基于数据库的径向滑动轴承—转子系统非线性动力学行为研究
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摘要
对于大型旋转机械来说,转子运行是否稳定关系到整个系统的安全,这就要求我们必须对转子的非线性动力学响应进行全面的分析。本文针对流体动压径向滑动轴承支承的转子非线性动力系统进行分析,主要的研究内容包括以下几个方面：
1.详细阐述了径向滑动轴承非线性油膜力数据库方法。本文基于动态Reynolds方程和Reynolds破膜条件,运用Castelli法求解Reynolds方程,通过对动态Reynolds方程的特殊处理,建立了单块轴瓦的非线性油膜力数据库,同时介绍了数据库的结构以及快速检索和精确插值的方法。以固定瓦轴承为研究对象,介绍了固定瓦轴承几何参数的求解计算和轴承静态特性的组装计算过程。最后,针对各种固定瓦滑动轴承,通过与参考文献[1]的计算结果进行对比计算,验证了数据库方法的快速、精确的特点。
2.对可倾瓦滑动轴承和固定瓦-可倾瓦组合滑动轴承的非线性油膜力进行了分析计算。首先建立了单块轴瓦坐标系,然后将轴承坐标系下的几何参数分解为单块轴瓦坐标系下的几何参数。根据单块轴瓦的几何参数,通过调用单块轴瓦的非线性油膜力数据库,并利用瓦块的平衡条件计算出单块轴瓦坐标系下的油膜力,运用组装技术求解可倾瓦轴承的非线性油膜力,并对可倾瓦轴承的静态性能计算程序进行了验证与分析。在此基础上,计算了固定瓦-可倾瓦组合滑动轴承的非线性油膜力。
3.建立了固定瓦-可倾瓦组合径向滑动轴承-Jeffcott刚性转子系统的动力学模型。运用Poincare映射和Runge-Kutta方法得到了固定瓦-可倾瓦组合滑动轴承支承的对称刚性转子系统的不平衡响应,数据结果展现了固定瓦-可倾瓦组合滑动轴承-转子系统的周期解、倍周期解、准周期解等非线性现象。分析了轴瓦的支点位置系数和预负荷系数对固定瓦-可倾瓦组合滑动轴承-刚性转子系统稳定性的影响。结果表明,瓦块的支点位置系数和预负荷系数对系统的稳定性有较大的影响。因此,在选取系统参数时应选取适当的预负荷系数和一定的偏支。
4.建立了固定瓦-可倾瓦组合径向滑动轴承-Jeffcott柔性转子系统的动力学模型。运用Poincare映射和Runge-Kutta法,分析了支点比分别为0.5和0.6,预负荷系数为0.4时,固定瓦-可倾瓦组合滑动轴承支承的对称柔性转子系统的不平衡响应。数据结果展现了组合轴承-转子系统的周期解、倍周期解和准周期解等非线性现象。
上述研究为分析解决实际的径向滑动轴承-转子系统中的非线性问题和稳定性问题提供了理论参考。
For large rotating machinery, the system's security is influenced by the operation stability of the rotor, which requires us to conduct a comprehensive analysis to the nonlinear dynamic response of the rotor. In this thesis, nonlinear dynamic systems of the rotor supported by hydrodynamic journal bearing are analyzed. The contents are as follows:
1. Nonlinear oil film force database method is discussed here in detail. Based on the dynamic Reynolds equation with Reynolds boundary condition, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By special treatment to the dynamic Reynolds equation, a profile of nonlinear oil film force of single-pad journal bearing is established. At the same time, the structure of the database, as well as fast retrieval and accurate interpolation method are introduced. Taking fixed-pad bearing as the object, and the calculation of the geometric parameters and the assembly calculation of static characteristics of bearing are introduced. By comparison of the results of a variety of fixed-pad journal bearings, the database method is validated to be rapid and accurate.
2. The nonlinear oil film forces of tilting-pad journal bearing and fixed-tilting pads journal bearing are calculated. A single pad coordinate system is established, and then the geometric parameters in the bearing coordinate system are transformed into the geometric parameters in a single pad coordinate system. According to the geometric parameters and the pad equilibrium condition in a single pad coordinate system, the nonlinear oil film forces are calculated by calling the nonlinear oil film forces database. The nonlinear oil film force of the tilting pad bearing is obtained by the assembly method. The calculation program for the static characteristics of tilting pad bearing is verified, and then the nonlinear oil film force of the fixed-tilting pads combination bearing is calculated.
3. The dynamic model of a symmetric rigid rotor supported by fixed-tilting pads journal bearing is established. The unbalanced responses of the symmetrical rigid rotor dynamic system supported by fixed-tilting pads journal bearings are analyzed by self-adaptive Runge-Kutta method and Poincare mapping. The numerical results reveal nonlinear behaviors of the system, such as periodic, periodic-doubling, quasi-periodic, etc. The effects of the pivot ratio and the preload on the stability of the rotor system are analyzed. The results show that the pivot ratio and the preload have an important influence on the system's stability. Therefore, when selecting the system parameters, the appropriate preload and pivot ratio should be chosen.
4. The dynamic model of a symmetric flexible rotor supported by fixed-tilting pads journal bearing is established. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the. nonlinear motions of the center of the rotor are calculated by self-adaptive Runge-Kutta method and Poincare mapping during different rotational speed tests, . when the pivot ratio is 0.5 or 0.6, and the preload is 0.4. Numerical results reveal nonlinear behaviors, such as periodic, periodic-doubling, quasi-periodic, etc.
The preceding research provides theoretical references for analyzing and settling nonlinear and stability problems of a practical rotor system supported by fixed-tilting pads journal bearings..
1.详细阐述了径向滑动轴承非线性油膜力数据库方法。本文基于动态Reynolds方程和Reynolds破膜条件,运用Castelli法求解Reynolds方程,通过对动态Reynolds方程的特殊处理,建立了单块轴瓦的非线性油膜力数据库,同时介绍了数据库的结构以及快速检索和精确插值的方法。以固定瓦轴承为研究对象,介绍了固定瓦轴承几何参数的求解计算和轴承静态特性的组装计算过程。最后,针对各种固定瓦滑动轴承,通过与参考文献[1]的计算结果进行对比计算,验证了数据库方法的快速、精确的特点。
2.对可倾瓦滑动轴承和固定瓦-可倾瓦组合滑动轴承的非线性油膜力进行了分析计算。首先建立了单块轴瓦坐标系,然后将轴承坐标系下的几何参数分解为单块轴瓦坐标系下的几何参数。根据单块轴瓦的几何参数,通过调用单块轴瓦的非线性油膜力数据库,并利用瓦块的平衡条件计算出单块轴瓦坐标系下的油膜力,运用组装技术求解可倾瓦轴承的非线性油膜力,并对可倾瓦轴承的静态性能计算程序进行了验证与分析。在此基础上,计算了固定瓦-可倾瓦组合滑动轴承的非线性油膜力。
3.建立了固定瓦-可倾瓦组合径向滑动轴承-Jeffcott刚性转子系统的动力学模型。运用Poincare映射和Runge-Kutta方法得到了固定瓦-可倾瓦组合滑动轴承支承的对称刚性转子系统的不平衡响应,数据结果展现了固定瓦-可倾瓦组合滑动轴承-转子系统的周期解、倍周期解、准周期解等非线性现象。分析了轴瓦的支点位置系数和预负荷系数对固定瓦-可倾瓦组合滑动轴承-刚性转子系统稳定性的影响。结果表明,瓦块的支点位置系数和预负荷系数对系统的稳定性有较大的影响。因此,在选取系统参数时应选取适当的预负荷系数和一定的偏支。
4.建立了固定瓦-可倾瓦组合径向滑动轴承-Jeffcott柔性转子系统的动力学模型。运用Poincare映射和Runge-Kutta法,分析了支点比分别为0.5和0.6,预负荷系数为0.4时,固定瓦-可倾瓦组合滑动轴承支承的对称柔性转子系统的不平衡响应。数据结果展现了组合轴承-转子系统的周期解、倍周期解和准周期解等非线性现象。
上述研究为分析解决实际的径向滑动轴承-转子系统中的非线性问题和稳定性问题提供了理论参考。
For large rotating machinery, the system's security is influenced by the operation stability of the rotor, which requires us to conduct a comprehensive analysis to the nonlinear dynamic response of the rotor. In this thesis, nonlinear dynamic systems of the rotor supported by hydrodynamic journal bearing are analyzed. The contents are as follows:
1. Nonlinear oil film force database method is discussed here in detail. Based on the dynamic Reynolds equation with Reynolds boundary condition, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By special treatment to the dynamic Reynolds equation, a profile of nonlinear oil film force of single-pad journal bearing is established. At the same time, the structure of the database, as well as fast retrieval and accurate interpolation method are introduced. Taking fixed-pad bearing as the object, and the calculation of the geometric parameters and the assembly calculation of static characteristics of bearing are introduced. By comparison of the results of a variety of fixed-pad journal bearings, the database method is validated to be rapid and accurate.
2. The nonlinear oil film forces of tilting-pad journal bearing and fixed-tilting pads journal bearing are calculated. A single pad coordinate system is established, and then the geometric parameters in the bearing coordinate system are transformed into the geometric parameters in a single pad coordinate system. According to the geometric parameters and the pad equilibrium condition in a single pad coordinate system, the nonlinear oil film forces are calculated by calling the nonlinear oil film forces database. The nonlinear oil film force of the tilting pad bearing is obtained by the assembly method. The calculation program for the static characteristics of tilting pad bearing is verified, and then the nonlinear oil film force of the fixed-tilting pads combination bearing is calculated.
3. The dynamic model of a symmetric rigid rotor supported by fixed-tilting pads journal bearing is established. The unbalanced responses of the symmetrical rigid rotor dynamic system supported by fixed-tilting pads journal bearings are analyzed by self-adaptive Runge-Kutta method and Poincare mapping. The numerical results reveal nonlinear behaviors of the system, such as periodic, periodic-doubling, quasi-periodic, etc. The effects of the pivot ratio and the preload on the stability of the rotor system are analyzed. The results show that the pivot ratio and the preload have an important influence on the system's stability. Therefore, when selecting the system parameters, the appropriate preload and pivot ratio should be chosen.
4. The dynamic model of a symmetric flexible rotor supported by fixed-tilting pads journal bearing is established. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the. nonlinear motions of the center of the rotor are calculated by self-adaptive Runge-Kutta method and Poincare mapping during different rotational speed tests, . when the pivot ratio is 0.5 or 0.6, and the preload is 0.4. Numerical results reveal nonlinear behaviors, such as periodic, periodic-doubling, quasi-periodic, etc.
The preceding research provides theoretical references for analyzing and settling nonlinear and stability problems of a practical rotor system supported by fixed-tilting pads journal bearings..
引文
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[2]虞烈,刘恒.轴承一转子系统动力学[M].西安：西安交通大学出版社,2001.
[3]郑惠萍.大型旋转机械中非线性因素综述[J].河北科技大学学报,1999,20(3)：82-86.
[4]Rankine, W. J. M. On the centrifugal force of rotating shafts[J]. The Engineer,1869,27(3):249-256.
[5]Jeffcott H. H. The lateral vibration of loaded shafts in the neighbourhood of a whirling speed-the effect of want of balance[J]. Philosophical Magazine, Series 6,1919,37(219):304-314.
[6]Stodola A. Steam and gas turbines[M]. New York:McGraw-Hill,1927.
[7]Green R. B. Gyroscopic effects on the critical speeds of flexible rotors[J]. Journal of Applied Mechanics,1948,15:369-376.
[8]Newkirk B. L. Shaft whipping[J]. General Electric Review,1924,27(3):169-178.
[9]Newkirk B. L. and Taylor H. D. Shaft whipping due to oil action in journal bearings[J]. General Electric Review,1925,28(8):559-568.
[10]Frene J., Nicolas D., Degueurce B., Berthe D. and Godet M. Hydrodynamic lubrication:bearings and thrust bearings[M]. Amsterdam:Elsevier Science,1997.
[11]Smith D. M. The motion of a rotor carried by a flexible shaft in flexible bearings[J]. Proceedings of the Royal Society of London,1933,142(846):92-118.
[12]Black H. F. The stabilizing capacity of bearings for flexible rotors with hysteresis[J]. Journal of Engineering for Industry,1976,98(1):87-91.
[13]Barrett L. E., Gunter E. J., and Allaire P. E. Optimum bearing and support damping for unbalance response and stability of rotating machinery[J]. Journal of Engineering for Power,1978,100(1): 89-94.
[14]Lund J. W. and Sternlicht B. Rotor-bearing dynamics with emphasis on attenuation[J]. Journal of Basic Engineering,1962,84:491-502.
[15]Lund J. W. The stability of an elastic rotor in journal bearings with flexible, damped supports[J]. Journal of Applied Mechanics,1965,87(4):911-920.
[16]Gunter E. J. Dynamic stability of rotor-bearing systems[R]. Washington:NASA SP-113,1966.
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