A simple method of analysis using force polygon diagrams is proposed for determining roll torque and pressing load, in particular plane-strain ring rolling processes. Pressing velocity together with driven roll rotation is incorporated in constructing the hodograph for the upper-bound analysis in order to find an optimized tangential velocity pattern. Results from two types of tangential velocity discontinuity patterns and related force polygon diagrams are compared at optimized values. The ratio of resultant friction force and pressing load, or an equivalent coefficient of friction is determined from the force polygon diagrams. Experiments were carried out with AISI 1045 steel blanks in a hot condition. Theoretical torques and pressing loads are in good agreement with the experimental values. It is shown that the present method can be efficiently used for predicting pressing load and roll torque in ring rolling; the method has a flexibility and simplicity which recommends it for engineering analytical purposes and for explaining related physical phenomena.

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