Studies on melt spinning. II. Steady-state and transient solutions of fundamental equations compared with experimental results

In the part installment of the present paper, the authors formulated the dynamics of melt spinning by introducing a set of fundamental equations that consist of the equations of heat, force, and material balances. Some steady-state solutions were also given. Additional steady-state solutions corresponding to many different spinning conditions for polyester and polypropylene filament yarns consistently show good agreement with experimental results. These steady-state solutions that give filament cross-section A (x) and filament temperature t(x) as functions of position x are correlated with yarn qualities: yarn density and birefringence, crystallinity and molecular orientation, are correlated respectively with the speed of Polymer cooling at 100°C. and the maximum tensile stress (F/A)_w acting on the filament. A transient solution of the fundamental equations computed on an IBM 1401 machine shows that the filament cross-section A at the take-up roll forms a large transient peak after a stepwise increase in the speed v_y of cooling air. This agrees with experiments fairly well. The fundamental equations, therefore, clarify the dynamic relations between cooling air speed and yarn weight variations.