Response evaluation of imbalance-rub-pedestal looseness coupling fault on a geometrically nonlinear rotor system
Introduction
Thrust-weight ratio and efficiency of rotating machine can be enhanced via precisely manufactured bearings with reduced clearances. However, under this engineering circumstance, the probability of rotor-stator rub is increased sharply, which may result in decreased machine life and adverse thermal effects. The rub is termed as the contact between rotor and stator, which may be a dominant factor of rotordynamic behavior [1]. As one of secondary faults occurring in the rotating machine, rotor-stator rub is usually represented in the form of coupling failure. The sources for primary causes could be rotor imbalance, misalignment, fluid forces, shaft crack and pedestal looseness [2], [3], [4], [5], [6]. As far as the stability and safety of the rotating machine are concerned, the coupling failures are more harmful and uncertain than single faults. That is to say it is essential to master the unique vibration signature of the rotor system with rub coupling fault from state monitoring point of view.
During the past decades, the rotor-stator rub coupling fault has been under comprehensive investigations. Considering this issue that the Jeffcott rotor was subjected to imbalance and rub, Chu et al. [7] revealed the distribution rule among periodic region, quasi periodic region and chaotic region at different rotational speed. As for an asymmetric double-disc rotor-bearing system, Xiang et al. [8] adopted the numerical method to study the nonlinear dynamic behavior of the system varying with the model parameters. The electromagnetic vibration of electrical machines with an eccentric rotor was addressed in the reference [9], in which the electromagnetic excitation, mass imbalance and rub were taken into account. Hou et al. [10] focused on the influence of aircraft hovering flight on the rub rotor system and they investigated the nonlinear dynamic phenomenon. AlZibdeh et al. [11] proposed a three degree-of-freedom extended Jeffcott rotor for describing the drill string, and then they captured the vibration response of the rotor system with rub fault in an approximate solution. Under the periodic excitation caused by the mass eccentricity of disc, Vlajic et al. [12] analytically and numerically investigated the torsional vibration of a Jeffcott rotor system subjected to continuous contact of stationary components. For a rotating continuous flexible shaft-disc system with rotor-stator rub, Khanlo et al. [13] emphasized the torsional coupling effect on the chaotic characteristic and gave the conclusion that this effect could primarily change the speed ratios at which rub occurred. Popprath and Ecker [14] presented the nonlinear dynamic response of a Jeffcott rotor system having intermittent contact with a stator and discussed the effect of the visco-elastically suspended stator on the rotor motion. Wang et al. [15] theoretically studied the sudden unbalance and rub-impact caused by blade loss, in particular investigated the response of the rotor on a rotor test rig. Cong et al. [16] proposed an Impact Energy Model (IEM) to evaluate the probability or severity of rub-impact fault. Meanwhile, they conducted the experiment in two steps i.e. hammer test and rub-impact fault validation. Based on variational mode decomposition, Wang et al. [17] gave a novel method of rubbing fault diagnosis and proved the effectiveness of the method. Ma et al. [18] investigated the fault characteristics of a single span rotor system with two disc when the rub-impact between a disc and an elastic limiter occurred. By using conventional scalograms and reassigned scalograms, Peng et al. [19] explained the cause of rubbings, its occurrence and phenomenon if the severity of rubbing became serious. Thus, there is no denying that the complicated nonlinear phenomenon is generally associated with a rub rotor and then this is supposed to be worthy of intensive study [20], [21], [22], [23], [24], [25].
Because of the poor quality of installation or long period of vibration, the pedestal looseness becomes one of the common faults that happen in rotating machine [26]. The looseness fault will reduce the elastic constraint stiffness of pedestal and cause the violent vibration of the rotor system. It is suggested that the work on the topic of pedestal looseness is indeed significant to aviation industry in terms of safe operation. Ma et al. [27], [28] established a single-span rotor model with two discs, where the looseness fault was described by a piecewise linear spring-damper model, and analyzed the nonlinear vibration characteristic. For a rotating machine with only one pedestal looseness, Goldman and Muszynska [29], [30] observed the synchronous and sub-synchronous frictional components referring to the numerical results and experimental data. Jiang et al. [31] developed a nonlinear measure to quantify the degree of nonlinear behaviors in a bearing-rotor system and predicted the dynamic behavior under different looseness clearances. In the reference [32], a method of multiple scales was adopted to analyze the free vibration and forced vibration of the nonlinear rotor-bearing system. Besides, the influences involved in this bearing pedestal model were also revealed in detail. According to the vibration sensitive time-frequency feature, Chen et al. [33] proposed a novel method to recognize the pedestal looseness extent of rotating machine and then successfully examined the validity of the method.
It should be noted that the looseness fault has a higher potential risk to induce the rotor-stator rub and causes the complicated nonlinear vibration. In other word, there is a close relation between pedestal looseness and rub in the most of actual cases. Meanwhile, the coupling fault of looseness-rub can easily aggravate the whirling motion, so that the geometrical nonlinearity of shaft should not be ignored. Meanwhile, it becomes an extremely crucial component in dynamic design of rotating machine. In the previous authors’ work [34], the geometrically nonlinear relation between strain and displacement of flexible shaft was characterized by the equivalent spring and equivalent damper. However, the pioneering contributions to the dynamic response of the rotor system considering geometrical nonlinearity of shaft, rotor-stator rub and pedestal looseness have not been observed in existing literature.
In view of this case, the main contribution of this paper is to investigate the close interaction between geometrical nonlinearity and coupling fault acting on the rotor system. According to the Hamilton principle, a general dynamic model for geometrically nonlinear rotor system subjected to imbalance-rub-pedestal looseness coupling fault is established in this paper. To reveal the normal impact mechanism in the condition of thermal barrier coatings, a novel force model and its modified forms [35], [36] are employed at the different penetration stages. In the tangential direction, the Coulomb model [37] is used to describe the friction characteristic. Then the numerical simulation is applied to obtain the nonlinear vibration response of the rotor system at different rotational speed. Briefly speaking, there are five parts in the present work, including (1) sweep frequency analysis of linear/nonlinear rotor system without any fault, (2) imbalance-rub coupling fault under different initial clearance, (3) imbalance-pedestal looseness coupling fault under different looseness stiffness, (4) nonlinear dynamic characteristic of the rotor system with imbalance-rub-looseness coupling fault, (5) hammering test and vibration test on the rotor test rig. To some extent, this work can enrich our understanding to the vibration mechanism of rotating machine and may promote the development of fault diagnosis.
Section snippets
Formulation of vibrating equations
The mathematical formulation of the geometrically nonlinear rotor system with single pedestal looseness is briefed in this section. Due to the severe imbalance excitation and pedestal looseness, the whirling motion with larger amplitude usually happens. Thus, for the flexible shaft, the relation between strain and displacement becomes nonlinear rather than linear. This may change the resonant frequency of the system and lead to the complicated vibration behavior. At the same time, the
Results and discussion
Because of these features, such as geometrical nonlinearity of shaft, mass imbalance, rotor-stator rub and pedestal looseness, performing the theoretically qualitative analysis becomes relative difficult, so that this case becomes impossible to obtain the solutions in a closed form. So the numerical methods have to be resorted in this paper.
Referring to the existing research on the nonlinear vibration, the Runge-Kutta method is chosen, in which the time step of direct numerical integration is
Experimental operation on a rotor test rig
In order to show the effectiveness of modeling method and relavant dynamic phenomena observed in this paper, the hammering test and vibration experiment are conducted on the rotor test rig, which is set up in the ADVC (Aircraft Dynamics Vibration and Control) Laboratory, HIT. There are two main research contents in the vibration experiment: (1) measuring the vertical vibration under imbalance fault and (2) measuring the vertical vibration under imbalance-pedestal looseness coupling fault. There
Conclusion
In this paper, taking into account the coupling fault of imbalance-rub-pedestal looseness, the dynamic model of a three-degree-of-freedom rotor system has been proposed, in which the geometrically nonlinear property of the shaft has been presented. Under the influence of severe imbalance and pedestal looseness, the rotor-stator rub has a higher potential risk and then the mechanical mechanism has been described by the novel impact force model and Coulomb friction model. By using the Runge-Kutta
Acknowledgment
This work was supported by the National Nature Science Foundation of China (Grant No. 11702228), (Grant No. 11772273) and the Fundamental Research Funds for the Central Universities (2682017CX087).
References (42)
- et al.
Investigations on bending-torsional vibrations of rotor during rotor-stator rub using Lagrange multiplier method
J. Sound Vib.
(2017) - et al.
Coupled bending-torsional vibration analysis of rotor with rub and crack
J. Sound Vib.
(2009) - et al.
Nonlinear dynamic analysis of fractional order rub-impact rotor system
Commun. Nonlinear Sci. Numer. Simul.
(2011) Effects of a crack on the stability of a non-linear rotor system
Int. J. Nonlin. Mech.
(2007)- et al.
Bifurcation and chaos in rub-impact Jeffcott rotor system
J. Sound Vib.
(1998) - et al.
Nonlinear coupled dynamics of an asymmetric double-disc rotor-bearing system under rub-impact and oil-film forces
Appl. Math. Model.
(2016) - et al.
A general electromagnetic excitation model for electrical machines considering the magnetic saturation and rub impact
J. Sound Vib.
(2018) - et al.
Nonlinear vibration phenomenon of an aircraft rub-impact rotor system due to hovering flight
Commun. Nonlinear Sci. Numer. Simul.
(2014) - et al.
Effects of high frequency drive speed modulation on rotor with continuous stator contact
Int. J. Mech. Sci.
(2017) - et al.
Torsional oscillations of a rotor with continuous stator contact
Int. J. Mech. Sci.
(2014)
The effects of lateral-torsional coupling on the nonlinear dynamic behavior of a rotating continuous flexible shaft-disk system with rub-impact
Commun. Nonlinear Sci. Numer. Simul.
Nonlinear dynamics of a rotor contacting an elastically suspended stator
J. Sound Vib.
Theoretical and experimental investigation on the sudden unbalance and rub-impact in rotor system caused by blade off
Mech. Syst. Signal Process.
Experimental validation of impact energy model for the rub-impact assessment in a rotor system
Mech. Syst. Signal Process.
Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system
Mech. Syst. Signal Process.
Fixed-point rubbing fault characteristic analysis of a rotor system based on contact theory
Mech. Syst. Signal Process.
Detection of the rubbing-caused impacts for rotor-stator fault diagnosis using reassigned scalogram
Mech. Syst. Signal Process.
Nonlinear effects caused by coupling misalignment in rotors equipped with journal bearings
Mech. Syst. Signal Process.
Nonlinear coupled dynamics of flexible blade-rotor-bearing systems
Tribology Int.
Dynamic characteristics analysis of a rotor system with two types of limiters
Int. J. Mech. Sci.
A finite element-based algorithm for rubbing induced vibration prediction in rotors
J. Sound Vib.
Cited by (57)
Numerical and experimental investigations on dynamic behaviors of a bolted joint rotor system with pedestal looseness
2024, Journal of Sound and VibrationRole of image feature enhancement in intelligent fault diagnosis for mechanical equipment: A review
2024, Engineering Failure AnalysisDynamics simulation-based deep residual neural networks to detect flexible shafting faults
2023, Knowledge-Based SystemsNumerical and experimental analysis of rotor-bearing system for axial piston pump with misalignment–rubbing coupling fault
2023, Journal of Sound and VibrationErosion-damage-induced vibration response of aero-gas generator rotor system
2023, Mechanical Systems and Signal ProcessingElectromechanical coupling modeling and motor current signature analysis of bolt loosening of industrial robot joint
2023, Mechanical Systems and Signal Processing