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本文给出的方程,原则上适用于任何可缠绕的几何曲面,也适用于任何给定的纱嘴运动形式。方程的建立,涉及到“落点稳定”和“支点稳定”概念;前者用于一般连续曲面缠绕,后者用于粗台曲面的凸棱过过渡缠绕。在以落点稳定为基础建立的方程中引入了“替换因子”,它使方程在运动形式的选择上具有广泛性。方程一般都以几何参数形式表示,这样利于数学表达,也使方程推导简化;此外,在参数运方程的基础上建立速度方程也比较容易。文中结出了几何参数与时间参数之间的数学关系,以便工程应用。
The equations given in this paper apply in principle to any wraparound geometric surface and to any given yarn movement. The establishment of equations involves the concepts of “falling stability” and “fulcrum stability”. The former is used for general continuous surface winding and the latter is used for the over-edge transition winding of rough surface. The “substitution factor” was introduced into the equation based on the stability of the landing point, which made the equation extensive in the choice of the form of motion. Equations are generally expressed in the form of geometric parameters, which is conducive to mathematical expression, but also to simplify the equation derived; In addition, the parameters of the equation based on the establishment of the speed equation is relatively easy. The article concludes the mathematical relationship between geometric parameters and time parameters for engineering application.