area is undergoing compression stress, and the stress neutral layer moves close to the inner area, which is in good accordance with practice;(3) the maximal wall thinning ratio in the outer tensile area changes only a little with increase of the bending angle, and the maximal wall thickening ratio in the inner compression area increases linearly with bending angle. The above results show that 3D FE simulation is an important and valid tool for analyzing the NC bending process of tube. this research being beneficial for the practical tube bending process, and may serve as a significant guide to the practice of the relevant processes.

The axial compression of a thin-walled tube over a simple radiused die can make the tube invert to form a complicated part that is diffcult to be manufactured by any other technique. However, the behavior of the free deformation under dieless constraint existing in the process has an essential effect on the degree of precision of the product obtained by the process and the advantages of the process. This paper explores the mechanism of the free deformation on the basis of the development of a rigid-plastic FEM. It is found from the results obtained that:(1)for a givento/do or rp/to, the free deformation behavior of the tube under dieless constraint depends mainly on the value of rp/do and little on the properties of the tube material and the friction condition, which, however, have a significant influence on the deforming force; (2) before reaching steady-state, the radius of curvature at each point in the free deformation zone may be different from that at the other points, and it changes continuously with time; (3)the free deformation zone relative to the die fillet decreases with increasing rp/do, and there is a critical parameter k for a given td/do or rp/to，such that when rp/do>k, the free deformation will go within a circle with the same radius as the die; correspondingly, the relative gap Δ/2rp of the double-walled tube obtained decreases with increasing rp/do, and when rp/do>k, then Δ/2rp<1; contrarily, the free deformation will then extend beyond the circle, and Δ/2rp>1. The achievements of this research may serve as a significant guide to the practice of the relevant processes. ©2001 Elsevier Science B.V. All rights reserved.

The process optimization of the inverting-forming of a thin-walled tube, when a radiused die is used for the process, involves identifying the optimum value of the radius. This paper explores an optimization design of the process from the viewpoint of the deformation force to identify the optimum radius, allowing for the effects of thickness variation, strain hardening, normal anisotropy, and friction. After taking the minimum of the deformation force and the radius limits as the objective function and the critical equations respectively, an optimization model of the process is established, and an optimization algorithm based on the computer simulation of the process is presented, the program for which can be run on a personal computer. The results show that the process optimization is good: an optimized process not only minimizes the deformation force and make the inverting forming progress steady, but also prolongs the die life and improves the quality of the part.