叶片—转子系统振动特性与参数辨识方法研究
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摘要
高速旋转机械作为一类被广泛使用的机械设备,在许多行业(如航空航天、电力、冶金等)中都发挥着重要的作用,转子系统作为高速旋转机械的重要组成部分,其研究一直受到广泛关注,近年来由于转子系统的故障产生的恶性事故给企业造成过极大的损失,因此对转子系统进行准确的建模以及故障和参数的辨识,逐渐受到关注。
本文以转子系统为主要研究对象,建立了叶片-转子-轴承耦合系统的非线性动力学模型,并将改进的差分进化算法应用到失谐叶盘系统的优化排序以及转子系统的结构参数和故障参数的辨识中。为了进一步提高运算效率,提出了多点加点Kriging代理模型和改进的差分进化算法相结合的参数辨识方法,高效准确的实现了线性和非线性转子系统的参数辨识工作。本文的主要工作有以下几个方面：
1、建立了能够全面考虑叶片弯曲振动的叶片-转子-轴承系统的非线性动力学模型。首先,利用集中质量法将转子系统离散。其次,为分析叶片对转子系统的惯性效应并考虑系统的时变性,将叶片模化为悬臂梁结构,利用假设模态法对叶片进行离散分析,同时根据叶片的循环对称性对系统的微分方程进行简化降阶。对于叶片数量较多的叶片-转子-轴承系统可以实现明显的维数降低的效果。利用数值方法对系统动力学方程进行求解,并通过分岔图、最大Lyapunov指数曲线、相图、Poincar6截面映射、时域波形、幅值谱图等分析了该系统在非线性油膜力作用下的弯扭耦合振动特性。最后,讨论了叶片的存在以及叶片长度对系统非线性演化过程的影响。
2、建立了叶片-圆盘系统的集中参数化模型,分析了叶盘系统自由振动和受迫振动下的振动特性,并讨论了失谐叶盘系统各阶模态的局部化程度以及失谐叶盘系统响应影响的一般规律。结合所得规律,提出了一种评价失谐叶盘系统振动优劣的新的评价参数。最终将差分进化算法应用到失谐叶盘系统叶片排序的优化研究中。在兼顾降低振幅和平衡叶片间振幅大小的情况下,使各叶片较均匀的分担系统的整体振动能量,以达到降低疲劳、延长寿命的目的。
3、在基本差分进化算法的基础上提出了适用于转子系统参数辨识的遗传-自适应混合差分进化算法。由于转子系统待辨识参数过大或者过小同时待辨识区间范围较大,因此首先引入具有全局搜索能力的遗传算法以缩小问题的寻优区间,其次为了防止问题陷入局部最优,提出了自适应Cauchy变异和自适应Caussian变异策略,用以修正差分进化算法原有的变异策略。并以考虑不平衡量的线性转子模型和考虑油膜力和碰摩力共同作用下的非线性转子模型为对象进行仿真分析,验证了所提出方法在转子系统参数辨识中的可行性和准确性。最后与基本差分进化算法和遗传算法进行比较,结果显示本文提出的GA-AHDE优化算法能够快速有效的逼近全局最优解。
4、在原有Kriging代理模型的基础上,结合改进的自适应混合差分进化算法设计了新的转子系统参数辨识方法,在每次更新Kriging代理模型时,增加当前由差分进化算法得到的最优设计点,以提高模型的全局预测精度。通过数值算例和实验,验证了该方法在转子系统参数辨识中的高效性和准确性。在此基础上又将新的多点加点准则引入到Kriging代理模型中,即在每次更新模型时除了增加当前最优设计点外,还根据搜索进程加入相关度较大或较小的点,从而进一步提高了Kriging代理模型的精度,更大程度的提高了搜索效率。最后通过完成线性算例和非线性算例的辨识工作,讨论了多点加点的Kriging代理模型与改进的差分进化算法相结合的参数辨识方法在不同情况下的的辨识结果,并分析了该方法的适用条件。
High speed rotating machinery is widely used in many fields, such as aerospace, electric power, metallurgical and so on. It is necessary to pay close attention to build an effective modelling strategy and identify the faults and parameters of high speed rotating machinery, which can reduce the mechanical faults and improve the safety and reliability of high speed rotating machinery.
In this paper, we research on the rotor system. Firstly, a coupling nonlinear dynamical model of the blade-rotor-bearing system is developed to analyse the interaction of the rotor, blade and bearing. Secondly, the improved differential evolution is used to optimize the installation arrangement of mistuned blades and identify the faults and parameters of the rotor system. To improve the operation efficiency, a new identification method combined with multi-points added Kriging surrogate model and improved differential evolution algorithm is presented, which identifies the faults and parameters of linear and nonlinear rotor system effectively and exactly. The main works in this paper are as follows:
1. The nonlinear coupling model of blade-rotor-bearing system is established by the Lagrange approach. Simplifying the rotor system with the lumped mass method. The baldes are modeled as a cantilever beam and simplified with the assumed mode method. The motion equations are simplified owing to cyclic symmetric property. According to this, the dimension of blade-rotor-bearing system can be reducted, especially for too many blades. Considering the bending-torsion coupling motion with nonlinear oil film, the motion differential equations are solved. The bifurcation diagrams, maximum Lyapunov exponent diagrams, phase plane portraits, Poincare maps, time domain waveform, amplitude-frequency curve are used to analyse the motion state of blade-rotor-bearing system. The nonlinear dynamic characteristics of the rotor system with or without blades and the effect of blade length on onlinear dynamic characteristics are discussed.
2. A lumped parameter model of blade-disk system is established. At the beginning, we analyse the dynamic characteristics of free vibration and forced vibration and discuss the effect of mistuning on mode localization of various orders. Based on the rules, a new formula which evaluates the degree of mode localization of mistuned blade-disk is proposed. At the end, the differential evolution algorithm is used to optimize the installation arrangement of mistuned blades. Both reducing vibration and tuning amplitudes are considered which makes each blade share vibration energy evenly and bring down the material fatigue of blades.
3. An improved differential evolution algorithm is proposed. It is suitable for identifying the faults and parameters of rotor system. Because of the large range of parameter interval, the genetic algorithm based on its global searching ability is used to reduce the optimization interval firstly. Secondly, in order to prevent reaching the dilemma problem and the local optimal solution, the adaptive Cauchy mutation and adaptive Gaussian mutation are put forward to modify the original mutation strategy of the differential evolution. A linear rotor system with unbalance and a nonlinear rotor system are as the numerical examples. The results prove that the improved differential evolution algorithm is efficient and accurate on faults and parameters identification of rotor system.
4. A new parameter identification method is designed based on the Kriging surrogate model and the improved differential evolution algorithm. This identification method updates the Kriging surrogate model by adding current optimal point, which improves the accuracy of the Kriging surrogate model in global approximation. A numerical example and the experiment are analysed to vertify the effectiveness and accuracy of the method on parameter identification of rotor system. After that, a new multi-points addition criterion is joined in the Kriging surrogate model. It means that not only the current optimal point, but also the correlated points are add to update the Kriging surrogate model, which can improve the precision of Kriging surrogate model in a short time. At the end, the linear and nonlinear examples are analysed. We discuss the identification results using the multi-points added Kriging-AHDE, and the applicable condition of this method.
本文以转子系统为主要研究对象,建立了叶片-转子-轴承耦合系统的非线性动力学模型,并将改进的差分进化算法应用到失谐叶盘系统的优化排序以及转子系统的结构参数和故障参数的辨识中。为了进一步提高运算效率,提出了多点加点Kriging代理模型和改进的差分进化算法相结合的参数辨识方法,高效准确的实现了线性和非线性转子系统的参数辨识工作。本文的主要工作有以下几个方面：
1、建立了能够全面考虑叶片弯曲振动的叶片-转子-轴承系统的非线性动力学模型。首先,利用集中质量法将转子系统离散。其次,为分析叶片对转子系统的惯性效应并考虑系统的时变性,将叶片模化为悬臂梁结构,利用假设模态法对叶片进行离散分析,同时根据叶片的循环对称性对系统的微分方程进行简化降阶。对于叶片数量较多的叶片-转子-轴承系统可以实现明显的维数降低的效果。利用数值方法对系统动力学方程进行求解,并通过分岔图、最大Lyapunov指数曲线、相图、Poincar6截面映射、时域波形、幅值谱图等分析了该系统在非线性油膜力作用下的弯扭耦合振动特性。最后,讨论了叶片的存在以及叶片长度对系统非线性演化过程的影响。
2、建立了叶片-圆盘系统的集中参数化模型,分析了叶盘系统自由振动和受迫振动下的振动特性,并讨论了失谐叶盘系统各阶模态的局部化程度以及失谐叶盘系统响应影响的一般规律。结合所得规律,提出了一种评价失谐叶盘系统振动优劣的新的评价参数。最终将差分进化算法应用到失谐叶盘系统叶片排序的优化研究中。在兼顾降低振幅和平衡叶片间振幅大小的情况下,使各叶片较均匀的分担系统的整体振动能量,以达到降低疲劳、延长寿命的目的。
3、在基本差分进化算法的基础上提出了适用于转子系统参数辨识的遗传-自适应混合差分进化算法。由于转子系统待辨识参数过大或者过小同时待辨识区间范围较大,因此首先引入具有全局搜索能力的遗传算法以缩小问题的寻优区间,其次为了防止问题陷入局部最优,提出了自适应Cauchy变异和自适应Caussian变异策略,用以修正差分进化算法原有的变异策略。并以考虑不平衡量的线性转子模型和考虑油膜力和碰摩力共同作用下的非线性转子模型为对象进行仿真分析,验证了所提出方法在转子系统参数辨识中的可行性和准确性。最后与基本差分进化算法和遗传算法进行比较,结果显示本文提出的GA-AHDE优化算法能够快速有效的逼近全局最优解。
4、在原有Kriging代理模型的基础上,结合改进的自适应混合差分进化算法设计了新的转子系统参数辨识方法,在每次更新Kriging代理模型时,增加当前由差分进化算法得到的最优设计点,以提高模型的全局预测精度。通过数值算例和实验,验证了该方法在转子系统参数辨识中的高效性和准确性。在此基础上又将新的多点加点准则引入到Kriging代理模型中,即在每次更新模型时除了增加当前最优设计点外,还根据搜索进程加入相关度较大或较小的点,从而进一步提高了Kriging代理模型的精度,更大程度的提高了搜索效率。最后通过完成线性算例和非线性算例的辨识工作,讨论了多点加点的Kriging代理模型与改进的差分进化算法相结合的参数辨识方法在不同情况下的的辨识结果,并分析了该方法的适用条件。
High speed rotating machinery is widely used in many fields, such as aerospace, electric power, metallurgical and so on. It is necessary to pay close attention to build an effective modelling strategy and identify the faults and parameters of high speed rotating machinery, which can reduce the mechanical faults and improve the safety and reliability of high speed rotating machinery.
In this paper, we research on the rotor system. Firstly, a coupling nonlinear dynamical model of the blade-rotor-bearing system is developed to analyse the interaction of the rotor, blade and bearing. Secondly, the improved differential evolution is used to optimize the installation arrangement of mistuned blades and identify the faults and parameters of the rotor system. To improve the operation efficiency, a new identification method combined with multi-points added Kriging surrogate model and improved differential evolution algorithm is presented, which identifies the faults and parameters of linear and nonlinear rotor system effectively and exactly. The main works in this paper are as follows:
1. The nonlinear coupling model of blade-rotor-bearing system is established by the Lagrange approach. Simplifying the rotor system with the lumped mass method. The baldes are modeled as a cantilever beam and simplified with the assumed mode method. The motion equations are simplified owing to cyclic symmetric property. According to this, the dimension of blade-rotor-bearing system can be reducted, especially for too many blades. Considering the bending-torsion coupling motion with nonlinear oil film, the motion differential equations are solved. The bifurcation diagrams, maximum Lyapunov exponent diagrams, phase plane portraits, Poincare maps, time domain waveform, amplitude-frequency curve are used to analyse the motion state of blade-rotor-bearing system. The nonlinear dynamic characteristics of the rotor system with or without blades and the effect of blade length on onlinear dynamic characteristics are discussed.
2. A lumped parameter model of blade-disk system is established. At the beginning, we analyse the dynamic characteristics of free vibration and forced vibration and discuss the effect of mistuning on mode localization of various orders. Based on the rules, a new formula which evaluates the degree of mode localization of mistuned blade-disk is proposed. At the end, the differential evolution algorithm is used to optimize the installation arrangement of mistuned blades. Both reducing vibration and tuning amplitudes are considered which makes each blade share vibration energy evenly and bring down the material fatigue of blades.
3. An improved differential evolution algorithm is proposed. It is suitable for identifying the faults and parameters of rotor system. Because of the large range of parameter interval, the genetic algorithm based on its global searching ability is used to reduce the optimization interval firstly. Secondly, in order to prevent reaching the dilemma problem and the local optimal solution, the adaptive Cauchy mutation and adaptive Gaussian mutation are put forward to modify the original mutation strategy of the differential evolution. A linear rotor system with unbalance and a nonlinear rotor system are as the numerical examples. The results prove that the improved differential evolution algorithm is efficient and accurate on faults and parameters identification of rotor system.
4. A new parameter identification method is designed based on the Kriging surrogate model and the improved differential evolution algorithm. This identification method updates the Kriging surrogate model by adding current optimal point, which improves the accuracy of the Kriging surrogate model in global approximation. A numerical example and the experiment are analysed to vertify the effectiveness and accuracy of the method on parameter identification of rotor system. After that, a new multi-points addition criterion is joined in the Kriging surrogate model. It means that not only the current optimal point, but also the correlated points are add to update the Kriging surrogate model, which can improve the precision of Kriging surrogate model in a short time. At the end, the linear and nonlinear examples are analysed. We discuss the identification results using the multi-points added Kriging-AHDE, and the applicable condition of this method.
引文
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