Abstract:

In order to obtain the lateral displacement of an axially moving yarn at any point under arbitrary load, the dimensionless dynamic differential equation of the axially moving yarn in Hamilton system is established. The axial movement of the yarn system conjugate symplectic eigenvalue was solved using minimum yarn dual variational principle of motion equation together with the variable separation method. A nonsingular modal function was obtained using the linear characteristic eigenvalues, and a modal function of conjugate symplectic orthogonal to a relationship was deduced. According to the eigenvalues and the bifurcation, the stability of the lateral movement of yarns was studied. Based on the approximate solution of the nonlinear lateral vibration, the dynamic behavior of the yarn under various operating conditions were studied. The results show that the yarn speed have obvious effect on the response cycle, the response amplitude of the different points and the yarn configuration. The yarn displacement can be obtained by superposition of the first two configurations.

Key words: moving yarn, Hamiltonian system, vibration, symplectic conjugation, stability