【作者】 周娜；

【导师】 张义民；

【作者基本信息】 东北大学 ， 机械设计及理论， 2012， 博士

【摘要】 可靠性作为衡量产品质量的一个重要指标,越来越受到工程界的重视,可靠性学科的迅速发展以及广泛的应用,也远非一般应用科学所比。机械结构设计追求的目标之一就是结构的可靠性满足要求,且具有稳定性。但是,机械结构的可靠性受到一些不确定性因素的影响,而且这些不确定性因素对机械结构可靠性的影响程度是不相同的,且不容忽视。为了确定各因素对机械结构可靠性的影响程度,以便于在机械结构设计、制造等过程中把握重点,降低成本、提高效率,对机械结构进行可靠性灵敏度设计是十分必要的。齿轮是机械结构的重要组成部分,对其进行设计及分析非常重要。因此基于可靠性灵敏度分析的可靠性优化设计,即可靠性稳健设计,该方法为使所设计的齿轮传动乃至机械结构的可靠性具有稳定性提供了一种切实可行的方法。本文主要研究内容如下：1.阐述了可靠性分析理论、可靠性灵敏度设计、可靠性优化设计及其稳健设计的研究进展与国内外现状,对选题的背景、目的和意义进行了论述,指出了对随机动态结构系统进行可靠性研究和稳健设计的重要性。2.研究了多失效模式齿轮传动的可靠性优化设计问题。介绍了随机摄动方法、Edgeworth级数方法及相应的经验修正公式、多失效模式的可靠性理论和可靠性优化设计。本章将可靠性分析理论与优化设计方法相结合,提出了具有任意分布参数的齿轮传动的可靠性优化设计,发展了具有任意分布参数的齿轮传动的可靠性设计理论。在考虑失效模式相关性的前提下,研究了多失效模式齿轮传动可靠性评价方法。在基本随机参数的前四阶矩已知的情况下,通过计算机程序可以实现具有任意分布参数的齿轮传动的可靠性优化设计,及多失效模式下的齿轮传动的可靠性优化设计,并通过实例验证了所提方法的有效性。3.研究了多失效模式齿轮传动的可靠性灵敏度设计问题。本章将可靠性设计理论与灵敏度分析方法相结合,以可靠性数学模型为基础,建立了齿轮传动可靠性灵敏度设计的计算方法,给出了可靠性灵敏度的变化规律,研究了设计参数的改变对齿轮传动可靠性的影响程度,为齿轮传动的可靠性设计提供了理论依据。在随机参数前四阶矩已知的情况下,应用随机摄动方法、利用Edgeworth级数方法及相应的经验修正公式,把未知的状态函数的概率分布展开成标准的正态分布的方式,确定了参数为任意分布的齿轮传动的可靠度的计算公式,并应用灵敏度求解方法,’推导出相应的可靠性灵敏度的计算公式。对随机参数的概率分布类型没有任何限制,使之更接近于工程实际中的机械结构的可靠性问题,并通过实例验证了所提方法的有效性。4.研究了多失效模式齿轮传动的可靠性稳健设计问题。将可靠性灵敏度理论与稳健设计方法相结合,基于可靠性优化模型研究了齿轮传动的可靠性稳健设计问题,提出了可靠性稳健设计的数值计算方法。把可靠性灵敏度融入到优化设计模型的目标中,将可靠性稳健设计归结为满足可靠性要求的多目标优化问题,在满足可靠性要求的前提下,实现了多失效模式齿轮传动的稳健性设计,并通过实例验证了所提方法的有效性。5.研究了强度退化时的多失效模式齿轮传动的渐变可靠性和可靠性灵敏度分析问题。在考虑强度退化情况下,将渐变可靠性设计理论与灵敏度分析方法相结合,以可靠性数学模型为基础,建立了多失效模式齿轮传动的渐变可靠性和可靠性灵敏度设计的计算方法,给出了强度退化下的渐变可靠性灵敏度的变化规律,研究了设计参数的改变对齿轮传动可靠性的影响程度,为齿轮传动的可靠性设计提供了理论依据。更多还原

【Abstract】 An essential index of product’s quality, reliability attracts more and more attention in engineering with its rapid development and widely application. One of the objectives of mechanical structure design is that the reliability of the structure meets the requirements with its stability. However, the reliability of mechanical structure is influenced by some uncertain factors which affect the structure in different extent and cannot be ignored. For the sake of determining the degrees that each factor affects the structure, grasping key points in mechanical structure design and manufacturing, reducing costs and improving efficiency, reliability sensitivity design is very necessary for mechanical structures. Gear is an important part of mechnical transmission. As a result, it is necessary to analyze and design the structural parameters of gear system. Reliability-based robust design, a reliability optimization design based on reliability sensitivity analysis, provides a realistic approach for a gear transmission and mechanical structure in which reliability is needed.The contents of this thesis are as follows:1. Reliability analysis theories, domestic and foreign development of reliability sensitivity design and reliability optimization design are elaborated. It also discusses the background, objectives and meaning of the subject selected, and the importance of research on reliability and robust design for a stochastic dynamic structure system.2. Reliability optimization design of gear transmission system with multi-failure modes is investigated. This part presents the stochastic perturbation method, the Edgeworth series method and its related empirical revised formulas, and the reliability theories and optimization design of multi-failure modes. Combining reliability analysis theories with optimization design methods, a reliability optimization design approach for gear transmission with arbitrary distribution parameters is proposed in this part, which is a development of gear transmission reliability design theories with arbitrary distribution parameters. Taking into account of correlation of failure models, the reliability evaluation method of mechanical system with multi-failure modes is investigated. Moreover, it suggests that the reliability optimization design of gear transmission with arbitrary distribution parameters and with multi-failure mode can be processed through computer software provided that the first four moments of basic random parameters are given. Finally, the approach proposed is verified with examples.3. Reliability-based sensitivity design of gear transmission is researched. Combining reliability design theories and sensitivity analysis method, with the foundation of reliability mathematics, a calculating method for reliability-based sensitivity design for gear transmission is proposed, which gives the changing rule of reliability sensitivities, researches on the influential degrees of design parameters’variety to components’reliability, and more over provides a theoretical basis for gear transmission’reliability design. Given the first four moments of random parameters, the unknown state functions’probability distribution can be expressed by standard normal distribution using stochastic perturbation method and the Edgeworh series method and its empirical modified formulas. The reliability calculating formulas for gear transmission with arbitrary parameter distribution is then determined, and the related reliability-based sensitivity’s calculating formulas is deduced using sensitivity solving method. There is no limitation of random parameters’probability distribution types on the method proposed, thus it is more accessible to solve the realistic mechanical components’ reliability problems in engineering. Similarly, this approach is verified by examples in the following.4. Reliability-based robust design of gear transmission system is studied. Combining reliability-based sensitivity theories with robust design methods, gear transmission’s reliability-based robust design is investigated based on the reliability optimization model, a numerical calculating method for reliability-based robust design is proposed. Adding the reliability based sensitivity to aims of the optimization designing model, the reliability-based robust design is then come down to multi-objective optimization problems which also satisfy the reliability requirements. Therefore, reliability-based robust design of gear transmission with multi failure modes is achieved provided that the reliability requirements are satisfied. Examples are checked out to verify the effectiveness of the method proposed.5. The gradual varying reliability and reliability based-sensitivity problems of the gear transmission system with multi failure modes are investigated. In consideration of the strength degradation, combining the gradual varying reliability theory and the reliability based sensitivity analysis method, with the foundation of reliability mathematics, the evaluating method of the gradual varying reliability and reliability-based sensitivity analysis of the gear transmission system with multi failure modes is build. The changing rule of the reliability-based sensitivity taking the strength degradation into accordance is given, and the influence level of the designing parameters’ varying to the gear transmission systems’ reliability is studied. It provides the theory support for the gear transmission systems’ reliability design.更多还原