【作者】 魏永祥；

【导师】 陈建军；

【作者基本信息】 西安电子科技大学 ， 机械制造及其自动化， 2011， 博士

【摘要】 本学位论文以随机或区间参数机构为研究对象,探索性地研究了当构件参数和外载荷为区间变量或随机变量时弹性机构的动力特性分析方法,动力响应分析和动力可靠性方法。主要内容如下：1、随机参数齿轮-转子系统扭转振动的动力特性分析和区间参数平面弹性连杆的动力特性分析应用拓广的随机因子法分析了物理参数和几何参数均为随机变量的齿轮-转子系统的时变固有频率。将系统的刚度矩阵和质量矩阵分解为具有相同随机因子的矩阵之和的形式,再由求解系统固有频率的瑞利商公式出发,将系统频率展成部分频率分量之和的形式,利用求解随机函数数字特征的代数综合法求解系统固有频率的数字特征。通过算例分析了随机参数对系统固有频率的影响,并验证了方法的可行、有效和正确性。应用区间因子法分析了具有区间参数弹性连杆机构的固有频率。将系统的刚度矩阵和质量矩阵分解为具有相同区间因子的矩阵之和的形式,然后利用区间因子法将区间变量表示为其区间因子和确定性量的乘积,再由求解系统固有频率的瑞利商公式出发,应用区间算法,推导出了系统固有频率上、下限与均值的计算表达式。通过算例,分析了机构物理参数和几何尺寸的不确定性对机构固有频率的影响。2、随机参数时变齿轮副的动力响应分析和随机参数齿轮-转子系统的扭转振动分析研究基于概率的齿轮副动力响应问题。考虑齿轮副的物理参数、几何参数和作用荷载幅值同时具有随机性和齿轮时变刚度时,从Duhamel积分关系式出发利用随机因子法导出齿轮副动力响应的数字特征计算表达式。通过算例考察齿轮副的物理参数、几何参数和作用荷载幅值的随机性对其动力响应的影响,研究结果表明：几何参数的随机性对系统位移响应的随机性影响较大,系统的时变刚度对系统响应有冲击作用。建立了考虑物理参数和几何参数均为随机变量的齿轮-转子扭转振动系统在随机荷载激励下的动力学方程。利用Newmark-β逐步积分法将此随机参数时变刚度系统的动力学方程转换为拟静力学控制方程。利用求解随机变量函数数字特征的矩法,导出了系统动态位移反应的均值和方差计算公式。通过算例得出了：系统的时变刚度对系统响应有冲击作用,系统的物理参数、几何参数和外荷载幅值的随机性对系统动力响应的影响不可忽略,其中几何参数的随机性对系统位移响应的随机性影响较大。3、随机参数齿轮系统的非线性动力响应分析和基于可靠性的随机参数齿轮-转子系统的动态优化建立了物理参数和几何参数均为随机变量,并考虑具有齿轮侧隙、轴承间隙、时变刚度、齿间摩擦力和静态传递误差的齿轮-转子系统非线性振动的动力学方程。利用Newmark-β逐步积分法将此随机参数时变刚度系统的非线性动力学方程转换为随机参数的拟静力学控制方程,然后利用求解随机变量函数数字特征的代数综合法和矩法,导出了系统动态位移响应的均值和均方差计算公式。分析了系统中的诸随机参数、间隙和摩擦系数对系统非线性动力响应的影响,并获得了一些有意义的结论。在考虑系统物理参数、几何参数和作用载荷同时具有随机性时,建立了以齿轮-转子系统的各参数为设计变量,以振动加速度的均方根值最小为目标函数,同时具有齿间振动应力、轴扭矩可靠性约束和齿轮静态约束的优化设计模型,并将其中的可靠性概率约束等价转换为对应的数字特征约束,利用遗传算法进行优化。算例表明：系统中参数的随机性对优化的结果影响不可忽视。4、随机参数刚弹耦合平面连杆的动力分析和区间参数平面连杆机构的动力分析建立了考虑物理参数、几何参数及荷载均为不确定变量的平面连杆机构的动力学方程,在建模中计入了刚弹耦合项和运动副的粘性摩擦。利用Newmark-β逐步积分法将此不确定参数机构系统的动力学方程转换为随机参数的拟静力控制方程。利用求解随机变量函数数字特征的矩法和代数综合法或区间算法,导出了机构动态弹性位移的均值和方差计算公式或区间上下限。通过算例考察了机构的杆长、截面半径、质量密度、弹性模量的不确定性,以及刚弹耦合项和运动副摩擦对机构动力响应的影响。5、随机参数机构的动力可靠性分析将一对啮合齿轮等效为单自由度随机振动系统,研究随机参数齿轮副在平稳随机激励下的动力可靠度的求解方法。从其平稳随机响应的表达式出发,同时考虑齿轮物理参数、几何尺寸的随机性,利用求解随机变量数字特征的矩法和代数综合法,导出随机参数齿轮副在平稳随机激励下位移及其导数响应的数字特征,再由动力可靠度的公式导出随机参数齿轮副动力可靠度的均值和方差的计算公式。通过与Monte Carlo方法结果的比较,验证文中方法的可行性和有效性。研究了随机参数弹性连杆机构在平稳随机激励下的动力响应分析。首先利用拓广的随机因子法,从求解系统固有频率的瑞利商公式出发,得出了物理参数和几何参数均为随机变量的弹性连杆的时变固有频率的均值和方差。然后再从动力平稳随机响应在频域上的表达式出发,利用求解随机变量函数的矩法和数字特征的代数综合法,计算出了随机参数弹性连杆机构在平稳随机激励下弹性位移和速度的均方值的均值、方差的表达式。再由动力可靠度的公式导出了其动力可靠度的均值和方差的计算公式。通过算例,分析了机构物理参数和几何尺寸的随机性对机构动力可靠度随机性的影响。更多还原

【Abstract】 Mechanisms with random parameters or interval parameters is considered in this paper. The system dynamic characteristic, dynamic response and dynamic reliability are investigated in the scenario that physical parameters of system, geometric dimensions of components and applied loads are all random or interval variables. The main research works can be described as follows:1. Dynamic characteristic analysis for torsional vibration of a gear-rotor system with random parameters and dynamic characteristics analysis of elastic linkage mechanism with interval parameters.Firstly, based on the generalized random factor method, the time-variable natural frequencies were analyzed for the torsional vibration of a gear-rotor system with random physical and geometrical parameters. The stiffness and mass. matrices of the system were discomposed into a sum of matrices with same random factors, respectively. Based on the Rayleigh quotient formula, the natural frequencies of this system were represented as a sum of partial ones. And then the mathematic characteristics expressions of the natural frequencies were obtained by utilizing the algebra synthesis method for solving a random function. Finally, numerical examples showed that the influence of the randomness of the physical and geometrical parameters on the natural frequencies, and verified the feasibility of the proposed method. Secondly, based on the interval factor method, the analysis of system dynamic characteristic for interval elastic linkage mechanism is presented. The stiff and mass matrices of the system are discomposed into a sum of matrices with same interval factors, respectively. By using interval factor method, all of the interval parameters can be expressed as the products of two parts corresponding to the interval factors and deterministic value. Based on the Rayleigh’s quotient formula, the computational expressions for the lower, upper bonds and mean value of system dynamic characteristic are developed using the interval operations. The effects of the uncertainty of the bar length and radius, mass density, and elastic modulus on mechanism dynamic characteristic are studied through an example.2. Dynamic response of gear with random parameters and torsional vibration of Gear-Rotor with random parametersFirstly, the dynamic response of gear based on probability is investigated. Considering the randomness of the system physical parameters, and the geometric dimensions parameters, as well as the randomness of the amplitude peak of applied load and the time-varying stiffness of gear pairs, the numerical characteristics of the system dynamic response are formulated from the dynamic expression of Duhamel integral by the random factor method. The influences of the randomness of physical parameters and geometric dimensions parameters on the randomness of the mean square value of system displacement are inspected and some significant conclusions are obtained as follows:the randomness of geometric parameters have greater effected on displacement response of system and the time-varying stiffness of system have impacted on the response of system through the example. Secondly, the vibration equations of torsional vibration of Gear-Rotor with random physical parameters and geometrical parameters under random excitation were established. Dynamic equations with random parameters and time-varying stiffness were reformulated as static governing equations by using the Newmark-βstep-by-step integration method. Considering system parameters and force as inhomogeneous random parameters, the mean value and the variance of dynamic displacement response were calculated by moment method for solving the characteristic of a function with random variable. It can be shown from the numerical examples that the time-varying stiffness of system have impacted on the response of system, the influences of the randomness of physical parameters, geometrical parameters and the amplitude of loads on system dynamic response can not be ignored, and the randomness of geometric parameters have greater effected on displacement response of system.3. Nonlinear dynamic analysis of response of gear-rotor with random parameters and dynamic response optimization for gear-rotor with random parameters based on reliability.Firstly, the nonlinear dynamical model of gear-rotor is established, where the random physical and geometrical parameters, the backlash, the time-varying stiffness, and the friction between teeth and the static transmission error are all included. Nonlinear dynamic equations are transformed into static governing equations by exploiting the Newmark-βstep-by-step integration method. The mean value and the variance of dynamic displacement response are calculated by algebra synthesis method and moment method for obtaining the numerical characteristics of a function with random variables. The influences of the randomness of physical parameters, geometrical parameters, the backlash and the friction coefficient on system dynamic response are studied through an example and some useful conclusions are obtained. Secondly, the randomness of the physical parameters, geometrical parameters and the stochastic loads applied Gear-Rotor with random parameters is considered. In this case, the various parameters of the system are regarded as the design variables, the root of stochastic vibration acceleration minimum is considered as the objective function with the reliability constraints of dynamic stress between teeth of gear and bearing torque and gear static constraint. Genetic algorithm is applied, where constraints based on reliability probability are converted to equivalent constraints based on corresponding numerical characteristics. Example shows that the randomness of the parameters of system can not be neglected.4. Dynamic response of rigid-elastic coupling linkage mechanism with uncertain parameters.The vibration equations of rigid-elastic coupling linkage mechanism with random or interval physical and geometrical parameters are established by incorporating random or interval excitation into the equations. Dynamic equations with random or interval parameters are transformed into static governing equations by the Newmark-βstep-by-step integration method. The mean value and variance or the upper and lower limit of dynamic displacement response are calculated by algebra synthesis method.and moment method or interval algorithm. The influences of the uncertainty of the bar length and radius, mass density, and elastic modulus on mechanism dynamic response are studied through an example and some useful conclusions are obtained.5. Dynamic reliability analysis of gear with stochastic parameters under stationary random excitation and dynamic reliability analysis of elastic linkage mechanism with stochastic parameters under stationary random excitation.Firstly, a method for calculating dynamic reliability of gear with stochastic parameters stationary random excitation is proposed under the condition of single degree random vibration. Considering the randomness of the structural physical parameters and the geometric dimensions parameters, the mean value and the variance of the mean square value of the structural displacement and stationary random excitation are computed firstly from the expressions of system stationary response in frequency domain by utilizing the random variable’s functional moment method and the algebra synthesis method. And then the expressions of the mean value and the variance of stochastic gear dynamic reliability are deduced from the Poisson formula for calculating dynamic reliability. Finally, the influence of the randomness of system physical and geometric dimensions parameters on the system dynamic reliability is analyzed through comparing with the Monte Carlo method, validating the feasibility of this method. Secondly, the stationary random vibration analysis of elastic linkage mechanism with random with random parameters was investigated. Firstly, based on the Rayleigh quotient formula, the expressions of the mean value and the variance of the time-variable natural frequencies of elastic linkage mechanism with random physical and geometrical parameters were formulated by using the generalized random factor method. From the expression of dynamic stationary random response of the frequency domain, the computational expressions of the mean value, variance and variation coefficient of the mean square value of elastic displacement and velocity responses under the stationary random excitation were developed by means of the random variable’s functional moment method and the algebra synthesis method. And then the expressions of the mean value and the variance of system dynamic reliability are deduced from the Poisson formula of calculating dynamic reliability. Finally, the influence of the random of mechanism physical and geometric dimensions parameters on the system dynamic reliability is analyzed through the examples, validating the feasibility of this method.更多还原