可倾瓦轴承—转子系统的非线性动力学分析与主动控制
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摘要
随着大型旋转机械向高转速、高负载、高精度等方向发展,其核心部件轴承—转子系统的非线性动力失稳问题越来越突出。因此,需要深入研究轴承—转子系统的非线性动力学特性和失稳机理以及其结构参数和运行参数对稳定性的影响规律。滑动轴承的油膜力是其中极为典型的非线性因素之一,建立一个合理且易于解析处理的油膜力模型对于轴承—转子系统运动稳定性分析和工程应用都具有重要意义。另一方面,要对导致轴承—转子系统动力失稳的因素加以控制,采用有效措施提高系统的运动稳定性,转子在工作中一旦出现异常振动现象,要立即采取有效的纠正措施,避免动力失稳后产生更加严重的后果。对于轴承—转子系统的振动控制问题,控制装置的设计与控制器参数的调节在很大程度上决定了控制性能的好坏。
本文的研究工作主要集中在两个方面,即可倾瓦轴承非线性油膜力解析模型的建立和轴承—转子系统的振动主动控制。首先建立了可倾瓦滑动轴承的非线性油膜力解析模型,接着针对可倾瓦轴承—转子系统油膜失稳等问题采用主动润滑系统进行控制,并设计了多种行之有效的控制器,计算分析在各种控制器作用下转子系统油膜失稳的控制情况,取得的主要成果有:
1.基于短轴承假设,建立了可倾瓦轴承非线性油膜力的解析模型。首先根据轴承单个瓦块与转子的运动平衡关系和几何关系,推导出了瓦块摆角的计算公式,基于短轴承假设和Reynolds边界条件求得了每个瓦块上的油膜压力分布,并采用油膜压力的修正函数来确定油膜力的自由边界条件,对每个瓦块的油膜压力进行积分得到其油膜力,进而将所有瓦块的油膜力进行矢量求和得到了整个可倾瓦轴承的非线性油膜力的解析表达式。利用油膜力解析模型分析了可倾瓦轴承—非对称转子系统的动力学特性,通过和有限差分法导出的油膜力模型的计算结果进行比较,证实了本文油膜力解析模型的有效性和实用性。
2.针对可倾瓦轴承—非对称转子系统存在的油膜涡动等失稳现象,设计了基于PI、PID的主动润滑控制系统。本文建立了基于电液控制系统的主动可倾瓦轴承的动力学模型,包括在主动润滑下可倾瓦轴承的油膜厚度,主动润滑Reynolds方程,电液控制系统方程等。为便于控制的实现,采用工程上常用的PI、PID控制器对可倾瓦轴承—非对称转子系统进行控制,并分析其动力学响应。研究结果表明,在主动润滑控制系统的作用下,转子系统的振动得到很好的抑制,系统发生油膜涡动时的转速得到提高,系统稳定工作的转速范围得到拓宽,并且发生油膜涡动时系统的振幅也得到了抑制。
3.针对电液控制系统存在的高度非线性、时变不确定性等问题,采用神经网络技术对主动润滑控制系统进行改进。利用RBF神经网络和BP神经网络来优化常规的PID控制器的参数,处理液压系统中的不确定性,以满足液压伺服系统的动态性能和静态性能要求。针对主动润滑控制系统设计了RBF神经网络PID和BP神经网络PID控制器。并采用基于这两种控制器的主动润滑系统对可倾瓦轴承—非对称转子系统进行控制,数值计算的结果表明,与PI、PID控制器的作用效果相比,基于神经网络PID控制的主动润滑系统在控制精度和动态性能等方面的都有明显的优越性。
4.在利用神经网络技术优化PID控制器参数的基础上,进一步设计了模糊PID和模糊神经网络PID控制器来改进主动润滑控制系统。将模糊控制不依赖精确模型、算法灵活而神经网络具有很强的鲁棒性和非线性映射能力等特点相结合,采用模糊控制和模糊神经网络控制在线整定PID控制器的参数。分析计算了基于模糊PID和模糊神经网络PID控制器作用下可倾瓦轴承—非对称转子系统的动力学响应,与之前设计的控制器比较,模糊PID和模糊神经网络PID控制具有更好的控制性能。
5.研究了一类可倾瓦轴承双盘外伸转子系统的非线性动力学分析和主动控制问题。基于有限元法建立了系统的非线性动力学方程,油膜力采用本文导出的可倾瓦轴承非线性油膜力解析模型。采用数值方法对该系统的耦合动力学方程进行求解,分析了转子系统的非线性动力学特性。在没有主动润滑的情况下,随着转速的升高会出现油膜涡动和油膜振荡等失稳现象,采用基于模糊PID和模糊神经网络PID控制器的主动润滑对该系统进行控制的结果表明,主动润滑系统能够完全消除油膜振荡现象,较好的抑制油膜涡动时转子系统的振幅,极大的拓宽转子系统稳定运行的转速范围。比较而言,模糊神经网络PID控制的效果优于模糊PID控制。
With the trending to high speed, high precision and high load of the large scale rotating machinery, the increasingly nonlinear dynamic instability of rotor-bearing system have become the most serious problem. It is necessary to investigate the nonlinear dynamic behaviors, instability and the influences of operating parameters on dynamic stability of rotor-bearing systems. The fluid film force model is crucial to the nonlinear dynamics analysis of a rotor-bearing system. The formulation of a reasonable and manageable analytical fluid film force model is of great significance to the stability analysis and its engineering applications of rotor-bearing systems. On the other hand, the dynamic instability factors of the rotor-bearing system must be kept under control and the effective measures must be taken to improve the dynamic stability of the system. Once the abnormal phenomenon occurs, the effective corrective measures have to be put into action in case of the more serious consequences. The effectiveness of the active control to the rotor-bearing system mainly depends on the design of the control device and the regulation of the controller parameters.
In this dissertation two challenging issues in the investigation of large-scale rotor-bearing system are investigated, i.e. the formulation of analytical fluid film force model of a tilting pad bearing and active control of the self-excited vibration problem. Firstly, the nonlinear fluid film force model of a tilting pad journal bearing is deduced based on the short bearing assumption. And then an active lubrication device is adopted to eliminate the self-induced vibration of the rotor-bearing system. Correspondingly, several active control strategies are designed to regulate the electro-hydraulic control system. The nonlinear dynamic responses of the active lubricated rotor-bearing system based on different controllers are worked out and the inhibitions of self-excited vibration of the systems with various controllers are compared. The main achievements are listed below:
1. Based on the assumption of the short journal bearing,the fluid force model of the tilting pad journal bearing is formulated. Taking as a reference of the Capone model which is formulated based on the assumption of the short journal bearing,the fluid film pressure distribution is derived in each pad’s own local reference frame. The relation of the pad rotation angle and motion of the rotor is figured out. Then the fluid film pressure distribution of the tilting pad bearing in global reference frame is obtained by coordinate transformations. The nonlinear fluid force model of the tilting pad is formulated by integrating the fluid film pressure distribution. A numerical model for an unsymmetrical flexible-rotor supported by two tilting pad bearings is given and the dynamic response is worked out. The fluid force model based on the finite difference model for the tilting pad journal bearing are deduced to confirm that the analytical model is valid to deal with the problem of nonlinear dynamics of the rotor-bearing system. The calculated results show that the analytical model proposed can be used to analyze the dynamical behavior of the rotor-bearing system qualitatively and to save the computing cost for solving the system.
2. To eliminate the whirl and whip instability of the rotor bearing system, the active lubrication action is adopted to simultaneous reduction of wear and vibration between rotating and stationary machinery parts. The dynamic model of the electro-hydraulic active control system including the active lubricated tilting pad journal bearing and the electro-hydraulic system is formulated. In order to facilitate the realization of the control device, the design strategies of PI and PID controllers, applied to a tilting-pad journal bearing, are analyzed and discussed. Numerical results show that an effective vibration reduction of the unbalance response of an asymmetric rotor is performed for the system with PI or PID controllers. The feasibility of eliminating rotor-bearing instabilities (phenomena of whirl) by using active lubrication is also investigated, that illustrates clearly one of its most promising applications.
3. To deal with the disadvantages of highly nonlinear, time-varying uncertainty and delay characteristics in the electro-hydraulic control system, the neural network (NN) technology is applied to improve the active lubricated control system. The most efficient neural network, radical basis function (RBF) and back propagation (BP) are designed to optimize the parameters of the PID controller to settle the uncertainty and inaccuracy of the hydraulic system. Then the dynamic performance requirements of hydraulic servo system are achieved. Then two kinds of NN-PID controllers are applied to an active lubricated tilting-pad bearing system, and the dynamic responses of the asymmetric rotor-bearing system are analyzed and calculated. Comparing with the results based on the PI and PID controllers, the NN-PID controller show better performance.
4. The fuzzy PID control and fuzzy neural network PID control are designed to improve the active lubricated system after the successful application of neural network technology in optimizing PID parameters. Fuzzy controller does not rely on accurate models and possess flexible algorithms especially is suitable for the control of the system with nonlinear, large delay, time-varying characteristics. While the neural network has the advantage of strong robustness, memory capacity, non-linear mapping capabilities and a self-learning ability. So the fuzzy PID controller and fuzzy neural network PID controller are designed to regulate the active lubrication of the tilting pad bearing. Then the dynamic responses of the asymmetrical rotor-bearing system with fuzzy PID and fuzzy neural network PID controllers are worked out. Comparing with the results based on the other control laws, the fuzzy neural network PID controller shows better performance.
5. The nonlinear dynamics analysis and active control of the overhang rotor system with double disks supported by two tilting pad journal bearings is investigated. The nonlinear dynamic model of the overhang rotor system is formulated based on the finite element theory. The analytical fluid film force model of the tilting pad journal bearing proposed in this dissertation are applied to analyze the nonlinear dynamic characteristics of the rotor system. Numerical method is used to solve the coupled dynamic equations and the result shows that whirl and whip phenomena occur when the rotational speed is increasing upto the critical case. Thus the active lubrication systems based on both fuzzy PID and fuzzy neural network PID controller are designed to suppress the vibration of the overhang rotor system. The results show that by active lubrication the whirl amplitude of the system is greatly suppressed and whip instability is totally eliminated. The stable operating speed range of the rotor system is widely broadened. The control performance of the fuzzy neural network PID controller is better than that of fuzzy PID controller.
本文的研究工作主要集中在两个方面,即可倾瓦轴承非线性油膜力解析模型的建立和轴承—转子系统的振动主动控制。首先建立了可倾瓦滑动轴承的非线性油膜力解析模型,接着针对可倾瓦轴承—转子系统油膜失稳等问题采用主动润滑系统进行控制,并设计了多种行之有效的控制器,计算分析在各种控制器作用下转子系统油膜失稳的控制情况,取得的主要成果有:
1.基于短轴承假设,建立了可倾瓦轴承非线性油膜力的解析模型。首先根据轴承单个瓦块与转子的运动平衡关系和几何关系,推导出了瓦块摆角的计算公式,基于短轴承假设和Reynolds边界条件求得了每个瓦块上的油膜压力分布,并采用油膜压力的修正函数来确定油膜力的自由边界条件,对每个瓦块的油膜压力进行积分得到其油膜力,进而将所有瓦块的油膜力进行矢量求和得到了整个可倾瓦轴承的非线性油膜力的解析表达式。利用油膜力解析模型分析了可倾瓦轴承—非对称转子系统的动力学特性,通过和有限差分法导出的油膜力模型的计算结果进行比较,证实了本文油膜力解析模型的有效性和实用性。
2.针对可倾瓦轴承—非对称转子系统存在的油膜涡动等失稳现象,设计了基于PI、PID的主动润滑控制系统。本文建立了基于电液控制系统的主动可倾瓦轴承的动力学模型,包括在主动润滑下可倾瓦轴承的油膜厚度,主动润滑Reynolds方程,电液控制系统方程等。为便于控制的实现,采用工程上常用的PI、PID控制器对可倾瓦轴承—非对称转子系统进行控制,并分析其动力学响应。研究结果表明,在主动润滑控制系统的作用下,转子系统的振动得到很好的抑制,系统发生油膜涡动时的转速得到提高,系统稳定工作的转速范围得到拓宽,并且发生油膜涡动时系统的振幅也得到了抑制。
3.针对电液控制系统存在的高度非线性、时变不确定性等问题,采用神经网络技术对主动润滑控制系统进行改进。利用RBF神经网络和BP神经网络来优化常规的PID控制器的参数,处理液压系统中的不确定性,以满足液压伺服系统的动态性能和静态性能要求。针对主动润滑控制系统设计了RBF神经网络PID和BP神经网络PID控制器。并采用基于这两种控制器的主动润滑系统对可倾瓦轴承—非对称转子系统进行控制,数值计算的结果表明,与PI、PID控制器的作用效果相比,基于神经网络PID控制的主动润滑系统在控制精度和动态性能等方面的都有明显的优越性。
4.在利用神经网络技术优化PID控制器参数的基础上,进一步设计了模糊PID和模糊神经网络PID控制器来改进主动润滑控制系统。将模糊控制不依赖精确模型、算法灵活而神经网络具有很强的鲁棒性和非线性映射能力等特点相结合,采用模糊控制和模糊神经网络控制在线整定PID控制器的参数。分析计算了基于模糊PID和模糊神经网络PID控制器作用下可倾瓦轴承—非对称转子系统的动力学响应,与之前设计的控制器比较,模糊PID和模糊神经网络PID控制具有更好的控制性能。
5.研究了一类可倾瓦轴承双盘外伸转子系统的非线性动力学分析和主动控制问题。基于有限元法建立了系统的非线性动力学方程,油膜力采用本文导出的可倾瓦轴承非线性油膜力解析模型。采用数值方法对该系统的耦合动力学方程进行求解,分析了转子系统的非线性动力学特性。在没有主动润滑的情况下,随着转速的升高会出现油膜涡动和油膜振荡等失稳现象,采用基于模糊PID和模糊神经网络PID控制器的主动润滑对该系统进行控制的结果表明,主动润滑系统能够完全消除油膜振荡现象,较好的抑制油膜涡动时转子系统的振幅,极大的拓宽转子系统稳定运行的转速范围。比较而言,模糊神经网络PID控制的效果优于模糊PID控制。
With the trending to high speed, high precision and high load of the large scale rotating machinery, the increasingly nonlinear dynamic instability of rotor-bearing system have become the most serious problem. It is necessary to investigate the nonlinear dynamic behaviors, instability and the influences of operating parameters on dynamic stability of rotor-bearing systems. The fluid film force model is crucial to the nonlinear dynamics analysis of a rotor-bearing system. The formulation of a reasonable and manageable analytical fluid film force model is of great significance to the stability analysis and its engineering applications of rotor-bearing systems. On the other hand, the dynamic instability factors of the rotor-bearing system must be kept under control and the effective measures must be taken to improve the dynamic stability of the system. Once the abnormal phenomenon occurs, the effective corrective measures have to be put into action in case of the more serious consequences. The effectiveness of the active control to the rotor-bearing system mainly depends on the design of the control device and the regulation of the controller parameters.
In this dissertation two challenging issues in the investigation of large-scale rotor-bearing system are investigated, i.e. the formulation of analytical fluid film force model of a tilting pad bearing and active control of the self-excited vibration problem. Firstly, the nonlinear fluid film force model of a tilting pad journal bearing is deduced based on the short bearing assumption. And then an active lubrication device is adopted to eliminate the self-induced vibration of the rotor-bearing system. Correspondingly, several active control strategies are designed to regulate the electro-hydraulic control system. The nonlinear dynamic responses of the active lubricated rotor-bearing system based on different controllers are worked out and the inhibitions of self-excited vibration of the systems with various controllers are compared. The main achievements are listed below:
1. Based on the assumption of the short journal bearing,the fluid force model of the tilting pad journal bearing is formulated. Taking as a reference of the Capone model which is formulated based on the assumption of the short journal bearing,the fluid film pressure distribution is derived in each pad’s own local reference frame. The relation of the pad rotation angle and motion of the rotor is figured out. Then the fluid film pressure distribution of the tilting pad bearing in global reference frame is obtained by coordinate transformations. The nonlinear fluid force model of the tilting pad is formulated by integrating the fluid film pressure distribution. A numerical model for an unsymmetrical flexible-rotor supported by two tilting pad bearings is given and the dynamic response is worked out. The fluid force model based on the finite difference model for the tilting pad journal bearing are deduced to confirm that the analytical model is valid to deal with the problem of nonlinear dynamics of the rotor-bearing system. The calculated results show that the analytical model proposed can be used to analyze the dynamical behavior of the rotor-bearing system qualitatively and to save the computing cost for solving the system.
2. To eliminate the whirl and whip instability of the rotor bearing system, the active lubrication action is adopted to simultaneous reduction of wear and vibration between rotating and stationary machinery parts. The dynamic model of the electro-hydraulic active control system including the active lubricated tilting pad journal bearing and the electro-hydraulic system is formulated. In order to facilitate the realization of the control device, the design strategies of PI and PID controllers, applied to a tilting-pad journal bearing, are analyzed and discussed. Numerical results show that an effective vibration reduction of the unbalance response of an asymmetric rotor is performed for the system with PI or PID controllers. The feasibility of eliminating rotor-bearing instabilities (phenomena of whirl) by using active lubrication is also investigated, that illustrates clearly one of its most promising applications.
3. To deal with the disadvantages of highly nonlinear, time-varying uncertainty and delay characteristics in the electro-hydraulic control system, the neural network (NN) technology is applied to improve the active lubricated control system. The most efficient neural network, radical basis function (RBF) and back propagation (BP) are designed to optimize the parameters of the PID controller to settle the uncertainty and inaccuracy of the hydraulic system. Then the dynamic performance requirements of hydraulic servo system are achieved. Then two kinds of NN-PID controllers are applied to an active lubricated tilting-pad bearing system, and the dynamic responses of the asymmetric rotor-bearing system are analyzed and calculated. Comparing with the results based on the PI and PID controllers, the NN-PID controller show better performance.
4. The fuzzy PID control and fuzzy neural network PID control are designed to improve the active lubricated system after the successful application of neural network technology in optimizing PID parameters. Fuzzy controller does not rely on accurate models and possess flexible algorithms especially is suitable for the control of the system with nonlinear, large delay, time-varying characteristics. While the neural network has the advantage of strong robustness, memory capacity, non-linear mapping capabilities and a self-learning ability. So the fuzzy PID controller and fuzzy neural network PID controller are designed to regulate the active lubrication of the tilting pad bearing. Then the dynamic responses of the asymmetrical rotor-bearing system with fuzzy PID and fuzzy neural network PID controllers are worked out. Comparing with the results based on the other control laws, the fuzzy neural network PID controller shows better performance.
5. The nonlinear dynamics analysis and active control of the overhang rotor system with double disks supported by two tilting pad journal bearings is investigated. The nonlinear dynamic model of the overhang rotor system is formulated based on the finite element theory. The analytical fluid film force model of the tilting pad journal bearing proposed in this dissertation are applied to analyze the nonlinear dynamic characteristics of the rotor system. Numerical method is used to solve the coupled dynamic equations and the result shows that whirl and whip phenomena occur when the rotational speed is increasing upto the critical case. Thus the active lubrication systems based on both fuzzy PID and fuzzy neural network PID controller are designed to suppress the vibration of the overhang rotor system. The results show that by active lubrication the whirl amplitude of the system is greatly suppressed and whip instability is totally eliminated. The stable operating speed range of the rotor system is widely broadened. The control performance of the fuzzy neural network PID controller is better than that of fuzzy PID controller.
引文
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