【作者】 王俊杰；

【导师】 叶南海； 曹学华；

【作者基本信息】 湖南大学 ， 机械工程（专业学位）， 2021， 硕士

【摘要】 机械设计中存在着诸多不确定性的因素,例如材料属性,几何尺寸与外加载荷。这些不确定性作为输入进入系统,通过系统中各种物理关系的相互作用,最终导致了整体失效的不确定性。作为输入的不确定性误差虽小,但作用于系统累加后的影响是不容小觑的,工程师设计机械时应着重考虑所设计机械可靠性,在概率可靠性模型的基础上,大量学者对非线性极限状态函数可靠度问题求解进行了研究,但很少有方法可以平衡计算消耗与求解精度。因此本文提出了一种新的可靠性指标及其求解方法,以两个数值算例为例给出了两个基本变量与三个基本变量下的参数优选值,并与其他算法进行了性能对比。以一个材料力学中的管状悬臂梁与一个基于现有国产某型号RV(Rotate Vector)减速器为应用案例,提出一套较为完整的可靠度求解技术方案,论文主要工作如下:(1)提出区域等效转换指标的概念。对概率可靠性模型中的可靠度经典算法进行了系统的研究和介绍,在此基础上提出刻画失效域的区域等效转换指标,并对其求解方法进行了说明。(2)推导区域等效转换指标表达式。从图形刻画与积分微元两个角度对区域等效转换指标表达式进行了推导,建立了基本变量个数为2,3,4情况下的区域等效转换指标与失效率间的映射关系,并对映射关系进行了分析。(3)通过算例分析得到参数优选值。通过两个个数值算例,获得了采样参数对可靠度相对误差的影响,分析其原因并给出在不同维度下优选的参数值数值。结合参数分析的两个数值算例与一个管状悬臂梁力学算例与传统经典算法进行比较,验证该算法在效率与精度上具有一定的优越性。(4)摆线轮机构可靠性分析。以国产某型号RV减速器作为研究对象,对其中第二级传动机构关键部分摆线针轮机构建立三维数模与有限元仿真模型,针对其中四个关键几何参数通过试验设计方法产生一系列样本点,仿真后构建响应面。基于BP(Back Propagation)神经网络,拟合得到RV减速器的极限状态函数,基于本文AFOSM(Advanced First Order and Second Moment)采样转换方法进行求解,验证该方法对于实际问题求解的有效性。本文基于传统的改进一次二阶矩法提出了区域等效转换指标,通过采样而不是寻找最可能失效点来求解可靠度,在一定情况下有效提高地提高了求解效率与稳定性,对工程应用有一定的指导价值。更多还原

【Abstract】 There are naturally various types of uncertainties in machine design,namely material characteristics,geometric properties and imposed loads.The combination of these uncertainties in machinery ultimately leads to uncertainty in mechanical failure.While pursuing low cost and light weight,machine design should also pursue the reliability of the designed machine.Therefore,the accurate calculation of mechanical reliability becomes a critical issue.A lot of work has been done in solving nonlinear performance function,but there are few ways to coordinate accuracy and computational cost.Therefore,a new reliability index and its solution method are proposed in this paper to solve the reliability.Taking two numerical examples as examples,the optimal values of parameters under two basic variables and three basic variables are given,and the performance is compared with other algorithms.A cantilever tube in mechanics of materials and an existing domestic RV reducer are taken as application case,a set of relatively complete mechanical reliability solution technical scheme is proposed.The main work of the paper is as follows:(1)The concept of regional equivalent of conversion index is proposed.The classical reliability algorithm in probabilistic reliability model is systematically studied and introduced.The regional equivalent of conversion index used to describe the failure region is proposed,and its solution method is explained.(2)The expression of regional equivalent of conversion index is deduced.The expression of regional equivalent of conversion index is deduced from two perspectives of graphic description and integral infinitesimal,and the mapping relationship between regional equivalent of conversion index and failure rate is established when the number of basic variables is 2,3,4,and the mapping relationship is analyzed.(3)The optimal value of parameters was obtained by example analysis.Through two numerical examples,the influence of sampling parameters on the relative error of reliability is obtained,the reasons are analyzed,and the optimized parameter values under different dimensions are given.Two numerical examples of parameter analysis and a mechanical example of cantilever tube are compared with the traditional classical algorithm,and the proposed algorithm is proved to have certain advantages in efficiency and precision.(4)Reliability analysis of cycloid gear mechanism.Taking a certain type of RV reducer made in China as the research object,a three-dimensional mathematical model and finite element simulation model are established for the cycloidal pin gear mechanism,a key part of the second stage transmission mechanism.A series of sample points are generated by experimental design method according to four key geometric parameters,and the response surface was constructed after simulation.Based on the BP neural network,the limit state function of the RV reducer is fitted,and the AFOSM sampling conversion method was used to solve the problem,and the validity of the method for solving practical problems is verified.In this paper,regional equivalent conversion index is proposed based on the traditional advanced first order and second moment,which solves the reliability by sampling instead of searching for the most probable point,effectively improving the solution efficiency and stability under certain circumstances,which has certain engineering application value.更多还原