三相驱动下非光滑振动驱动系统的动力学分析

朱诗慧; 周震; 吕敬; 王琪

doi:10.6052/0459-1879-20-177

三相驱动下非光滑振动驱动系统的动力学分析

doi: 10.6052/0459-1879-20-177

北京航空航天大学航空科学与工程学院, 北京 100083

基金项目: 1) 国家自然科学基金项目(11772021);国家自然科学基金项目(11972055)

详细信息

作者简介:
2) 吕敬, 副教授, 主要研究方向: 动力学与控制. E-mail: lvjing@buaa.edu.cn

通讯作者:
吕敬

中图分类号: O313
计量
- 文章访问数: 1084
- HTML全文浏览量: 240
- PDF下载量: 71
- 被引次数: 0
出版历程
- 收稿日期: 2020-05-30
- 刊出日期: 2020-12-10

KINETICS ANALYSIS OF NON-SMOOTH VIBRATION-DRIVEN SYSTEM WITH THREE-PHASE CONTROL

School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China

摘要

摘要: 可移动式机器人已成为机器人研究领域的重要分支,为实现其在狭小特殊环境中的运动, 学者们提出并研究了振动驱动移动系统.本文基于二维LuGre摩擦模型和拉格朗日方程,给出了一类振动驱动系统在各向同性摩擦环境中的动力学建模方法和数值算法.这类振动驱动系统结构简单且密封性好,依靠箱体与地面间的摩擦力实现自身的定向运动.该系统由一个外部箱体和两个内部质量块构成,两个质量块在箱体内的两个平行轨道上作三相振动驱动,箱体通过三个刚性支撑足与地面保持接触. 二维LuGre摩擦模型的利用,可有效避免库伦摩擦模型的不连续性给动力学方程的数值求解带来的困难,且可有效揭示该系统在运动过程中的黏滞-滑移切换现象. 数值仿真结果表明,通过调整其内部质量块的驱动参数,可实现箱体的直线平移、定轴转动和平面一般运动,且箱体在移动和转动过程中会出现擦滑、穿滑、回滑和不黏等4种现象; 另外,通过调节驱动参数, 不仅可以改变箱体移动和转动的快慢,还可以改变箱体形心运动轨迹的曲率半径.
- 振动驱动系统 /
- 三相驱动 /
- 黏滞-滑移 /
- LuGre摩擦模型
Abstract: Mobile robot has become an important branch in the domain of robotics. In order to achieve its movement in some narrow and special environments, the vibration-driven system has been proposed and researched by domestic and foreign scholars. In this paper, such a vibration-driven system consisting of an external rigid box and two internal mass blocks which are driven by three-phase control on two parallel orbits is researched. And the box is always in contact with the rough ground via three rigid support elements. This kind of vibration-driven system has simple structure, good sealing performance, and relies on the friction force between the box and the rough ground to realize its directional movement. Based on the two-dimensional LuGre friction model and Lagrange equations of the second kind, the dynamic modeling method and numerical algorithm of the vibration-driven system are presented in an isotropic friction environment. The use of the two-dimensional LuGre friction model can effectively avoid the difficulty of solving the dynamic equations caused by the discontinuity of the Coulomb friction model, and can accurately reveal the stick-slip switching phenomenon during the movement of vibration-driven systems. The numerical simulation results show that the driving parameters of the internal mass blocks can be adjusted to realize rectilinear translation, rotation about a fixed-axis and general plane motion of the rigid box. And four types of stick-slip motion with different sliding regions can occur during the translation and rotation of the rigid box, such as grazing sliding, crossing sliding, switching sliding and no stick. In addition, the translational speed and rotational speed of the box body and the radius of curvature of the box centroid trajectory can be changed by adjusting the driving parameters.
- vibration-driven system /
- three-phase control /
- stick-slip /
- LuGre friction model

HTML全文

参考文献(1)

[1]	朱磊磊, 陈军. 轮式移动机器人研究综述. 机床与液压, 2009,37(8):242-247
[1]	( Zhu Leilei, Chen Jun. A review of wheeled mobile robots. Machine Tool & Hydraulics, 2009,37(8):242-247 (in Chinese))
[2]	王鹏飞, 孙立宁, 黄博. 地面移动机器人系统的研究现状与关键技术. 机械设计, 2006,23(7):1-4
[2]	( Wang Pengfei, Sun Lining, Huang Bo. Present situation and key technology of ground mobile robot system. Journal of Machine Design, 2006,23(7):1-4 (in Chinese))
[3]	Chernous'ko FL. Analysis and optimization of the motion of a body controlled by means of a movable internal mass. Journal of Applied Mathematics & Mechanics, 2006,70(6):819-842
[4]	Chernous'ko FL. The optimum rectilinear motion of a two-mass system. Journal of Applied Mathematics & Mechanics, 2002,66(1):1-7
[5]	Sergey J, Vyacheslav D, Andrey Y, et al. Modelling of robot's motion by use of vibration of internal masses// The Second European Conference on Mechanism Science. Cassino, Italy, September 17-20, 2008: 263-270
[6]	Chernous'ko FL. Dynamics of a body controlled by internal motions// Iutam Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty, 2007: 227-236
[7]	Chernous'ko LF. On the optimal motion of a body with an internal mass in a resistive medium. Journal of Vibration & Control, 2008,14(2):197-208
[8]	Li H, Furuta K, Chernousko FL. A pendulum-driven cart via internal force and static friction// Physics & Control, International Conference, IEEE, 2005: 15-17
[9]	Sobolev NA, Sorokin KS. Experimental investigation of a model of a vibration-driven robot with rotating masses. Journal of Computer and Systems ences International, 2007,46(5):826-835
[10]	Fang HB, Xu J. Dynamics of a mobile system with an internal acceleration-controlled mass in a resistive medium. Journal of Sound & Vibration, 2011,330(16):4002-4018
[11]	Fang BH, Xu J. Dynamic analysis and optimization of a three-phase control mode of a mobile system with an internal mass. Journal of Vibration & Control, 2010,16(1):19-26
[12]	Xu J, Fang H. Stick-slip effect in a vibration-driven system with dry friction: Sliding bifurcations and optimization. Journal of Applied Mechanics, 2014,81(5):1-10 (051001)
[13]	Du Z, Fang H, Zhan X, et al. Experiments on vibration-driven stick-slip locomotion: A sliding bifurcation perspective. Mechanical Systems & Signal Processing, 2018,105(15):261-275
[14]	陈祺, 占雄, 徐鉴. 振动驱动移动机器人直线运动的滑移分岔. 力学学报, 2016,48(4):792-803
[14]	( Chen Qi, Zhan Xiong, Xu Jian. Sliding bifurcations of rectilinear motion of a three-phase vibration-driven system subject to Coulomb dry friction. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(4):792-803 (in Chinese))
[15]	Qi C, Jian X, Xiong Z. A three-phase vibration-driven system's locomotion on an isotropic rough surface// 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE, 2015: 2193-2198
[16]	Volkova LY, Yatsun SF. Simulation of the plane controlled motion of a three-mass vibration system. Journal of Computer & Systems Sciences International, 2012,51(6):859-878
[17]	殷蓬勃, 占雄, 徐鉴. 三相驱动下含两质量块刚体的平面运动. 固体力学学报, 2016,37(5):421-437
[17]	( Yin Pengbo, Zhan Xiong, Xu Jian. Planar locomotion of a rigid body driven by the three-phase motion of two internal masses. Chinese Journal of Solid Mechanics, 2016,37(5):421-437 (in Chinese))
[18]	Zhan X, Xu J. Locomotion analysis of a vibration-driven system with three acceleration-controlled internal masses. Advances in Mechanical Engineering, 2015,7(3):1-12
[19]	Xiong Z, Jian X, Fang H. Planar locomotion of a vibration-driven system with two internal masses. Applied Mathematical Modelling, 2016,40(2):871-885
[20]	张敏, 徐鉴. 振动驱动移动系统平面避障运动分析. 力学学报, 2017,49(2):397-409
[20]	( Zhang Min, Xu Jian. Analysis on planar obstacle avoidance locomotion of vibration-driven system. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(2):397-409 (in Chinese))
[21]	Bolotnik NN, Zeidis IM, Zimmermann K, et al. Dynamics of controlled motion of vibration-driven systems. Journal of Computer and Systems ences International, 2006,45(5):831-840
[22]	Bernardo MD, Kowalczyk P, Nordmark A. Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dry friction oscillators. International Journal of Bifurcation & Chaos, 2003,13(10):2935-2948
[23]	Kowalczyk P, Piiroinen PT. Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator. Physica D-nonlinear Phenomena, 2008,237(8):1053-1073
[24]	刘丽兰, 刘宏昭, 吴子英等. 机械系统中摩擦模型的研究进展. 力学进展, 2008,38(2):201-213
[24]	( Liu Lilan, Liu Hongzhao, Wu Ziying, et al. An overview of friction models in mechanical systems. Advances in Mechanics, 2008,38(2):201-213 (in Chinese))
[25]	Marques F, Flores P, Pimenta Claro JC, et al. A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dynamics, 2016,86(3):1407-1443
[26]	王晓军, 吕敬, 王琪. 含摩擦滑移铰平面多刚体系统动力学的数值算法. 力学学报, 2019,51(1):209-217
[26]	( Wang Xiaojun, Lü Jing, Wang Qi. A numeraical method for dynamics of planar multi-rigid-body system with frictional translational joints based on LuGre friction model. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):209-217 (in Chinese))
[27]	邢航, 郑旭东, 王琪. 基于LuGre模型非光滑柱铰链平面多体系统动力学的建模和数值方法. 动力学与控制学报, 2019,17(5):413-418
[27]	( Xing Hang, Zheng Xudong, Wang Qi. Modeling and simulation of planar multibody systems with frictional revolute joints based on LuGre friction model. Journal of Dynamics and Control, 2019,17(5):413-418 (in Chinese))
[28]	Pennestrì E, Rossi V, Salvini P, et al. Review and comparison of dry friction force models. Nonlinear Dynamics, 2016,83(4):1785-1801
[29]	Johanastrom K, Canudas-De-Wit C. Revisiting the LuGre friction model. Control Systems IEEE 2009,28(6):101-114
[30]	郑鹏, 王琪, 吕敬等. 摩擦与滚阻对被动行走器步态影响的研究. 力学学报, 2020,52(1):162-170
[30]	( Zheng Peng, Wang Qi, Lü Jing, et al. Study on the influence of friction and rolling resistance on the gait of passive dynamic walker. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(1):162-170 (in Chinese))
[31]	Xiao T, Guoping C, Dongyang S, et al. Dynamic analysis of planar mechanical systems with clearance joint based on LuGre friction model. Journal of Computational & Nonlinear Dynamics, 2018, 13(6): 1-9 (061003)
[32]	Nikoli? M, Borovac B, Rakovi? M. Dynamic balance preservation and prevention of sliding for humanoid robots in the presence of multiple spatial contacts. Multibody System Dynamics, 2018,42(2):197-218
[33]	曲子芳, 张正娣, 彭淼等. 双频激励下Filippov系统的非光滑簇发振荡机理. 力学学报, 2018,50(5):1145-1155
[33]	( Qu Zifang, Zhang Zhengdi, Peng Miao, et al. non-smooth bursting oscillation mechanisms in a filippov-type system with multiple periodic excitations. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(5):1145-1155 (in Chinese))