Study on the twist compression forming of cylinder based on the upper bound and slab methods

In this work, slab method and upper bound method are proposed to investigate the twist compression forming of cylinder. Both upper bound method and slab method assume the friction between the cylinder and the die as constant shear friction (τ = mk). The total power rate of the energy consumption with a 3D velocity field based on the upper bound method is constructed. An optimum variable parameter is obtained by using the energy minimization method. The upper and lower dies are rotated in different directions, so the cylinder is compressed with the twist circumstance, and the frictional shear stresses (τ) are not acted in the radial direction. The stresses (τ) are acted in an arbitrary direction at angle α from the radial direction relative to the r-axis. According to the velocity relations between radial direction and circumferential direction, angle ( can be determined. Combining the upper bound method with the slab method, the effects of frictional factor, aspect ratio, height reduction, and angular velocity etc on the twist compression forming characteristics are explored effectively. The feasibility of both models can be realized by comparisons of two models and the experiments.