轴向移动绳振动能量计算及非线性动力学实验研究

发布时间：2018-04-25 05:05

本文选题：轴向移动绳 + 横向振动能量　；参考：《合肥工业大学》2017年硕士论文

【摘要】：轴向移动绳系统是机械传动重要形式之一,具有运行效率高、运动路线布置灵活的优点。然而移动绳系统弯曲刚度小,表现柔性结构特征,系统在受到外界激励时很容易产生横向振动,严重影响系统的平稳性和精确性,限制了移动绳系统的应用。因此,研究轴向移动绳系统横向振动特性是对其有效控制的前提。本文主要研究了轴向移动绳系统横向振动能量的计算分析以及非线性动力学。本文以轴向移动绳系统为研究对象,首先对轴向移动绳系统进行了简化,建立了移动绳自由振动的力学模型。基于有限元法将空间上的绳长离散为长度相同的有限单元,实现移动绳横向振动问题转化为有限单元的横向振动问题。其次,对定长度轴向移动绳横向振动能量表达式适当化简,得到了移动绳横向振动能量的一般表达式,从理论上和数值仿真上证明了定长度轴向移动绳横向振动能量呈周期性变化的规律。接着,基于工程应用实例,建立了具有Kelvin模型的粘弹性轴向移动绳系统横向非线性振动方程,应用Galerkin离散法和改进的四阶Runge-Kutta法得到非线性方程的数值解。分别研究了粘弹性移动绳横向非线性振动以及系统出现的非线性动力学现象。最后,从实验角度研究轴向运动带的横向振动,证明了轴向运动带系统存在丰富的周期运动、倍周期运动、混沌运动和拍频现象,为轴向运动带横向非线性振动理论研究提供实验参考依据。
[Abstract]:The axial moving rope system is one of the important forms of mechanical transmission, which has the advantages of high running efficiency and flexible movement route arrangement. However, the bending stiffness of the mobile rope system is small, which shows the characteristics of flexible structure. It is easy to produce lateral vibration when the system is subjected to external excitation, which seriously affects the stability and accuracy of the system, which limits the application of the mobile rope system. Therefore, the study of lateral vibration characteristics of axial moving rope system is the premise of its effective control. In this paper, the calculation and analysis of transverse vibration energy and nonlinear dynamics of the axial moving rope system are studied. In this paper, the axial moving rope system is taken as the research object. Firstly, the axial moving rope system is simplified, and the mechanical model of the free vibration of the moving rope is established. Based on the finite element method, the length of the rope in space is discretized into a finite element of the same length, and the lateral vibration problem of the moving rope is transformed into the transverse vibration problem of the finite element. Secondly, the general expression of lateral vibration energy of moving rope is obtained by properly simplifying the expression of lateral vibration energy of moving rope with fixed length. It is proved theoretically and numerically that the lateral vibration energy of the fixed length axial moving rope varies periodically. Then, based on an engineering application example, the transverse nonlinear vibration equation of viscoelastic axial moving rope system with Kelvin model is established. The numerical solution of the nonlinear equation is obtained by using the Galerkin discrete method and the improved fourth-order Runge-Kutta method. The transverse nonlinear vibration of viscoelastic moving rope and the nonlinear dynamic phenomena of the system are studied respectively. Finally, the transverse vibration of the axial motion band is studied from the experimental point of view. It is proved that there are abundant periodic motion, periodic motion, chaotic motion and beat frequency phenomena in the axial motion band system. The experimental reference is provided for the theoretical study of lateral nonlinear vibration of axial moving band.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH132

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