基于非线性转子动力学的水轮发电机组振动机理研究
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摘要
水力发电系统是一类机械、电磁和水力等因素相互影响、相互制约的复杂非线性动力系统,其运行过程中水电机组振动故障的产生和发展包含了大量不确定性因素,难以用传统建模理论与方法进行精确的数学模型描述。同时,随着水电在电力能源结构中所占比重逐渐增大,且机组单机容量和水头的大幅提高,机组振动问题日益突出,对电网的安全稳定运行造成的影响也日益凸显。因此,迫切需要深入研究不同机组振动故障的产生及其相互作用机理,揭示系统参数对机组轴系振动稳定性及失稳影响的规律,为进一步提高我国水电机组的设计和运行水平提供重要的理论依据和技术支撑。本文以非线性转子动力学理论和方法为基础,建立不同振动故障作用下机组轴系非线性动力学模型和运动微分方程,综合运用分岔图、Poincare截面图、轴心轨迹图、时域波形图和幅值谱图等多种手段,系统地研究了转定碰摩与轴承松动耦合故障下机组轴系的动态响应、联轴器综合不对中下机组的动力学行为、机组轴系的非线性电磁振动特性和水轮机密封系统对机组振动及稳定性的影响等。论文主要的研究成果如下：
(1)综合考虑裂纹深度对转轴刚度的影响以及开闭函数的连续性,提出一种新的裂纹开闭规律,构建了裂纹和碰摩耦合故障转子系统的运动微分方程,分析了不同故障下转子系统的分岔与混沌行为,研究了定子径向刚度、裂纹深度和裂纹角度等系统参数对耦合故障转子系统动力学特性的影响。研究表明,随着定子径向刚度的增大,转子碰摩力不断增大逐渐成为主导因素,使系统响应由混沌运动不断向周期运动演变；不同裂纹深度和裂纹角度下转子系统随转速变化表现出不同的分岔演化过程,在临界转速附近,其响应逐渐由复杂的混沌运动向周期4运动不断演变,在超临界转速区则以拟周期运动为主要形式,且出现了不同的倍周期运动。
(2)针对轴承松动易导致发电机转子与定子发生碰摩的问题,考虑发电机定子与基础间的连接刚度和阻尼,建立了轴承松动与碰摩耦合故障下水轮发电机组非线性动力学模型,分析了机组转频比、转子质量偏心及摩擦系数等参数对转子、定子及松动轴承的振动影响,重点研究了发生碰摩时定子响应的非线性动力学行为。分析发现,刚度比不影响碰摩的发生区域,系统响应随转频比和摩擦系数变化存在周期运动、倍周期运动和拟周期运动等,幅值频谱中出现幅值较大的谐波分量；随着转子质量偏心的增大,转子与定子发生碰摩的区域不断增大,且在两个不同的转频区间内都有碰摩现象发生,其响应出现了拟周期运动。
(3)在分析刚性联轴器综合不对中运动机理的基础上,建立了水轮发电机组轴系综合不对中的动力学模型,分析了该系统随机组转速、不对中平行量及不对中偏角等参数变化的非线性动力学行为。研究发现,随着不对中故障的增大,系统响应存在有周期运动、周期3运动及复杂的拟周期运动。在拟周期运动区域,转子和转轮的幅值谱图中除1倍频外,还存在幅值较大的低频分量,特别是在0.3-0.4倍频处,且不对中平行量对转子的振动影响较大；在转速上升的过程,转子和转轮响应均为周期运动,其振幅不断变化,当转速进一步增大时,系统响应会由周期运动演变为拟周期运动,呈现出丰富的非线性动力学行为。
(4)根据电磁拉力与转子偏心的非线性关系,将气隙磁导展开为Fourier级数,推导出不平衡磁拉力的具体解析表达式,建立了水轮发电机组轴系非线性电磁振动的动力学模型,研究了机组转速、励磁电流及转子质量偏心等系统参数对机组轴系振动的影响。结果表明,随着机组转速上升过程中,发电机转子在1-1.5倍频和0.5-1倍频处出现了谐波分量,转轮则在0.5-1倍频处存在幅值较大的低频分量；随着励磁电流和转子质量偏心的增大的变化,系统响应存在周期运动和复杂的拟周期等,系统振幅不断变化,转子的1倍频幅值不断增大,高频分量不断减少,而转轮的1倍频幅值不断减小,低频分量不断增多。
(5)针对随着水轮发电机组轴系结构参数的提高,作用在水轮机转轮上的密封水流激振力将显著增大,容易导致机组异常振动的问题,采用Muszynska非线性密封力模型,建立了密封激振力作用下水轮发电机组密封轴系非线性动力学模型,系统地分析了机组导轴承的振动特性和水轮机转轮的动态稳定性。研究表明,各导轴承运动振幅随转子质量偏心的增大不断变化；水轮机转轮受到非线性密封力作用后发生自激振动,呈现出复杂的动力学行为；密封结构的各主要参数对机组主轴系统稳定性有很大的影响。
Hydroelectric system is a complex nonlinear dynamic hydro-mechanical-electrical system. As the system is running, there are a number of uncertain factors in the generation and development of vibration fault of hydropower generating unit, which are difficult to describe accurately using mathematical models. And, with the proportion of energy in the power structure, and the rapid increase of the single unit capacity and head of the hydropower generating units, vibration problems have become increasingly prominent, which serious threaten to the safe and reliable operation of the hydroelectric plant, even power grid. Once a failure for generating units occurs, it may cause the plant to non-planned shutdown or reduce capacity, even serious heavy casualties and serious damage to the system. Therefore, to further improve our design and operation of hydroelectric generating units and provide important theoretical and technical support, we must study on mechanism of different vibration faults and interaction between them and reveal influence of fault factors to the unit vibration stability and instability law. In this paper, based on nonlinear rotor dynamics theory and methods, many approaches such as bifurcation diagram, Poincare map, axis orbit, time domain waveform and amplitude spectrum diagram are employed to analyze the vibration characteristics on shaft system which including dynamic behavior of the rotor system with rotor rub-impact and bearing loose coupling faults, the dynamic response of generator rotor and turbine runner with comprehensive misalignment, nonlinear electromagnetic vibration characteristics of unit shaft and the analysis of turbine vibration and stability of the turbine seal system with considering the vibration of universal operation of the unit. The main contents of the paper as follows:
(1) With considering the crack depth to shaft stiffness and continuous of switching function of crack, an improved switching crack model in a beam is presented. Dynamic characteristics of a rotor-bearing system with rub-impact and transverse crack are attempted. Due to the presence of coupling faults, the system becomes highly nonlinear. The stiffness of stator, crack depth, crack angle effects on the response of a rotor are investigated using numerical method. Various nonlinear phenomena compressing periodic, quasi-periodic and chaotic motions with rotating speed as a control parameter in the rotor system are analyzed. The research results show that as the increase of the stiffness, rub forces increase and gradually come to be the dominant factor, leading responses of the rotor evolving from chaos to periodic motions. In the cases of different cracks depth and crack angular, the responses of the rotor system present different bifurcation trajectory. Within the subcritical speed range responses of the rotor evolves from complex chaotic motion to four-periodic motion and within supercritical speed range mainly are quasi-periodic motions.
(2) In order to solve the fault problems of the bearing looseness and rotor local rubbing caused by some nonlinear factors, considering the rigidity and damping between the stator and foundation, a dynamic model for the hydroelectric generating unit with coupling faults of bearing looseness and rub-impact is established. The nonlinear dynamic behaviors of the shaft system are analyzed, as ratio of rotation frequency, mass eccentricity of rotor and friction coefficient varied. The focus is mainly on the process of the stator-rotor rub-impact. The results show that the stiffness is unrelated to the range of rub occurring, and various non-linear phenomena compressing periodic, three-period and quasi-periodic motions occurs at different speed and there are some low frequencies with large amplitude in the amplitude spectrum Moreover, the speed range of rotor rub-impact enlarges constantly and dynamic responses of the system are complex as the increasing of mass eccentricity of the rotor.
(3) Based on movement mechanism of rigid coupling with misalignment, a dynamic model for the shaft system with coupling faults of misalignment and rub-impact is established. The dynamic behaviors of the generator rotor and turbine runner are investigated, as rotating speed, parallel misalignment and angular misalignmen varied. Various nonlinear phenomena compressing periodic, three-periodic and quasi-periodic motions in the system are observed. The results reveal that when response is quasi-periodic motion, there are some low frequencies with large amplitude, especially at the 0.3-0.4X-ratational speed. While the speed goes up, their responses are periodic motion and the amplitudes are constantly changing and the responses will evolve from periodic motion to quasi-periodic motion as the increase of the speed.
(4) According to nonlinear relation of unbalanced magnetic pull (UMP) and mass eccentricity of the rotor, the air-gap permeance is expressed as a Fourier series. Then the analytical expression of UMP is derived and the kinetic equation is set up to describe electromagnetic vibration of the shaft system. Numerical method is adopted to analyze the nonlinear dynamic response of the rotor and runner with rotation speed, exciting current and mass eccentricity of the rotor as a control parameter, respectively. Simulation results display that There are many harmonics with large amplitude at the 1～1.5X and 0.5～1X for generator rotor and at the 0.5～1X for turbine runner as the speed increasing. As the increase of exciting current and mass eccentricity, various nonlinear phenomena compressing periodic and complicated quasi-periodic motions in the system are observed, and the amplitude at the 1X increases and high frequency components decrease for the generator rotor, but it is opposite for the turbine runner.
(5) As the structural parameters of hydroelectric generating units shaft increase, the flow induced force imposed on the hydraulic turbine runner will significantly increase, which easily causes abnormal vibration of the unit. According to the problem, the Muszynska's model of the nonlinear seal force is applied to building the dynamic equation of the shaft system with flow induced force. The vibration characteristics of the guide bearings at different mass eccentricity and dynamic stability of the hydraulic turbine rotor is analyzed. The results show that the vibration amplitude of three guide bearings is constantly changing with the increase of mass eccentricity. There is occurrence of Hopf bifurcation after threshold speed is exceeded and rich nonlinear motions such as periodic and quasi-periods, for hydraulic turbine runner. The main parameters of the sealed structure have important impaction the stability of the rotor system.
(1)综合考虑裂纹深度对转轴刚度的影响以及开闭函数的连续性,提出一种新的裂纹开闭规律,构建了裂纹和碰摩耦合故障转子系统的运动微分方程,分析了不同故障下转子系统的分岔与混沌行为,研究了定子径向刚度、裂纹深度和裂纹角度等系统参数对耦合故障转子系统动力学特性的影响。研究表明,随着定子径向刚度的增大,转子碰摩力不断增大逐渐成为主导因素,使系统响应由混沌运动不断向周期运动演变；不同裂纹深度和裂纹角度下转子系统随转速变化表现出不同的分岔演化过程,在临界转速附近,其响应逐渐由复杂的混沌运动向周期4运动不断演变,在超临界转速区则以拟周期运动为主要形式,且出现了不同的倍周期运动。
(2)针对轴承松动易导致发电机转子与定子发生碰摩的问题,考虑发电机定子与基础间的连接刚度和阻尼,建立了轴承松动与碰摩耦合故障下水轮发电机组非线性动力学模型,分析了机组转频比、转子质量偏心及摩擦系数等参数对转子、定子及松动轴承的振动影响,重点研究了发生碰摩时定子响应的非线性动力学行为。分析发现,刚度比不影响碰摩的发生区域,系统响应随转频比和摩擦系数变化存在周期运动、倍周期运动和拟周期运动等,幅值频谱中出现幅值较大的谐波分量；随着转子质量偏心的增大,转子与定子发生碰摩的区域不断增大,且在两个不同的转频区间内都有碰摩现象发生,其响应出现了拟周期运动。
(3)在分析刚性联轴器综合不对中运动机理的基础上,建立了水轮发电机组轴系综合不对中的动力学模型,分析了该系统随机组转速、不对中平行量及不对中偏角等参数变化的非线性动力学行为。研究发现,随着不对中故障的增大,系统响应存在有周期运动、周期3运动及复杂的拟周期运动。在拟周期运动区域,转子和转轮的幅值谱图中除1倍频外,还存在幅值较大的低频分量,特别是在0.3-0.4倍频处,且不对中平行量对转子的振动影响较大；在转速上升的过程,转子和转轮响应均为周期运动,其振幅不断变化,当转速进一步增大时,系统响应会由周期运动演变为拟周期运动,呈现出丰富的非线性动力学行为。
(4)根据电磁拉力与转子偏心的非线性关系,将气隙磁导展开为Fourier级数,推导出不平衡磁拉力的具体解析表达式,建立了水轮发电机组轴系非线性电磁振动的动力学模型,研究了机组转速、励磁电流及转子质量偏心等系统参数对机组轴系振动的影响。结果表明,随着机组转速上升过程中,发电机转子在1-1.5倍频和0.5-1倍频处出现了谐波分量,转轮则在0.5-1倍频处存在幅值较大的低频分量；随着励磁电流和转子质量偏心的增大的变化,系统响应存在周期运动和复杂的拟周期等,系统振幅不断变化,转子的1倍频幅值不断增大,高频分量不断减少,而转轮的1倍频幅值不断减小,低频分量不断增多。
(5)针对随着水轮发电机组轴系结构参数的提高,作用在水轮机转轮上的密封水流激振力将显著增大,容易导致机组异常振动的问题,采用Muszynska非线性密封力模型,建立了密封激振力作用下水轮发电机组密封轴系非线性动力学模型,系统地分析了机组导轴承的振动特性和水轮机转轮的动态稳定性。研究表明,各导轴承运动振幅随转子质量偏心的增大不断变化；水轮机转轮受到非线性密封力作用后发生自激振动,呈现出复杂的动力学行为；密封结构的各主要参数对机组主轴系统稳定性有很大的影响。
Hydroelectric system is a complex nonlinear dynamic hydro-mechanical-electrical system. As the system is running, there are a number of uncertain factors in the generation and development of vibration fault of hydropower generating unit, which are difficult to describe accurately using mathematical models. And, with the proportion of energy in the power structure, and the rapid increase of the single unit capacity and head of the hydropower generating units, vibration problems have become increasingly prominent, which serious threaten to the safe and reliable operation of the hydroelectric plant, even power grid. Once a failure for generating units occurs, it may cause the plant to non-planned shutdown or reduce capacity, even serious heavy casualties and serious damage to the system. Therefore, to further improve our design and operation of hydroelectric generating units and provide important theoretical and technical support, we must study on mechanism of different vibration faults and interaction between them and reveal influence of fault factors to the unit vibration stability and instability law. In this paper, based on nonlinear rotor dynamics theory and methods, many approaches such as bifurcation diagram, Poincare map, axis orbit, time domain waveform and amplitude spectrum diagram are employed to analyze the vibration characteristics on shaft system which including dynamic behavior of the rotor system with rotor rub-impact and bearing loose coupling faults, the dynamic response of generator rotor and turbine runner with comprehensive misalignment, nonlinear electromagnetic vibration characteristics of unit shaft and the analysis of turbine vibration and stability of the turbine seal system with considering the vibration of universal operation of the unit. The main contents of the paper as follows:
(1) With considering the crack depth to shaft stiffness and continuous of switching function of crack, an improved switching crack model in a beam is presented. Dynamic characteristics of a rotor-bearing system with rub-impact and transverse crack are attempted. Due to the presence of coupling faults, the system becomes highly nonlinear. The stiffness of stator, crack depth, crack angle effects on the response of a rotor are investigated using numerical method. Various nonlinear phenomena compressing periodic, quasi-periodic and chaotic motions with rotating speed as a control parameter in the rotor system are analyzed. The research results show that as the increase of the stiffness, rub forces increase and gradually come to be the dominant factor, leading responses of the rotor evolving from chaos to periodic motions. In the cases of different cracks depth and crack angular, the responses of the rotor system present different bifurcation trajectory. Within the subcritical speed range responses of the rotor evolves from complex chaotic motion to four-periodic motion and within supercritical speed range mainly are quasi-periodic motions.
(2) In order to solve the fault problems of the bearing looseness and rotor local rubbing caused by some nonlinear factors, considering the rigidity and damping between the stator and foundation, a dynamic model for the hydroelectric generating unit with coupling faults of bearing looseness and rub-impact is established. The nonlinear dynamic behaviors of the shaft system are analyzed, as ratio of rotation frequency, mass eccentricity of rotor and friction coefficient varied. The focus is mainly on the process of the stator-rotor rub-impact. The results show that the stiffness is unrelated to the range of rub occurring, and various non-linear phenomena compressing periodic, three-period and quasi-periodic motions occurs at different speed and there are some low frequencies with large amplitude in the amplitude spectrum Moreover, the speed range of rotor rub-impact enlarges constantly and dynamic responses of the system are complex as the increasing of mass eccentricity of the rotor.
(3) Based on movement mechanism of rigid coupling with misalignment, a dynamic model for the shaft system with coupling faults of misalignment and rub-impact is established. The dynamic behaviors of the generator rotor and turbine runner are investigated, as rotating speed, parallel misalignment and angular misalignmen varied. Various nonlinear phenomena compressing periodic, three-periodic and quasi-periodic motions in the system are observed. The results reveal that when response is quasi-periodic motion, there are some low frequencies with large amplitude, especially at the 0.3-0.4X-ratational speed. While the speed goes up, their responses are periodic motion and the amplitudes are constantly changing and the responses will evolve from periodic motion to quasi-periodic motion as the increase of the speed.
(4) According to nonlinear relation of unbalanced magnetic pull (UMP) and mass eccentricity of the rotor, the air-gap permeance is expressed as a Fourier series. Then the analytical expression of UMP is derived and the kinetic equation is set up to describe electromagnetic vibration of the shaft system. Numerical method is adopted to analyze the nonlinear dynamic response of the rotor and runner with rotation speed, exciting current and mass eccentricity of the rotor as a control parameter, respectively. Simulation results display that There are many harmonics with large amplitude at the 1～1.5X and 0.5～1X for generator rotor and at the 0.5～1X for turbine runner as the speed increasing. As the increase of exciting current and mass eccentricity, various nonlinear phenomena compressing periodic and complicated quasi-periodic motions in the system are observed, and the amplitude at the 1X increases and high frequency components decrease for the generator rotor, but it is opposite for the turbine runner.
(5) As the structural parameters of hydroelectric generating units shaft increase, the flow induced force imposed on the hydraulic turbine runner will significantly increase, which easily causes abnormal vibration of the unit. According to the problem, the Muszynska's model of the nonlinear seal force is applied to building the dynamic equation of the shaft system with flow induced force. The vibration characteristics of the guide bearings at different mass eccentricity and dynamic stability of the hydraulic turbine rotor is analyzed. The results show that the vibration amplitude of three guide bearings is constantly changing with the increase of mass eccentricity. There is occurrence of Hopf bifurcation after threshold speed is exceeded and rich nonlinear motions such as periodic and quasi-periods, for hydraulic turbine runner. The main parameters of the sealed structure have important impaction the stability of the rotor system.
引文
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