轴向运动纱线束的非线性横向振动特性

纺织学报 ›› 2013, Vol. 34 ›› Issue (12): 37-0.

轴向运动纱线束的非线性横向振动特性

高晓平¹ 李友国² 孙以泽³ 王晓清¹

1. 内蒙古工业大学轻工与纺织学院
2. 信阳农林学院计算机系
3. 东华大学机械工程学院

收稿日期:2013-01-04 修回日期:2013-08-01 出版日期:2013-12-15 发布日期:2013-12-16
通讯作者: 高晓平 E-mail:gaoxp@imut.edu.cn
基金资助:
内蒙古自治区自然科学基金资助项目

Transverse nonlinear-vibration of axially moving yarn strand

Received:2013-01-04 Revised:2013-08-01 Online:2013-12-15 Published:2013-12-16
Contact: GAO Xiao-Ping E-mail:gaoxp@imut.edu.cn

摘要/Abstract

摘要： 为控制纱线张力波动，提高毯面质量，研究了建立地毯织造过程中粘弹性纱线束振动模型及其影响因素。为此，应用三参数本构关系表征纱线束粘弹性，结合轴向几何非线性变形和材料非线性因素，应用牛顿第二定律建立纱线束横向振动方程。经无量纲化和一阶Galerkin截断，应用四阶Runge-Kutta法求解常微分方程，可得纱线束喂入速度、张力波动幅度以及阻尼系数对振动特性的影响。结果显示，在纱线束材料确定下，降低纱线束振动振幅从而减少张力波动的方法主要是增加阻尼系数，如增加提花罗拉表面摩擦系数。

关键词: 横向振动, 几何非线性, 本构关系, 张力波动

Abstract: It is essential to develop the dynamic vibration model of yarn strand and its influence during tufting process for controlling vibration amplitude of yarn tension and improve the carpet quality. The three-parameter constitutive relation was used for charactering the viscoelasticity of yarn strand, a partial differential equation governing the transverse vibration was derived from the Newton’s second law, in which geometric nonlinearity and material nonlinearity were all taken into account. The first-order Galerkin method was used for separating time variable from space variable, the nonlinear dynamics for transverse motion of axially moving yarn strand was developed. The effect of transport speed, amplitude of the tension perturbation, and the damping coefficient on the dynamic vibration behavior could be analyzed by applying the fourth order Runge-Kutta method in next paper. Based on above analysis, we can conclude that the main method for decreasing amplitude of vibration and vibration of tension is increasing damping coefficient, for example, increasing friction coefficient of jacquard roller.

Key words: transverse vibration, geometric nonlinearity, constitutive relation, tension fluctuation

高晓平李友国孙以泽王晓清. 轴向运动纱线束的非线性横向振动特性[J]. 纺织学报, 2013, 34(12): 37-0.

参考文献

参考文献
[1] Chen L, Yang X, Cheng C. Dynamic stability of an axially accelerating viscoelastic beam[J]. European Journal of Mechanics - A/Solids. 2004, 23(4): 659-666.
[2] Ghayesh M.H, Balar S. Non-linear parametric vibration and stability analysis for two dynamic models of axially moving Timoshenko beams[J]. Applied Mathematical Modelling. 2010, 34(10): 2850-2859.
[3] Ghayesh M.H. Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation[J]. International Journal of Non-Linear Mechanics. 2010, 45(4): 382-394.
[4] ?z H.R, Pakdemirli M, Boyac1 H. Non-linear vibrations and stability of an axially moving beam with time-dependent velocity[J]. International Journal of Non-Linear Mechanics. 2001, 36(1): 107-115.
[5] ?z H.R, Pakdemirli M. Vibrations of axially moving beam with time-dependent velocity [J]. Journal of Sound and Vibration. 1999, 227(2): 239-257.
[6] Usik L, Hyungmi Oh. Dynamics of an axially moving viscoelastic beam subject to axial tension[J]. International Journal of Solids and Structures. 2005, 42(8): 2381-2398.
[7] Ghayesh M.H, Balar S. Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams[J]. International Journal of Solids and Structures. 2008, 45(25-26): 6451-6467.
[8] Ghayesh M.H. Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide[J]. Journal of Sound and Vibration. 2008, 314(3-5): 757-774.
[9] Andrianov I.V, Awrejcewicz J. Dynamics of a string moving with time-varying speed[J]. Journal of Sound and Vibration. 2006, 292(3-5): 935-940.
[10] Zhang N, Chen L. Nonlinear dynamical analysis of axially moving viscoelastic strings[J]. Chaos, Solitons & Fractals. 2005, 24(4): 1065-1074.
[11] Chen L, Chen H, Lim C.W. Asymptotic analysis of axially accelerating viscoelastic strings[J]. International Journal of Engineering Science. 2008, 46(10): 976-985.
[12] Suweken G, Van Horssen W.T. On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: The string-like case[J]. Journal of Sound and Vibration. 2003, 264(1): 117-133.
[13] Marynowski K. Non-linear vibrations of an axially moving viscoelastic web with time-dependent tension[J]. Chaos, Solitons & Fractals. 2004, 21(2): 481-490.
[14] Suweken G, Van Horssen W.T. On the weakly nonlinear, transversal vibrations of a conveyor belt with a low and time-varying velocity[J]. Nonlinear Dynamics. 2003, 31(2): 197-223.
[15] Koivurova H. The numerical study of the nonlinear dynamics of a light, axially moving string[J]. Journal of Sound and Vibration. 2009, 320(1-2): 373-385.
[16] 沈丹峰，叶国铭. 织造过程中经纱振动特性的分析[J]. 纺织学报. 2007, 28(5): 41-46.
[17] Clark J.D, Fraser W.B, Stump D M. Modelling of tension in yarn package unwinding[J]. Journal of Engineering Mathematics. 2001, 40(1): 59-75.
[18] Kurilenko Z.N, Matyushev II, Goncharenko A F, et al. Yarn tension during unwinding from a package[J]. Fibre Chemistry. 1980, 12(3): 189-191.
[19] Vangheluwe L, Sleeckx B, Kiekens P. Numerical simulation model for optimisation of weft insertion on projectile and rapier looms[J]. Mechatronics. 1995, 5(2-3): 183-195.
[20] Murakami F, Watanabe T, Tazaki H, et al. Dynamic tension on yarns being unwound from a beam.[J]. Journal of the Textile Machinery Society of Japan. 1979, 25(4): 93-99.
[21] Koo Y. Yarn tension variation on the needle during the knitting process[J]. Textile Research Journal. 2004, 74(4): 314-317.
[22] Gao X, Sun Y, Meng Z, et al. Analytical approach of mechanical behavior of carpet yarn by mechanical models[J]. Materials Letters. 2011, 65(14): 2228-2230.
[23] 张伟，胡海岩. 非线性动力学理论与应用的新进展[M]. 第一版. 北京: 科学出版社, 2009.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed