铰接摆杆截面尺寸对高速共轭凸轮引纬机构弹性动力学影响

Impact of articulated swing bar’s cross-section size on elastodynamics of high-speed conjugate cam’s weft insertion mechanism

针对共轭凸轮引纬机构中铰接摆杆的截面尺寸影响引纬机构运动精度与可靠性问题,将引纬机构中的铰接杆件等效为梁单元,考虑铰接杆件的横向位移、纵向位移和扭转变形,基于有限元法和拉格朗日方程建立了铰接杆件运动微分方程,进而推导出系统弹性运动微分方程。采取运动弹性动力分析方法,分析摆杆的截面尺寸和主轴转速对杆件动态响应、动应力的影响。研究结果表明:增加摆杆的高度比增加宽度更能减少摆杆的动应力和弹性变形,摆杆的高度提高50%,与机架相连的摆杆端点处的扭转变形峰值将减少约54%,摆杆的动应力峰值将减少约71%;随着主轴转速的提高,相同结构尺寸下摆杆的动态响应和动应力将增大。

Since the articulated swing bar’s cross-section size in the conjugate cam’s weft insertion mechanism affects the motion accuracy and reliability of the weft insertion mechanism, the articulated bar in the weft insertion mechanism is equivalent to a beam element. With the articulated bar’s transverse displacement, longitudinal displacement and torsional deformation taken into consideration, the motion differential equation is set up based on the finite-element method and the Lagrange equation, and then the motion elasticity differential equation of the system is derived. The impacts of the cross-section size and the spindle speed on both the dynamic response and the dynamic stress of the swing bar are explored by means of the dynamic analysis on motion elasticity. The results show that the swing bar’s ever-increasing height, compared with its ever-increasing width, reduces greater dynamic stress and elastic deformation. The height of the swing bar increases by 50%, and the peak value of torsional deformation at the end of the swing bar connected with the frame decreases by about 54%. The peak value of the swing bar’s dynamic stress decreases by about 71%. With the ever-growing spindle speed, both the dynamic response and the dynamic stress of the swing bar with the same structure size will increase.