起重机n阶伸缩臂架稳定性的递推公式及数值解法  

Recursive Formula and Numerical Solution of Stability with n-stepped Crane Telescopic Booms

作　　者：姚峰林[1] 孟文俊[1] 赵婕[2] 张志德[3] 申昌宏 闫俊慧[3] 刘海波[3] YAO Fenglin;MENG Wenjun;ZHAO Jie;ZHANG Zhide;SHEN Changhong;YAN Junhui;LIU Haibo(School of Mechanical Engineering,Taiyuan University of Science&Technology,Taiyuan,030024;Computer Engineering Department,Taiyuan University,Taiyuan,030032;Construction Machinery Sub-Co.,Taiyuan Heavy Industry Co.,Ltd.,Taiyuan,030024)

机构地区：[1]太原科技大学机械工程学院,太原030024 [2]太原大学计算机工程系,太原030032 [3]太原重工股份有限公司工程机械分公司,太原030024

出　　处：《中国机械工程》2019年第21期2533-2538,共6页China Mechanical Engineering

基　　金：国家自然科学基金资助项目（51575370）;国家高技术研究发展计划（863计划）资助项目（2013AA041104）;山西省自然科学基金资助项目（201701D221130)

摘　　要：基于纵横弯曲理论建立了n阶伸缩臂阶梯柱的微分方程组,并利用数学归纳法推导出n阶阶梯柱压杆稳定性的递推公式。针对递推公式中的超越方程,结合结构受力特征,列写补充方程,使用Levenberg-Marquardt数值最优化算法求解了具有n个未知数的超越方程组。利用此算法求解出的长度系数与GB/T3811—2008中的结果和ANSYS 17.0结果进行对比,结果表明,此算法的精度优于其他算法的精度,并且长度系数具有一定的非线性,因此在实用过程中,小范围内的线性插值是可行的。对于大截面的阶梯柱,使用线性插值计算,临界力的误差较大。Differential equations of n-stepped telescopic boom were established based on the vertical and horizontal bending theory.The recursive formula of the stability of n-stepped telescopic booms was deduced by the mathematical induction method.For the transcendental equation in recursive formula,combined with the structural force characteristics,the Levenberg-Marquardt numerical optimization algorithm was used to solve the equations with n unknowns.Length coefficients that solved by the method were compared with those in GB3811—2008 and the outcomes calculated by ANSYS 17.0.The results show that the accuracy of this algorithm is better than that of the other algorithms,and the length coefficient has certain nonlinearity.Therefore,linear interpolation is feasible in a small scope in practical processes.For the large sections of the stepped column,linear interpolation method will lead larger errors in critical forces.

关 键 词：伸缩臂 阶梯柱 递推公式 超越方程 数值求解 

分 类 号：TH213.1[机械工程—机械制造及自动化]