On The Theory Of Ring Spinning Balloon

Ring spinning is the dominant system of manufacturing high quality yarns from fibres for apparel applications. Because of the careful fibre control during the spinning process, ring spinning produces relatively high quality yarns and the quality of ring spun yarns has been used as a benchmark against which quality of yarns produced on other spinning system is judged. With the progress of the Times and the development of science and technology, higher request has been put forward to ring spinning system, so it is necessary to deeply analyze the ring spinning process in essential. This dissertation is focus on spinning balloon phenomena, which is studied by method of the combination of theory derivation, analytical and numerical calculating as well as experiment validation.Based on yarn dynamics, ordinary differential equations of balloon shape and boundary conditions are derived incorporating normal air drag. The resulting equations which are nonlinear boundary value problem are solved by shooting method and finite difference method. Various parameters affecting balloon profile and yarn tension are discussed in detail, such as traveler mass, balloon height, bobbin radius, friction coefficient of traveler and ring collar, friction coefficient of yarn and traveler, friction coefficient of normal air drag, ring radius and spindle speed.For an equation, analytical solution is more willing to be obtained. Approximate analytical solution of the ring spinning formula in zero air drag is given using perturbation method. Since the equation does not exist the so-called 'small parameter', the artificial small parameter is used into the appropriate place in the equation. Parameter expansion method is also used to enlarge the convergence area. In addition, homotopy perturbation method is introduced, which can effectively solve the above problem with smaller error.Models incorporating yarn elasticity are set up, incorporating linear elastic yarn assumption and nonlinear elastic yarn assumption. Model of linear elastic yarn is used to analyze the significance of various yarn elasticity parameters on balloon profile and yarn tension, which gives quantitative conclusions. For different spinning materials, curve fitting are used to match two parameters proposed in nonlinear elastic model and quantitative conclusions are drawn.It is found that balloon shape and yarn tension are not unique in solving steady-state equations. In certain parameter conditions, ring spinning equations have 3 answers, namely Hopf-like bifurcation phenomena. In order to study the stability of the whole system, transient model is developed and the stability of representative quasi-stationary balloons subjected to a small velocity impulse is investigated. The results of single-loop balloon, one-and-a-half-loop balloon and double-loop balloon are given.Finally, experimental platform is built by the existing equipment (stroboscope, tensiometer). Space curves of yarn balloons are collected by digital camera and yarn tensions at guide-eye are acquired by programmed Labview software. Tension data are extracted by data processing technology which is proposed based on Empirical Mode Decomposition principle and compared with numerical calculation.