不确定弹性机构可靠性分析及其优化设计研究
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摘要
现代机构日益向着高速化、轻量化、精密化的方向发展,因此开展基于弹性动力学的不确定参数机构的可靠性分析和优化设计研究有着重要的理论和现实意义。本文将机构的不确定参数分别视为随机变量、模糊变量和区间变量,在对机构进行弹性动力学分析的基础上,分别构建了机构的随机可靠性、模糊可靠性和非概率可靠性分析模型并进行了基于可靠性和非概率可靠性的机构优化设计研究,其主要内容如下:
1、对工程中广泛使用的连杆机构、螺旋机构和齿轮传动机构分别进行了弹性动力学分析。通过相应算例对上述机构的动力响应特点进行了分析研究,算例表明进行基于弹性动力学的机构分析及设计的必要性。从而为后序章节的研究奠定基础。
2、在对机构进行动力学分析的基础上,考虑机构参数(几何参数、物理参数)的随机性,建立了机构动态可靠性分析模型。对连杆机构、螺旋机构和齿轮传动机构分别进行了动态精度可靠性分析。通过算例,考查了机构参数对机构动态精度可靠性的影响,获得了有意义的结论,该结论对机构动态设计具有指导意义。
3、针对机构动力响应分析过程的复杂性和耗时性,将神经网络应用到机构的弹性动力学分析之中。根据训练好的网络给出的机构动力响应的近似表达式,导出了机构响应的灵敏度计算公式。并通过相关算例,验证了这一新的动力学分析方法的可行性和有效性。这一方法的应用,缩短了机构动力响应计算时间、提高了设计效率,使得弹性机构的可靠性模拟得以实现。此外,由于可以得到响应及其灵敏度的近似表达式,使得优化中的某些隐式约束显式化成为可能,从而加速优化过程。
4、对机构模糊可靠性问题展开了较为详细的讨论,进行了模糊极限状态及其设计准则下的机构模糊可靠性分析;进行了模糊强度和应力下的机构模糊可靠性分析;利用模糊变量的等效正态变换法,对含有模糊参数的机构进行了动力响应分析和模糊可靠性分析。相关算例表明,文中采用的方法是合理和有效的,算例同时考查了机构参数对机构模糊可靠度的影响,获得了与随机可靠性类似的结论。
5、针对可靠性分析和设计时,由于样本较少,某些不确定量缺乏必要的统计信息而难以有效利用现有可靠性模型的情况,将弹性机构的不确定参数描述为区间变量,分别应用泰勒展开法和本文提出的基于神经网络求解动力响应的Monte-Carlo模拟法,对机构的动力响应进行了区间分析。在此基础上,建立了弹性机构的非概率可靠性分析模型。通过算例,对两种区间分析方法进行了对比,验证了模型的合理性和本文方法的可行性和有效性。
6、讨论了基于可靠性的不确定参数弹性机构的优化问题。构建了弹性连杆机构基于刚度和强度可靠性约束的优化设计模型,并用梯度法结合可行方向法进行求解,文中的算例验证了优化模型的合理性和所采用算法的有效性;构建了弹性连杆机构基于刚度和强度非概率可靠性约束的优化设计模型,提出了两步优化的求解策略。通过算例,进行了模型和求解策略的验证,并获得了相关结论。
Modern mechanisms are trending to high speed, light mass and high precision, the research on the reliability analysis and optimization design based on Kineto-Elastiodynamics has important theoretical significance and research worthiness. In this paper, the random reliability model, fuzzy reliability model and non-probabilistic reliability model are established by taking the uncertain parameters of the elastic mechanism as random variables, fuzzy variables and interval variables respectively. And the optimization design of the elastic mechanism based on reliability is made. The main research works can be described as follows:
1. The planar linkages, screw mechanism and gear driven mechanism, which are used widely in engineering, are taken as analytic objects. The Kineto-Elastodynamics analytic models of the mechanisms are built respectively, and then the Kineto-Elastodynamics analyses are made. The necessity of mechanism analysis based on Kineto-Elastodynamics.is proved by examples. Thereby, the theoretical basis for the further research is offered.
2. Based on above, the dynamic reliability models of the mechanism are given by taking the uncertain parameters of the mechanism as random variables, and the dynamic reliability analyses are made. Through examples, the influence of the mechanism's parameters on the reliability of the output kinematic accuracy of the mechanism is investigated, some instructive conclusions are obtained, and those conclusions contribute to improving design quality.
3. In accordance with the complexity and time-consuming character of the dynamic analysis of the elastic mechanism, a new dynamic analysis method is presented that is based on BP(Back-propagation) network. By using the approximate functional relationship between the input parameters and the output parameters given by the trained network, the formula of the sensitivity of the network output parameters is derived. The feasibility and validity of the method presented here are verified through examples. Application of the method decreases the time for the dynamic analysis obviously, increases the design efficiency effectively and makes the reliability numerical simulation can be actualized. Furthermore, for the formula of the sensitivity of the dynamic response can be given, so the equivalent treatment of some probability constraints can be actualized, this will accelerate the optimum procedure.
4. The fuzzy reliability problem of mechanisms is discussed detailedly. Fuzzy reliability analysis based on fuzzy limit state and fuzzy design rule is made first. Then the fuzzy reliability analysis based on fuzzy strength and stress is studied. Finally, the fuzzy reliability of the elastic mechanism with fuzzy parameters is analyzed by transforming the fuzzy variables into equivalent normal random variables. The relevant examples show that the method is practicable and effective, and the influence of the mechanism's parameters on the reliability of the output kinematic accuracy of the mechanism is investigated, with the similar conclusion as attained from random reliability obtained.
5. In according with the difficult of applying the existing probability reliability model under conditions of small sample and poor information in the reliability analysis and design, the interval analysis of the elastic mechanism is made by taking the uncertain parameters as interval variables, applying Taylor series expansion and Monte-Carlo simulation based on BP (Back-propagation) network respectively. Based on above, the non- probabilistic reliability model is established. Finally, through examples, the results comparison of Taylor series expansion and Monte-Carlo show the model is rational and the method is practicable and effective.
6. The optimization problem of the uncertain elastic mechanism based on reliability is discussed. The optimization model of the elastic linkage mechanism based on reliability is built by taking the reliability of strength and stiffness of the mechanism as constraints. In the optimum iterative procedure, the gradient and feasible direction algorithms are adopted to calculate. The rationality of the model and the availability of the arithmetic are verified through an example. The optimization model of the elastic linkage mechanism based on non-probabilistic reliability is built by taking the non-probabilistic reliability of strength and stiffness of the mechanism as constraints. The two steps optimization method is presented to calculate. Finally, the model and method given here are inspected by example, with some instructive conclusions obtained.
1、对工程中广泛使用的连杆机构、螺旋机构和齿轮传动机构分别进行了弹性动力学分析。通过相应算例对上述机构的动力响应特点进行了分析研究,算例表明进行基于弹性动力学的机构分析及设计的必要性。从而为后序章节的研究奠定基础。
2、在对机构进行动力学分析的基础上,考虑机构参数(几何参数、物理参数)的随机性,建立了机构动态可靠性分析模型。对连杆机构、螺旋机构和齿轮传动机构分别进行了动态精度可靠性分析。通过算例,考查了机构参数对机构动态精度可靠性的影响,获得了有意义的结论,该结论对机构动态设计具有指导意义。
3、针对机构动力响应分析过程的复杂性和耗时性,将神经网络应用到机构的弹性动力学分析之中。根据训练好的网络给出的机构动力响应的近似表达式,导出了机构响应的灵敏度计算公式。并通过相关算例,验证了这一新的动力学分析方法的可行性和有效性。这一方法的应用,缩短了机构动力响应计算时间、提高了设计效率,使得弹性机构的可靠性模拟得以实现。此外,由于可以得到响应及其灵敏度的近似表达式,使得优化中的某些隐式约束显式化成为可能,从而加速优化过程。
4、对机构模糊可靠性问题展开了较为详细的讨论,进行了模糊极限状态及其设计准则下的机构模糊可靠性分析;进行了模糊强度和应力下的机构模糊可靠性分析;利用模糊变量的等效正态变换法,对含有模糊参数的机构进行了动力响应分析和模糊可靠性分析。相关算例表明,文中采用的方法是合理和有效的,算例同时考查了机构参数对机构模糊可靠度的影响,获得了与随机可靠性类似的结论。
5、针对可靠性分析和设计时,由于样本较少,某些不确定量缺乏必要的统计信息而难以有效利用现有可靠性模型的情况,将弹性机构的不确定参数描述为区间变量,分别应用泰勒展开法和本文提出的基于神经网络求解动力响应的Monte-Carlo模拟法,对机构的动力响应进行了区间分析。在此基础上,建立了弹性机构的非概率可靠性分析模型。通过算例,对两种区间分析方法进行了对比,验证了模型的合理性和本文方法的可行性和有效性。
6、讨论了基于可靠性的不确定参数弹性机构的优化问题。构建了弹性连杆机构基于刚度和强度可靠性约束的优化设计模型,并用梯度法结合可行方向法进行求解,文中的算例验证了优化模型的合理性和所采用算法的有效性;构建了弹性连杆机构基于刚度和强度非概率可靠性约束的优化设计模型,提出了两步优化的求解策略。通过算例,进行了模型和求解策略的验证,并获得了相关结论。
Modern mechanisms are trending to high speed, light mass and high precision, the research on the reliability analysis and optimization design based on Kineto-Elastiodynamics has important theoretical significance and research worthiness. In this paper, the random reliability model, fuzzy reliability model and non-probabilistic reliability model are established by taking the uncertain parameters of the elastic mechanism as random variables, fuzzy variables and interval variables respectively. And the optimization design of the elastic mechanism based on reliability is made. The main research works can be described as follows:
1. The planar linkages, screw mechanism and gear driven mechanism, which are used widely in engineering, are taken as analytic objects. The Kineto-Elastodynamics analytic models of the mechanisms are built respectively, and then the Kineto-Elastodynamics analyses are made. The necessity of mechanism analysis based on Kineto-Elastodynamics.is proved by examples. Thereby, the theoretical basis for the further research is offered.
2. Based on above, the dynamic reliability models of the mechanism are given by taking the uncertain parameters of the mechanism as random variables, and the dynamic reliability analyses are made. Through examples, the influence of the mechanism's parameters on the reliability of the output kinematic accuracy of the mechanism is investigated, some instructive conclusions are obtained, and those conclusions contribute to improving design quality.
3. In accordance with the complexity and time-consuming character of the dynamic analysis of the elastic mechanism, a new dynamic analysis method is presented that is based on BP(Back-propagation) network. By using the approximate functional relationship between the input parameters and the output parameters given by the trained network, the formula of the sensitivity of the network output parameters is derived. The feasibility and validity of the method presented here are verified through examples. Application of the method decreases the time for the dynamic analysis obviously, increases the design efficiency effectively and makes the reliability numerical simulation can be actualized. Furthermore, for the formula of the sensitivity of the dynamic response can be given, so the equivalent treatment of some probability constraints can be actualized, this will accelerate the optimum procedure.
4. The fuzzy reliability problem of mechanisms is discussed detailedly. Fuzzy reliability analysis based on fuzzy limit state and fuzzy design rule is made first. Then the fuzzy reliability analysis based on fuzzy strength and stress is studied. Finally, the fuzzy reliability of the elastic mechanism with fuzzy parameters is analyzed by transforming the fuzzy variables into equivalent normal random variables. The relevant examples show that the method is practicable and effective, and the influence of the mechanism's parameters on the reliability of the output kinematic accuracy of the mechanism is investigated, with the similar conclusion as attained from random reliability obtained.
5. In according with the difficult of applying the existing probability reliability model under conditions of small sample and poor information in the reliability analysis and design, the interval analysis of the elastic mechanism is made by taking the uncertain parameters as interval variables, applying Taylor series expansion and Monte-Carlo simulation based on BP (Back-propagation) network respectively. Based on above, the non- probabilistic reliability model is established. Finally, through examples, the results comparison of Taylor series expansion and Monte-Carlo show the model is rational and the method is practicable and effective.
6. The optimization problem of the uncertain elastic mechanism based on reliability is discussed. The optimization model of the elastic linkage mechanism based on reliability is built by taking the reliability of strength and stiffness of the mechanism as constraints. In the optimum iterative procedure, the gradient and feasible direction algorithms are adopted to calculate. The rationality of the model and the availability of the arithmetic are verified through an example. The optimization model of the elastic linkage mechanism based on non-probabilistic reliability is built by taking the non-probabilistic reliability of strength and stiffness of the mechanism as constraints. The two steps optimization method is presented to calculate. Finally, the model and method given here are inspected by example, with some instructive conclusions obtained.
引文
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