Three dimensional vibration of a ballooning string

Kevin J. Hall, Fang Zhu, Christopher D. Rahn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In many textile manufacturing processes, yarn is rotated at high speed forming a balloon. In this paper, Hamilton's principle is used to derive the nonlinear partial differential equations of a ballooning string. Jacobian elliptical sine functions satisfy the nonlinear steady state equations. The steady state eyelet tension is related to the string length for a constant balloon height. For high tension and low string length cases, single loop balloons occur. As the string length increases, tension decreases and multiple loop solutions are obtained. The nonlinear partial differential equations are linearized about the steady state solutions, resulting in three coupled equations with spatially varying coefficients. The equations involve a positive definite mass matrix operator, skew symmetric gyroscopic matrix operator, and symmetric stiffness matrix operator. It is shown using a Galerkin approach that only single loop balloons are stable for practical yarn elasticity. The natural frequencies of the single loop balloon increase with decreasing balloon size and increasing yam stiffness. The effect of yam elasticity on the first three vibration modes of a single loop balloon is analyzed. The steady state and stability analyses are experimentally verified.

Original languageEnglish (US)
Title of host publication15th Biennial Conference on Mechanical Vibration and Noise - Acoustics, Vibrations, and Rotating Machines
PublisherAmerican Society of Mechanical Engineers (ASME)
Pages1411-1418
Number of pages8
ISBN (Electronic)9780791897652
DOIs
StatePublished - 1995
EventASME 1995 Design Engineering Technical Conferences, DETC 1995, collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium - Boston, United States
Duration: Sep 17 1995Sep 20 1995

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume3B-1995

Conference

ConferenceASME 1995 Design Engineering Technical Conferences, DETC 1995, collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium
Country/TerritoryUnited States
CityBoston
Period9/17/959/20/95

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

Fingerprint

Dive into the research topics of 'Three dimensional vibration of a ballooning string'. Together they form a unique fingerprint.

Cite this