高速動平衡機的隨機可靠性分析方法研究
發(fā)布時間：2018-08-10 18:16
【摘要】：隨著工程可靠性觀念的普及,機械裝備性能的可靠性在裝備的設計、制造和使用中也逐漸成為必要的性能評價指標。因而,在研究典型機械裝備靜動力學性能的同時對其相應的可靠性和壽命評估方法進行研究將具有重要的工程實用價值。本文依托國家863項目(2009AA04Z419)“典型在役重大裝備的可靠性和壽命再評估與增長技術(shù)”,以高速動平衡機為主要分析對象,系統(tǒng)而深入地研究高速動平衡機的靜動力學性能和隨機可靠性分析方法,以期在旋轉(zhuǎn)機械類重大裝備的性能分析和隨機可靠性評估方面提供理論支持和實踐經(jīng)驗。高速動平衡機的力學系統(tǒng)屬于轉(zhuǎn)子動力學范疇。其力學研究可分為兩個層次:一是等剛度擺架部分;二是擺架-軸承-轉(zhuǎn)子耦合動力系統(tǒng)(簡稱擺架-轉(zhuǎn)子系統(tǒng))。前者以單獨的擺架為研究對象,被平衡轉(zhuǎn)子則以外載的形式考慮;后者還需考慮與被平衡柔性轉(zhuǎn)子間的相互耦合作用。全面掌握這兩個力學系統(tǒng)的靜動力學性能對高速動平衡機的動平衡精度和運行安全尤為重要。但是,由于各種偶然的、不確定性的因素作用,高速動平衡機的性能會表現(xiàn)出諸多不確定性,這使得確定性的性能評價結(jié)果無法反映機械裝備的真實性能情況。隨機不確定性分析與可靠性評估是處理含不確定性因素問題的主要途徑。從隨機可靠性角度評價裝備性能將能有助于提高高速動平衡機安全、可靠運行的裕度。事實上,高速動平衡機屬于小樣本高可靠性設備,并且通常還具有模型復雜、計算量大、高非線性、高維度的特點�？紤]到這些因素,本文在系統(tǒng)分析靜動力學性能的基礎上,重點研究了高速動平衡機的隨機可靠性分析方法,包括對重要失效模式的可靠度計算方法以及關(guān)鍵響應的隨機不確定性分析方法等的研究。主要內(nèi)容可歸納為:(1)研究了高速動平衡機等剛度擺架的靜承載力、靜/動剛度特性以及應力疲勞壽命。首先,建立擺架靜力有限元模型,并分析了幾種典型噸位轉(zhuǎn)子下的擺架靜承載能力和徑向靜剛度變化特點。之后,基于錘擊法測得了擺架動剛度曲線并詳細剖析了擺架當前的動剛度特性。并在少量試驗動剛度數(shù)據(jù)基礎上,給出一種便于工程應用的擺架模態(tài)信息的有限元輔助識別方案。最后,基于準不平衡力下的擺架應力狀態(tài)以及估算的一階臨界轉(zhuǎn)速和不平衡力放大系數(shù)對幾種典型噸位轉(zhuǎn)子下的擺架主彈性支承的應力疲勞壽命進行了估算。(2)研究了高速動平衡機的梁元有限元建模理論和響應敏感性分析的直接微分解法,并給出了擺架-軸承部分的等效剛度阻尼特性系數(shù)公式,推導了一階臨界轉(zhuǎn)速和不平衡力放大系數(shù)的估算公式。首先,基于轉(zhuǎn)子系統(tǒng)梁有限元理論建立了高速動平衡機的有限元方程。在全面分析了方程中涉及到的定義參數(shù)后,給出了模態(tài)特征值和臨界轉(zhuǎn)速對定義參數(shù)敏感性的直接微分法求解公式,以及相應方程系數(shù)矩陣對定義參數(shù)直接微分的層次關(guān)系。給出了忽略交叉特性影響時的擺架-軸承部分的等效剛度和阻尼系數(shù)公式。并在此基礎上推導了基于簡單的擺架-軸承-轉(zhuǎn)子系統(tǒng)模型的一階臨界轉(zhuǎn)速估算公式以及不平衡力荷載作用在擺架上的力放大系數(shù)估算公式。這些公式對擺架主支承應力疲勞壽命估算非常有用。最后,分析了某50mw汽輪機轉(zhuǎn)子動平衡系統(tǒng)的動力學性能和一階特征值響應的敏感性。(3)研究了高速動平衡機隨機因素空間變換的rackwitz-fiessler方法,詳細探討了rackwitz-fiessler方法的正逆變換過程和相關(guān)性變化規(guī)律,并提出了增強r-f方法。首先,從提出的等效r-f條件和數(shù)學推導兩個角度證實了r-f方法中由物理x空間到標準正態(tài)y空間的正變換過程與nataf-pearson(n-p)方法中的等概率邊緣映射變換的一致性。基于這一結(jié)論可以分析出r-f方法中當量正態(tài)化過程的相關(guān)性變化公式同樣是由derkiureghian和liu的公式表示的,并由此提出了增強r-f方法。最后,討論了增強r-f方法與n-p方法的計算量和計算效率。(4)基于copula理論對rackwitz-fiessler方法進行了改進和廣義化推廣,分別提出了改進r-f法和廣義r-f法。首先,針對線性相關(guān)系數(shù)的不足,提出了基于spearman和kendall相關(guān)系數(shù)的改進r-f方法。進而,考慮到傳統(tǒng)r-f方法中的gaussiancopula假設,提出了基于橢圓copula族的廣義r-f法。同時,為了使一次可靠度方法與廣義r-f方法相適應,在不相關(guān)的標準球u空間中基于最可能失效點的概念提出了廣義的一次可靠度指標和廣義的一次可靠度方法。最后,以工程算例的方式,分析了擺架主彈性支承具有無限疲勞壽命的可靠性。(5)提出了一種自適應的mpp快速搜索算法——ahlrf方法,并給出相應的收斂性證明以及討論了影響算法效率的幾個關(guān)鍵問題。首先,在已有基于hlrf的mpp搜索方法基礎上,提出了一種利用已有迭代信息自適應地估算算法參數(shù)的mpp搜索算法——ahlrf�？梢宰C明,ahlrf具有全局收斂性且收斂率至少是線性的。討論了幾個影響aHLRF方法效率的關(guān)鍵問題,并選取了11個工程算例驗證aHLRF方法。最后,以工程算例的方式,分析了擺架主彈性支承的應力疲勞壽命以及轉(zhuǎn)子系統(tǒng)工作轉(zhuǎn)速下穩(wěn)定裕度的可靠性問題。(6)研究了基于譜方法的高速動平衡機臨界轉(zhuǎn)速和不平衡穩(wěn)態(tài)響應的隨機不確定性問題。首先,探討了基于小波基-伽遼金求解方案的Karhunen-Loeve(K-L)展開方法對高斯隨機場近似的誤差來源和影響程度。基于這一K-L展開方案分別處理了轉(zhuǎn)軸彈性模量高斯隨機場和轉(zhuǎn)子分布不平衡量高斯隨機場。進一步,在Sudret提出的盒子-球填充方案基礎上,詳細地給出了一種自動生成具有任意維數(shù)和階數(shù)的多項式混沌基函數(shù)的編程方案。為了將譜隨機有限元方程右端項改寫為以多項式混沌基展開的表達形式,提出了一種遞歸的實現(xiàn)方案。這種遞歸方案只適用于以多項式形式表達的右端項。最后,基于非侵入式的譜隨機有限元解法分析了50MW汽輪機轉(zhuǎn)子動平衡系統(tǒng)臨界轉(zhuǎn)速的不確定性;基于嵌入式的譜隨機有限元解法分析了50MW汽輪機轉(zhuǎn)子動平衡系統(tǒng)在轉(zhuǎn)子隨機點不平衡量和分布不平衡量共同作用下不平衡響應的不確定性。總之,本文在充分考慮高速動平衡機具有的模型復雜、計算量大、高非線性、高維的特點以及屬于小樣本高可靠性設備的事實,完成了對高速動平衡機的靜動力學性能分析和隨機可靠性分析方法的研究。所采用的Rackwitz-Fiessler隨機空間變換方法、具有自適應性的MPP搜索算法——aHLRF方法、以及基于譜方法的隨機不確定性分析方法對其他旋轉(zhuǎn)類機械裝備的隨機可靠性分析也非常適用。
[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.
【學位授予單位】：上海交通大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TB114.3
本文編號：2175808
[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.
【學位授予單位】：上海交通大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TB114.3
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