The computer-aided optimal heating schedule of forging ingots using the finite element method

Abstract

This thesis presents the computer simulated thermal stress analysis of forging ingots during the heating and soaking periods. These results are then used to obtain the optimal heating schedule of these ingots. -- The equations for the transient nonlinear temperature distribution within the ingot due to the convective and radiative heat flux are derived using the nonlinear finite element analysis. The nonlinearities due to the variation of material properties have been taken into account by calculating the temperature at different time steps first and then at each time step the elemental property matrices are recalculated. The nonlinear algebraic equations are solved using three techniques and then the best technique is selected from these three for further analysis. -- The mathematical model for the thermal stress analysis has also been formulated using the finite element analysis. The temperatures obtained from the heat transfer analysis are used to calculate the force vector for the stress analysis. These finite element models are then used to calculate the effects of axial heat flux, the slenderness ratio of the ingot, and the linearization of the heat flux on the transient temperature and stress distributions within the ingot. -- The optimal heating schedule has been obtained considering two types of constraints; the first type of the constraint is that the stresses developed should not exceed certain value established by some of the commonly known failure theories, and the second type is that the temperature in the ingot during the heating or soaking period does not exceed a specified value for a particular type of material. The method of optimization of the furnace heating schedule is selected after considering three alternate ways of carrying out the optimization.