高速动平衡机的随机可靠性分析方法研究

发布时间：2018-08-10 18:16

【摘要】：随着工程可靠性观念的普及,机械装备性能的可靠性在装备的设计、制造和使用中也逐渐成为必要的性能评价指标。因而,在研究典型机械装备静动力学性能的同时对其相应的可靠性和寿命评估方法进行研究将具有重要的工程实用价值。本文依托国家863项目(2009AA04Z419)“典型在役重大装备的可靠性和寿命再评估与增长技术”,以高速动平衡机为主要分析对象,系统而深入地研究高速动平衡机的静动力学性能和随机可靠性分析方法,以期在旋转机械类重大装备的性能分析和随机可靠性评估方面提供理论支持和实践经验。高速动平衡机的力学系统属于转子动力学范畴。其力学研究可分为两个层次:一是等刚度摆架部分;二是摆架-轴承-转子耦合动力系统(简称摆架-转子系统)。前者以单独的摆架为研究对象,被平衡转子则以外载的形式考虑;后者还需考虑与被平衡柔性转子间的相互耦合作用。全面掌握这两个力学系统的静动力学性能对高速动平衡机的动平衡精度和运行安全尤为重要。但是,由于各种偶然的、不确定性的因素作用,高速动平衡机的性能会表现出诸多不确定性,这使得确定性的性能评价结果无法反映机械装备的真实性能情况。随机不确定性分析与可靠性评估是处理含不确定性因素问题的主要途径。从随机可靠性角度评价装备性能将能有助于提高高速动平衡机安全、可靠运行的裕度。事实上,高速动平衡机属于小样本高可靠性设备,并且通常还具有模型复杂、计算量大、高非线性、高维度的特点。考虑到这些因素,本文在系统分析静动力学性能的基础上,重点研究了高速动平衡机的随机可靠性分析方法,包括对重要失效模式的可靠度计算方法以及关键响应的随机不确定性分析方法等的研究。主要内容可归纳为:(1)研究了高速动平衡机等刚度摆架的静承载力、静/动刚度特性以及应力疲劳寿命。首先,建立摆架静力有限元模型,并分析了几种典型吨位转子下的摆架静承载能力和径向静刚度变化特点。之后,基于锤击法测得了摆架动刚度曲线并详细剖析了摆架当前的动刚度特性。并在少量试验动刚度数据基础上,给出一种便于工程应用的摆架模态信息的有限元辅助识别方案。最后,基于准不平衡力下的摆架应力状态以及估算的一阶临界转速和不平衡力放大系数对几种典型吨位转子下的摆架主弹性支承的应力疲劳寿命进行了估算。(2)研究了高速动平衡机的梁元有限元建模理论和响应敏感性分析的直接微分解法,并给出了摆架-轴承部分的等效刚度阻尼特性系数公式,推导了一阶临界转速和不平衡力放大系数的估算公式。首先,基于转子系统梁有限元理论建立了高速动平衡机的有限元方程。在全面分析了方程中涉及到的定义参数后,给出了模态特征值和临界转速对定义参数敏感性的直接微分法求解公式,以及相应方程系数矩阵对定义参数直接微分的层次关系。给出了忽略交叉特性影响时的摆架-轴承部分的等效刚度和阻尼系数公式。并在此基础上推导了基于简单的摆架-轴承-转子系统模型的一阶临界转速估算公式以及不平衡力荷载作用在摆架上的力放大系数估算公式。这些公式对摆架主支承应力疲劳寿命估算非常有用。最后,分析了某50mw汽轮机转子动平衡系统的动力学性能和一阶特征值响应的敏感性。(3)研究了高速动平衡机随机因素空间变换的rackwitz-fiessler方法,详细探讨了rackwitz-fiessler方法的正逆变换过程和相关性变化规律,并提出了增强r-f方法。首先,从提出的等效r-f条件和数学推导两个角度证实了r-f方法中由物理x空间到标准正态y空间的正变换过程与nataf-pearson(n-p)方法中的等概率边缘映射变换的一致性。基于这一结论可以分析出r-f方法中当量正态化过程的相关性变化公式同样是由derkiureghian和liu的公式表示的,并由此提出了增强r-f方法。最后,讨论了增强r-f方法与n-p方法的计算量和计算效率。(4)基于copula理论对rackwitz-fiessler方法进行了改进和广义化推广,分别提出了改进r-f法和广义r-f法。首先,针对线性相关系数的不足,提出了基于spearman和kendall相关系数的改进r-f方法。进而,考虑到传统r-f方法中的gaussiancopula假设,提出了基于椭圆copula族的广义r-f法。同时,为了使一次可靠度方法与广义r-f方法相适应,在不相关的标准球u空间中基于最可能失效点的概念提出了广义的一次可靠度指标和广义的一次可靠度方法。最后,以工程算例的方式,分析了摆架主弹性支承具有无限疲劳寿命的可靠性。(5)提出了一种自适应的mpp快速搜索算法——ahlrf方法,并给出相应的收敛性证明以及讨论了影响算法效率的几个关键问题。首先,在已有基于hlrf的mpp搜索方法基础上,提出了一种利用已有迭代信息自适应地估算算法参数的mpp搜索算法——ahlrf。可以证明,ahlrf具有全局收敛性且收敛率至少是线性的。讨论了几个影响aHLRF方法效率的关键问题,并选取了11个工程算例验证aHLRF方法。最后,以工程算例的方式,分析了摆架主弹性支承的应力疲劳寿命以及转子系统工作转速下稳定裕度的可靠性问题。(6)研究了基于谱方法的高速动平衡机临界转速和不平衡稳态响应的随机不确定性问题。首先,探讨了基于小波基-伽辽金求解方案的Karhunen-Loeve(K-L)展开方法对高斯随机场近似的误差来源和影响程度。基于这一K-L展开方案分别处理了转轴弹性模量高斯随机场和转子分布不平衡量高斯随机场。进一步,在Sudret提出的盒子-球填充方案基础上,详细地给出了一种自动生成具有任意维数和阶数的多项式混沌基函数的编程方案。为了将谱随机有限元方程右端项改写为以多项式混沌基展开的表达形式,提出了一种递归的实现方案。这种递归方案只适用于以多项式形式表达的右端项。最后,基于非侵入式的谱随机有限元解法分析了50MW汽轮机转子动平衡系统临界转速的不确定性;基于嵌入式的谱随机有限元解法分析了50MW汽轮机转子动平衡系统在转子随机点不平衡量和分布不平衡量共同作用下不平衡响应的不确定性。总之,本文在充分考虑高速动平衡机具有的模型复杂、计算量大、高非线性、高维的特点以及属于小样本高可靠性设备的事实,完成了对高速动平衡机的静动力学性能分析和随机可靠性分析方法的研究。所采用的Rackwitz-Fiessler随机空间变换方法、具有自适应性的MPP搜索算法——aHLRF方法、以及基于谱方法的随机不确定性分析方法对其他旋转类机械装备的随机可靠性分析也非常适用。
[Abstract]:With the popularization of the concept of Engineering reliability, the reliability of mechanical equipment performance has gradually become a necessary performance evaluation index in the design, manufacture and use of equipment. Relying on the National 863 Project (2009 AA04Z419) "Reliability and Life Reassessment and Growth Technology of Typical in-service Major Equipments", this paper systematically and thoroughly studies the static and dynamic performance and stochastic reliability analysis method of high-speed dynamic balancing machine, with the high-speed dynamic balancing machine as the main analysis object, in order to make it possible for the rotating machinery major equipment. The mechanical system of high-speed dynamic balancing machine belongs to the category of rotor dynamics. Its mechanical research can be divided into two levels: one is equal stiffness pendulum part; the other is pendulum-bearing-rotor coupling dynamic system (referred to as pendulum-rotor system). For the research object, the balanced rotor is considered in the form of load; the latter also needs to consider the interaction between the balanced flexible rotor and the balanced flexible rotor. As a result, the performance of high-speed dynamic balancer will show many uncertainties, which makes the deterministic performance evaluation results can not reflect the real performance of mechanical equipment. Random uncertainty analysis and reliability evaluation are the main ways to deal with uncertain factors. In order to improve the margin of safe and reliable operation of high-speed dynamic balancing machine, in fact, high-speed dynamic balancing machine belongs to small sample high-reliability equipment, and usually has the characteristics of complex model, large amount of calculation, high non-linearity and high dimension. The main contents can be summarized as follows: (1) The static bearing capacity, static/dynamic stiffness characteristics and stress fatigue life of the equi-stiffness pendulum of high-speed dynamic balancer are studied. Firstly, the pendulum is established. The static finite element model of the frame is established, and the static load-bearing capacity and radial static stiffness of the pendulum under several typical tonnage rotors are analyzed. Then, the dynamic stiffness curve of the pendulum frame is measured based on the hammering method, and the current dynamic stiffness characteristics of the pendulum frame are analyzed in detail. Finally, the stress fatigue life of the main elastic support of the pendulum under several typical tonnage rotors is estimated based on the stress state of the pendulum under quasi-unbalanced force and the estimated first-order critical speed and unbalanced force amplification coefficient. (2) The beam element finite element method of the high-speed dynamic balancer is studied. Based on the modeling theory and the direct differential method of response sensitivity analysis, the equivalent stiffness damping coefficient formulas of the pendulum-bearing part are given, and the estimation formulas of the first-order critical speed and the unbalanced force amplification coefficient are deduced. After analyzing the defining parameters involved in the equation, the formulas for solving the sensitivity of modal eigenvalues and critical speeds to the defining parameters are given, and the hierarchical relations between the coefficients of the corresponding equations and the direct derivatives of the defining parameters are given. On the basis of these formulas, the first-order critical speed estimation formula based on a simple swing-bearing-rotor system model and the force amplification coefficient estimation formula under unbalanced load on the swing frame are derived. These formulas are very useful for the fatigue life estimation of the main support stress of the swing frame. Finally, the rotor motion of a 50 MW steam turbine is analyzed. (3) The rackwitz-fiessler method for space transformation of stochastic factors in high-speed dynamic balancing machine is studied. The forward-inverse transformation process and the correlation variation law of the rackwitz-fiessler method are discussed in detail. The enhanced R-F method is proposed. Firstly, the equivalent R-F condition and the corresponding correlation are given. Mathematical deduction proves the consistency between the positive transformation from physical X-Space to standard normal Y-Space in the r-f method and the equal probability edge mapping transformation in the nataf-pearson (n-p) method. Based on this conclusion, it can be concluded that the correlation variation formula of the equivalent normalization process in the r-f method is also derived by derkiureghian and Liu Finally, the computational complexity and efficiency of the enhanced R-F method and the N-P method are discussed. (4) Based on the copula theory, the rackwitz-fiessler method is improved and generalized, and the improved R-F method and the generalized R-F method are proposed respectively. Firstly, to overcome the shortcomings of the linear correlation coefficient, the basis method is proposed. Then, considering the Gaussian opula hypothesis in the traditional R-F method, a generalized R-F method based on the elliptic copula family is proposed. In order to make the first-order reliability method fit the generalized R-F method, a concept based on the most likely failure point in the unrelated standard sphere u space is proposed. The generalized first-order reliability index and the generalized first-order reliability method are given. Finally, the reliability of the main elastic support of the pendulum with infinite fatigue life is analyzed by means of an engineering example. (5) An adaptive MPP fast search algorithm, ahlrf method, is proposed, and the convergence proof is given. The efficiency of the algorithm is discussed. Firstly, on the basis of the existing MPP search method based on hlrf, a MPP search algorithm, ahlrf, is proposed to estimate the parameters of the algorithm adaptively by using the existing iterative information. It can be proved that ahlrf has global convergence and the convergence rate is at least linear. Eleven engineering examples are selected to validate the aHLRF method. Finally, the stress fatigue life of the main elastic support and the reliability of the stability margin of the rotor system at operating speed are analyzed by means of an engineering example. (6) The stochastic uncertainties of the critical speed and the unbalanced steady-state response of the high-speed dynamic balancer based on the spectral method are studied. Firstly, the error sources and the influence degree of the Karhunen-Loeve (K-L) expansion method based on the wavelet basis-Galerkin solution for Gaussian random field approximation are discussed. Based on the sub-sphere filling scheme, a programming scheme for automatically generating polynomial chaotic basis functions with arbitrary dimension and order is given in detail. In order to rewrite the right-hand-end term of the spectral stochastic finite element equation into the expression of polynomial chaotic basis expansion, a recursive implementation scheme is proposed. Finally, the uncertainty of the critical speed of the 50 MW turbine rotor dynamic balancing system is analyzed based on the non-invasive spectral stochastic finite element method, and the common unbalance between the random point unbalance and the distributed unbalance of the 50 MW turbine rotor dynamic balancing system is analyzed based on the embedded spectral stochastic finite element method. In a word, the static and dynamic performance analysis and stochastic reliability analysis methods of high-speed dynamic balancer are studied in this paper, taking into account the characteristics of complex model, large amount of calculation, high nonlinearity, high dimension and the fact that it belongs to small sample and high reliability equipment. The Rackwitz-Fiessler random space transformation method, the adaptive MPP search algorithm aHLRF method and the random uncertainty analysis method based on the spectral method are also very suitable for the random reliability analysis of other rotating machinery equipment.
【学位授予单位】：上海交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TB114.3

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