起重机n阶伸缩臂带超起装置的临界力数值解法研究  

Study on the numerical solution method of critical force of crane n-step telescopic boom with super-lifting device

作　　者：姚峰林[1,2] 李建东 高有山[1,2] 杨浩 孟文俊[1,2] YAO Fenglin;LI Jiandong;GAO Youshan;YANG Hao;MENG Wenjun(School of Mechanical Engineering,Taiyuan University of Science and Technology,Taiyuan 030024;Shanxi Provincial Key Laboratory of Intelligent Logistics Equipment,Taiyuan University of Science and Technology,Taiyuan 030024;Shanxi Taigang Stainless Steel Co.,Ltd.,Taiyuan 030002;Orit Cranes(Beijing)Co.,Ltd.,Beijing 101103)

机构地区：[1]太原科技大学机械工程学院,山西太原030024 [2]太原科技大学智能物流装备山西省重点实验室,山西太原030024 [3]山西太钢不锈钢股份有限公司,山西太原030002 [4]奥力通起重机(北京)有限公司,北京101103

出　　处：《机械设计》2025年第1期70-77,共8页Journal of Machine Design

基　　金：国家自然科学基金项目(52075356);山西省自然科学基金项目(201901D111236);山西省教学改革项目(J2021411)。

摘　　要：起重机伸缩臂的受力状况和起升性能可以通过安装超起装置进行改善和提高。然而,目前还没有有效、精确的数值方法来求解带超起装置的伸缩臂临界力。文中将带超起装置的伸缩臂简化为阶梯柱加双拉索模型,并基于纵横弯曲理论建立了挠曲微分方程组,推导了屈曲特征方程及递推公式。同时,建立了联合超越方程组,采用Levenberg-Marquardt最优化算法求解临界力及长度系数。通过与ANSYS有限元仿真结果的对比分析,验证了所提方法的正确性和准确性。文中所提方法可适用于任意臂节数、臂节长度、截面惯性矩、拉索长度及两拉索夹角的情况,并对带超起装置的伸缩臂结构设计具有工程应用价值。Both the stress status and the lifting performance of the telescopic boom can be improved by installing a super-lifting device.However,there is no effective and accurate numerical method to solve the critical force exerted on the telescopic boom with a super-lifting device.In this article,the telescopic boom with a super-lifting device is simplified as a stepped column with a model of double cables;according to the longitudinal and transverse bending theory,a deflection differential equation group is set up;then,both the buckling characteristic equation and the recursive formula are derived.At the same time,a joint super-lifting equation group is constructed,and the Levenberg-Marquardt optimization algorithm is used to solve the critical force and the length coefficient.The results are compared with those obtained from the ANSYS finite-element simulation;it is verified that this method is correct and accurate.It,which is applied to any number of arm sections,arm section length,cross-section inertia moment,cable length and angle between two cables,is valuable to structural design of telescopic booms with super-lifting devices in different projects.

关 键 词：伸缩臂 超起装置 屈曲特征方程 递推公式 超越方程组 数值求解 

分 类 号：TH213.1[机械工程—机械制造及自动化]