Inter-shaft Bearing Research Articles

Research on early weak structural damage detection of aeroengine intershaft bearing based on acoustic emission technology

Until now, there is no effective method to detect the early weak structural damage of the aero engine intershaft bearing. In this article, an online method based on acoustic emission technology is used to detect the early weak structural damage of aeroengine intershaft bearing. The combination of maximum correlated kurtosis deconvolution and bandpass filter is proposed to enhance and denoise fault characteristic signals of the aero engine intershaft bearing. The Hilbert envelope demodulation is used to extracting the bear fault characteristic frequency. Under aeroengine working conditions, the experiment of an intershaft bearing with outer ring fault is carried out. The result shows that bearing outer ring fault characteristic frequency and bearing vibration frequencies clearly appear in the envelope spectrum of the acoustic emission signal. Therefore, online detection of early weak structure damage of aeroengine intershaft bearing is realized by acoustic emission technology under the background of strong noise.

Analytical Analysis for the Nonlinear Phenomena of a Dual-Rotor System at the Case of Primary Resonances

This paper proposes an analytical method to study the nonlinear phenomena of a simple dual-rotor system in the case of primary resonances. According to the assumed mode method (AMM), the dynamic equations of the system with four degrees of freedom (4DOF) are established by considering the nonlinearities of the inter-shaft bearing as a nonlinear spring. The 4DOF dynamic equations in real coordinate are transferred into 2DOF dynamic equations in complex coordinate because of the symmetry of the system in two directions. Then the amplitude-frequency response equations for both primary resonances are obtained by the multiple scales method and the numerical verification shows that the simplified method of the dynamic equation is correct. Moreover, the primary resonances affected by the typical parameters such as the linear stiffness and the nonlinear stiffness of the inter-shaft bearing, and the rotation speed ratio are discussed in detail afterwards. The results show that the system will show the jump phenomenon and resonance hysteresis phenomenon when the linear stiffness is rather small and the nonlinear stiffness is rather large. The linear stiffness will suppress these nonlinear phenomena while the nonlinear stiffness will promote them. The results obtained in this paper will contribute to the mechanism analysis of the nonlinear phenomena in a dual-rotor system, which is beyond the reach of the numerical method.

Spectrum Analysis of a Coaxial Dual-Rotor System with Coupling Misalignment

The finite element model of a dual-rotor system was established by Timoshenko beam element. The dual-rotor system is a coaxial rotor whose supporting structure is similar to that of an aero-engine rotor system. The inner rotor is supported by three bearings, which makes it a redundantly supported rotor. The outer rotor connects the inner rotor by an intershaft bearing. The spectrum characteristics of the dual-rotor system under unbalanced excitation and misalignment excitation were analysed in order to study the influence of coupling misalignment of the inner rotor on the spectral characteristics of the rotor system. The results indicate that the vibration caused by the misaligned coupling of the inner rotor will be transmitted to the outer rotor through the intershaft bearing. Multiple harmonic frequency components, mainly 1x and 2x, will be excited by the coupling misalignment. The amplitudes of all harmonic frequencies increase with the misalignment in both the inner and outer rotors. The vibration level of the outer rotor affected by the misalignment is lower than that of the inner rotor because it is far from the misaligned coupling. Harmonic resonance occurs when any harmonic frequencies of the misalignment response coincide with a natural frequency of the system. In order to verify the theoretical model, experiments are performed on a test rig. Both the experimental and simulation results are in good accordance with each other.

Nonlinear thermal behaviors of the inter-shaft bearing in a dual-rotor system subjected to the dynamic load

This paper proposes a new theoretical method to investigate the thermal behaviors of the inter-shaft bearing considering the nonlinear dynamic characteristics of a dual-rotor system by combining heat transfer and nonlinear dynamics. The nonlinearities of the inter-shaft bearing, including the Hertzian contact and the radial clearance, are considered during the dynamic modeling for the system. The dynamic load of the inter-shaft bearing is defined according to the nonlinear dynamic responses of the system. Therefore, some fundamental nonlinear phenomena, i.e., jump and bi-stable phenomena happen to the dynamic load. It makes the dynamic load more appropriate to describe the actual load of the inter-shaft bearing than the static load. Furthermore, a steady-state heat transfer model for the inter-shaft bearing subjected to the dynamic load can be set up with the help of Palmgren’s empirical formula. The variation of temperatures with the rotation speed is obtained by using the Gauss–Seidel iteration. Temperatures of the inter-shaft bearing also show nonlinear thermal behaviors, i.e., jump and bi-stable phenomena. It implies the nonlinear dynamic behaviors of the system have a great impact on the thermal behaviors of the inter-shaft bearing. Moreover, an exhaustive parametric analysis for temperatures and nonlinear thermal behaviors of the inter-shaft bearing affected by dynamic parameters (including the rotation speed ratio, unbalances of rotors, the radial clearance, the stiffness and the roller number of the inter-shaft bearing) and thermal parameters (including the lubricant viscosity and the ambient temperature) is carried out. The results show that the rotation speed ratio has a significant influence on both temperatures and nonlinear thermal behaviors, other dynamic parameters mainly affect nonlinear thermal behaviors, while thermal parameters only affect temperatures. This unique discovery indicates the thermal behaviors of the inter-shaft bearing could be much more complex because of the nonlinear dynamic characteristics of the dual-rotor system. The obtained results will contribute to a better understanding of the nonlinear thermal behaviors of bearings and profoundly reveal the mechanism of the nonlinear thermal behaviors of bearings.

Bifurcation Analysis for a Simple Dual-Rotor System with Nonlinear Intershaft Bearing Based on the Singularity Method

This paper aims to classify bifurcation modes for two interrelated primary resonances of a simple dual-rotor system under double frequency excitations. The four degree-of-freedom (4DOF) dynamic equations of the system considering the nonlinearity of the intershaft bearing can be obtained by using the assumed mode method (AMM) and Lagrange’s equation. A simplified method for dynamic equations is developed due to the symmetry of rotors, based on which the amplitude frequency equations for two interrelated primary resonances are obtained by using the multiple scales method. Furthermore, the validity of the simplified method for dynamic equations and the amplitude frequency equations solved by the multiple scales method are confirmed by numerical verification. Afterwards, the bifurcation analysis for two interrelated primary resonances is carried out according to the two-state-variable singularity method. There exist a total of three different types of bifurcation modes because of double frequency excitations of the dual-rotor system and the nonlinearity of the intershaft bearing. The second primary resonance is more prone to have nonlinear dynamic characteristics than the first primary resonance. This discovery indicates that two interrelated primary resonances of the dual-rotor system may have different bifurcation modes under the same dynamic parameters.

Research of the internal resonances on a nonlinear dual-rotor based on the energy tracks shifting

The complex coupling characteristics of a dual-rotor system make the mechanism of nonlinear vibrations different from that of a single rotor system. Research of nonlinear vibration of the dual-rotor is beneficial to improve the stability of an aero-engine. Based on nonlinear spring characteristics of rotors, a novel nonlinear dual-rotor dynamics model coupled by the inter-shaft bearing is proposed, and internal resonances on the dual-rotor system are systematically studied. Considering nonlinearities, internal resonance phenomena occurring in the vicinity of the coupling critical rotational speed are systematically analyzed by numerical simulation results such as time histories, Poincare maps, bifurcation maps and largest Lyapunov exponents. Theoretical solutions are calculated based on the improved shooting method and stabilities of theoretical solutions are investigated by using the Floquet theory. The theoretical solutions are consistent with numerical simulation results well. The concepts of the energy track shifting, the energy-Poincare map, stabilities of energy tracks and the energy supplying function are introduced to analyze nonlinear vibration characteristics for the first time. The internal resonance phenomena of the low pressure rotor and the complex nonlinear vibrations of the high pressure rotor are qualitatively analyzed based on the energy viewpoint, and the energy tracks are verified by experiments. Research shows that energy tracks can characterize vibration characteristics well and the energy supplying function provide a possible way to quantify the energy transfer between rotors in the multi-rotor system.

An Intelligent Fault Diagnosis Scheme Using Transferred Samples for Intershaft Bearings Under Variable Working Conditions

Machine learning methods have made great development in data-driven fault diagnosis of rolling bearings. But the intelligent fault diagnosis of intershaft bearing faces the following two dilemmas: 1) the fault vibration is extremely weak, and it is difficult to extract features that can distinguish different classes; 2) due to the complex and variable working condition, the intershaft bearing does not always fail in same working conditions. That is, the labeled training data is not sufficient for every source domain. These challenges lead to the failure of traditional machine learning based fault diagnosis for intershaft bearings. Therefore, a novel intelligent fault diagnosis scheme is investigated for intershaft bearings of dual-rotor equipment under variable working conditions. The paper focuses on two key issues: 1) developing a feature extraction approach with which the fault features with excellent clustering and separation are extracted from vibration signals. This approach addresses the dilemma of weak fault feature extraction of intershaft bearing and creates a feasible precondition for subsequent feature transfer; 2) proposing a feature transfer method transforming the labeled sample features in multiple source domains into the trainable sample features in the target domain. This new transfer achieves the sharing of labeled training samples under working conditions and enriches the trainable samples in target domain. Ultimately, the faults of intershaft bearings can be diagnosed with the help of the neural network classifier trained by the transferred samples with labels. Experimental results verify that this established scheme is effective and superior to other comparable methods for the transfer diagnosis task from multiple source domains to target domain.

Dynamic Modeling and Vibration Analysis for Inter-shaft Bearing Fault

Dynamic Modeling and Vibration Analysis for Inter-shaft Bearing Fault

Multi-Domain Entropy-Random Forest Method for the Fusion Diagnosis of Inter-Shaft Bearing Faults with Acoustic Emission Signals.

Inter-shaft bearing as a key component of turbomachinery is a major source of catastrophic accidents. Due to the requirement of high sampling frequency and high sensitivity to impact signals, AE (Acoustic Emission) signals are widely applied to monitor and diagnose inter-shaft bearing faults. With respect to the nonstationary and nonlinear of inter-shaft bearing AE signals, this paper presents a novel fault diagnosis method of inter-shaft bearing called the multi-domain entropy-random forest (MDERF) method by fusing multi-domain entropy and random forest. Firstly, the simulation test of inter-shaft bearing faults is conducted to simulate the typical fault modes of inter-shaft bearing and collect the data of AE signals. Secondly, multi-domain entropy is proposed as a feature extraction approach to extract the four entropies of AE signal. Finally, the samples in the built set are divided into two subsets to train and establish the random forest model of bearing fault diagnosis, respectively. The effectiveness and generalization ability of the developed model are verified based on the other experimental data. The proposed fault diagnosis method is validated to hold good generalization ability and high diagnostic accuracy (~0.9375) without over-fitting phenomenon in the fault diagnosis of bearing shaft.

Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method

In this paper, a dynamic model of a complex dual rotor-bearing system of an aero-engine is established based on the finite element method with three types of beam elements (rigid disc, cylindrical beam element and conical beam element), as well as taking into account the nonlinearities of all of the supporting rolling element bearings. To rapidly and accurately analyze dynamic behaviors of the complex dual rotor-bearing system, a two-level model order reduction (MOR) method is proposed by combining component mode synthesis (CMS) method and proper orthogonal decomposition (POD) technique. The first-level reduced-order model (ROM) of the dual rotors is obtained by CMS method with a high precision for the original system. Then, the POD method is applied to second-level model order reduction to further decrease the degrees of freedom (DOFs) of first-level ROM. Second-level ROM with mode expansion and direct second-level ROM are obtained, and the nonlinear displacement responses of the two ROMs are compared with the first-level ROM. The numerical results demonstrate that the proposed method has a higher computational efficiency and accuracy in terms of mode expansion than the direct model reduction by using POD method. In addition, the nonlinear vibration responses of the dual rotor-bearing system are studied by this second-level ROM in the case of different clearances of the inter-shaft bearing. The results indicate that the dynamic characteristics of the dual rotor-bearing system are very complicated for a large clearance.

Vibration signal model of an aero-engine rotor-casing system with a transfer path effect and rubbing

This paper addresses modeling of vibration signals produced by rotor-localized excitation and modulated by multi-paths in an aero-engine rotor-casing system. The aim is to provide a better understanding of specific features of measurement point signals at the casing. Multi-paths effects are incorporated, including rubbing and rotor-casing paths through backup and inter-shaft bearings. The vibration waveforms and spectral signatures of signals with and without rubbing are derived and simulated. The most critical features of the resulting vibration signal are a prominent double rotating frequency and smaller overall amplitudes of frequencies due to rubbing, and bearing varying compliance (VC) frequencies due to the rotor-casing paths. A novel pneumatic-driven dual-rotor-casing test bench with a pneumatic rubbing structure is designed to initiate rubbing and acquire vibration signals at the casing. The test results provide sound verification for the proposed signal models. The analysis may prove useful for simulation purposes and rubbing fault diagnosis.

Dynamic modeling and simulation of inter-shaft bearings with localized defects excited by time-varying displacement

To accurately describe the dynamic features of inter-shaft bearings with localized defect under operation, the dynamic model of inter-shaft bearing with localized defects was established with respect to time-varying displacement excitation. Based on fault simulations on a birotor experimental rig, the developed dynamic model of inter-shaft bearing is validated to have high accuracy (over 99%) when localized defects happen on inner and outer race with co- and counter-rotation, which indicates that the model can be adopted to simulate the faults of inter-shaft bearing instead of experiment. Through investigation of the square-root (SR) amplitudes of bearing vibration with different defect sizes, radial loads, and rotational directions, we find that the SR amplitudes of bearing vibration increase with increasing defect size and radial load for both co- and counter-rotation. The amplitudes of counter-rotation are larger than those of co-rotation for inner race and outer race, and the amplitude of inner race defect are larger than that of outer race defect for the same defect size or same radial load. This work reveals the SR variation of bearing vibration with localized surface defects under different defect sizes and radial loads, and accurately describes the dynamic characteristics of inter-shaft bearing with localized defects. The efforts of this study open a door to adopt a dynamic model in the future to evaluate and monitor the health condition of inter-shaft bearings in an aeroengine or other rotating machinery.

Nonlinear response analysis for an aero engine dual-rotor system coupled by the inter-shaft bearing

This paper focuses on the nonlinear response characteristics of an aero engine dual-rotor system coupled by the cylindrical roller inter-shaft bearing. The motion equations of the system are formulated considering the unbalance excitations of the two rotors, vertical constant forces acting on the rotor system and the gravities. By using numerical calculation method, the motion equations are solved to obtain the nonlinear responses of the dual-rotor system. Accordingly, complex nonlinearities affected by the bearing radical clearance, the vertical constant force and the rotating speed ratio are discussed in detail. The jump phenomenon, hard resonant hysteresis characteristics are shown for a relatively large bearing clearance, and the soft resonant hysteresis characteristics can be observed for a relatively large vertical constant force. Moreover, the super-harmonic frequency components and the combined frequency components caused by the inter-shaft bearing are observed for both rotors. But the corresponding frequency components for the low-pressure rotor are more complex than that for the high-pressure rotor in same condition. These results would be helpful to recognize the nonlinear dynamic characteristics of dual-rotor bearing system.

Application of Kernel Auto-encoder Based on Firefly Optimization in Intershaft Bearing Fault Diagnosis

Application of Kernel Auto-encoder Based on Firefly Optimization in Intershaft Bearing Fault Diagnosis

Local defect modelling and nonlinear dynamic analysis for the inter-shaft bearing in a dual-rotor system

• A force model for the inter-shaft bearing with a local defect on surface of the outer or inner race. • The system may resonant in some non-critical-speed region due to the local defect. • Parameters affecting the resonant frequencies and vibration amplitudes of the abnormal resonances. • A comprehensive parametric analysis is carried out to show the nonlinear resonant response characteristics. This paper presents a force model for the inter-shaft bearing with a local defect on the surface of the outer race or the inner race, and the nonlinear dynamic characteristics of a dual-rotor system affected by the local defect are investigated. A simplified dual-rotor system is presented with the consideration of the inter-shaft bearing's nonlinearities such as the Hertzian contact force and the radial clearance. The local defect is considered as a regular dent with a constant depth, thus the radial clearance will increase when rolling elements go through the range of the local defect. The motion equations of the system with eight degrees of freedom are formulated by using the Lagrange's equation. The nonlinear vibration responses of the dual-rotor system affected by the local defect are obtained using numerical method. The results show that there exist four abnormal resonances on the amplitude frequency curves of the system due to the effect of the local defect, apart from the couple of primary resonances excited by the unbalance excitations of the two rotors. With the aid of the characteristic defect frequency analysis, it is revealed that one pair of the abnormal resonances are excited by the characteristic defect frequency, and the other pair of the abnormal resonances are excited by the combination frequency. Furthermore, a comprehensive parametric analysis is carried out to give an insight into the nonlinear resonant response characteristics affected by parameters such as the depth and the span of the defect, the rotation speed ratio, the unbalances of two rotors, the stiffness and the damping of the linear elastic spring, and the radial clearance, the stiffness and the roller number of the inter-shaft bearing. The results show that the vibration amplitudes for the abnormal resonances are mainly determined by the depth and the span of the defect, while the resonant frequencies for the abnormal resonances are mainly influenced by the rotation speed ratio and the roller number of the inter-shaft bearing. However, the rotors’ unbalances mainly affect the corresponding primary resonance rather than the abnormal resonances. The obtained results will contribute to a better understanding of the nonlinear resonant response characteristics of dual-rotor systems with a local defect on the inter-shaft bearing, which are helpful for the fault diagnostics of the inter-shaft bearing in a dual-rotor system.

Casing vibration response prediction of dual-rotor-blade-casing system with blade-casing rubbing

Abstract This paper focuses on the dynamic responses of whole aero-engine with blade-casing rubbing. The vibration response of casing is simulated and the dynamic behaviors of casing acceleration under blade-casing rubbing are investigated to diagnose the blade-casing rubbing fault effectively. Firstly, the finite element model of a dual-rotor-blade-casing (DRBC) system with inter-shaft bearing is proposed. The shear deformations and inertias of the rotor and casing are taken into account. The gyroscopic moments of the rotors are evaluated. Secondly, the effects of the blade-casing clearance and the number of blades on the vibration responses of DRBC system with blade-casing rubbing are considered. Finally, the casing acceleration responses of the DRBC system with blade-casing faults are solved numerically, and the influences of some variables, such as the rotating speed ratio, eccentricity of disk and rubbing stiffness, on the dynamic behaviors have been investigated by time waveform of acceleration, frequency spectrum and waterfall. The results indicate that (1) blade-casing rubbing can cause impulsive load to the casing and rotor, and lead to abrupt increase of the vibration amplitude; (2) the obvious periodic impact characteristics are contained in the casing vibration acceleration signals, and the impact frequency equals the product of the rotational frequency and the numbers of blades; (3) the fraction frequency component of rotating speed difference of dual rotors is excited on both sides of impact frequency and its multiple frequency components.

Dynamic response analysis for the aero-engine dual-rotor-bearing system with flexible coupling misalignment faults

This paper focuses on the nonlinear response characteristics of an aero-engine dual-rotor-bearing system with flexible coupling misalignment faults in the low-pressure rotor system (rotor 2). The motion equations of the system are formulated by using finite element method, in which the excitations induced by the misalignment faults, the dual-unbalance excitations of the two rotors (the high-pressure rotor system-rotor 1 and the low-pressure rotor system-rotor 2), the gravities, and the nonlinear force induced by the inter-shaft bearing are all considered. By using numerical calculation method, the motion equations are solved to obtain the nonlinear responses of the system. Then, the nonlinear responses for the alignment dual-rotor-bearing system are analyzed, the hardening type hysteresis characteristics with jump phenomenon are shown. Accordingly, the nonlinear responses affected by the amount of parallel misalignment and angular misalignment are discussed in detail. The results show that, with the increase of by the amount of parallel misalignment (angular misalignment), the frequency components 2 times rotational speed of rotor 2 appear, and the amplitudes of the responses at the super-harmonic frequency components and combined frequency components get larger for not only rotor 2 but also rotor 1, which indicates that the vibration characteristics of misalignment faults in rotor 2 can be transmitted to the rotor 1 and can be used to diagnose the misalignment faults. The results obtained in this paper will contribute to the response analysis for the aero-engine dual-rotor-bearing system with flexible coupling misalignment faults.

Fault Diagnosis of Intershaft Bearings Using Fusion Information Exergy Distance Method

For the fault diagnosis of intershaft bearings, the fusion information exergy distance method (FIEDM) is proposed by fusing four information exergies, such as singular spectrum exergy, power spectrum exergy, wavelet energy spectrum exergy, and wavelet space spectrum exergy, which are extracted from acoustic emission (AE) signals under multiple rotational speeds and multimeasuring points. The theory of FIEDM is investigated based on four information exergy distances under multirotational speeds. As for rolling bearings, four faults and one normal condition are simulated on a birotor test rig to collect the AE signals, in which the four faults are inner ring fault, outer ring fault, rolling element fault, and inner race‐rolling element coupling fault. The faults of the intershaft bearings are analyzed and diagnosed by using the FIEDM. From the investigation, it is demonstrated that the faults of the intershaft bearings are accurately diagnosed and identified, and the FIEDM is effective for the analysis and diagnosis of intershaft bearing faults. Furthermore, the fault diagnosis precision of intershaft bearings becomes higher with increasing rotational speed.

Dynamic characteristics analysis of a dual-rotor system with inter-shaft bearing

The dual-rotor structure is susceptible to vibration, causing the malfunction of the entire operating system. In order to avoid the resonance during operation, it is significant and necessary to conduct modal analysis of such rotors. The dynamic analysis of the full dual-rotor system under operating conditions is also necessary to study dynamic characteristics of the rotating system. In this paper, one-dimension Timoshenko beam-type model, including the effects of gyroscopic moments, rotary inertias, bending and shear deformations, and three-dimension model for dual-rotor system with inter-shaft bearing are developed. Critical speed tests of dual-rotor are carried out to verify the analytical results. Based on the finite element models, the first critical speed excited by inner rotor and the first two critical speeds excited by outer rotor are calculated. The comparisons between both finite element models indicate that 1D model costs less time, which can be used to predict the critical speeds. Good agreement between the theoretical and experimental results shows the accuracy of the FE models. The Campbell diagram, critical speeds, operational deflection shapes and unbalance response of the dual-rotor are obtained to fully study the dynamic characteristics of the dual-rotor system.

Weak Fault Feature Extraction Scheme for Intershaft Bearings Based on Linear Prediction and Order Tracking in the Rotation Speed Difference Domain

Because both the inner and outer rings rotate, the intershaft bearings used in gas turbines do not have fixed bearing housings. As a result, the vibration of intershaft bearings cannot be measured directly. Therefore, a vibration signal can only be collected through indirect measurement. First, it must be transferred to adjacent bearings through the shafting. Then, it should be transferred by the elastic supports and complex structure of the thin-walled strut. The vibration signal is severely weakened during transmission under the influences of the transfer path. In the meantime, in the vibration of other components, a huge amount of noise is produced by the air flow, and the variable speeds of the inner and outer rings of the intershaft bearings make it harder to analyze the signal. Hence, it is very difficult to extract the vibration fault features of intershaft bearings. To deal with the variable speed of dual rotors, as well as the weak signal, a fault feature extraction scheme for the weak fault signals of intershaft bearings is proposed in this paper. This scheme is based on linear prediction, spectral kurtosis, and order tracking in the rotation speed difference domain. First, a prewhitening process, based on linear prediction, is applied to the fault signal of the intershaft bearings to eliminate the stationary component. Thus, the remaining components, including the impulse signal of faulty bearings and nonstationary noise, can retain the features of the vibrational bearings, in addition to reducing the noise. Second, the optimal center frequency and bandwidth of the band-pass filter, applied to resonant demodulation, are selected by spectral kurtosis. Subsequently, the enveloped signal containing the features of the faults found in the intershaft bearings is obtained by resonance demodulation. The quasi-stationary signal in the angle domain is acquired by the even angle resampling of the nonstationary envelope signal, as a result of the variable speed. The final order spectrum is obtained through a Fourier transform. Fault diagnosis can be conducted for the intershaft bearings by comparing this spectrum with the feature order of the bearing fault. Experiments were conducted to verify the validity of the proposed scheme.