不确定结构动力分析及星载天线展开机构可靠性研究
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摘要
本学位论文首先以区间和区间随机结构为研究对象,探索性地研究了当结构参数和外载荷为区间变量或区间随机变量时结构的动力特性分析和动力响应分析;然后以在研的国家863高技术研究发展计划项目《大型星载可展开天线结构系统多状态全过程的可靠性综合分析研究》为工程背景,分别基于区间、模糊和灰色理论,针对小样本、贫信息事件,对星载天线展开机构系统的可靠性进行了计算、预测、分配和分析。主要内容如下:
1、区间参数桁架结构的动力特性和动力响应分析方法研究。
在考虑结构单元的物理参数、几何尺寸和载荷幅值具有不确定性时,利用区间因子法建立了结构的刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构特征值不确定变量的计算表达式;从结构响应的Duhamel积分式出发,利用区间因子法、区间运算和振型叠加法导出结构动力响应区间变量的表达式。通过算例分析区间桁架结构参数的区间分散性对其动力特性和动力响应的影响。
2、区间随机参数桁架结构的动力特性和动力响应分析方法研究。
当结构的物理参数和几何尺寸同时具有区间随机性时,利用区间因子法和随机因子法建立了结构的刚度矩阵和质量矩阵;由结构振动的Rayleigh商表达式,利用区间运算推导了结构动力特性区间随机变量的计算式;进而利用随机变量的矩法和代数综合法,推导出了结构特征值的数字特征的计算式。然后从Duhamel积分式出发,利用振型叠加法求出了结构动力响应区间随机变量的表达式;最后再由随机函数的矩法推导出结构区间随机动力响应的区间数字特征。从而分析区间随机桁架结构物理参数和几何参数的区间随机分散性对其动力特性和动力响应的影响。
3、星载天线展开机构可靠性指标的计算方法研究。
首先在周边桁架式星载天线展开机构运动机理分析的基础上,建立了展开机构的力学分析模型,并推导了桁架杆内力的计算式。从桁架展开要满足的功能函数出发,给出机构运动可靠性的分析模型。综合考虑尺寸误差和太空环境因素的影响,将运动功能函数视为区间变量函数,利用非概率方法导出可靠性计算公式,对机构在整个展开过程中的运动可靠性进行预测和仿真;然后对展开机构中的齿轮运动副的卡滞失效形式进行了研究,从齿轮啮合的极限位置出发,推导出了同步齿轮副不发生卡滞的条件。在综合考虑齿轮加工误差、装配误差和太空环境温度等因素的基础上,利用优化算法,构建了齿轮副防卡滞的非概率可靠度计算公式。最后,对同步齿轮副在不同装配误差和不同温度环境下的防卡滞的非概率可靠度进行了预测。
4、星载天线展开系统可靠性分配方法研究。
针对星载天线展开机构系统设计可靠性数据缺乏的实际情况,应用系统可靠性分配的模糊数学方法,在综合评分为权的系统可靠性加权分配法的基础上,将模糊数学引入可靠性分配的权系数矩阵中,建立了星载天线展开机构系统可靠性分配的模糊模型。利用模糊数学的运算规则,推导出星载天线展开机构系统可靠性分配的权系数表达式。最后以某星载天线展开机构系统为例,给出系统可靠性的分配结果,表明该方法的可行性和有效性。
5、星载天线展开系统故障树的区间分析方法研究。
在对星载天线展开系统故障树分析的基础上,针对传统故障树分析中存在的不确定性难以量化的问题,结合D-S(dempster-shafer)理论和区间概率理论,提出星载天线展开机构故障树的区间分析方法,构造失效独立和失效相关情况下故障树区间分析的与门区间算子和或门区间算子,在此基础上对系统的展开可靠度进行分析和预测。
6、基于灰色关联法的星载天线展开机构系统故障树分析研究。
针对星载天线展开机构系统设计中可靠性数据缺乏的实际情况,将灰色关联法引入到星载天线展开机构系统可靠性分析中,并采用该方法在星载天线展开机构系统的故障诊断中研究系统的故障特征与内部特征之间的相关性,确定实际模式归属于某个标准模式,并对故障树诊断进行综合分析。
Firstly, structures with interval parameters or interval-random parameters are taken as research objects in this paper. The structural dynamic characteristic and dynamic response are derived under the condition that physical parameters of structural materials, geometric dimensions of truss structures and applied loads are all interval or interval-random variables.Secondly, based on the engineering background of national 863 project, reliability computation, allocation, prediction and analysis on deployment mechanism system of satellite antenna are derived by means of non-stochastic theory. The main research works can be described as follows:
1. The analysis of dynamic characteristic and dynamic response on interval truss structures.
Under the condition that the uncertainty of physical parameters of structural materials, geometric dimensions of truss structures and considering uncertainty of applied load simultaneously, the structural stiffness matrix and mass matrix are constructed by using interval factor method. From the Rayleigh quotient of structural vibration, the computation expression of interval variable of structural characteristic is obtained on the basis of interval operation principles. From Duhamel integral, the expressions of structures interval dynamic response are deduced by combining mode superposition method with calculus, interval factor method and interval arithmetic, and membership functions of dynamic response can be derived in the end.Through some engineering examples, the influence of the interval structural parameters and interval applied load on structural interval dynamic characteristic and dynamic response are inspected.
2. The study on dynamic characteristic and dynamic response of interval stochastic truss structures.
Considering the interval randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices were constructed based on the interval factor method and random factor method; from the Rayleigh’s quotient of structural vibration, the structural interval random dynamic characteristic was obtained by means of the interval arithmetic; the interval numeric characteristics of dynamic characteristic were then derived by using the random variable’s moment function method and algebra synthesis method. From the Duhamel integral, structural dynamic responses are derived by the mode superposition method. Then, the interval numerical characteristics of interval random dynamic responses are derived by using the moment function method for random variables. Some numerical examples were provided to illustrate the validity and feasibility of the present method.
3. The study on reliability index in the deployment mechanism of a large satellite antenna.
Firstly, by studying the movement principium of hoop-truss satellite antenna, a mechanical analysis model of the deployment mechanism and the calculating formula for the interval forces of trusses were presented. Based on the function deployment of the hoop-truss must accord with, a movement reliability analysis model of the mechanism was given. Synthetically considering the effects of dimension errors and the space environment factors, we treated the mechanism movement-function as a function of some interval variables, and derived the reliability formula by using the method of non-probabilistic reliability. The movement reliability of the deployment mechanism was predicted and simulated in the whole process of deployment. Secondly, the seizure-preventing reliability of synchronous gears in the deployment mechanism is studied, from the ultimate position of the gearing mesh, the seizure-preventing condition for the gear pair is given in this paper. With gears’machining tolerances and fitting allowances and the space temperature considered synthetically, an analytical model of seizure-preventing non-probabilistic reliability of the gear pair is presented by using optimization. The seizure-preventing reliability of synchronous gears is predicted in different fitting allowances and different temperature conditions, and some significant conclusions are obtained.
4. The study on the reliability allocation of satellite antenna deployment mechanism system.
Fuzzy comprehensive evaluation method for system reliability allocation was proposed in the initial stages of the design of spaceborne antenna deployment mechanism. This method was based on the weight allocation method. Through introduced the fuzzy information into the matrix of weight coefficients, the fuzzy model for the reliability allocation of spaceborne antenna deployment mechanism was built. By the arithmetic operation rules of fuzzy mathematics, the expression of fuzzy weight coefficient was derived. Finally, the reliability allocation of a spaceborne antenna deployment mechanism was given as an example. The possible reliability of the system was obtained. The rationality and validity of the presented method were demonstrated.
5. Interval analysis method of faulty tree for the deployment system of a large satellite antenna
To formulate the uncertainties of conventional fault tree analysis, the method of fault tree interval analysis based on D-S(dempster-shafer) theory and interval probability theory is proposed. On the condition that the premises in FTA(faulty tree analysis) is dependence or independence between basic events, the AND operator and the OR operator are proposed to compute interval probability of FTA, and upon which the system reliability was forecasted.
6. Fault analysis of the deployment mechanism system of satellite antenna based on grey relation method
For the shortage of the system reliability datum in the initial stages of the design of satellite antenna deployment mechanism, grey relation method for system reliability allocation was proposed. It was used to study the relativity of the mechanism system’s failure characters and inside characters of the satellite antenna, and to confirm what kind of standard mode the actual mode belonged to. And it was also used in the fault tree’s synthetically analysis.
1、区间参数桁架结构的动力特性和动力响应分析方法研究。
在考虑结构单元的物理参数、几何尺寸和载荷幅值具有不确定性时,利用区间因子法建立了结构的刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构特征值不确定变量的计算表达式;从结构响应的Duhamel积分式出发,利用区间因子法、区间运算和振型叠加法导出结构动力响应区间变量的表达式。通过算例分析区间桁架结构参数的区间分散性对其动力特性和动力响应的影响。
2、区间随机参数桁架结构的动力特性和动力响应分析方法研究。
当结构的物理参数和几何尺寸同时具有区间随机性时,利用区间因子法和随机因子法建立了结构的刚度矩阵和质量矩阵;由结构振动的Rayleigh商表达式,利用区间运算推导了结构动力特性区间随机变量的计算式;进而利用随机变量的矩法和代数综合法,推导出了结构特征值的数字特征的计算式。然后从Duhamel积分式出发,利用振型叠加法求出了结构动力响应区间随机变量的表达式;最后再由随机函数的矩法推导出结构区间随机动力响应的区间数字特征。从而分析区间随机桁架结构物理参数和几何参数的区间随机分散性对其动力特性和动力响应的影响。
3、星载天线展开机构可靠性指标的计算方法研究。
首先在周边桁架式星载天线展开机构运动机理分析的基础上,建立了展开机构的力学分析模型,并推导了桁架杆内力的计算式。从桁架展开要满足的功能函数出发,给出机构运动可靠性的分析模型。综合考虑尺寸误差和太空环境因素的影响,将运动功能函数视为区间变量函数,利用非概率方法导出可靠性计算公式,对机构在整个展开过程中的运动可靠性进行预测和仿真;然后对展开机构中的齿轮运动副的卡滞失效形式进行了研究,从齿轮啮合的极限位置出发,推导出了同步齿轮副不发生卡滞的条件。在综合考虑齿轮加工误差、装配误差和太空环境温度等因素的基础上,利用优化算法,构建了齿轮副防卡滞的非概率可靠度计算公式。最后,对同步齿轮副在不同装配误差和不同温度环境下的防卡滞的非概率可靠度进行了预测。
4、星载天线展开系统可靠性分配方法研究。
针对星载天线展开机构系统设计可靠性数据缺乏的实际情况,应用系统可靠性分配的模糊数学方法,在综合评分为权的系统可靠性加权分配法的基础上,将模糊数学引入可靠性分配的权系数矩阵中,建立了星载天线展开机构系统可靠性分配的模糊模型。利用模糊数学的运算规则,推导出星载天线展开机构系统可靠性分配的权系数表达式。最后以某星载天线展开机构系统为例,给出系统可靠性的分配结果,表明该方法的可行性和有效性。
5、星载天线展开系统故障树的区间分析方法研究。
在对星载天线展开系统故障树分析的基础上,针对传统故障树分析中存在的不确定性难以量化的问题,结合D-S(dempster-shafer)理论和区间概率理论,提出星载天线展开机构故障树的区间分析方法,构造失效独立和失效相关情况下故障树区间分析的与门区间算子和或门区间算子,在此基础上对系统的展开可靠度进行分析和预测。
6、基于灰色关联法的星载天线展开机构系统故障树分析研究。
针对星载天线展开机构系统设计中可靠性数据缺乏的实际情况,将灰色关联法引入到星载天线展开机构系统可靠性分析中,并采用该方法在星载天线展开机构系统的故障诊断中研究系统的故障特征与内部特征之间的相关性,确定实际模式归属于某个标准模式,并对故障树诊断进行综合分析。
Firstly, structures with interval parameters or interval-random parameters are taken as research objects in this paper. The structural dynamic characteristic and dynamic response are derived under the condition that physical parameters of structural materials, geometric dimensions of truss structures and applied loads are all interval or interval-random variables.Secondly, based on the engineering background of national 863 project, reliability computation, allocation, prediction and analysis on deployment mechanism system of satellite antenna are derived by means of non-stochastic theory. The main research works can be described as follows:
1. The analysis of dynamic characteristic and dynamic response on interval truss structures.
Under the condition that the uncertainty of physical parameters of structural materials, geometric dimensions of truss structures and considering uncertainty of applied load simultaneously, the structural stiffness matrix and mass matrix are constructed by using interval factor method. From the Rayleigh quotient of structural vibration, the computation expression of interval variable of structural characteristic is obtained on the basis of interval operation principles. From Duhamel integral, the expressions of structures interval dynamic response are deduced by combining mode superposition method with calculus, interval factor method and interval arithmetic, and membership functions of dynamic response can be derived in the end.Through some engineering examples, the influence of the interval structural parameters and interval applied load on structural interval dynamic characteristic and dynamic response are inspected.
2. The study on dynamic characteristic and dynamic response of interval stochastic truss structures.
Considering the interval randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices were constructed based on the interval factor method and random factor method; from the Rayleigh’s quotient of structural vibration, the structural interval random dynamic characteristic was obtained by means of the interval arithmetic; the interval numeric characteristics of dynamic characteristic were then derived by using the random variable’s moment function method and algebra synthesis method. From the Duhamel integral, structural dynamic responses are derived by the mode superposition method. Then, the interval numerical characteristics of interval random dynamic responses are derived by using the moment function method for random variables. Some numerical examples were provided to illustrate the validity and feasibility of the present method.
3. The study on reliability index in the deployment mechanism of a large satellite antenna.
Firstly, by studying the movement principium of hoop-truss satellite antenna, a mechanical analysis model of the deployment mechanism and the calculating formula for the interval forces of trusses were presented. Based on the function deployment of the hoop-truss must accord with, a movement reliability analysis model of the mechanism was given. Synthetically considering the effects of dimension errors and the space environment factors, we treated the mechanism movement-function as a function of some interval variables, and derived the reliability formula by using the method of non-probabilistic reliability. The movement reliability of the deployment mechanism was predicted and simulated in the whole process of deployment. Secondly, the seizure-preventing reliability of synchronous gears in the deployment mechanism is studied, from the ultimate position of the gearing mesh, the seizure-preventing condition for the gear pair is given in this paper. With gears’machining tolerances and fitting allowances and the space temperature considered synthetically, an analytical model of seizure-preventing non-probabilistic reliability of the gear pair is presented by using optimization. The seizure-preventing reliability of synchronous gears is predicted in different fitting allowances and different temperature conditions, and some significant conclusions are obtained.
4. The study on the reliability allocation of satellite antenna deployment mechanism system.
Fuzzy comprehensive evaluation method for system reliability allocation was proposed in the initial stages of the design of spaceborne antenna deployment mechanism. This method was based on the weight allocation method. Through introduced the fuzzy information into the matrix of weight coefficients, the fuzzy model for the reliability allocation of spaceborne antenna deployment mechanism was built. By the arithmetic operation rules of fuzzy mathematics, the expression of fuzzy weight coefficient was derived. Finally, the reliability allocation of a spaceborne antenna deployment mechanism was given as an example. The possible reliability of the system was obtained. The rationality and validity of the presented method were demonstrated.
5. Interval analysis method of faulty tree for the deployment system of a large satellite antenna
To formulate the uncertainties of conventional fault tree analysis, the method of fault tree interval analysis based on D-S(dempster-shafer) theory and interval probability theory is proposed. On the condition that the premises in FTA(faulty tree analysis) is dependence or independence between basic events, the AND operator and the OR operator are proposed to compute interval probability of FTA, and upon which the system reliability was forecasted.
6. Fault analysis of the deployment mechanism system of satellite antenna based on grey relation method
For the shortage of the system reliability datum in the initial stages of the design of satellite antenna deployment mechanism, grey relation method for system reliability allocation was proposed. It was used to study the relativity of the mechanism system’s failure characters and inside characters of the satellite antenna, and to confirm what kind of standard mode the actual mode belonged to. And it was also used in the fault tree’s synthetically analysis.
引文
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