An upper bound analysis for closed-die forging of spur gear forms

스퍼어 기어의 밀폐단조에 관한 상계해석

A kinematically admissible velocity field for the numerical analysis of closed-die forging process of spur gear is proposed. The velocity field is divided into three regions of deformation. In the analysis, the involute curve is approximated to be straight line and the upper-bound method is used to calculate energy dissipation rate. A constant frictional frictional factor has been assumed on the contacting surfaces. The effects of root diameter, number of teeth, and friction factor are determined on the relative forging pressure. The frictionless relative pressure is independent of root diameter for the same number of teeth, but increases with the number of teeth on a given root diameter. In the presence of friction, the relative forging presure increasing root diameter at the start of forging, but decreases with increasing root diameter in the processing of forging.