Analytic model of outer rib height for thin-walled cylindrical rings in spin-extrusion forming processing

Thin-walled cylindrical rings with outer cross ribs (TCROCR) have the advantages of lightweight, high stiffness, and high bearing capacity, which is widely used in aerospace equipment. Usually, these kinds of parts are split manufacturing with welding, and integrated manufacturing has received more attention now. Spin-extrusion forming (SEF) processing which draws inspiration from the principle of the gear-generating method is proposed and has been preliminarily applied. This method can improve rib height-width ratio, and TCROCR can be formed efficiently and integrally. However, as a new method, there is still a lack of research on how to design the target parts contour. Using FE models to simulate the forming of a set of geometric parameters takes a week or even longer. If this method is used for the preliminary design and optimization of TCROCR, the efficiency will be eminently low. This article proposes an analytic model for predicting the rib height variation to assist the preliminary design and improve work efficiency. The rib height of TCROCR is determined by two factors: one is the skin thickness reduction, which can be conveniently calculated based on the feeding amount of the feeding roll, and the other is the rib growth, which is caused by the material of the skin flowing towards the cavities. Therefore, the key to creating the analytic model is to obtain the material volume of the skin allocated to the longitudinal and transverse cavities, respectively. Utilizing Newton’s second law, the proportion of material flowing into the transverse and longitudinal ribs can be correlated with the stress state of the skin, and the stress state during SEF processing can be calculated by the slab method and upper bound method. Then, the material flowing into the longitudinal ribs and transverse ribs can be obtained based on the principle of volume invariance, and the analytic model is established to predict the rib height variation. Subsequently, the accuracy of the analytic model is verified through experiments and simulations, and the growth patterns of rib height are detailed research.