立体织机打纬机构动力学方程的对称性解法

Symmetry Solution of Dynamic Equations of Weft Beating Mechanism of Stereo Loom

曲柄滑块式打纬机构广泛应用于立体织机平行打纬中,对其进行全面深入准确的动力学特性研究,将有助于提升织机整体性能,提高生产效率。本文主要基于Lie对称性理论精确计算了立体织机打纬机构的动力学方程,以此克服位置非线性数值分析以及与设计参数定量显示关系的困难。首先,在考虑打纬机构的非线性几何约束,依据分析力学方法建立了两自由度打纬机构动力学模型;其次,运用首次积分法得到机构性能指标打纬力的解析动态响应曲线,并进行了连续性局部参数灵敏度分析;最后,实际算例表明用对称性理论研究机构非线性动力学特性,方法新颖,适用范围广,结果可靠准确,本文的研究内容也为织机打纬机构更精确地动态优化设计和先进控制奠定了理论基础。

The slider crank beating up mechanism is widely used in th~ parallel beating up of three dimensional looms. It is helpful to improve the overall performance of the loom and increase the production efficiency by studying the dynamics characteristics comprehensively and accurately. In this paper, the dynamic equations of the weft beating mechanism of a solid loom are calculated accurately based on the Lie symmetry method, in order to overcome the difficulty of the position nonlinear numerical analysis and the quantitative display of the design parameters. First, considering the nonlinear geometric constraint of beating up mechanism, a dynamic model of two degree of freedom beating up mechanism is established according to the analytical mechanics method; secondly, the analytical dynamic response curve of beating force of mechanism performance index is obtained by the first integral method, and the continuous local parameter sensitivity analysis is also carried out; finally, the practical example shows that the theory of symmetry can be used to study the nonlinear dynamic characteristics of mechanisms. The method is novel, applicable to a wide range, reliable and accurate. The research content of this paper lays a theoretical foundation for more accurate dynamic optimization design and advanced control of loom beating up mechanism.