梁岗 程天聪 王桂昇

摘要：为保证桥机安全可靠工作，桥机振动问题是大型起重设备中十分重要的研究课题，而传统所采用的是单一能域建模方法。鉴于此，针对小车-吊重-桥机主梁耦合系统，利用键合图分块建模的特点，分别建立小车运动系统和简支梁承重结构对应的键合图模型。根据两个子系统之间的功率守恒，组合完成耦合系统的键合图模型，借此建立耦合系统的状态方程。针对小车运行加速-匀速-减速的实际工况，根据状态方程计算系统的耦合频率，采用状态空间迭代解法求解主梁跨中动力响应。分析吊重与小车质量比、绳长和吊重摆动对系统耦合频率和主梁跨中动力响应的影响。结果表明：利用键合图法可以快速有效地构建复杂耦合系统的动力学模型;小车-吊重-桥机主梁耦合系统的动力学特性不仅与小车运行的速度、加速度有关，而且与吊重与小车质量比、绳长和吊重摆动有关。

关键词： 键合图; 状态空间迭代解法; 桥式起重机; 耦合频率

中图分类号： TH215    文献标志码： A

Modeling and dynamics analysis on trolley-lifting weight-bridge crane

main girder coupling system with bond graphs

LIANG Gang， CHENG Tiancong， WANG Guisheng

（Logistics Engineering College， Shanghai Maritime University， Shanghai 201306， China）

Abstract： In order to ensure the safe and reliable work of the bridge crane， the vibration of the bridge crane is a very important research topic in the large lifting equipment， while the traditional method is a single energy domain modeling method. In view of this， for the trolley-lifting weight-bridge crane main girder coupling system， using the characteristic of block modeling of bond graphs， the bond graph models of the trolley motion system and the simply supported girder bearing structure are established， respectively. According to the power conservation between the two subsystems， the bond graph model of the coupling system is completed， and the state equation of the coupling system is built. According to the working conditions of acceleration-uniform speed-deceleration of the trolley， the coupling frequency of the system is calculated by the state equation， and the mid-span dynamic response of the main girder is solved by the state space iterative method. The influences of the mass ratio of the lifting weight to the trolley， the length of wire and the lifting weight swing on the system coupling frequency and the mid-span dynamic response of the main girder are analyzed. The results show that： using the bond graph method， the dynamic model of complex coupling systems can be constructed quickly and effectively; the dynamic characteristics of the trolley-lifting weight-bridge crane main girder coupling system are not only related to the speed and acceleration of the trolley， but also related to the mass ratio of the lifting weight to the trolley， the length of wire and the lifting weight swing.

Key words： bond graph; state space iterative method; bridge crane; coupling frequency

0 引 言

橋式起重机（以下简称桥机）是用于港口货物装卸的主要设备，其装卸能力和工作效率直接决定码头作业生产率。随着港口机械朝着大型化、高速化方向发展，桥机起升的重量不断加大，小车运行速度也加快，吊重与桥机主梁的耦合作用增强，因此研究其动态特性有重要意义。

考虑桥机主梁结构与小车的耦合振动时，由于货物在起吊过程中会发生摆动，往往将模型简化为移动质量-吊重-简支梁耦合系统。……