| Summary: | 碩士 === 國立中央大學 === 機械工程研究所 === 93 === Abstract
The objective of this thesis is to investigate the effect of neutral radius on the upper-bound solution of the upset forging of rings using a variational approach. To this end, the neutral radius of the upset ring is considered an explicit function of polynomials during deformation process, and the upper-bound energy equation is formulate in terms of the explicit function as well as the velocity field derived from the theory of stream function. Since the velocity field was considered unknown functions before the upper-bound energy equation is extremized, a variational approach is required. As a result, a set of boundary conditions can be derived. To determine the upper-bound solution, the set of boundary conditions, which include the so-called natural boundary conditions, was imposed in the optimization procedure. In numerical analysis, an optimization program "NCONF" of the IMSL［25］is utilized.
Some experimental results of the upset disks［6,18］and ring［5,9］were employed for discussion and comparison among the theories. It also discussion the effect of working factors, such as the friction condition and the reduction in height on upper-bound solution. From the result we can clearly indicate that the solution in predicting the calibration curve as well as the bulged profiles of the upset disks and ring would be better when it is based on the model of neutral radius considered, and satisfies the natural boundary condition.
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