【作者】 李辉；

【导师】 谢进；

【作者基本信息】 西南交通大学 ， 机械设计及理论， 2023， 博士

【摘要】 机构中的混沌运动直接影响到机械性能。对于一般机构,混沌运动会使机构产生较大的冲击和振动,从而影响机械寿命,对于这种情况应设法抑制或减小混沌运动;而对于可以通过混沌运动提高机构效率的设备,则应激发或增强混沌运动。另外,机构中可能会同时存在多个非线性因素的耦合作用,这样的耦合作用也会对机构的混沌运动产生影响。对诸如此类混沌现象进行分析,则需要建立一种能够定量地表示混沌强度判定方法,用于衡量混沌运动作用的大小。鉴于目前还没有被广泛接受的、有效的混沌强度判定方法。本文开展了混沌强度判定方法的研究工作。混沌现象的主要特征是对初值的敏感性以及混沌轨道的遍历性。对应于这两个特征的常用定量分析指标分别是最大Lyapunov指数和均匀度。基于对Logistic映射,Duffing混沌振子和Lorenz系统等典型非线性动力系统的分析可知:最大Lyapunov指数无法涵盖混沌轨道的遍历性;均匀度无法确保系统的确是处于混沌状态。另外,Pearson相关系数表明:随着动力系统维数的增加,Lyapunov指数和均匀度的相关性减弱,由Logistic映射的强相关变为在Lorenz系统中弱相关。基于上述分析,提出将两个指标结合起来形成混沌强度判定方法。首先,在无外界因素扰动的条件下,以Lyapunov指数是否大于0,判断系统是否处于混沌运动状态;再根据系统运动相图的均匀度值确定混沌运动的强度。其主要难点是:当系统处于混沌运动时,随着系统参数的变化而变化的均匀度值为连续的随机变量,无明显的规律性。针对这个问题,本文首先将均匀度按照其值的大小分为五个混沌强度等级;再对系统进行动力分析、得到了均匀度的变化曲线之后,利用高斯核密度估计法和均匀度变化曲线的数据,确定出均匀度变化的概率密度曲线,进而确定出其分布函数;由分布函数确定出系统均匀度变化范围的混沌强度等级及对应各个等级的概率。以其中最高的混沌强度等级及其概率作为系统混沌运动强度的定量分析指标。围绕着混沌强度及其判定在机构动力学中的应用开展了系统性的研究工作。首先将混沌强度判定方法应用于平面闭链欠驱动五杆机构、含转动副间隙曲柄滑块机构,以及含转动副间隙平面闭链欠驱动五杆机构的混沌现象分析,重点研究了运动副间隙和欠驱动这两种非线性因素之间的耦合作用对机构混沌运动的影响;其次,研究了面向混沌控制的机构设计方法,即如何根据混沌强度的设计要求进行机构设计的问题。在机构运动的动力学分析方面,基于混沌强度的定量分析方法,本文得到的主要研究结论是:无论是机构的动力学参数,还是机构的运动几何参数,均会对机构运动的混沌强度产生影响,只是影响的程度有所不同;机构中含运动副间隙的大小及数量均对机构运动的混沌强度有明显的影响,一般情况下,运动副间隙值越大,其混沌强度也越高。但是,在相同的运动副间隙值的条件下,含有两个运动副间隙机构运动的混沌强度并非总是高于含有一个运动副间隙机构运动的混沌强度;同样,在欠驱动与运动副间隙两个非线性因素耦合作用下,并不存在运动副间隙值越大机构运动的混沌强度越高的规律,只是间隙值不为零的机构运动混沌强度一定大于间隙值为零的机构运动混沌强度。这表明:运动副间隙中的构件弹性变形及摩擦具有降低机构运动中混沌强度的作用。在含有运动副间隙的平面连杆机构动力分析中,采用了一种新的动力学建模方法。将含间隙转动副处理为一个两端为转动副的虚拟构件,虚拟构件的杆长为转动副中销、孔中心之间的距离,虚拟构件的转角为销、孔中心位置连线与坐标轴正向之间的夹角,并将虚拟杆长及转角作为系统的两个独立广义坐标,写入运动约束方程,再利用第一类拉格朗日方程建立系统的动力学方程。实验结果验证了该方法的准确性。在面向混沌控制的机构设计方法的研究中,将含转动副间隙的平面闭链欠驱动五杆机构的驱动转速、转动副间隙值及连杆长度作为设计变量,而将设计要求的Lyapunov指数、均匀度及滑块行程作为设计目标,采用多目标优化设计中的权函数方法建立优化模型,利用粒子群方法对优化模型进行求解。为了克服求解过程中需要大量的仿真计算而造成的耗时巨大、利用一般的计算机甚至不可能完成的问题,利用正交试验的方法建立一个数据库;在优化设计时,从数据库中搜索出与设计要求值相近的解及对应的设计变量值,进而确定出多目标优化设计中的权值,以及粒子群方法中的初始种群。采用这样的策略,避免了大量的仿真计算,大大减少了面向混沌控制机构设计的耗时。文中通过四个实现不同混沌强度的示例说明了这种面向混沌控制的机构设计方法和策略的有效性。更多还原

【Abstract】 Chaotic motion in a mechanism directly affects the performance of a machinery.For the general mechanism,it will cause undesired impact and vibration,furthermore reduce the life span of the machinery,then it should be suppressed or controlled.For some special application,however,it is beneficial to improve the performance of the mechanism,then it should be excited or enhanced.In addition,there is coupling of several nonlinear factors existing in the mechanism,and such coupling will also affect the chaotic motion of a mechanism.In all these circumstances,for the analysis and design of mechanism,it is necessary to establish a method to differ chaos intensity(MDCI),or in other word,to measure the effect of chaotic motion.However,there has not been widely accepted and effective MDCI until now.In order to fill this need,this paper focuses on establishment of MDCI.The main characteristics of chaos are sensitivity to the initial values and ergodicity of its orbit.For these two characteristics,the commonly used quantitative indexes are the maximum Lyapunov exponent and the uniformity respectively.Through analysis of several typical nonlinear dynamical systems,i.e.one-dimensional Logistic mapping,twodimensional Duffing chaotic oscillator and three-dimensional Lorenz system,it can be seen that the maximum Lyapunov exponent is unable to reveal the ergodicity of the chaotic orbit,and uniformity is unable to ensure the system actually in chaos.The result has shown that with the increase of the dimension of the dynamical system,the Pearson correlation coefficient between maximum Lyapunov exponent and uniformity changes from large into small,which means that correlation between these two indexes decrease.It is to say that the correlation between these two indexes changes from strong into weak as the dynamic system changes from Logistic mapping to Lorenz system.Based on the above observations,a MDCI is proposed by combining the two indexes.Firstly,under the circumstance that there on existence of any external disturbance,to determine whether the dynamic system is in chaos or not by the condition that if the maximum Lyapunov exponent is larger than zero;Then,to determine the chaos intensity by the uniformity obtained from the phase portrait of the dynamic system,in which the challenge is the value of uniformity is in the form of continuous random variable,and without any regularity when the dynamic system is in chaos.To meet this challenge,five chaos intensity levels is divided up according to the values of uniformity.While the varying curve of uniformity is yielded with the results of analysis,its probability density curve can be obtained by the Gaussian kernel density estimation method with the data on the varying curve of uniformity,further,the distribution function is determined.Together with chaos intensity levels,one can compute the probability for each intensity level.In this way,the highest chaos intensity level and its probability can be determined,which is used as chaos intensity of the dynamic system.The application of MDCI in mechanism dynamics is studied systematically in this paper.Firstly,it was applied to analyzing the chaos of the planar closed-chain underactuated five-bar mechanism,slider-crank mechanism with revolute clearance joints,and the planar closed-chain underactuated five-bar mechanism with a revolute clearance joint.The emphasis was place on the coupling effects of the two nonlinear factors,the revolute clearance joint and the underactuated mechanism,on the chaotic motion of the mechanism.After that,the control-chaos-oriented method of mechanism design was studied,i.e.to design the parameters of mechanism to meet the requirements on chaos intensity.In the dynamics analysis of mechanism,the main outcomes by MDCI are more convinced due to the its quantification.They are as followings: both the dynamic parameters and kinematic geometric parameters of mechanism can affect the chaos intensity of mechanism motion,but the influence extent is different;The value and the number of the clearance joint in the mechanism have obvious influence on the chaos intensity.In general,the larger the clearance value is,the higher the chaos intensity of the mechanism motion will be.However,with the same clearance value,the chaos intensity of the mechanism with two such revolute joints are not certainly higher than that with one such revolute joint.Similarly,under the coupling effect of two nonlinear factors,i.e.underactuated mechanism and clearance joint,it is not a general rule that a larger clearance value definitively results in higher chaos intensity of the mechanism motion.The conlusion can be drawn is that the chaos intensity of mechanism with unequal to zero clearance value is ceatainly higher than that of mechanism with equal to zero clearance value.It indicates that the elastic deformation and friction of mechanical elements in the revolute joints can reduce the chaos intensity of the mechanism motion.In the dynamic analysis of crank-slider mechanism with clearance,a new method to establish the dynamic model is proposed.In this method,the clearance joint is treated as virtual component,its length is the distance between the centers of the pin and the hold in the revolute joint,and the rotating angle of the virtual component is the angle between the virtual component and the positive direction of the coordinate axis.The length and rotating angle of the virtual component are involved in the kinematic constraints as two independent general coordinates,and are introduced into Lagrange equation of the first kind.Experimental results verify the accuracy of the method.In the control-chaos-oriented design of planar closed-chain underactuated five-bar mechanism with clearance joint,the driving angular velocity,the clearance value and the length of coupler are taken as the variables,and the desired maximum Lyapunov exponent,the uniformity and the stroke of the slider are taken as the objectives.And a multi-objective optimization is presented.To solving this optimization problem,the weight function method in the multi-objective optimization and particle swarm optimization method are employed.Whereas in the optimization,it needs lots of simulation of the dynamics for the mechanism,which is great time-consuming,and even cannot be implemented by means of a normal person computer.To break down this barrier,a database is established with orthogonal test method.Have searched out the solutions approaching to the optimization objectives from the database,one is able to determine the weights for multi-objective optimization model and the initial populations for the particle swarm optimization method.By this strategy,some of simulations are avoided,the time-consuming is reduced greatly.Four examples of mechanism design with different chaos intensity are presented to demonstrate efficiency of the method and strategy proposed in this paper.更多还原