基于Hermite多项式的打纬运动学方程及其应用

Establishment and application of kinematics equations of beating-up motion based on Hermite polynomials

为使打纬机构运行平稳,性能达到理想的织造要求,采用由理想运动学方程反求机构参数的方法,用4段光滑拼接的三次Hermite多项式建立剑杆织机打纬机构加速度曲线方程,再由加速度曲线方程及其边界条件推导出剑杆织机打纬机构速度、位移和跃度曲线方程,并对运动学方程中参数的计算进行了说明。将所建立的运动学方程用在共轭凸轮打纬机构的参数反求,得到了机构参数和曲率变化均匀的共轭凸轮廓线。研究结果表明,建立的运动学方程不仅能够满足共轭凸轮打纬机构参数反求的要求,而且所求共轭凸轮具有较好的力学特性。

In order to let the beating-up mechanism operate smoothly and stably and meet the desired weaving requirement,this paper applies ideal kinematics equations to derive mechanism parameters in reverse.The acceleration curve equation of beating-up mechanism on a rapier loom is established using 4 sections of cubic Hermite interpolation polynomials.Then based on the acceleration curve equation and its corresponding boundary conditions,the velocity,displacement and jerk equations of beating-up mechanism on the rapier loom is deduced.The calculation of parameters in these kinematics equations is illustrated.By applying these kinematics equations to conjugate cam beating-up mechanism reverse calculation,the parameters of mechanism and the profile of conjugate cam with uniform changing curvature are obtained.The research results indicate that these established kinematics equations can satisfy the requirements of reverse calculation of conjugate cam beating-up mechanism′s parameters,and the required conjugate cam has good mechanical performance.