Substantial unbalance may be caused by fan blade off during the operation period of gas turbine engines,and related dynamic problems are very critical to the safety design of rotor system in aero-engine.This article a...Substantial unbalance may be caused by fan blade off during the operation period of gas turbine engines,and related dynamic problems are very critical to the safety design of rotor system in aero-engine.This article aims to understand lateral-torsional coupled vibration of the rotor system with substantial unbalance.The governing equation of a modified unbalanced rotor system is established based on Lagrangian approach.Then,a mathematical analytical method is proposed in which a linear approximation is derived and the Floquet theory and Hill’s method are incorporated,from which the modal characteristics of the unbalanced rotor are obtained.The modal characteristics of the unbalanced rotor system are revealed comprehensively for the first time.Furthermore,the relation between the modes and responses of the unbalanced rotor is discussed in detail.The results show that the lateral vibration and torsional vibration of the unbalanced rotor are coupled through the inertial terms in the governing equations.Due to the coupling,veering and lock-in phenomena occur between the frequencies of the forward whirl mode and the torsional mode.Furthermore,lock-in can lead to a kind of principal instability.With regard to the response of the unbalanced rotor,both natural vibration components and enforced vibration components appear in the lateral response,while only natural vibration components appear during torsional vibration.Moreover,natural vibration components play a crucial role in the response within the principal instability region and cause divergence of the vibration amplitudes in the lateral and torsional directions.展开更多
调频气压液柱阻尼器(tuned liquid column gas damper,TLCGD)是一种从调频液柱阻尼器发展而来的新型而有效的结构减震装置。在U/V形阻尼器液柱上加上封闭式气压不仅增加了它的使用范围,使频率扩大到5Hz,并且提高了结构的有效阻尼。由广...调频气压液柱阻尼器(tuned liquid column gas damper,TLCGD)是一种从调频液柱阻尼器发展而来的新型而有效的结构减震装置。在U/V形阻尼器液柱上加上封闭式气压不仅增加了它的使用范围,使频率扩大到5Hz,并且提高了结构的有效阻尼。由广义Bernoulli方程推导出液体在管道中的运动方程并等价线性化。本文分析了非对称结构平移-扭转耦联振动的动力特性。当结构在地震和强风作用下发生以平移为主的动力反应,该阻尼器的最佳位置使到速度中心的距离最大。通过振型优化,Den Hartog公式得到阻尼器的最优参数(阻尼比和调谐频率比),考虑邻近多个振型的相互影响,状态空间优化使得结果更为合理。用1个3层的偏心结构作为算例,进行优化计算。数值结果表明,这种优化方法得到的参数使得调频气压阻尼器对结构的平动-扭转反应起到较好的减振效果。展开更多
Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined interna...Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.展开更多
Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into acco...Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.展开更多
基金the support from the National Natural Science Foundation of China(Nos.11772022,51575022 and 51475021)the support by the Academic Excellence Foundation of BUAA for Ph.D.Students。
文摘Substantial unbalance may be caused by fan blade off during the operation period of gas turbine engines,and related dynamic problems are very critical to the safety design of rotor system in aero-engine.This article aims to understand lateral-torsional coupled vibration of the rotor system with substantial unbalance.The governing equation of a modified unbalanced rotor system is established based on Lagrangian approach.Then,a mathematical analytical method is proposed in which a linear approximation is derived and the Floquet theory and Hill’s method are incorporated,from which the modal characteristics of the unbalanced rotor are obtained.The modal characteristics of the unbalanced rotor system are revealed comprehensively for the first time.Furthermore,the relation between the modes and responses of the unbalanced rotor is discussed in detail.The results show that the lateral vibration and torsional vibration of the unbalanced rotor are coupled through the inertial terms in the governing equations.Due to the coupling,veering and lock-in phenomena occur between the frequencies of the forward whirl mode and the torsional mode.Furthermore,lock-in can lead to a kind of principal instability.With regard to the response of the unbalanced rotor,both natural vibration components and enforced vibration components appear in the lateral response,while only natural vibration components appear during torsional vibration.Moreover,natural vibration components play a crucial role in the response within the principal instability region and cause divergence of the vibration amplitudes in the lateral and torsional directions.
基金Supported by National Natural Science Foundation of China(Grant No.51475084)
文摘Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.
基金supported by the National Natural Science Fundation of China(51105063)the Fundamental Research Funds for the Central Universities(N120403004)
文摘Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.
