伸缩臂式起重机阶梯柱模型的临界力计算对比  

Comparison of Calculation Methods of Critical Force of Stepped Column Model of Telescopic Crane

作　　者：姚峰林[1] 孟文俊[1] 赵婕[2] 石国善 YAO Feng-lin;MENG Wen-jun;ZHAO Jie;SHI Guo-shan(School of Mechanical Engineering,Taiyuan University of Science and Technology,Shanxi Taiyuan030024,China;Department of Computer Engineering,Taiyuan University,Shanxi Taiyuan030032,China)

机构地区：[1]太原科技大学机械工程学院,山西太原030024 [2]太原大学计算机工程系,山西太原030032

出　　处：《机械设计与制造》2020年第5期23-27,共5页Machinery Design & Manufacture

基　　金：国家高技术研究发展规划(863计划)项目(SS2013AA041104);国家自然科学基金资助项目(51575370);山西省自然科学基金(201701D221130)。

摘　　要：为解决大型全地面起重机伸缩臂稳定性的临界力的问题,针对五阶以上n阶阶梯柱理论计算的空白和国家标准的缺失。基于微弯曲理论列写微分方程,得到理想柱的挠曲线,使用此曲线和瑞利李兹法可得理想柱欧拉临界力。对于n阶阶梯柱,使用理想柱挠曲线和抛物线两种假设曲线结合瑞利李兹法,可分别求得阶梯柱的临界力和等效长度系数。基于纵横弯曲理论,建立n阶伸缩臂的阶梯柱的分段微分方程组,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。针对递推公式当中的超越方程,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具有n个未知数的超越方程组,利用此算法能够求解出n阶阶梯柱的长度系数。以上三种方法得到的长度系数与GB3811-2008,ANSYS 17.0结果进行对比。研究结果表明,提出数值算法的精度最高;并且在阶梯柱的阶数较高时,传统的前两种算法将产生较大误差。The calculation of the critical force of telescopic boom is the key to stability calculation of all-terrain crane due to the absence of theoretical calculation method and national standard for the stepped column number is more than 5. In slightly bending theory,differential equation can be build up,and then the deflection curve of ideal column can be obtained. Using this curve and the Rayleigh-Ritz method,the Euler force of the ideal column can be gotten. For n-stepped columns,Euler forces and the effective length coefficients can be acquired by using defection curve of the ideal column and parabolic curve respectively. Differential equations of the n-stepped telescopic boom are established based on the vertical and horizontal bending theory. The recursive formula of the stability of n-stepped telescopic boom is deduced by mathematical induction method. For the transcendental equation in recursive formula,combined with structural characteristics and supplementary formulas,the Levenberg-Marquardt numerical optimization algorithm is used to solve the equations with n unknowns. Length coefficients that obtained by the three method are compared with GB3811-2008 and ANSYS 17.0.The results show that the accuracy of the numerical algorithm is the highest,and the first two methods will produce large errors when the stepped columns have more steps.

关 键 词：伸缩臂 阶梯柱 递推公式 数值求解 瑞利李兹法 

分 类 号：TH16[机械工程—机械制造及自动化] TH213.1