桥式起重机吊重摆动的参变振动模型

Parametric oscillation model of the load swing of bridge crane

针对起重机吊重摆动问题,着重探讨了吊重垂直运动对摆振的影响,在允许的假设条件下建立了起重机吊重摆动的数学模型,用坐标变换把起重机微分方程转化为Hill方程标准形式,通过研究Hill方程找出起重机吊重做减幅摆动的条件。最后引入参数平面,绘制Hill方程稳定图,即起重机吊重做减幅摆动的图示。结果表明:通过控制摆长实现起重机吊重的消摆需要综合考虑初始摆长、摆长的变化幅度和变化周期这三个参数,由这三个参数结合引入的参数平面求得一个坐标点,当这个点落在参数平面的减幅振动区域就可以实现吊重的消摆。

Regarding the problem of crane loads swing,the effect of vertical movement of the load on shimmy was discussed;the mathamatical model of crane load sway under permitted supposed conditions was established;through coordingate transformation,the differential equation was teansformed into the standard form of Hill equation;and with analysis on Hill equation the condition about damped oscillation was obtained.Introducing the parametric plane,the stable map of Hill equation was drawn,i.e.the map of damped oscillation of crane load.The results show that,if control of the pendulum length is used to realize the anti-sway of crane,three parameters including initial pendulum length,amplitude of variation and period of variation of pendulum length should be considered comprehensively,a specific coordinate point can be determined by these three parameters on the parametric plane,if this point is in the area of damped oscillation on the parametric plane,the anti-sway of crane can be realized.