缠绕式多点提升系统钢丝绳变形失谐动力学分析

摘要

为了对缠绕式多点提升系统变形失谐时动力学响应特性进行研究,建立一种考虑卷筒缠绕半径误差的多点提升系统纵向振动模型,采用瑞利法对钢丝绳质量进行处理,同时将钢丝绳等效为刚度随绳长变化且具有一定阻尼的黏弹性体,然后应用Lagrange方程建立系统的振动方程.运用Matlab中ode45函数对转换后的一阶线性微分方程进行求解,计算结果表明:对于提升高度为43 m、卷筒缠绕半径误差为1 mm的实验提升系统,变形失谐情况下钢丝绳纵向运动加速度呈四段波动变化且位于0 ～1.5 m/s2内波动,且提升钢丝绳最终绳长差为3.6 mm,张力差达到657 N.同时采用软件进行仿真对比,发现仿真提升容器速度、加速度变化曲线和数值计算变化曲线基本吻合;仿真进一步表明:钢丝绳之间动张力差在绳长差为3.0 mm和4.2 mm时达到了平均张力的5％和10％,说明由于卷筒缠绕误差带来的变形失谐对张力差会造成显著的影响.研究结果对于设计和制造超深井缠绕式多点提升机卷筒和控制钢丝绳变形失谐量有重要理论和应用参考价值.%To study dynamic response characteristics of a multi-point winding hoisting system under the condition of discordance among wire ropes,a longitudinal vibration model for the multi-point hoisting system considering winding radius error of its drum was established.Rayleigh method was used to deal with the mass of the wire rope.The rope was equivalent to a viscoelastic body with a certain damping and stiffness varying with the rope' s length.The vibration equation of the system was built with Lagrange equation.Then the first order linear differential equation converted from the vibration equation was solved with the ode45 subroutine of MATLAB.The calculation results showed that for a tested hoisting system with the lifting height of 43 m and the rope winding error of 1 mm,the wire ropes' longitudinal vibration acceleration has four fluctuating stages within a range of 0-1.5 m/s2,the final length difference and tension difference of hoisting ropes are 3.6 mm and 657 Newton,respectively.The computing software was applied to do simulation and comparison.It was shown that the simulated rope' s hoisting velocity and acceleration versus time curves match those of the above calculation with MATLAB well;the dynamic tension differences among ropes reach 5％ and 10％ of the average tension with the rope length differences of 3.0 mm and 4.2 mm,respectively;the discordance among wire ropes caused by the drum' s winding radius error has a large influence on tension difference.The study results provided a theoretical basis and a reference for design of drum and control of discordance among wire ropes inmulti-point winding hoisting systems.