【作者】 王建平；

【导师】 刘宏昭；

【作者基本信息】 西安理工大学 ， 机械设计及理论， 2002， 博士

【摘要】 随着现代机械工业的发展，高速轻量化设计在工程中已被广泛应用，随之而来的机构弹性振动，疲劳破坏时有发生。如何简单可靠地消除和抑制机械系统的有害振动，提高其精度和寿命是机械科学领域一个重要的理论和实践问题，因此考虑阻尼的弹性连杆机构建模理论与分析方法是目前一个需要迫切研究的领域。结晶器四偏心式振动机构是大型连铸机上广泛采用的一种振动装置，随着拉速的提高，其弹性振动效应非常明显，对其复杂弹性动力学性能进行深入研究是合理设计该系统的基础。本文的主要研究工作及结论如下： 从材料应力应变本构关系出发，导出了滞变阻尼模型、复阻尼模型、非线性阻尼模型、粘弹性阻尼模型下的有限单元分析模型，进而给出了含阻尼合金构件弹性连杆机构系统动力学模型。讨论了运用复阻尼理论时应遵循的对偶原则，分析了含复阻尼系统运动方程数值解的稳定性。针对阻尼合金夹层梁提出了一种2节点10自由度梁单元模型，给出了该单元运动微分方程。 导出了一类非线性振动系统的状态空间模型，在此模型中给出了非线性振动系统的隐式解析解，提出了相应的数值计算方法，并利用迭代法有效地提高了计算精度，最后将该数值方法推广应用到复刚度振动方程的数值求解计算中。和传统的非线性振动方程数值计算方法如Euler法、中心差分法、Houbolt法、Wilson-θ法和Newmark-β法等相比，本文方法具有更高的计算精度和效率。研究了所提 西安理工大学博士学位论文数值计算方法的误差、稳定性、收敛性等数学性质，在计算精度和计算效率两方面提出了一些改进措施，构造了零矩阵法、常数矩阵法、雅可比矩阵法等计算格式，给出了利川Pade逼近计算矩阵指数函数的求解步骤。 以铝基和锌基阻尼合金制成的试件为实验对象，测定了这两类阻尼合金的阻尼值。通过实验测试和数值拟合获得了阻尼合金的阻尼性能随应变的非线性变化规律。给出了二次曲线模型、反双曲线模型、指数模型、反指数模型、位错阻尼模型等阻尼模型并将按这些模型进行数值计算所得结果和实验结果进行了对比研究。以铰链四杆机构为研究对象，测试了铝基、锌基阻尼合金及阻尼合金夹层梁的阻尼减振效果，并与数值分析结果进行了对比研究，结果表明实验结果和数值计算结果基本吻合。在等刚度条件下对铝基、锌基阻尼合金和45＃钢阻尼减振作川进行了对比实验，实验结果表明摇杆为铝基和锌基阻尼合金材料时，连杆中点动态应变曲线幅值只有45＃钢时的一半左右，而且随着曲柄转速的提高，阻尼合金的减振效果更加明显。 建立了集儿何非线性和载荷非线性于一体的大型连铸机四偏心式多连杆振动系统运动弹性动力学分析力学与数学模型。考虑了碟形平衡弹簧非线性、导向板弹簧儿何非线性、导向板弹簧的阻尼、铸坯摩擦力，以及传动轴扭转刚度等多种冈素。给出了系统方程装配的位移协调关系式。对系统的动态【响应进行了仿真求解，给出了各个1‘义坐标方向的弹性位移、各铰接点的反力、系统各构件相关点的动应力。研究了弹性振动位移在频域内的特性，绘制了相应的幅频、相频、实频和虚频曲线，找出了系统的一阶固有频率。研究了结晶器中心点弹性位移与激振频率之间的关系曲线，指出该机构系统在运动过程中存在明显的分频共振现象，对影响系统分频共振的因素进行了研究，说明摩擦力激励是引起系统分频振动最主要的因素。以结晶器中心点径向位移为目标函数，就其随主要结构参数的变化规律进行了分析，对系统的现有状态提出了改进意见。h6制了具有良好用户界面的计算及仿真软件。 本研究得到国家自然科学基金（50075068）、陕西省自然科学基金（98C12）和内安理工人学优秀博十生研究基金的资助。更多还原

【Abstract】 With the development of modern mechanical industry, fatigue destruction and precision decrease due to elastic vibration occur much frequently because machine operation speeds became faster and faster and the parts of machines are designed lighter and lighter. How to reduce vibrations of the mechanism systems simply and reliably and how to improve precision and fatigue life time of the machine are important in theory and practice of mechanical engineering, so dynamic models and analysis methods of elastic mechanism systems considering damping effects are necessary. Oscillator mechanism with four-eccentric axes is widely used in modem continuous casting machine. With the increase of operation speeds of the machine, elastic vibrations of the machine parts became much obviously. In order to design the machine reasonably, the complex dynamic property of the system must be studied deeply. The main research works and conclusions of this thesis are listed as follows.The dynamic analysis model of elastic mechanism system with damping alloy parts is deduced based on the relationship between stress and strain of the material, also the analysis model under viscous damping model, complex damping model, nonlinear damping model and viscous-elastic damping model is put forward using the finite element method. Dual principle is discussed while complex constitutive theory is used. The numerical solution stability of differential equations with complex damping is analyzed. A beam element of 2 nodes and 10 degrees of freedom with interlayer damping alloy is presented and the element differential equation of motion is put forward.A state space model for parts of non-linear oscillation systems is put forward, and the concealed analytical solution for the systems is deduced. A numerical calculation method is presented and the calculation precision is improved greatly through using iterative method. Finally the presented numerical method is extended to solve differential equations with complex stiffness matrix. Compared with traditional numerical methods such as Houbolt Method, Wilson-0 Method, and Newmark-p Method,A Dissertation Submitted to Xi’an University of Technology for Degree of Doctor Philosophythe presented numerical method has higher calculation precision and efficiency. The astringency, error and stability of the numerical method are researched. Zero matrix method, constant matrix method, and Jacobian matrix method are constructed in order to improve numerical precision and efficiency. The steps for calculating matrix exponential function using Pade approach method are given out.The damping values of damping aluminum-alloy and zinc-alloy are measured. Nonlinear laws between damping value and strain of damping alloy are obtained by mean of experiment and numerical fitting. Base on the experimental data some damping models such as conic model, inverse hyperbola model, exponent model, inverse exponent model, dislocation-induced damping model are put forward, and the results between numerical calculations base on above models and experiments are studied contrastively. The vibration absorption effects of damping aluminum-alloys, zinc-alloys and damping alloy interlayer beam are tested through a four bar linkage mechanism and the test results are carried out a contrastive research with numerical analysis results, and it is found that response curves obtained by test are similar with those given out by numerical calculation. Contrastive tests of damping aluminum-alloys, zinc-alloys and 45# steel are carried out at the case of equal stiffness. The test results show that when the rocker bar is made of damping aluminum-alloys or damping zinc-alloys, the strain amplitude at the middle point of connecting bar is half of the one when the rocker bar is made of 45# steel.The mechanical and mathematical models for the kineto-elastodynamic analysis of a multiple linkage oscillator mechanism with four-eccentric axis used in continuous casting machine are presented, which consider both the geometrical non-linearity and lo更多还原