Inter-shaft Bearing Research Articles

Dynamic Modeling and Simulation Analysis of Inter-Shaft Bearings with Local Defects Considering Elasto-Hydrodynamic Lubrication

As an important component of large engines, inter-shaft bearing is easily damaged due to its poor working conditions. By analyzing the time–frequency distribution rules of fault signals and the evolution law of micro-faults, the bearing failure mechanism can be revealed, and the bearing failure can be monitored in real time and prevented in advance. For the purpose of studying the mechanism of inter-shaft bearing faults, a 4-DOF (degree of freedom) dynamic model of inter-shaft bearing with local defects considering elasto-hydrodynamic lubrication (EHL) is proposed. Based on the established dynamic model, the impact characteristics and distribution rules of the fault signals of the bearing are accurately simulated, and the evolution law of the micro-faults is also analyzed. The effects of different speeds, loads and defect widths on maximum value (MV), absolute mean value (AMV), effective value (EV), amplitude of square root (AST), kurtosis factor (KF), impulse factor (IF), peak factor (PF) and shape factor (SF) are obtained. The findings show that the vibration amplitude of the bearing increases with the increase in defect size, and the faults are easier to diagnose accordingly. At the same time, PF, KF and IF are very sensitive to the initial failure of bearings. With the development of faults, the overall trend of AMV, AST and EV are relatively stable. The PF is sensitive to the change of rotating speeds and defect widths. The SF is insensitive to the change of rotating speeds, loads and defect widths. This lays a foundation for the research of monitoring and diagnosis methods of aeroengine inter-shaft bearing fault.

A novel intelligent method for inter-shaft bearing-fault diagnosis based on hierarchical permutation entropy and LLE-RF

Since the transmission path of inter-shaft bearing-fault signal is complex, a fault feature extraction method based on hierarchical permutation entropy (HPE) and locally linear embedding (LLE) algorithm is proposed in this paper. In this method, HPE is utilized to extract fault information of signals, and LLE is utilized to reduce and fuse high-dimensional fault features of multi-sensors to construct fault samples. Then, the random forest (RF) model is established to diagnose the faults of the inter-shaft bearings. The fault simulation test rig with the inter-shaft bearing is built to simulate the normal bearing, inner ring fault, outer ring fault, and rolling ball fault, and the data are collected to verify the HPE-LLE-RF fault diagnosis algorithm of inter-shaft bearings established in this paper. The experimental results show that the proposed algorithm can extract the fault features of inter-shaft bearings effectively with a fault diagnosis accuracy of 93.3% without overfit phenomenon.

Analysis of backward whirling characteristics of a dual-rotor system caused by unbalance

In this paper, a dual-rotor system with five-point support is established, considering the nonlinearity of the inter-shaft bearing. Based on the full-spectrum analysis theory, the whirling characteristics of the dual-rotor system are analyzed. In a counter-rotating dual-rotor system, the backward whirling phenomenon caused by the unbalanced excitation is found, and the effects of rotation direction, unbalanced excitation, speed ratio, and inter-shaft bearing on this phenomenon are discussed. Finally, the simulation results are verified based on the dual-rotor test rig. The results show that a negative speed ratio is a necessary condition to generate the backward whirling of the rotor; in the counter-rotating dual-rotor, a large unbalance of one rotor is an important factor causing the backward whirling of the other rotor. The larger the unbalance is, the more likely the backward whirl will occur; changing the speed ratio will mainly affect the initial speed and speed range at which backward whirl occurs; The radial clearance and stiffness of the intermediate bearing mainly affect the coupling degree of the inner and outer rotors, thereby affecting the whirl characteristics of the dual-rotor. The above research helps understand the whirl characteristics of the counter-rotating dual-rotor deeply.

Improved spiking neural network for intershaft bearing fault diagnosis

The intershaft bearing is located between the high and low-pressure rotors of the aero-engine, where the working environment is harsh, the load variation range is large, and the lubrication and heat dissipation are poor. The fault of the intershaft bearing is sudden and will cause the engine to hold the shaft and break the shaft, which is more harmful than the ordinary bearings. In recent years, bearing intelligent fault diagnosis methods based on deep learning have been widely applied. However, most of the existing methods are mainly proposed based on second-generation neural networks. Spiking neural network (SNN), also known as the third-generation neural network, mimics the dynamics of the biological brain and is more powerful for processing time-series information. As we know, vibration data is a typical time-series data, SNN would have stronger feature extraction potential for it. In this paper, we propose an improved spiking neural network (ISNN) for intershaft bearing fault diagnosis. Specifically, we propose an encoding method to encode raw data into spike sequences and demonstrate that the encoding method is accurate and efficient. Then we derive the gradient relation in the ISNN and mathematically prove the replacement of invalid gradients in it. Furthermore, we compensate for the loss of information in forward propagation and simplify the process of backpropagation by constructing suitable spiking neurons. Finally, we test the ISNN on the fault dataset of intershaft bearings, and the results show that the proposed ISNN outperforms previous SNNs and typical second-generation neural networks.

Nonlinear dynamics analysis of a dual-rotor-bearing-casing system based on a modified HB-AFT method

This paper presents a modified harmonic balance-alternating frequency/time domain (HB-AFT) method to analyze the nonlinear dynamics of a dual-rotor-bearing-casing system. The motion equations of a dual-rotor-bearing-casing system subjected to the unbalanced excitations of the two rotors are formulated with 284 degrees of freedom, in which, the complex nonlinear factors of the inter-shaft bearing such as exponential nonlinear restoring force, radial clearance and varying stiffness excitation are taken into consideration. The HB-AFT method is modified by applying the AFT procedure to obtain the harmonic expending coefficients of the harmonic balance residuals rather than that of the nonlinear terms, hence, the Jacobian matrix is calculated programmatically and efficiently, as a result the performance of the HB-AFT method is improved greatly. The primary resonance of the system is analyzed by employing the three-dimensional diagrams of amplitude-frequency responses of each node of the system, including the inner casing and the outer casing. In addition, the amplitude-frequency response curves with separated frequencies and orbits of the two rotors are also discussed. Furthermore, the pseudo-arclength continuation procedure is introduced into the modified HB method, then all periodic solution branches of the system including the unstable solutions are obtained. The results show that there are two resonant peaks in the amplitude-frequency response curves of the system and the vibration of each part of the system, i.e., LPC, LPT, HPC, HPT, inner casing and outer casing, is synchronous. Besides, the nonlinear dynamic behaviors such as vibration jumping, bi-stable and resonance hysteresis are revealed. Accordingly, the dynamic load of the inter-shaft bearing is calculated. The results show that the evolution of the inter-shaft bearing’s dynamic load is associated with the vibration responses of the two rotors. The nonlinear characteristics of the force-frequency responses of the inter-shaft bearing are consistent with that of the two rotors and casings. In addition, with the increase of the inter-shaft bearing clearance, the nonlinear characteristics of the force-frequency responses of the inter-shaft bearing are more significant. In comparison with the Newmark method, the modified HB-AFT method proposed in this paper has a great advantage in computing efficiency, and it can also grasp all solution branches of the system including the unstable solutions. Consequently, it has great potential to deal with high-dimensional systems with complex nonlinearities and multifrequency excitations in practical engineering.

Combination resonances of rotor systems with asymmetric residual preloads in bolted joints

For highly-loaded rotor systems of aero-engines, residual preloads in the same row of bolts are generally asymmetric after multiple operational cycles. The asymmetry in residual bolt preloads could lead to time-varying stiffness of rotors, which become parametrically excited systems. This paper investigates the combination resonances of bolted rotor systems with asymmetric preloads under multi-frequency excitation. A new breathing model induced by asymmetric bolt preloads is proposed, which takes the rotor whirling position into account, instead of using the assumption of weight dominance. Theoretical studies are conducted on a Jeffcott rotor with asymmetric bolt preloads under two-frequency excitation, whose approximate analytical solution is obtained through the Harmonic Balance Method. Results show that combination tones arise in the vibration spectra, whose frequencies are the combinations of two excitation frequencies. The amplitude of a combination tone reaches the maximum value when its frequency is in the vicinity of natural frequencies, which correspond to the combination resonance. To extend these results to practical rotors with more complex structures, the finite element modeling method of bolted joints with asymmetric preloads is presented based on the Euler-Bernoulli beam theory. Experimental validations are performed on a practical aero-engine dual rotor system with an inter-shaft bearing. Good agreement is shown in the comparison between numerical and experimental results, which indicate that combination resonances of practical dual rotor systems could occur in the vicinity of dual-rotor coupled vibration mode.

Vibration Characteristic Analysis of a Coupling System for Compound Biaxial and Inter-Shaft Bearings

In order to analyse the system spatial vibration of compound biaxial and inter-shaft bearings during unbalanced excitation, the theory of rotor dynamics and bearing contact deformation are combined to establish a coupling system model of compound biaxial and inter-shaft bearings. Considering the moment of inertia, gyro effect, and structural damping, a one-dimensional beam model is used to perform the MATLAB numerical calculation of the coupling system to obtain the modal characteristics of the system, and based on the ANSYS simulation analysis of the three-dimensional model, a modal test is used to obtain the system modal shape and test frequency response function to verify the rationality of the coupling system model. Based on the Runge-Kutta iterative method and Hamilton’s principle, the nonlinear amplitude-frequency response of the system is calculated while taking into account the influence of the compound biaxial eccentricity, as well as the stiffness and radial clearance of the inter-shaft bearing. The results show that the changes in the eccentricity of the compound biaxial and the structural parameters of the inter-shaft bearing cause the unbalanced excitation of the system, additional external load changes, and different coupled vibrations between the composite compound biaxial and inter-shaft bearings. Therefore, it is reasonable to match the structural parameters of the coupling system and improve the dynamic performance to avoid system resonance.

Feature extraction of mixed faults of intershaft bearing based on homologous information and Hjorth parameters

To make correct judgment on the mixed faults of intershaft bearing of aeroplane engine, the paper has proposed a feature option method. This method works by decomposing cross-correlation function (CCF) of homogeneous information from casing with intrinsic time scale decomposition (ITD) for the separation and blending of signals. Furthermore, option of proper rotation components (PRCs) for fault identification is made by abandoning the PRC related with the least Complexity parameter in Hjorth parameters. Moreover, signal is reconstructed based on the autocorrelation function (AF) of residual PRCs. Finally, according to the frequency spectrum of signal reconstructed, fault features corresponding to intershaft bearing are extracted and fault types estimated. The result indicates that the Complexity parameter in Hjorth parameter can be used as an evaluation index to implement the selecting of sensitive fault components. Furthermore, the mixed fault types which come from intershaft bearing of aeroplane engine could be judged correctly.

Dynamic Characteristics of a Dual-Rotor System with Parallel Non-Concentricity Caused by Inter-Shaft Bearing Positioning Deviation

Dynamic Characteristics of a Dual-Rotor System with Parallel Non-Concentricity Caused by Inter-Shaft Bearing Positioning Deviation

Dynamic Load of the Inter-Shaft Bearing and Its Influence on Bearing’s Temperature

Dynamic Load of the Inter-Shaft Bearing and Its Influence on Bearing’s Temperature

Durability evaluation of the inter-shaft bearing by the contact bearing stress

Durability evaluation of the inter-shaft bearing by the contact bearing stress

Compound faults feature extraction of inter-shaft bearing based on vibration signal of whole aero-engine

To effectively extract the information of compound faults of inter-shaft bearing of an aero-engine based on casing vibration signals, the paper has introduced the concept of weighted Katz fractal dimension and proposed the method combining information fusion, wavelet transform (WT), singular value decomposition (SVD), and Katz fractal dimension, the cross-correlation function (CCF-WT-SVD-Katz algorithm). The method includes homologous information fusion achieved by the CCF of horizontal and vertical vibration signals of the rotor from the same section; signal separation and denoising of blended signals through WT and SVD; reinforcement of fault characteristics of signals according to weighted Katz fractal dimension; and extraction of characteristic frequencies of compound faults of inter-shaft bearing by frequency spectrum of weighted and reconstructed signals. The result indicates that the proposed CCF-WT-SVD-Katz algorithm is capable of effectively extracting compound fault characteristics of inter-shaft bearing and precisely identifying a fault type based on whole casing vibration signals and will be of very good application value in engineering.

A study on the feature separation and extraction of compound faults of bearings based on casing vibration signals

The autocorrelation function is combined with wavelet transform and cyclostationary theory (WT-AF-CT) in place of threshold denoising, and meanwhile the mean power ratio (MPR) is calculated by the proposed method. Furthermore, extracted characteristic as well as calculated MPR is used to identify compound faults of rolling bearings in aero-engine based on casing vibration acceleration signal-including the ones of common rolling bearing (inner race rotates and outer race is constant) and intershaft bearing (co-rotates with outer and inner race). A comparative analysis was carried out between conventional researches (cyclostationary theory (CT) or wavelet transform combined with threshold value denoising (WT-TD)) and proposed WT-AF-CT method. Additionally, the effect of sensors installation direction for feature separation and extraction of compound faults is considered. The results indicate that the proposed WT-AF-CT method can separate and extract characteristics of compound faults exactly and identify fault types of bearings precisely, no matter sensors are installed horizontally or vertically, while CT or WT cannot.

Quantum entropy‐based hierarchical strategy for inter‐shaft bearing fault detection

To effectively conduct the fault diagnosis of inter-shaft bearings in precision and stability, hierarchical quantum entropy (HQE) method is proposed by absorbing quantum theory into hierarchical entropy, to precisely extract the features of fault signals with strong robustness. Firstly, we investigate HQE method and HQE-based fault diagnosis thought based on quantum theory and hierarchical thought. Then the HQE method is validated by numerical simulation in feature extraction precision and stability (robustness) under the influence of key parameters. The HQE method is applied to the fault diagnosis of inter-shaft bearing based on the test data of four faults (i.e., normal state, inner ring fault, outer ring fault, and rolling ball fault) simulated in birotor experimental rig. As revealed in this study, (1) the HQE method can precisely extract and fully reflect the feature information of vibration signals by regarding the information of full-scale components comprising low- and high-frequency components and a series of bit ground states; (2) the HQE of signals is insensitive and stable against the key parameters (i.e., dimension number and data length), due to more scales acquired by quantum entropy and hierarchical decomposition, which is promising to improve the robustness and stability of fault diagnosis; (3) the proposed HQE possesses high diagnostic accuracy, high efficiency, and robustness under few experiment data, which indicates the good diagnostic performance of HQE method in the fault diagnosis of inter-shaft bearing. The efforts of this study provide a useful way to effectively conduct structural health monitoring besides inter-shaft bearing fault diagnosis.

Dynamic load and thermal coupled analysis for the inter-shaft bearing in a dual-rotor system

Dynamic load and thermal coupled analysis for the inter-shaft bearing in a dual-rotor system

A 3D CFD simulation of oil spray-collection and delivery process in an aeroengine inter-shaft bearing

Under-race lubrication applied to the inter-shaft bearing of aeroengine is characterized by spray oil collection and oil delivery to the bearing via flow-path structure. Droplet splashing induced by the collision between spray oil and the scoop as well as oil flowing characteristics in the flow-path influence bearing lubrication efficiency. In previous investigations, the spray oil collection and oil delivery analysis were separated, and the effect of droplet splashing on bearing lubrication efficiency was not considered. Moreover, time-varying characteristics of oil delivered to the bearing were not accounted for. This is caused by time variations of the circumferential position of rollers and under-race feed holes. To overcome these limitations, a numerical model which integrates the spray oil collection and oil delivery analysis is proposed in this paper. The model is embedded with the function of calculating the flow rate of splashing droplets and analyzing time-varying characteristics of the oil fed to the bearing. Furthermore, the numerical model is validated by experimental investigation. The proposed numerical model facilitates the accurate calculation of bearing lubrication efficiency as well as the design of an efficient lubrication structure.

Paroxysmal impulse vibration phenomena and mechanism of a dual–rotor system with an outer raceway defect of the inter-shaft bearing

This paper focuses on the dynamic phenomena, physical mechanism and occurrence condition of paroxysmal impulse vibrations in a dual-rotor system with inter-shaft bearing defect. The equations of motion of the dual-rotor system are established considering the force model for the inter-shaft bearing with an outer raceway defect. The fourth order Runge-Kutta method is adopted to investigate the vibration acceleration signals of the rotor system. The results show that there are paroxysmal impulse vibration phenomena when the dual-rotor system reaches some special rotation speed ratios. The time-domain waveforms, Hilbert envelope spectrums and inter-shaft bearing contact force curves of paroxysmal impulse vibrations are markedly distinguished from those of general impulse vibrations. The physical reason of paroxysmal impulse vibration phenomena is that the inter-shaft bearing loading position and defect position are intermittently anti-phase. It is found that the paroxysmal impulse vibration phenomena will occur if the rotation frequency of the high-pressure rotor (HP rotor) is equal to the fractional or multiple defect frequencies of the dual-rotor system. Based on this finding, an analytical formula related to the rotation speed ratio is derived, which can well predict the occurrence condition of paroxysmal impulse vibrations. At last, according to the guidance of the analytical formula, 6 experimental cases are executed, proving the dynamic phenomena and occurrence condition of the paroxysmal impulse vibrations.

Nonlinear resonance characteristics of a dual-rotor system with a local defect on the inner ring of the inter-shaft bearing

In this paper, the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system. A simplified model of the dual-rotor system is proposed by considering that there is a local defect on the inner ring of inter-shaft bearing. The local defect is modelled as an inverted isosceles trapezoidal groove, which can make great influence on the inter-shaft bearing force due to the change of radial clearance of the inter-shaft bearing. The motion equations of the dual-rotor system are formulated by using the Lagrange equation. The Runge-Kutta method is employed to solve the motion equation. The amplitude-frequency response curve of the dual-rotor system is obtained, the abnormal resonance characteristics are analyzed. In addition, the influence of defect parameters, rotors and support parameters and inter-shaft bearing parameters on the amplitude-frequency characteristics of the system are discussed. The results show that there are two main resonance peaks and four abnormal resonance peaks on the amplitude-frequency response curve of the dual-rotor with a local defect on the inner ring of the inter-shaft bearing. Through analyzing the vibration response of the abnormal resonance peaks, it is found that the first two abnormal resonances are caused by the combined resonance, which are related to the inner ring fault and the rotational speed of high or low pressure rotors, and the last two resonances are caused by the induced resonance of the inner ring fault. At the same time, when the parameters of defect, rotors and support and inter-shaft bearing change, the resonance of the system also shows the corresponding change law.

Fault Diagnosis of Intershaft Bearing Using Variational Mode Decomposition with TAGA Optimization

To efficiently extract the features of aeroengine intershaft bearing faults with weak signal, the variational mode decomposition (VMD) method based on the tolerant adaptive genetic algorithm (TAGA) (TAGA-VMD) is proposed by introducing the idea of tolerance into the traditional adaptive genetic algorithm in this paper. In this method, the tolerant genetic algorithm was adopted to find the optimum empirical parameters K and α of VMD. A fault simulation experiment system of intershaft bearings was built for the inner ring fault and outer ring fault of bearings to verify the proposed TAGA-VMD method. The results show that the proposed method can effectively extract the fault feature frequency of intershaft bearings, and the error between the extracted fault feature frequency and the theoretical value of fault frequency is less than 0.1%. The efforts of this study provide one promising fault feature extraction approach for aeroengine intershaft bearing fault diagnosis with weak signal.

NONLINEAR THERMAL ANALYSIS FOR THE INTER-SHAFT BEARING UNDER THE DYNAMIC LOAD

As an important supporting part between the higher pressure rotor and the lower pressure rotor in a dual-rotor system, inner and outer races are rotating with the lower and higher pressure rotors, the heat transfer of the inter-shaft bearing is more prominent. This paper studies the nonlinear thermal behaviors of the inter-shaft bearing under the nonlinear dynamic load. The dynamic load of the inter-shaft bearing is defined based on the dynamic responses of the dual-rotor system, where the nonlinear factors of the inter-shaft bearing such as the radial clearance, the fractional exponential nonlinearity and the parameter excitation are taken into consideration. Thus the nonlinear behaviors such as the jump and the bi-stable phenomena happen to the dynamic load. According to Palmgren's empirical formula, a heat transfer model of the inter-shaft bearing under the dynamic load is established with considering the viscosity-temperature relationship of the lubricant. Steady-state temperatures of the inter-shaft bearing are obtained by the numerical integration. It shows that the nonlinear thermal behaviors of the inter-shaft bearing such as the jump and the bi-stable phenomena are caused by the nonlinear behaviors of the dynamic load. Furthermore, effects of the rotation speed ratio, the unbalances, the inter-shaft bearing's radial clearance, Hertz contact stiffness and roller number on the temperatures and the nonlinear thermal behaviors of the inter-shaft bearing are analyzed. The results show that the unbalances, the radial clearance and the stiffness only affect the nonlinear thermal behaviors of the inter-shaft bearing; the rotation speed ratio and the roller number have a magnificent influence on both. This discovery implies that the dynamic load is more appropriate to describe the actual load of the inter-shaft bearing than the static load. The thermal behaviors of the inter-shaft bearing become nonlinear, which is much more complicated than before, due to nonlinear dynamic characteristics of the dual-rotor system.