摘要
为实现大空间转动弹性梁的高速、高精度平稳控制,首先需解决弹性梁的非线性动力学建模问题,并完成动力学解耦。假设柔性连杆为欧拉-伯努利梁,应用假设模态法进行坐标离散,采用Galerkin法和Hamilton最小变微分原理建立弹性梁柔性动力学模型;基于摄动理论构建正则摄动式,应用多尺度法对摄动式进行改进,对比分析了常规正则摄动法、改进后摄动法的解耦精度,应用四阶Runge-Kutta法验证了所提出方法的有效性与可行性。数值仿真结果表明,改进后的摄动法解耦精度高,解耦误差比常规正则摄动误差降低一个数量级,解决了低阶正则摄动法解耦精度低的问题,避免了采用高阶摄动来提高解耦精度而产生庞大计算量的弊端。
In order to realize the stable and precision control of elastic beams in large overall rotation at high speed,its nonlinear dynamic model must be built and the decoupling work should be completed.Flexible rod was assumed by Euler-Bernoulli beam.The approach of assumed modes was applied to discrete the coordinates,and the Galerkin method and Hamilton principle were adopted to establish the flexible dynamic model.The regular perturbation formula was deduced with perturbation theory.Multiscale method was used to improve the perturbation formula by separating two-time parameters.The decoupling accuracy was deeply analyzed for the regular perturbation method and the improved perturbation method.The validity and feasibility of the proposed method were verified by Runge-Kutta method.The simulation data indicated that the improved perturbation solution owned high decoupling accuracy,little computation and good rapidity.The problem of low decoupling accuracy was solved compared with the common regular perturbation method which was limited by effective time series.The proposed decoupling method also avoided much calculation caused by high-order perturbation to improve the computation’s accuracy.It provided an important theoretical basis and data support for dynamic decoupling about complex multi-body flexible systems.
作者
赵磊
赵新华
李彬
周海波
杨玉维
刘凉
ZHAO Lei;ZHAO Xinhua;LI Bin;ZHOU Haibo;YANG Yuwei;LIU Liang(School of Mechanic Engineering,Tianjin University of Technology,Tianjin 300384,China;Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechatronical System,Tianjin 300384,China;National Demonstration Center for Experimental Mechanical and Electrical Engineering Education,Tianjin University of Technology,Tianjin 300384,China)
出处
《农业机械学报》
EI
CAS
CSCD
北大核心
2020年第1期391-397,共7页
Transactions of the Chinese Society for Agricultural Machinery
基金
国家重点研发计划项目(2017YFB1303502、2018YFB1308900)
天津市自然科学基金面上项目(18JCYBJC87900、17JCYBJC18300)
关键词
弹性梁
柔性动力学
摄动解耦
多尺度法
误差
elastic beam
flexible dynamics
perturbation decoupling
multiple scales method
error
