起重机n阶伸缩臂架稳定性的递推公式及数值解法

中国机械工程

起重机n阶伸缩臂架稳定性的递推公式及数值解法

姚峰林1;孟文俊1;赵婕2;张志德3;申昌宏3;闫俊慧3;刘海波3

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

出版日期:2019-11-10 发布日期:2019-11-08
基金资助:
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）

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

YAO Fenglin1;MENG Wenjun1;ZHAO Jie2;ZHANG Zhide3;SHEN Changhong3;YAN Junhui3;LIU Haibo3

1.School of Mechanical Engineering，Taiyuan University of Science & Technology，Taiyuan， 030024
2.Computer Engineering Department,Taiyuan University,Taiyuan，030032
3.Construction Machinery Sub-Co.,Taiyuan Heavy Industry Co.,Ltd.,Taiyuan,030024

Online:2019-11-10 Published:2019-11-08

摘要/Abstract

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。

关键词: 伸缩臂, 阶梯柱, 递推公式, 超越方程, 数值求解

Abstract: 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.

Key words: telescopic boom； stepped column； recursive formula； transcendental equation, numerical solution

中图分类号:

TH213.1

姚峰林1;孟文俊1;赵婕2;张志德3;申昌宏3;闫俊慧3;刘海波3. 起重机n阶伸缩臂架稳定性的递推公式及数值解法[J]. 中国机械工程.

YAO Fenglin1;MENG Wenjun1;ZHAO Jie2;ZHANG Zhide3;SHEN Changhong3;YAN Junhui3;LIU Haibo3. Recursive Formula and Numerical Solution of Stability with n-stepped Crane Telescopic Booms[J]. China Mechanical Engineering.

参考文献

[1]陆念力，都亮，兰朋.变截面阶梯压杆精确失稳特征方程及其稳定计算实用方法——《塔式起重机设计规范》中阶梯柱计算长度的快捷计算及精度分析[J].建筑机械，2014(6):76-81.
LU Nianli， DU Liang， LAN Peng. Accurate Buckling Characteristic Equation of Stepped Column Bar and Its Stability Analysis with Practical Method：Shortcut Calculation and Accuracy Analysis with the Effective Length of Stepped Column Given in Specification for Tower Crane Design[J].Construction Machinery,2014(6):76-81.
[2]LI Wenjun, ZHAO Jiong, JIANG Zhen, et al. A Numerical Study of the Overall Stability of Flexible Giant Crane Booms[J]. Journal of Constructional Steel Research, 2015, 105: 12-27.
[3]TIMOSHENKO S P, GERE J M. Theory of Elastic Stability[M]. New York: Mc Graw-Hill, 1961: 49-63.
[4]王欣，易怀军，赵日鑫，等.一种ｎ阶变截面压杆稳定性计算方法的研究[J].中国机械工程，2014，25（13）,1744-1747.
WANG Xin, YI Huaijun, ZHAO Rixin, et al. Research on Stability Analysis Method of n-order Variable Cross-Section Compression Bars[J]. China Mechanical Engineering,2014,25(13):1744-1747.
[5]张宏生，陆念力.动臂式塔机变截面吊臂的整体稳定性分析[J].哈尔滨工业大学学报，2010，42(9):1394-1397.
ZHANG Hongsheng，LU Nianli.Global Stability Analysis of the Tapered Luffing Jib of Tower Crane[J].Journal of Harbin Institute of Technology, 2010，42(9):1394-1397.
[6]刘庆潭.复杂细长压杆临界力计算的传递矩阵法[J].力学与实践，1997(6):51-54.
LIU Qingtan. Transfer Matrix Method for the Complex Compressed Bar [J]. Mechanics in Engineering,1997(6):51-54.
[7]孙建鹏，李青宁，曹现雷.压弯杆弹性弯曲分析的精细传递矩阵法[J].北京工业大学学报，2012,38(4):536-539.
SUN Jianpeng，LI Qingning，CAO Xianlei. Precise Transfer Matrix Method for Elastic Bending Analysis of a Compressive-bending Bar[J]. Journal of Beijing University of Technology, 2012,38(4):536-539.
[8]陆念力，兰朋，李良.二阶理论条件下的梁杆系统精确有限元方程及应用[J].哈尔滨建筑大学学报，1998,31(4):67-74.
LU Nianli, LAN Peng, LI Liang.Appilication of FEM of Beam Element with Theory of ⅡOrder[J].Journal of Harbin University of Civeil Engineering Architecture,1998，31(4)：67-74.
[9]陆念力，兰朋，白桦.起重机箱形伸缩臂稳定性分析的精确理论解[J].哈尔滨建筑大学学报，2000,33(2):89-93.
LU Nianli, LAN Peng, BAI Hua. Precise Stability Analysis of Telescopic Boom[J]. Journal of Harbin University of Civil Enineering Architecture,2000，33(2):89-93.
[10]陆念力，都亮.多级阶梯柱侧向刚度与轴压临界力的精确分析及其实用算式[J].工程力学,2015,32(8):217-222.
LU Nianli , DU Liang. Analysis of Lateral Stiffness and Critical Buckling Force of Stepped Columns and Their Practical Formulations[J].Engineering Mechanics ,2015,32(8):217-222.
[11]中华人民共和国国家质量监督检验检疫总局，中国国家标准化管理委员会.GB/T 3811—2008起重机设计规范[S]. 北京：中国标准出版社, 2008.
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China, Standardization Administration of the People's Repubic of China. GB/T3811—2008 Design Rules for Cranes [S]. Beijing: China Standard Press,2008.
[12]刘士明，陆念力，孟丽霞.牵绳非保向力作用下的起重臂稳定性分析[J].哈尔滨工业大学学报，2014,46(3):26-29.
LIU Shiming，LU Nianli，MENG Lixia.Stability Analysis of Telescopic Booms under Pull-rope Follower Force[J].Journal of Harbin Institute of Technology, 2014,46(3):26-29.
[13]刘士明.工程起重机伸缩臂系统结构稳定性及复合运动动力学研究[D].哈尔滨：哈尔滨工业大学,2013.
LIU Shiming. Research on Structural Stability and Complex Motion Dynamic of Telescopic Boom System in Construction Crane[D].Harbin:Harbin Institute of Technology ,2013.
[14]BAGHERI S, NIKKAR A. Higher Order Explicit Solutions for Nonlinear Dynamic Model of Column Buckling Using Variational Approach and Variational Iteration Algorithm-Ⅱ[J]. Journal of Mechanical Science and Technology, 2014, 28(11): 4605-4611.