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.

A simple and efficient method has been proposed in order to determine the dynamic speed boundary condition caused by the guide rolls for developing the 3D-FE model of cold ring rolling process rapidly. The concept of the motion track of guide rolls has been put forward firstly and an optimal motion track and track type are given by simulation. Meanwhile, an effect of the guide rolls on the ring tilting and ring circularity was simulated and analyzed. The result shows that the simulation results are in good agreement with experiment results from the literature.

The in-plane bending of a strip metal workpiece under unequal compression can be developed into an advanced precision forming process with high quality, high efficiency, low consumption, good flexibility for size changes, and a high forming limit, where the forming is diffcult to carry out using any other conventional process. To establish a coordination model of the process for the investigation and understanding Of the coordinated development of unequal deformation and its contribution to in-plane bending forming is one of the key problems urgently to be solved in the research and development of this advanced in-plane bending process. In this paper, on the basis of the rectilinear state of the unequally compressive deformation conducted with two conical rollers and the contribution of the unequal deformation to the in-plane bending forming. a coordination coefficient function of the unequal deformation is proposed. and further a coordination model of the in-plane bending of strip metal under unequal compression is established. Experimental research is carried out by means of the apparatus made in the authors'laboratory for performing the in-plane bending process under the unequal compression with LF21 M and LD2M strip workpieces in order to validate the model. The results obtained show the following: (1) The predictions by using the model are in good agreement with the experimental results. The model as a basic equation describing the process, characterizing the quantitative relationships between the deformation conditions and the forming results, reveals the precision forming law produced by the unequal deformation with its coordination. (2)The greater the unequally compressive deformation, the greater is its contribution to the stable in-plane bending forming. The proposed coordination coefficient used for describing this physical phenomenon is found to be practicable and sound. (3)The more notable the unequal compressive state, the higher the stable in-plane bending forming limit obtained, and the model provides the basis for the determination and optimization of the in-plane bending process. (4)The method described for establishing the coordination model is also of general significance to non-rectilinear states of unequally compressive deformation.

On the basis of establishing a mathematical model for adjusting and controlling the spiral flight-rolling process, a computer simulation theory and its realization algorithm step-wise approach are proposed in this paper. The proportional-function method and the combining direct-searching method are presented in order to determine the optimal approach direction and the optimal approaching step. The pressure, transfer, stability, and convergence conditions are given. The correctness and the reliability of the model and the principle of step-wise-approach simulation are verified by the results of engineering experiments. The achievement of this study makes it possible to predict the process parameters, the rolling results and the rolling law, which lays the foundation for realizing the optimal rolling process with the least consump-tion of man-power and raw material.

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.