TY - GEN
T1 - Three dimensional vibration of a ballooning string
AU - Hall, Kevin J.
AU - Zhu, Fang
AU - Rahn, Christopher D.
N1 - Funding Information:
The authors would like to thank Reiter-Scragg Corpo ration for their support of this research. This work was partially supported by the National Textile Center.
Publisher Copyright:
© 1995 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1995
Y1 - 1995
N2 - 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.
AB - 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.
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U2 - 10.1115/DETC1995-0542
DO - 10.1115/DETC1995-0542
M3 - Conference contribution
AN - SCOPUS:85103459178
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 1411
EP - 1418
BT - 15th Biennial Conference on Mechanical Vibration and Noise - Acoustics, Vibrations, and Rotating Machines
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 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
Y2 - 17 September 1995 through 20 September 1995
ER -