A New Analytical Solution of the Twist Wave Propagation Equation with its Application in a Modified Ring Spinning System

This paper is devoted to the formulation of new analytical solutions and exploration of physical interpretation for yarn twist propagation in staple yarn spinning. The wave equation governing the twist propagation is solved by using the complex exponential representation of the rotating angle of a yarn cross-section. Provided that the influence of twist blockage is allowed to be ignorable, the solution of the wave equation can be formulated by the superposition of two counterpropagating waves: one twist wave propagating in the positive s direction with a velocity of v(0) + v and the other one traveling along with the negative s direction with a velocity of v(0) - v. The Doppler effect could be found in the twist propagation process. Further, the proposed method is applied in a false twisting process and a modified low-torque ring spinning frame. Finally, the corresponding twist distribution and the torques of twisting devices are derived.