机构系统运动时变可靠性理论及其应用的研究

Methodologies of design under uncertainty have been widely used in mechanism synthesis where the effects of uncertainties on mechanism performances are taken into account, leading to improved mechanism reliability. The current mechanism reliability theory, however, is limited to point reliability that is defined at a specific instant of time. To this end, the reliability over the mechanism service time interval, which is termed as interval or time-dependent reliability, cannot be obtained from the point reliability. Interval reliability is much more critical than the point reliability. To fill the gap, this project is intended to establish theories, create models, and develop algorithms for time-dependent (interval) mechanism reliability. The major research tasks include the followings: (1) Investigate the effects of uncertainties, including tolerances, joint clearances, and elastic deformation, on the mechanism's kinematic performance. The mechanisms under consideration will be planar, spatial, and robotic mechanisms. (2) Propose new strategies and develop new algorithms for mechanism time-dependent reliability analysis. The analysis algorithms will be used to quantify the uncertainty effects specified in (1), and this will lead to the prediction of mechanism reliability over the mechanism service time, as well as the life distribution of the mechanism. (3) Develop time-dependent probabilistic synthesis methodologies so that (a) the mechanism will be more reliable - the probability of failure over its service time will be below a required level, (b) the mechanism will be more robust - the motion error will be small without eliminating the sources of uncertainties, and (c) the mechanism will be more affordable because of the increase reliability, robustness, and reduced cost. With the benefits, this project will not only enhance the current mechanism analysis and synthesis theories, but also provide powerful design tools for high performance mechanism systems.

不确定性设计方法已被广泛应用于机构设计中，从而考虑不确定性对机构运动性能的影响，进而提高机构的可靠性。但现有机构可靠性理论主要局限于机构在其运动区间上某点上的可靠度，无法给出更为重要的机构运动区间可靠度。为此，本项目提出并研究与时间相关的机构系统运动时变可靠度理论以获得机构在整个运动区间上的可靠度。其研究内容包括：考虑尺寸公差、运动副间隙、构件弹性变形等不确定性因素，应用随机过程理论研究平面、空间和机器人机构的随机运动误差的时变特性；提出机构运动时变可靠性分析策略与算法；开发机构时变概率综合方法及基于时变可靠性的机构精度设计新方法。本项目创新地提出机构系统运动时变可靠性新理论，以系统观点揭示机构系统中不确定性对机构运动输出的作用机理和影响规律。项目的研究成果，将在理论上丰富机构可靠性理论的知识内涵和拓展机构可靠性理论的外延，并为工程实践中高性能机构系统的设计提供有力的工具。

项目围绕真实机构系统的不确定性设计理论与方法展开研究，重点研究与时间相关的机构系统运动时变可靠度理论及其工程应用。在不确定性建模理论与方法方面，提出了基于变量降维的含尺寸公差、运动副间隙等多不确定性耦合建模方法，提出基于多失效模式和串联系统理论的多输出机构系统的可靠性建模方法。在求解策略和算法方面，开发出适用于各类型机构运动时变可靠性分析的高效、高精度求解算法——多极值联合概率分析方法和包络方法。在上述研究的基础上，开展了机构系统的可靠性设计、稳健设计方法研究。此外，在工程应用领域，基于机构系统的不确定性工程设计理论开展了工业机器人的运动规划和控制策略研究。项目研究初步建立了机构系统时变可靠性分析与设计理论框架。研究成果丰富和拓展了机构运动可靠性理论。所提出的建模理论和可靠性分析与设计理论为真实机构系统的运动精度可靠性、精度保持性、精度寿命的设计提供技术支撑和有效工具，也为解决机构系统乃至机械系统寿命周期内的可靠度分析与设计、稳健设计以及维修维护决策等提供新的思路。在装备制造领域提高系统运动精度、增强可靠性方面具有良好的应用前景。

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