Modal analysis of ballooning strings with small curvature

During the manufacture and transport of textile products, yarns are rotated at high speed. The surface of revolution generated by the rotation yarn is called a balloon. The dynamic response of the balloon to varying rotation speed, boundary excitation, and aerodynamic disturbances affects the qualit y of the associated textile product. Resonance, in particular, can cause la rge tension variations that reduce product quality and may cause yarn break age. In this paper, the natural frequencies and mode shapes of a single loo p balloon are calculated to predict resonance. The three-dimensional nonlin ear equations of motion are simplified under assumptions of small displacem ent and quasi-static axial motion. After linearization, Galerkin's method i s used to calculate the mode shapes and natural frequencies. Experimental m easurements of the steady-state balloon shape and the first two natural fre quencies and mode shapes are compared with theoretical predictions.