为解决舰船在恶劣海况下产生的大幅度、多维度的不规则摇荡运动，提出了一种6-DOF并联平台隔离舰船运动的方案，并对该方案的动力学特性进行了深入研究。首先，基于矢量关系推导该平台构件在惯性坐标下的速度、Jacobi矩阵和能量方程式，由拉格朗日方程和虚功原理得到其在非惯性系下的显式动力学方程。其次，利用Adams搭建该平台的虚拟缩比模型，采用P-M波谱和RAO模拟复杂海况下舰船的摇荡运动，基于Simulink实现MATLAB与Adams联合仿真。最后，计算分析5级海况下的运动实例，理论结果与仿真结果的驱动力误差在0.11%内，验证了本文动力学模型的正确性，且计算结果表明，平台可分别补偿船舶95.7%、97.7%和87.9%的横、纵和艏摇运动，验证了所提方案的有效性。研究结果对非惯性系下舰载稳定平台的动力学控制具有指导意义。
Abstract
In order to solve the large magnitude and multi-dimensional irregular rocking motions generated by ships in bad sea conditions, a 6-DOF parallel platform is proposed to isolate the ship's motion, and the dynamics characteristics of the scheme are thoroughly investigated. Firstly, the velocity, Jacobi matrix, and energy equations of the platform member in inertial coordinates are derived based on vector relations, and its explicit dynamical equations in a non-inertial system are obtained from the Lagrange equation and the principle of virtual work. Secondly, Adams is used to build a virtual scaling model of the platform, and P-M wave spectrum and RAO are used to simulate the rocking motion of the ship under a complex sea state, and the co-simulation of MATLAB and Adams is realized based on Simulink. Finally, the motion examples under 5 levels of sea state are calculated and analyzed, and the driving force error between the theoretical results and the simulation results is within 0.11%, which verifies the correctness of the dynamics model in this paper, and the computational results show that the platform can compensate the ship's roll, pitch, and yaw rocking motions by 95.7%, 97.7%, and 87.9%, respectively, which verifies the validity of the proposed scheme. The research results are of guidance for the dynamics control of the Ship-borne stabilized platform in the non-inertial system.
关键词
非惯性系 /
拉格朗日动力学建模 /
虚功原理 /
显示动力学方程 /
联合仿真
{{custom_keyword}} /
Key words
non-inertial system /
Lagrangian dynamics modeling /
virtual work principle /
explicit dynamical equations /
co-simulation
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] STEWART D. A platform with six degree of freedom[J]. Proceedings of the Institute of Mechanical Engineering, 1965, 1965.
[2] 胡俊峰, 张宪民, 徐贵阳. 基于模型预测控制的高速柔性并联机构振动控制[J]. 振动与冲击, 2014, 33(1): 24-32. DOI:10.13465/j.cnki.jvs.2014.01.013.
HU Junfeng，ZHANG Xianmin，XU Guiyang. Vibration control of a high-speed flexible parallel mechanism based on model predictive control[J]. Journal of Vibration and Shock, 2014, 33(1): 24-32.
[3] 刘晓, 赵铁石, 李二伟, 等. 非惯性系折叠式并联稳定平台机构建模及分析[J]. 机械工程学报, 2013, 49(17): 101-109.
LIU Xiao，ZHAO Tieshi，LI Erwei, et al. Modeling and Analysis of Foldable Parallel Stabilized Platform in Non-inertial System[J]. Journal of Mechanical Engineering， 2013, 49(17): 101-109.
[4] 罗波, 李伟鹏, 黄海. 基于Stewart平台的大柔性空间桁架结构振动控制[J]. 振动与冲击, 2012, 31(23): 148-153. DOI:10.13465/j.cnki.jvs.2012.23.035.
LUO Bo LI Weipeng HUANG Hai . Vibration control of large flexible space truss using a Stewart platform manipulator. Journal of Vibration and Shock, 2012, 31(23): 148-153.
[5] DAI X, SONG S, XU W, et al. Modal space neural network compensation control for Gough-Stewart robot with uncertain load[J]. Neurocomputing, 2021, 449: 245-257. DOI:10.1016/j.neucom.2021.03.119.
[6] 陈子明, 刘晓檬, 张扬, 等. 对称两转一移3-UPU并联机构的动力学分析[J]. 机械工程学报, 2017, 53(21): 46-53.
CHEN Ziming, LIU Xiaomeng, ZHANG Yang, et al. Dynamics Analysis of a Symmetrical 2R1T 3-UPU Parallel Mechanism[J]. Journal of Mechanical Engineering, 2017, 53(21): 46-53.
[7] DASGUPTA B, MRUTHYUNJAYA T S. A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator[J]. Mechanism and Machine Theory, 1998, 33(8): 1135-1152. DOI:10.1016/S0094-114X(97)00118-3.
[8] LU Y, DAI Z. Dynamics model of redundant hybrid manipulators connected in series by three or more different parallel manipulators with linear active legs[J]. Mechanism and Machine Theory, 2016, 103: 222-235. DOI:10.1016/j.mechmachtheory.2016.05.003.
[9] CHEN G, YU W, LI Q, et al. Dynamic modeling and performance analysis of the 3-PRRU 1T2R parallel manipulator without parasitic motion[J]. Nonlinear Dynamics, 2017, 90(1): 339-353. DOI:10.1007/s11071-017-3665-0.
[10] QIU J, QIU W, NIU A, et al. Modeling and Analysis of Offshore Gangway under Dynamic Load[J]. Journal of Marine Science and Engineering, 2023, 11(1): 77. DOI:10.3390/jmse11010077.
[11] NIU A, WANG S, SUN Y, et al. Dynamic modeling and analysis of a novel offshore gangway with 3UPU/UP-RRP series-parallel hybrid structure[J]. Ocean Engineering, 2022, 266: 113122. DOI:10.1016/j.oceaneng.2022.113122.
[12] 刘晓, 赵铁石, 高佳伟. 非惯性系下舰载稳定平台动力学建模及特性分析[J]. 机器人, 2014, 36(4): 411-418. DOI:10.13973/j.cnki.robot.2014.0411.
LIU Xiao，ZHAO Tieshi，GAO Jiawei. Dynamic Modeling and Analysis of Ship-based Stabilizing Platform in Non-inertial System[J]. Robot, 2014, 36(4): 411-418.
[13] 王力航, 郭菲, 卢文娟, 等. 3UPS/S舰船稳定平台非惯性系动力学建模[J]. 机械工程学报, 2020, 56(1): 20-29.
WANG Lihang, GUO Fei, LU Wenjuan, LI Yongquan, et al. Non-inertial System Dynamic Modeling of 3UPS/S Ship Stability Platform[J]. Journal of Mechanical Engineering, 2020, 56(1): 20-29.
[14] 沈庆, 陈徐均. 系泊多浮体系统流固耦合和浮体间耦合动力分析[J]. 中国造船, 2002(2): 83-86.
SHEN Qing，CHEN Xujun. Dynamic Analysis of a Mooring Multi-body System coupled with Fluid and among Bodies[J]. Shipbuilding of China, 2002(2): 83-86.
[15] 林富生, 黄其柏, 黄新乐, 等. 非惯性系动力学研究综述[J]. 武汉理工大学学报(信息与管理工程版), 2007(4): 67-71.
Lin F S, Huang Q B, Huang X L, et al. A survey of the dynamic investigation in non-inertial systems[J]. Journal of Wuhan University of Technology: Information & Management Engineering, 2007, 29(4): 67-71.
[16] 丁勤卫, 郝文星, 李春, 等. 漂浮式风力机结构动力学响应TMD控制及其参数优化研究[J]. 振动与冲击, 2018, 37(23): 61-70. DOI:10.13465/j.cnki.jvs.2018.23.009.
DING Qinwei, HAO Wenxing, LI Chun, YE Kehua, WANG Yuanbo. TMD Control and its parametric optimization for structural dynamic response of a floating wind turbine. Journal of Vibration and Shock, 2018, 37(23): 61-70.
[17] 邱建超, 陈海泉, 仇伟晗, 等. 船载串并混联海上稳定廊桥动力学建模与分析[J]. 中国造船, 2023, 64(1): 146-160.
QIU Jianchao, CHEN Haiquan, QIU Weihan, et al. Dynamic Modeling and Analysis of Shipborne Series-parallel Hybird Offshore Gangway[J]. Shipbuilding of China, 2023, 64(1): 146-160.
[18] 谢强, 党维. 舰载直升机着舰飞行特性评估方法研究[J]. 工程与试验, 2019, 59(1): 38–41.
Xie Qiang，Dang Wei. Study on Assessment Method for Flight Characteristics of Shipboard Helicopter[J].Engineering & Test, 2019, 59(1): 38–41.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(2624 KB)
