耦合故障复杂转子—轴承非线性系统的运行稳定性及其实验研究
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摘要
旋转机械是在工业部门中应用最为广泛的一类机械设备,它的稳定运行影响着整个工业的发展进程。随着社会的发展需要,现代旋转机械正朝着高速、重载、自动化和复杂化方向发展,由此所引发的问题也越来越多。由于运行环境比较恶劣,复杂高速的旋转机械时常由于非线性因素激发起各种故障,使系统失去稳定性甚至发生毁机事故,这些事故一般情况下所造成的经济损失、人员伤亡和社会危害是难以估量的,因此对旋转机械的稳定性研究是十分必要的。以往对转子系统的非线性特性及稳定性研究一般采用简单的动力模型,对于较为复杂的工程机组,这类模型已经不能胜任。因此,对复杂转子-轴承系统建模和运行稳定性研究有着十分重要的现实意义,目前国内外一些科技工作者也开始注意到这方面的问题,并取得了一定的成果。
本课题以东北大学与沈阳鼓风机(集团)有限公司联合进行的“大型压缩机转子振动实验系统”横向课题为背景,以闻邦椿教授提出的“基于系统工程的产品综合设计理论与方法”框架内的动态优化设计应用研究为目的,进行了含故障复杂转子-轴承系统,即含单故障/耦合故障的单跨双盘转子-轴承系统、含耦合故障的双跨多盘的转子-轴承系统的周期运行稳定性及分岔特性的理论和实验研究。具体研究内容和如下:
(1)研究了求解复杂转子-轴承非线性系统周期解及判断其稳定性、分岔的延拓打靶算法,以有限元理论为基础开发了转子-轴承非线性动力学工具箱,该工具箱共含50余个子函数,功能包括:计算临界转速,材料阻尼系数,弹性支承系统的时域及频域响应,单跨和多跨非线性转子系统时域、频域响应,以及分岔、混沌、稳定性等问题。其中非线性因素包括油膜支承、裂纹、碰摩等。为获得较高的计算精度和有效地节约计算成本,工具箱含有无量纲化和降维处理等功能。
(2)建立了油膜支承双盘转子-轴承系统非线性动力学模型,利用求解非线性系统周期解的延拓打靶方法,研究了系统在偏心量-转速、偏心相位-转速、轴承长径比-转速、轴承间隙-转速、润滑油动力粘度-转速参数域内的系统稳定性及分岔行为,得到了系统周期运行的失稳规律;搭建相应的实验装置,通过实验研究了油膜支承的转子-轴承系统失稳特性及非线性振动特征。研究发现系统的同频周期运动主要以倍周期、Hopf分岔失稳,并且随着某一参数的变化系统的拓扑结构和吸引域发生变化,使系统分岔曲线会发生跳跃突变现象,通常情况下,随着分岔类型的跳跃变化失稳转速也会发生突变。
(3)以油膜支承含碰摩故障双盘转子-轴承系统为研究对象,分析了碰摩转子-轴承系统对于不同碰摩位置在摩擦系数-转速、碰摩间隙-转速参数域内系统周期运动的失稳分岔行为及其规律;开发了配套的碰摩监测装置,并搭建了相应的实验装置,验证了主要的分析结果。研究发现不同的碰摩位置和偏心量对系统的稳定性和动态特性着很大的影响,这里认为碰摩故障比较容易改变系统的拓扑结构;当碰摩故障加重时容易干扰“油膜涡动”及“油膜振荡”的发生,使失稳转速出现延迟现象,碰摩故障容易使频域响应出现倍频成份。
(4)对于油膜支承含裂纹故障的双盘转子-轴承系统,分析了裂纹转子系统对于裂纹在偏心量-转速、裂纹深度-转速、裂纹位置-转速参数域内系统运行稳定性及失稳规律;并做了相应的验证实验。研究发现裂纹的存在以及位置的变化对系统失稳转速和失稳类型的影响并不是很大,随着裂纹的扩展失稳转速有缓慢升高趋势,主要原因是由于裂纹的存在干扰了油膜涡动的形成,但这并不是说裂纹的存在是有益的,它的存在将给机组带来很大隐患,对于数值计算当裂纹深度达到一定程度时将会发散而无法计算,对应于工程现场将会出现毁机事故,因此转子系统中的裂纹故障是必须避免的。
(5)对于含有碰摩-裂纹耦合故障的双盘多自由度转子-轴承系统,分析了其偏心量-转速、碰摩间隙-转速、裂纹深度-转速参数域内的运行稳定性及分岔规律,并做了相应的实验进行验证。研究发现随着偏心量的增加,系统失稳转速有降低趋势,当转盘的偏心量增大到一定程度时,由于定子对其限制作用会使系统的失稳转速升高:当碰摩间隙减小时,同样因为增大了碰摩力使系统失稳转速有升高现象;另外在碰摩和裂纹耦合故障的转子-轴承系统中,碰摩故障对系统的影响较为明显,裂纹对系统稳定性的影响相对于碰摩故障稍微弱一些。
(6)建立了考虑油膜支承含碰摩-裂纹耦合故障的双跨转子-轴承系统动力学模型,研究了其在偏心量-转速、碰摩间隙-转速、裂纹深度-转速参数域内研究稳定性及分岔行为,并做了相应的验证实验。研究表明双跨转子-轴承系统的失稳特性不同于前面单跨系统,其分岔类型和失稳转速并没有出现突变现象,这主要是由转子系统本身的结构特性所决定的。对于含耦合故障双跨系统的实验研究表明,由于弹性联轴器的作用,使两端转子的响应表现出一强一弱的现象;大偏心量使系统的失稳转速升高,并且碰摩故障的特性表现得较为明显一些。
Rotating machinery is one kind of mechanical equipments most widely used in the industrial department,its stable operation influences the development process of all the industry.With the development of the society,rotating machinery is developing in the direction of high speed,overloading,automation and complexity,which results in more and more questions.As the operating environment is quite bad,complex rotating machinery often breaks down for the nonlinear factors.This makes the system lose stability or even air crash accidents,which cause immeasurable economic losses,casualties and social harms.In the past, simple rotor model was often used to study the nonlinear characteristics and stability,but for the more complex engineering machinery,such model is no longer competent.Therefore, study of the modeling and operational stability of the complex rotor-bearing system has great practical significance.At present many scientific workers at home and abroad begin to realize this question and have achieved some results.
This paper is in the background of large-scale compressor rotor vibration experiment system studied by Northeastern University and Shenyang Blower Co.,Ltd.Cycle operation stability and bifurcation characteristics of the complex rotor-bearing system with faults,that single-span double-disk rotor-bearing system with single fault or coupling faults and double-span multiple-disk rotor-bearing system with coupling faults are studied for the purpose of the dynamic design appliance in the framework of the "Integrated Design Method Based on the System Engineering" put forward by Professor Wen Bangchun.Concrete contents are as follows:
(1) Continuation targeting algorithm is studied to solve the periodic solutions and to determine the stability and bifurcation of the nonlinear dynamic rotor-bearing system. Nonlinear dynamics toolbox of the rotor-bearing system is developed based on the finite element theory,this toolbox contains about 50 subfunctions,its functions are as follows: calculating critical speed,calculating material damping coefficient,calculating time and frequency domain response of the elastic supporting system,calculating time and frequency domain response of the single-span and double-span nonlinear rotor-bearing system, studying bifurcation,chaos,stability and so on.Nonlinear factors include oil film supporting, crack and rub-impact,etc.To get higher calculation accuracy and save calculation cost,the toolbox contains dimensionless and reduced-processing functions.
(2) Nonlinear dynamic model of the double-disk rotor-bearing system supported by oil film is established.Stability and bifurcation behaviors of the system are studied by the continuation targeting algorithm in the parameter domains of eccentric phase,eccentricityrotational speed,bearing aspect ratio-rotational speed,bearing clearance-rotational speed and oil viscosity-rotational speed.Instability characteristics and nonlinear vibration characteristics of the rotor-bearing system supported by oil film are studied by experiments.Research shows that synchronous periodic motion of the system mainly presents as period doubling and quasi periodic bifurcation phenomenon.And with the change of a parameter,the topological structure and domain of attraction of the system will also change,which results in the jump mutations phenomenon of the system bifurcation curve.Generally instability speed will also change as jump change of the bifurcation type.
(3) Instability and bifurcation behaviors of the double-disk rotor-bearing system supported by oil film with rub-impact faults are analyzed in the parameter domains of friction coefficient-rotational speed and rub-impact clearance-rotational speed for different rub-impact position.Rub-impact monitoring device and experimental device are established and the main results of the analysis are verified.Research shows that different rub-impact position and eccentric magnitude have great influence on the stability and dynamic characteristics of the system,so it can be said that topological structure of the system can be easily changed by the rub-impact faults.Rub-impact faults can influence the emergence of the oil whirl and oil whip. This can delay the instability speed and double frequency components will appear in the frequency domain response for the reason of rub-impact.
(4) Operation stability and instability rules of the double-disk rotor-bearing system supported by oil film with crack faults arc analyzed in the parameter domains of eccentric magnitude- rotational speed,crack depth- rotational speed and crack position- rotational speed. Research shows that existence and location change of the crack have little influence on the system instability speed and instability patterns.As the growth of the crack,instability speed increase slowly.The main reason is that existence of the crack interfere the formation of the oil whirl,but it not means that existence of the crack is beneficial:Its existence would bring about great hidden trouble,numerical calculation may not continue when the crack depth reach a certain level,so crack damage in the rotor system must be avoided.
(5) Operation stability and bifurcation rules of the continuous double eccentric rotorbearing system with rub-impact-crack coupling faults are analyzed in the parameter domains of eccentric magnitude- rotational speed,rub-impact clearance-rotational speed and crack depth- rotational speed.Research shows that with the increasing of the eccentric magnitude, instability speed has decreased tendency.When the eccentric magnitude reaches a certain level,instability speed will increase for the restriction of the stator.When the rub-impact clearance decreases,instability speed will increase for the increasing of the rub-impact force. In additon,rub-impact faults have bigger influence than the crack on the rotor-bearing system with rub-impact-crack coupling faults,but existence of the crack would bring about great hidden trouble for the normal operation of the system.
(6) Nonlinear dynamic model of the double-span rotor-bearing system with rub-impact-crack coupling faults supported by oil film is established.Stability and bifurcation behaviors of the system with rub-impact-crack coupling faults are studied in the parameter domains of eccentric magnitude- rotational speed,rub-impact clearance-rotational speed and crack depth- rotational speed.Research shows that instability characteristics of the double-span rotor-bearing system are different from that of the single-span system.Mutations phenomenon of bifurcation type and instability speed did not appear in the double-span rotor-bearing system,which is main decided by the structural characteristics of the rotor system.Study on the double-span rotor-bearing system with coupling faults shows that response of both ends of the rotor one appears strong and the other appears weak for the effect of the elastic coupling.Big eccentric magnitude makes the instability speed of the system increase and characteristic of rub-impact faults appears more obvious.
本课题以东北大学与沈阳鼓风机(集团)有限公司联合进行的“大型压缩机转子振动实验系统”横向课题为背景,以闻邦椿教授提出的“基于系统工程的产品综合设计理论与方法”框架内的动态优化设计应用研究为目的,进行了含故障复杂转子-轴承系统,即含单故障/耦合故障的单跨双盘转子-轴承系统、含耦合故障的双跨多盘的转子-轴承系统的周期运行稳定性及分岔特性的理论和实验研究。具体研究内容和如下:
(1)研究了求解复杂转子-轴承非线性系统周期解及判断其稳定性、分岔的延拓打靶算法,以有限元理论为基础开发了转子-轴承非线性动力学工具箱,该工具箱共含50余个子函数,功能包括:计算临界转速,材料阻尼系数,弹性支承系统的时域及频域响应,单跨和多跨非线性转子系统时域、频域响应,以及分岔、混沌、稳定性等问题。其中非线性因素包括油膜支承、裂纹、碰摩等。为获得较高的计算精度和有效地节约计算成本,工具箱含有无量纲化和降维处理等功能。
(2)建立了油膜支承双盘转子-轴承系统非线性动力学模型,利用求解非线性系统周期解的延拓打靶方法,研究了系统在偏心量-转速、偏心相位-转速、轴承长径比-转速、轴承间隙-转速、润滑油动力粘度-转速参数域内的系统稳定性及分岔行为,得到了系统周期运行的失稳规律;搭建相应的实验装置,通过实验研究了油膜支承的转子-轴承系统失稳特性及非线性振动特征。研究发现系统的同频周期运动主要以倍周期、Hopf分岔失稳,并且随着某一参数的变化系统的拓扑结构和吸引域发生变化,使系统分岔曲线会发生跳跃突变现象,通常情况下,随着分岔类型的跳跃变化失稳转速也会发生突变。
(3)以油膜支承含碰摩故障双盘转子-轴承系统为研究对象,分析了碰摩转子-轴承系统对于不同碰摩位置在摩擦系数-转速、碰摩间隙-转速参数域内系统周期运动的失稳分岔行为及其规律;开发了配套的碰摩监测装置,并搭建了相应的实验装置,验证了主要的分析结果。研究发现不同的碰摩位置和偏心量对系统的稳定性和动态特性着很大的影响,这里认为碰摩故障比较容易改变系统的拓扑结构;当碰摩故障加重时容易干扰“油膜涡动”及“油膜振荡”的发生,使失稳转速出现延迟现象,碰摩故障容易使频域响应出现倍频成份。
(4)对于油膜支承含裂纹故障的双盘转子-轴承系统,分析了裂纹转子系统对于裂纹在偏心量-转速、裂纹深度-转速、裂纹位置-转速参数域内系统运行稳定性及失稳规律;并做了相应的验证实验。研究发现裂纹的存在以及位置的变化对系统失稳转速和失稳类型的影响并不是很大,随着裂纹的扩展失稳转速有缓慢升高趋势,主要原因是由于裂纹的存在干扰了油膜涡动的形成,但这并不是说裂纹的存在是有益的,它的存在将给机组带来很大隐患,对于数值计算当裂纹深度达到一定程度时将会发散而无法计算,对应于工程现场将会出现毁机事故,因此转子系统中的裂纹故障是必须避免的。
(5)对于含有碰摩-裂纹耦合故障的双盘多自由度转子-轴承系统,分析了其偏心量-转速、碰摩间隙-转速、裂纹深度-转速参数域内的运行稳定性及分岔规律,并做了相应的实验进行验证。研究发现随着偏心量的增加,系统失稳转速有降低趋势,当转盘的偏心量增大到一定程度时,由于定子对其限制作用会使系统的失稳转速升高:当碰摩间隙减小时,同样因为增大了碰摩力使系统失稳转速有升高现象;另外在碰摩和裂纹耦合故障的转子-轴承系统中,碰摩故障对系统的影响较为明显,裂纹对系统稳定性的影响相对于碰摩故障稍微弱一些。
(6)建立了考虑油膜支承含碰摩-裂纹耦合故障的双跨转子-轴承系统动力学模型,研究了其在偏心量-转速、碰摩间隙-转速、裂纹深度-转速参数域内研究稳定性及分岔行为,并做了相应的验证实验。研究表明双跨转子-轴承系统的失稳特性不同于前面单跨系统,其分岔类型和失稳转速并没有出现突变现象,这主要是由转子系统本身的结构特性所决定的。对于含耦合故障双跨系统的实验研究表明,由于弹性联轴器的作用,使两端转子的响应表现出一强一弱的现象;大偏心量使系统的失稳转速升高,并且碰摩故障的特性表现得较为明显一些。
Rotating machinery is one kind of mechanical equipments most widely used in the industrial department,its stable operation influences the development process of all the industry.With the development of the society,rotating machinery is developing in the direction of high speed,overloading,automation and complexity,which results in more and more questions.As the operating environment is quite bad,complex rotating machinery often breaks down for the nonlinear factors.This makes the system lose stability or even air crash accidents,which cause immeasurable economic losses,casualties and social harms.In the past, simple rotor model was often used to study the nonlinear characteristics and stability,but for the more complex engineering machinery,such model is no longer competent.Therefore, study of the modeling and operational stability of the complex rotor-bearing system has great practical significance.At present many scientific workers at home and abroad begin to realize this question and have achieved some results.
This paper is in the background of large-scale compressor rotor vibration experiment system studied by Northeastern University and Shenyang Blower Co.,Ltd.Cycle operation stability and bifurcation characteristics of the complex rotor-bearing system with faults,that single-span double-disk rotor-bearing system with single fault or coupling faults and double-span multiple-disk rotor-bearing system with coupling faults are studied for the purpose of the dynamic design appliance in the framework of the "Integrated Design Method Based on the System Engineering" put forward by Professor Wen Bangchun.Concrete contents are as follows:
(1) Continuation targeting algorithm is studied to solve the periodic solutions and to determine the stability and bifurcation of the nonlinear dynamic rotor-bearing system. Nonlinear dynamics toolbox of the rotor-bearing system is developed based on the finite element theory,this toolbox contains about 50 subfunctions,its functions are as follows: calculating critical speed,calculating material damping coefficient,calculating time and frequency domain response of the elastic supporting system,calculating time and frequency domain response of the single-span and double-span nonlinear rotor-bearing system, studying bifurcation,chaos,stability and so on.Nonlinear factors include oil film supporting, crack and rub-impact,etc.To get higher calculation accuracy and save calculation cost,the toolbox contains dimensionless and reduced-processing functions.
(2) Nonlinear dynamic model of the double-disk rotor-bearing system supported by oil film is established.Stability and bifurcation behaviors of the system are studied by the continuation targeting algorithm in the parameter domains of eccentric phase,eccentricityrotational speed,bearing aspect ratio-rotational speed,bearing clearance-rotational speed and oil viscosity-rotational speed.Instability characteristics and nonlinear vibration characteristics of the rotor-bearing system supported by oil film are studied by experiments.Research shows that synchronous periodic motion of the system mainly presents as period doubling and quasi periodic bifurcation phenomenon.And with the change of a parameter,the topological structure and domain of attraction of the system will also change,which results in the jump mutations phenomenon of the system bifurcation curve.Generally instability speed will also change as jump change of the bifurcation type.
(3) Instability and bifurcation behaviors of the double-disk rotor-bearing system supported by oil film with rub-impact faults are analyzed in the parameter domains of friction coefficient-rotational speed and rub-impact clearance-rotational speed for different rub-impact position.Rub-impact monitoring device and experimental device are established and the main results of the analysis are verified.Research shows that different rub-impact position and eccentric magnitude have great influence on the stability and dynamic characteristics of the system,so it can be said that topological structure of the system can be easily changed by the rub-impact faults.Rub-impact faults can influence the emergence of the oil whirl and oil whip. This can delay the instability speed and double frequency components will appear in the frequency domain response for the reason of rub-impact.
(4) Operation stability and instability rules of the double-disk rotor-bearing system supported by oil film with crack faults arc analyzed in the parameter domains of eccentric magnitude- rotational speed,crack depth- rotational speed and crack position- rotational speed. Research shows that existence and location change of the crack have little influence on the system instability speed and instability patterns.As the growth of the crack,instability speed increase slowly.The main reason is that existence of the crack interfere the formation of the oil whirl,but it not means that existence of the crack is beneficial:Its existence would bring about great hidden trouble,numerical calculation may not continue when the crack depth reach a certain level,so crack damage in the rotor system must be avoided.
(5) Operation stability and bifurcation rules of the continuous double eccentric rotorbearing system with rub-impact-crack coupling faults are analyzed in the parameter domains of eccentric magnitude- rotational speed,rub-impact clearance-rotational speed and crack depth- rotational speed.Research shows that with the increasing of the eccentric magnitude, instability speed has decreased tendency.When the eccentric magnitude reaches a certain level,instability speed will increase for the restriction of the stator.When the rub-impact clearance decreases,instability speed will increase for the increasing of the rub-impact force. In additon,rub-impact faults have bigger influence than the crack on the rotor-bearing system with rub-impact-crack coupling faults,but existence of the crack would bring about great hidden trouble for the normal operation of the system.
(6) Nonlinear dynamic model of the double-span rotor-bearing system with rub-impact-crack coupling faults supported by oil film is established.Stability and bifurcation behaviors of the system with rub-impact-crack coupling faults are studied in the parameter domains of eccentric magnitude- rotational speed,rub-impact clearance-rotational speed and crack depth- rotational speed.Research shows that instability characteristics of the double-span rotor-bearing system are different from that of the single-span system.Mutations phenomenon of bifurcation type and instability speed did not appear in the double-span rotor-bearing system,which is main decided by the structural characteristics of the rotor system.Study on the double-span rotor-bearing system with coupling faults shows that response of both ends of the rotor one appears strong and the other appears weak for the effect of the elastic coupling.Big eccentric magnitude makes the instability speed of the system increase and characteristic of rub-impact faults appears more obvious.
引文
1.闻邦椿,顾家柳,夏松波,等.高等转子动力学—理论、技术与应用[M].北京:机械工业出版社,2000
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