摘要
深海采矿越来越重要,本文针对采矿船-缆索-水下机器人采矿系统的作业模式,考虑采矿船和水下机器人运动引起的非均匀张力缆索横向振动问题,建立了船-缆-机器人系统简化的数学模型,给出了二阶线性变系数偏微分控制方程和初边值条件。基于变量分离法求解模型得到非均匀张力缆自然频率和振动模态的Bessel函数解析表达式。分析了采矿船和水下机器人运动引起的端致运动规律,给出了上下端运动幅度和频率对缆索振动的影响。研究发现:端部运动幅度逐渐增大时,缆索的横向最大振幅均呈线性增长;端部运动频率与缆索各阶自然频率相等时,系统会发生共振现象,分析了各阶振型的响应函数,对非均匀张力缆的设计参数确定提供参考。
As deep-sea mining becomes increasingly important,in this study,the operation mode of a mining shipcable-underwater robot mining system was explored,and the lateral vibration of a non-uniform tension cable caused by the movement of a mining ship and an underwater robot was investigated.A simplified mathematical model was established targeting the ship-cable-robot system to analyze the lateral vibration.After providing the second-order linear variable coefficient partial differential control equation and the initial boundary value conditions,the variable separation method was used for model calculations,and the Bessel function analytic expression of the natural frequency and vibration mode of the non-uniform tension cable was derived.This model analysis indicates an end-induced motion law caused by the motions of the mining ship and the underwater robot.Furthermore,it proved that the cable vibration can be affected by the amplitude and frequency of the upper and lower ends.The results also revealed that the maximum lateral amplitude of the cable increases linearly as the end motion amplitude gradually increases.Moreover,when the motion frequency of the cable end is equal to the natural frequency of the cable at each order,resonance occurs in the system.Subsequently,the response function of each order vibration mode is analyzed,which provides a reference for determining the design parameters of non-uniform tension cables.
作者
程阳锐
马佳乐
王振
戴瑜
CHENG Yangrui;MA Jiale;WANG Zhen;DAI Yu(College of Mechanical and Electrical Engineering,Central South University,Changsha 410083,China;Changsha Research Institute of Mining and Metallurgy,Changsha 410012,China;State Key Laboratory of Deep-Sea Mineral Resources Development and Utilization Technology,Changsha 410012,China;School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China;School of Mathematical Sciences,Beihang University,Beijing 100191,China)
出处
《哈尔滨工程大学学报》
EI
CAS
CSCD
北大核心
2023年第9期1631-1637,共7页
Journal of Harbin Engineering University
基金
国家自然科学基金项目(U2106225,52171251)
湖南省科技重大专项(2020GK1020)
大连市科技创新基金项目(2022JJ12GX036).
