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

Abstract 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 vy 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.