汽轮发电机组轴系弯扭耦合振动研究
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摘要
随着电力工业的发展，汽轮发电机组振动问题越来越突出，人们对相应的振动机理开展了深入的研究，并积极探寻有效的故障预防和诊断方法。但目前的分析方法和结论对于某些类振动故障，难以准确诊断。机组弯扭耦合振动的研究以及非线性特性的研究，将有助于全面了解轴系动力学特性，增强振动分析手段，并提高故障诊断的准确性。
针对存在质量偏心的单圆盘Jeffcott转子模型，通过拉格朗日方程，建立了弯扭耦合振动模型。与以往分析方法不同，本文利用小参数法对弯扭耦合振动解析解进行了理论分析，并通过数值仿真手段验证了理论分析结果。弯振和扭振通过质量偏心发生耦合，由弯扭耦合共振而导致转子损坏的可能性很小，但这些耦合特征为转子的故障诊断提供了有益的信息。
建立了碰摩转子的弯扭耦合振动模型，利用标准的四阶Runge-kutta法对碰摩特性进行了数值分析，比较了有无考虑扭振的情况下，系统振动响应的主要区别和相应的扭振特性，并详细讨论了几种因素对碰摩转子弯振和扭振特性的影响。研究结果证实了扭振特征和非线性特性用于该类故障诊断的可行性：从发生碰摩起，扭振分频和倍频相伴出现，转速较低时，1/2X成分突出，随着转速升高，不但有1/3X及2/3X分量出现，而且出现了4/3X成分，分频幅值大于工频及倍频；弯振和扭振的非线性运动特性完全相似，扭振有抑制转子系统复杂运动的能力。
以重力占优的开闭裂纹模型为研究对象，研究了裂纹转子升速过程的弯扭耦合振动瞬态响应特性及影响因素，探讨了1／3阶及1／2阶亚谐共振特征；在考虑转速涡动情况下，比较了三种模型的分叉与混沌等非线性特性，并详细分析了轴承支承模型的弯扭耦合振动非线性特性。获得的裂纹转子扭振特征及分叉与混沌特性，对该类故障的诊断能起到很好的辅助作用：升速过程中，扭振出现1／2阶和1／3阶亚谐共振，扭振的1X、2x和3x分量共振峰对应转速下的相位角有180°的突变，同时，扭振在除各分量峰值转速外的其它转速处，如ω_(t0)、1/2ω_(t0)、2/3ω_(t0)、2/3ω_(t0)和ω_0，相位角也有一定的波动，且ω_0处的相角波动较剧烈；三种模型下，弯振和扭振在2/3ω_0、1/2ω_0、1/3ω_0及1/4ω_0处都出现了峰值，在1/2ω_0附近，可能出现拟周期及混沌运动，在2/3ω_0附近，各种周期、拟周期和混沌响应交替出现，阵发性特点非常明显。
将逐步积分法与传统传递矩阵法相结合，提出了增量传递矩阵法思想，文中相该方法应用于多段集中质量模型，并结合Riccati法，推导了汽轮发电机组轴系弯扭耦合振动响应计算的矩阵表达式，并开发了一套较完善的汽轮发电机组弯扭耦合振动分析软件。利用该软件，分析了低压缸和发电机转子发生质量飞脱事故，发电机出口端发生三相、两相短路故障，发电机非同期并网故障以及电网三相短路重合闸故障时，机组轴系的弯振、扭振及扭矩响应情况。研究结果表明：各种故障情况下，
华北电力大学博士学位论文
弯振和扭振之间都存在祸合关系，但弯扭祸合振动一般不会威胁机组安全运行:在
叶片丢失或滑环飞脱故障时，将产生很大的弯振，同时各转子扭振也将被激发出来，
它以工倍频和前三阶固有频率为主;在各种电气故障情况下，各转子都很快被激励
出较大幅值的扭振来，相应各转子弯振也发生一定的变化，但它的变化明显滞后于
扭振，扭振和扭矩主要以前三阶固有频率为主。该研究结果为指导大机组故障诊断
和安全生产提供了坚实的理论依据。
将文中的理论应用到生产实践中，研制开发了一套独具特色的汽轮发电机组轴
系弯扭祸合振动监测与诊断系统，文中详细介绍了该系统总体设计思想、具体功能
模块以及系统实现的关键技术等。该系统首次实现了机组轴系弯振和扭振同时监
测、统一管理功能，并将扭振特征应用于常见故障的诊断。
With the development of electric power, the problem of vibration on turbogenerator shafts stands out. A deep research on vibration mechanism is carried out. And valid method for preventing and diagnosing fault is explored. But the fact is that analysis method and conclusion can't be used for diagnosing some faults exactly. Research on coupled flexural and torsional vibrations and nonlinear characteristics will help to reveal dynamics property of shafts more perfectly and strengthen analysis technique of vibration and improve the accuracy of fault diagnosis.
Based on a Jeffcott rotor system with rigid support, the differential equations of coupled vibrations are established. Different from previous methods, litter parameter method is used for analyzing the characteristic of coupled vibrations. And the analytical results are validated through numerical simulation. Mass unbalance is necessary condition of coupling. The possibility of shaft damage led by coupled resonance is litter. Useful information for fault diagnosis is provided by the coupled characteristics.
The differential equations of coupled vibrations for rubbing rotor are established. Numerical analysis for rubbing characteristics is processed using standard four-step Runge-kutta method. Main differences and torsional property of system response are compared with and without considering torsional vibration. And the influences of several factors on rubbing rotor are discussed thoroughly. The feasibility that torsional vibration characteristic and nonlinear characteristic are used for the faults diagnosis of rubbing rotor is proved by the analysis results fully. From the happen time of rotor rubbing, fraction and multiple frequencies of torsional vibration always concomitant appear. As the speed is slow, 1/2X frequency is the main component. With the speed increment, not only 1/2X and 2/3X frequency component appear in low frequency segment, but also 4/3X frequency component begin to appear in high frequency segment. The amplitude of fraction frequency is usually larger than that of multiple frequencies. The
nonlinear characteristic of torsion for rubbing rotor is similar with that of flexural vibration completely. Torsion can restrain the complex motion of flexural vibration.
A breathing crack controlled by weight is the study object. Transient characteristics of coupled vibrations and influence factors are analyzed with the shaft accelerated. The properties of 1/3X and 1/2X sub-syntonic resonance are discussed. Nonlinear characteristics such as bifurcation and chaos under three kinds of models are compared. And nonlinear characteristics of coupled vibrations under the model supporting with bearings are analyzed detailedly. The acquired torsion properties and nonlinear characteristics of
cracked rotor have good assistant effect on diagnosing cracked fault. 1/3X and 1/2X sub-syntonic resonance of torsional vibration occur with the cracked rotor accelerated. The ωphases of torsional resonance peak of IX, 2X and 3X components change 180 degree. And the phases corresponding to ωt0, 1/2ωt0, 1/3ωt0, 2/3ω0 and ω0 fluctuate too. The phase of ω0 frequency fluctuates tempestuously. The resonance peaks of flexural and torsional vibrations response are present at 2/3ω0 1/2ω0 1/3ω0 and 1/4ω0 with three kinds cracked rotor models. Near 1/2ω0 frequency, quasi-periodic and chaotic motions maybe appear. Periodic, quasi-periodic and chaotic motions show on alternately when the rotating speed is near to 2/3ω0.
Combined step-by-step integral method with traditional transfer matrix method, an increment transfer matrix method is put forward. Based on Riccati method, the increment transfer matrix method is used in a multi-mass model. And matrix equations calculating the responses of coupled vibrations are deduced. A set of software analyzing coupled vibrations is developed. The responses of flexural vibration, torsional vibration and torsional torque are analyzed under some fault cases, including mass escaping of low-pressure and generator rotors
针对存在质量偏心的单圆盘Jeffcott转子模型，通过拉格朗日方程，建立了弯扭耦合振动模型。与以往分析方法不同，本文利用小参数法对弯扭耦合振动解析解进行了理论分析，并通过数值仿真手段验证了理论分析结果。弯振和扭振通过质量偏心发生耦合，由弯扭耦合共振而导致转子损坏的可能性很小，但这些耦合特征为转子的故障诊断提供了有益的信息。
建立了碰摩转子的弯扭耦合振动模型，利用标准的四阶Runge-kutta法对碰摩特性进行了数值分析，比较了有无考虑扭振的情况下，系统振动响应的主要区别和相应的扭振特性，并详细讨论了几种因素对碰摩转子弯振和扭振特性的影响。研究结果证实了扭振特征和非线性特性用于该类故障诊断的可行性：从发生碰摩起，扭振分频和倍频相伴出现，转速较低时，1/2X成分突出，随着转速升高，不但有1/3X及2/3X分量出现，而且出现了4/3X成分，分频幅值大于工频及倍频；弯振和扭振的非线性运动特性完全相似，扭振有抑制转子系统复杂运动的能力。
以重力占优的开闭裂纹模型为研究对象，研究了裂纹转子升速过程的弯扭耦合振动瞬态响应特性及影响因素，探讨了1／3阶及1／2阶亚谐共振特征；在考虑转速涡动情况下，比较了三种模型的分叉与混沌等非线性特性，并详细分析了轴承支承模型的弯扭耦合振动非线性特性。获得的裂纹转子扭振特征及分叉与混沌特性，对该类故障的诊断能起到很好的辅助作用：升速过程中，扭振出现1／2阶和1／3阶亚谐共振，扭振的1X、2x和3x分量共振峰对应转速下的相位角有180°的突变，同时，扭振在除各分量峰值转速外的其它转速处，如ω_(t0)、1/2ω_(t0)、2/3ω_(t0)、2/3ω_(t0)和ω_0，相位角也有一定的波动，且ω_0处的相角波动较剧烈；三种模型下，弯振和扭振在2/3ω_0、1/2ω_0、1/3ω_0及1/4ω_0处都出现了峰值，在1/2ω_0附近，可能出现拟周期及混沌运动，在2/3ω_0附近，各种周期、拟周期和混沌响应交替出现，阵发性特点非常明显。
将逐步积分法与传统传递矩阵法相结合，提出了增量传递矩阵法思想，文中相该方法应用于多段集中质量模型，并结合Riccati法，推导了汽轮发电机组轴系弯扭耦合振动响应计算的矩阵表达式，并开发了一套较完善的汽轮发电机组弯扭耦合振动分析软件。利用该软件，分析了低压缸和发电机转子发生质量飞脱事故，发电机出口端发生三相、两相短路故障，发电机非同期并网故障以及电网三相短路重合闸故障时，机组轴系的弯振、扭振及扭矩响应情况。研究结果表明：各种故障情况下，
华北电力大学博士学位论文
弯振和扭振之间都存在祸合关系，但弯扭祸合振动一般不会威胁机组安全运行:在
叶片丢失或滑环飞脱故障时，将产生很大的弯振，同时各转子扭振也将被激发出来，
它以工倍频和前三阶固有频率为主;在各种电气故障情况下，各转子都很快被激励
出较大幅值的扭振来，相应各转子弯振也发生一定的变化，但它的变化明显滞后于
扭振，扭振和扭矩主要以前三阶固有频率为主。该研究结果为指导大机组故障诊断
和安全生产提供了坚实的理论依据。
将文中的理论应用到生产实践中，研制开发了一套独具特色的汽轮发电机组轴
系弯扭祸合振动监测与诊断系统，文中详细介绍了该系统总体设计思想、具体功能
模块以及系统实现的关键技术等。该系统首次实现了机组轴系弯振和扭振同时监
测、统一管理功能，并将扭振特征应用于常见故障的诊断。
With the development of electric power, the problem of vibration on turbogenerator shafts stands out. A deep research on vibration mechanism is carried out. And valid method for preventing and diagnosing fault is explored. But the fact is that analysis method and conclusion can't be used for diagnosing some faults exactly. Research on coupled flexural and torsional vibrations and nonlinear characteristics will help to reveal dynamics property of shafts more perfectly and strengthen analysis technique of vibration and improve the accuracy of fault diagnosis.
Based on a Jeffcott rotor system with rigid support, the differential equations of coupled vibrations are established. Different from previous methods, litter parameter method is used for analyzing the characteristic of coupled vibrations. And the analytical results are validated through numerical simulation. Mass unbalance is necessary condition of coupling. The possibility of shaft damage led by coupled resonance is litter. Useful information for fault diagnosis is provided by the coupled characteristics.
The differential equations of coupled vibrations for rubbing rotor are established. Numerical analysis for rubbing characteristics is processed using standard four-step Runge-kutta method. Main differences and torsional property of system response are compared with and without considering torsional vibration. And the influences of several factors on rubbing rotor are discussed thoroughly. The feasibility that torsional vibration characteristic and nonlinear characteristic are used for the faults diagnosis of rubbing rotor is proved by the analysis results fully. From the happen time of rotor rubbing, fraction and multiple frequencies of torsional vibration always concomitant appear. As the speed is slow, 1/2X frequency is the main component. With the speed increment, not only 1/2X and 2/3X frequency component appear in low frequency segment, but also 4/3X frequency component begin to appear in high frequency segment. The amplitude of fraction frequency is usually larger than that of multiple frequencies. The
nonlinear characteristic of torsion for rubbing rotor is similar with that of flexural vibration completely. Torsion can restrain the complex motion of flexural vibration.
A breathing crack controlled by weight is the study object. Transient characteristics of coupled vibrations and influence factors are analyzed with the shaft accelerated. The properties of 1/3X and 1/2X sub-syntonic resonance are discussed. Nonlinear characteristics such as bifurcation and chaos under three kinds of models are compared. And nonlinear characteristics of coupled vibrations under the model supporting with bearings are analyzed detailedly. The acquired torsion properties and nonlinear characteristics of
cracked rotor have good assistant effect on diagnosing cracked fault. 1/3X and 1/2X sub-syntonic resonance of torsional vibration occur with the cracked rotor accelerated. The ωphases of torsional resonance peak of IX, 2X and 3X components change 180 degree. And the phases corresponding to ωt0, 1/2ωt0, 1/3ωt0, 2/3ω0 and ω0 fluctuate too. The phase of ω0 frequency fluctuates tempestuously. The resonance peaks of flexural and torsional vibrations response are present at 2/3ω0 1/2ω0 1/3ω0 and 1/4ω0 with three kinds cracked rotor models. Near 1/2ω0 frequency, quasi-periodic and chaotic motions maybe appear. Periodic, quasi-periodic and chaotic motions show on alternately when the rotating speed is near to 2/3ω0.
Combined step-by-step integral method with traditional transfer matrix method, an increment transfer matrix method is put forward. Based on Riccati method, the increment transfer matrix method is used in a multi-mass model. And matrix equations calculating the responses of coupled vibrations are deduced. A set of software analyzing coupled vibrations is developed. The responses of flexural vibration, torsional vibration and torsional torque are analyzed under some fault cases, including mass escaping of low-pressure and generator rotors
引文
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