【作者】 徐彦；

【导师】 刘杰； 孙光复；

【作者基本信息】 东北大学 ， 机械电子工程， 2008， 博士

【摘要】 大型、轻质和快速运行的机械部件的广泛应用促使柔性多体系统动力学得到了越来越多的关注,并为这一学科提供了广阔的发展空间。本文以柔性机械臂为研究对象,深入地研究了液压柔性机械臂动力学建模以及其相关的问题、柔性机械臂在标称运动附近振动的固有频率问题和对液压柔性机械臂末端位置的控制问题。论文的主要内容由以下四个方面组成：(1)与柔性机械臂建模相关的问题。主要分析了柔性机械臂结构的近似方法,这个问题是柔性机械臂建模的一个关键问题,完成的工作主要有：(a)个别文献对三维柔性机械臂质量矩阵公式表达不十分准确,本文基于三维有限元法推导了三维柔性机械臂的质量矩阵公式；(b)两节液压柔性机械臂臂架的约束条件较多,因此动力学边界问题较为复杂,不适合用假设模态法对柔性机械臂的结构进行近似处理。本文采用有限元法对柔性机械臂进行结构的近似,用单元节点的位移和转角表示柔性机械臂的弹性坐标,这种结构近似方法能够获得比较高的模型近似程度。还分析了基于密度函数法的带有末端质量的柔性机械臂建模方法,具体方法是将臂杆和末端质量视为一个整体,用狄拉克函数定义其密度。该方法的运用使柔性机械臂动力学模型的推导过程得到简化。(c)通过虚功原理求广义力也是用拉格朗日方程推导动力学模型的一个步骤,本文分析了拉杆内力对应的广义力的求解方法,在此基础上提出了弹性体广义内力的求解方法,即在弹性体所在的动坐标系下对广义内力进行求解。(2)液压柔性机械臂的建模问题。在对液压柔性机械臂建模的研究中,分别以CC2500起重机为例建立了单节柔性机械臂动力学模型和以两节液压柔性机械臂系统为研究对象,建立了机电液一体的完备动力学方程,并进行了柔性机械臂动力学行为的仿真研究。(3)柔性机械臂在非线性惯性场中随动坐标系大范围刚性转动的同时自身弹性振动的固有频率问题。柔性机械臂在随动坐标系作大范围刚性转动的同时,自身经历着弹性变形运动,而且这两种运动强烈耦合。刚柔耦合使得柔性机械臂在标称运动附近振动的固有频率问题的复杂性增大,固有频率不再是一个固定值,而是随着大范围刚性转动的角速度的变化而变化。在这个问题上学者们已经给出定性的结论,并为相关的后续研究提供了宝贵的经验,但是对固有频率产生变化的原因和对其进行定量计算的文献却比较鲜见。本文从固有频率发生变化的根本原因入手,以非线性位移场和动力刚化理论为基础,建立了柔性机械臂在标称运动附近振动的动力学模型,用复模态方法进行了模态分析。仿真结果显示,柔性机械臂在标称运动附近振动的固有频率随大范围刚性转动角速度的增大而增大,当转动角速度较高时,这种情况尤为明显。当转动角速度低时,固有频率接近于某个常数。(4)对单节和两节液压柔性机械臂末端位置控制的问题。在对单节液压柔性机械臂末端位置的控制方法研究中,以液压起重机为研究对象,采用模糊控制方法对起重机吊臂末端位置进行控制。由于模糊控制器语言变量控制规则能够使复杂系统解耦,因此模糊控制方法的运用使得对吊臂转角位移的轨迹跟踪控制和对吊臂的弹性振动控制可以各自独立地进行。参照有关文献的方法,本文同样将吊臂的转角系统称为慢变子系统,弹性振动系统称为快变子系统,通过对两个子系统的独立控制实现对吊臂末端位置的控制。由吊臂转角与吊臂末端标称位移的刚性几何关系确定吊臂转角期望值,首次将模糊PD控制运用到对大型起重机变幅过程吊臂转角位移的轨迹跟踪控制中；用模糊方法对吊臂的弹性振动加以控制。这方面的主要工作有：(a)分析了系统稳定性,并提出校正方案,确定了模糊PD控制器的参数初始值；(b)用模糊的非线性方法对模糊PD控制器两个参数的增量实现在线整定,对慢变子系统进行模糊PD控制；(c)用模糊控制法对吊臂弹性振动加以控制。在对两节液压柔性机械臂的末端位置控制的方法研究中,完成的工作有：(a)分别采用基本类型的模糊控制法和模糊PD控制法对上下两节臂关节转角进行位移的轨迹跟踪控制；(b)用上节臂末端在连续三个时刻的位移平均值与中间时刻的位移之差作为偏差,用模糊控制法消除上节臂的弹性振动,(c)通过对两节臂转角和弹性振动的控制实现对上节臂末端位置的控制。更多还原

【Abstract】 Theory of dynamics of flexible multibody system is now paid more attention to than before with the development of large,light-weight and high speed mechanics.Flexible arms are taken as an object in this paper.Theories about construction of dynamics model of the flexible arms,natural frequencies of the flexible arm vibrating about the nominal rigid rotation and control of the flexible arms are studied in this paper.There are four main topics:(1)The first topic is the research on the dynamic model of the arms. Approximation of the structure of the flexible arms is taken into consideration/which is one of the key points in modeling of the flexible system. Main tasks are as following (a)establishing mass matrix of the arm by three dimensional finite element method; (b) Infinite method is used to simulate the structure of the two-flexible links. Displacements and angles of the nodes are defined to be the elastic coordinates.This method can obtain a more accurate simulation of the flexible structure.Density of the beam with loads on the tip is expressed in density function,which is defined as the following:The expression of the function is simple and it cannot cause complex calculations when deducing the dynamic model of the beam; One of the steps to build models of flexible systems is expression of the generalized force, and always virtual energy theory is used to work it out,studies are also done on the method to calculate generalized force.(2) The second topic is developing dynamic models for the hydraulic flexible arms. A CC2500 crane is set as an object in this paper,model of this crane is developed and a whole model of the flexible two-links’ system which includes mechanical part,electric part and hydraulic part is also developed,simulation of the dynamics of the flexible two-links is done.(3)The third topic is the analysis of the natural frequencies of the arm’s elastic vibration in a nonlinear inertial frame.Flexible arm undergoes elastic vibration during it’s rigid rotation, and the two movements are coupled with each other, which makes the natural frequencies more complex, and it is no longer a constant, but a variable varying with the rotary speed of the arm. Based on nonlinear displacement frame and dynamic stiffening, vibrating model is established around the nominal movement. Complex modal analysis method is used in uncoupling the dynamic equation. The results turn out that the natural frequencies of the arm will increase when rotary speed of the arm increases, and it gets prominent if the rotary speed get higher. When rotary speed slows down especially when it is lower than the basic natural frequency of the arm which is obtained by means of structural mechanics, the frequencies turned to be a constant, and rigid flexible coupling can be ignored.(4)The forth topic is designing the controller for tracing the displacement of the tip of a flexible arm.This paper takes the hydraulic crane as an example. Linguistic variables of a Fuzzy controller has the decoupling function,so control of the angles and the control of the elastic vibration can be independent with each other.The angle subsystem is called slow subsystem and the elastic vibration system is called quick subsystem.In the slow subsystem, a fuzzy PD controller is designed for controlling the trajectory of the angle’s displacement.The expected angle of the arm joint is decided through the rigid geometry between the arm and angle of the joint.My work done in this aspects are as the followings,(a)Initial parameters of the Fuzzy PD controller are set according to Bode steady analysis;(b)the increments of the parameters are obtained through online fuzzy control.(c)In the quick subsystem,a fuzzy controller is designed to eliminate the elastic vibration of the arm.My work about controlling on the flexible two-links is:(a)fuzzy PD and basic Fuzzy method are used to control the angles of the arms’ moving trace.(b)Point error method are presented to be the error of the system, the tip’s trace of the upper arm is controlled by the above two independent controller. (c)Displacement of the tip is controlled through the control of the angles and the control on the elastic vibration.更多还原