Fault Characteristic Frequency Research Articles

Study on the Vibration Characteristics of the Helical Gear-Rotor-Bearing Coupling System of a Wind Turbine with Composite Faults

As the core component of the wind turbine generation gearbox, the gear-rotor-bearing transmission system typically operates in harsh environments, inevitably leading to the occurrence of composite faults in the system, which exacerbates system vibration. Therefore, it is necessary to study the vibration characteristics of wind turbine helical gear-rotor-bearing transmission systems with composite faults. This paper uses an improved energy method to calculate the theoretical time-varying mesh stiffness of a helical gear with a root crack failure. On the premise of considering the time-varying meshing stiffness of the faulty helical gear, the gear eccentric fault, and the nonlinear support force of the faulty bearing, a multi-degree-of-freedom helical gear-rotor-bearing transmission system with compound faults was established by using the lumped parameter method. The dynamic model of the system was solved based on the Runge–Kutta method, and the vibration response of the system under healthy conditions, single faults with gear eccentricity, single faults with tooth root cracks, and coupled bearing composite faults were simulated and analyzed. The results show that the simulation results based on KISSsoft software 2018 version verify the effectiveness of the improved energy method; the existence of single faults and composite faults will cause the fault characteristics in the time domain and frequency domain responses. In this paper, the influence of a single fault and a complex fault on the time domain and frequency domain of the system is mainly discovered through the fault study of the helical rotor-bearing system, and the influence of the fault degree on the vibration of the gear motion system is discussed. The greater the degree of the fault, the more vibration of the system occurs; accordingly, when the system is under the coupling of tooth root crack and bearing fault, there is a significant difference compared with the healthy system and the single fault system. The system vibration has obvious time domain and frequency domain signal characteristics, including periodic pulse impacts caused by gear faults and time domain impact caused by bearing. The fault characteristic frequencies can also be found in the frequency domain. In this paper, the fault study of a helical gear of wind turbine generation provides a reference for the theoretical analysis of the vibration characteristics of the helical gear-rotor-bearing system under various fault conditions, lays a solid foundation for the simulation and subsequent diagnosis of the composite fault signal of the system, and provides help for the fault diagnosis of wind turbine gearboxes in the future.

Incipient bearing fault detection using adaptive fast iterative filtering decomposition and modified Laplace of Gaussian filter

The impact components induced by faulty bearings can be readily concealed by environmental noise and other interferences due to their inherent weakness, especially during the incipient stages of fault development. A novel approach is presented in this study for the detection of incipient bearing faults, which combines an adaptive fast iterative filtering decomposition (FIFD) method with a modified Laplace of Gaussian filter. The first step involves proposing an adaptive FIFD (AFIFD) method employing improved sparrow search algorithm, enabling adaptive selection of the optimal parameter within the FIFD method. The AFIFD technique is able to adaptively decompose a complicated signal into a set of mono-components. Subsequently, a modified Laplace of Gaussian is used to highlight the fault-related cyclic impulse train from a sensitive mono-component decomposed by the AFIFD method. Finally, the envelope analysis performing on enhanced signals is applied to identify fault characteristic frequencies. Results from some case studies demonstrate that the proposed method is capable of extracting incipient fault signatures. The superiority of the proposed method is further validated through some comparative tests with recently developed fault detection methods.

Online Piecewise Convex-Optimization Interpretable Weight Learning for Machine Life Cycle Performance Assessment.

Machine life cycle performance assessment is of great significance to use a health index to inform the time of incipient fault initiation in a normal stage and realize fault identification and fault trending in a performance degradation stage. However, most existing works consider using unexplainable model parameters and historical data to build models and infer their off-line parameters for machine life cycle performance assessment. To overcome these limitations, an online piecewise convex-optimization interpretable weight learning framework without needing any historical abnormal and faulty data is proposed in this article to generate a piecewise health index to practically implement machine life cycle performance assessment. Firstly, based on a separation criterion, the first submodel in the proposed framework is built to detect the time of incipient fault initiation. Here, the piecewise health index generated by the first submodel is continuously updated by on-line monitoring data to timely detect the occurrence of any abnormal health conditions. Secondly, once the time of incipient fault initiation is informed, online updated model weights are highly correlated with fault characteristic frequencies and informative frequency bands for immediate fault identification. Simultaneously, the second submodel integrated with monotonicity and fitness properties in the proposed framework is triggered to generate the piecewise health index to realize overall monotonic fault trending. The significance of this article is that only online monitoring data are used to continuously update interpretable model weights as fault frequencies and informative frequency bands to generate the proposed piecewise health index so as to practically realize machine life cycle performance assessment. Two run-to-failure cases are studied to show the effectiveness and superiority of the proposed framework.

An adaptive threshold-selected symplectic geometry mode decomposition for application to multi-modulation complex fault signals

The signals obtained from complex mechanical systems are characterized by multilevel modulation and strong noise, which can lead to difficulties in fault feature extraction. Symplectic geometry mode decomposition (SGMD) proves to be a valid approach for decomposing signals. However, inaccurate threshold selection in the iterative decomposition process can compromise the quality of fault diagnosis results. To address the shortcomings of SGMD, this paper proposes adaptive SGMD with adaptive threshold selection for fault diagnosis. Based on minimum dispersion entropy indicators, correlation coefficient and stopping thresholds are adaptively chosen using the proposed enhanced dung beetle optimizer algorithm. Then the optimal symplectic geometry component (SGC) is filtered based on the value of the integrated indicators after decomposition. Finally, the optimal SGC is analyzed by envelope demodulation to extract gear fault information. Through simulation and experimental analysis, this method surpasses SGMD and other signal decomposition methods in the aspect of fault feature extraction and noise robustness. Additionally, the results indicate an increase in feature energy ratio by 2.14%–9.85% compared to SGMD. The paper demonstrates that the proposed method extracts the fault feature frequencies of gears more effectively in complex mechanical systems.

Bearings fault diagnosis under variable speed conditions by hypothesis-based FRFT technique

The vibration signals of faulty bearings under non-stationary conditions are inherently multi-component and time-varying, which presents a challenge for effective fault diagnosis. Considering the vibration characteristics of rolling bearings under non-stationary conditions and taking advantage of the Fractional Fourier Transform (FRFT), a novel diagnosis method based on the hypothesis-based FRFT has been proposed to separate the fault components. First, the fault characteristic frequencies (FCFs) are extracted from the time-frequency representation of the vibration signals, and the Vold-Kalman filtering is employed to eliminate the influence of noises and other interference components. Subsequently, the fractional feature model is constructed to obtain speed information by the hypothesis approach, whose central idea is that the rotational frequency (RF)-related frequencies under different fault types are estimated, based on the extracted FCFs and the fault characteristic orders. Finally, fault diagnosis is completed by the RF-related peaks in the final spectrum. The method eliminates the need for rotational speed measurement devices and angular resampling. Simulation and experiment estimation results show that the hypothesis-based FRFT method can accurately locate fault characteristic components of bearings under non-stationary conditions.

A Synchrosqueezed Transform Method Based on Fast Kurtogram and Demodulation and Piecewise Aggregate Approximation for Bearing Fault Diagnosis.

Synchrosqueezed transform (SST) is a time-frequency analysis method that can improve energy aggregation and reconstruct signals, which has been applied in the fields of medical treatment, fault diagnosis, and seismic wave processing. However, when dealing with time-varying signals, SST suffers from poor time-frequency resolution and is unable to deal with long signals. In order to accurately extract the characteristic frequency of variable speed rolling bearing faults, this paper proposes a synchrosqueezed transform method based on fast kurtogram and demodulation and piecewise aggregate approximation (PAA). The method firstly filters and demodulates the original signal using fast kurtogram and Hilbert transform to reduce the influence of background noise and improve the time-frequency resolution. Then, it compresses the signal by using piecewise aggregate approximation, so that the SST can deal with long signals and, thus, extract the fault characteristic frequency. The experimental data verification results indicate that the method can effectively identify the fault characteristic frequency of variable-speed rolling bearings.

Vibration characteristics of defective axle box bearings in high-speed trains under track irregularity excitation

Track irregularity is a type of excitation source for the wheel-rail system, and it is also the major cause of vibration and wheel-rail forces on the axle box bearings of vehicles, and it is commonly found on in-service lines. Therefore, this paper mainly focuses on the dynamic characteristics of high-speed train axle box bearings under track irregularity. Firstly, a nonlinear system containing a faulty double-row tapered roller bearings is established, the obtained equations of motion are solved numerically using the Runge–Kutta and comparing it with the varying compliance vibration frequency and fault characteristic frequency obtained by formula, the comparison results verify the effectiveness of the model. Then, the track irregularity is coupled to the above bearing system, the model is also verified by using the rolling and vibrating test rig of single wheelset. Secondly, the eigenvalue of covariance matrix is introduced as an index to analyze the influence trend of different fault sizes, loads, and inner rotational speeds on the axial trajectory. Finally, the influence trend of track irregularity on the stability of vertical acceleration is analyzed by simulating different operating conditions.

Calculation of Time-Varying Mesh Stiffness of Internal Gears based on Precise Tooth Profile and Dynamic Analysis of Planetary Systems with Root Cracks

The internal meshing spur gear pair is the research object, and the potential energy method is applied to calculate the time-varying meshing stiffness of the internal gear. The internal gear tooth profile is divided into two parts: involute and transition curves, and the gear tooth stiffness is calculated by numerical integration based on accurate tooth profile, which improves the calculation accuracy. Analyzed the influence of different crack size parameters on the stiffness of internal meshing gears. A coupled dynamic model of a planetary system with internal gear crack faults was established, and the influence of cracks on the dynamic response of the planetary system was studied using Zoom-FFT spectrum and cepstrum analysis methods. The simulation results show that as the crack parameter size increases, the mesh stiffness of the internal gear pair gradually weakens, and the periodic vibration impact of the planetary-internal gear pair is also more severe. Cepstrum analysis can easily capture weak fault characteristic frequency information in the system and discover their variation patterns. The research results can provide a theoretical basis for the state monitoring and fault diagnosis of gear systems with crack defects.

Two-stage benefits of internal and external noise to enhance early fault detection of machinery by exciting fractional SR

For early mechanical fault diagnosis, stochastic resonance (SR) breaks the previous perception that “noise is useless” and uses internal noise or external noise to enhance weak fault characteristics. Moreover, the fractional-order derivative can reinforce noise-enhanced weak fault detection. However, in the face of extremely low signal-to-noise ratio conditions, the enhancement effect of fractional SR induced by a single excitation of internal noise or external noise is unsatisfactory. To solve the above drawbacks, this paper investigates two-stage benefits of both internal and external noise to enhance early fault detection of machinery by exciting parallel array of fractional SR, and using the signal-to-noise ratio (SNR) to adjust these parameters of fractional SR. Then, two experiments including rolling element bearings and gearboxes were performed to validate it. Experimental results show that the proposed method takes on obvious detection ability for low SNR signals, where the amplitude at the fault characteristic frequency is amplified by beyond 300 times in bearing and gearbox fault experiments than one-stage those. In addition, it is also found that as the noise intensity and the number of iterations increase, the amplitude at the fault characteristic frequency tends to the peak value and then falls into a saturation value. Finally, compared with empirical mode decomposition (EMD), the proposed method can amplify the amplitude at the fault characteristic frequency beyond 1000 times in bearing and gearbox fault experiments. It was concluded that the proposed method has obvious advantages in extracting weak fault characteristics of machinery submerged by strong background noise.

A variable‐speed‐condition fault diagnosis method for crankshaft bearing in the RV reducer with WSO‐VMD and ResNet‐SWIN

AbstractDue to the noise interference and the weak characterization ability of the fault vibration signal of rotation vector (RV) reducer crankshaft bearing, it is difficult to obtain satisfactory results for the available fault diagnosis methods. For that, this paper proposes a variable‐speed‐condition fault diagnosis method with WSO‐VMD and ResNet‐SWIN. A signal reconstruction method with WSO‐VMD was carried out, Firstly, the performance of VMD algorithm is improved by using war strategy optimization algorithm to select parameters adaptively. Then the signal is reconstructed considering the fault characteristic frequency, so as to realize the noise reduction of the signal. By using the residual network module and attention mechanism to replace the first stage of the original SWIN model, a novel ResNet‐SWIN fault diagnosis model is established to enhance the feature extraction ability for the weak signal. The experiments with the constant‐operating‐condition and the variable‐operating‐condition are carried out to verify the effectiveness of the proposed method. The results show that, whether at variable‐speed or constant‐speed conditions, WSO algorithm has been proven to be the fastest convergence speed compared with WOA, SSA, and NGO optimization algorithms, and by the signal reconstruction with WSO‐VMD, the variance evaluation indicator of the reconstructed signal has 36%, 21%, 46%, and 40%, respectively. ResNet‐SWIN model has achieved the optimal diagnosis accuracy compared with SWIN, VIT, and CNN‐SVM models in both variable‐speed and constant‐speed conditions.

An improved tracking method for bearing characteristic frequencies in the time-frequency representation of vibration signal

Rolling bearing is one of the most critical components for support and energy conversion in machines. The fault characteristic frequency (FCF) of time–frequency representation has received increasing attention in bearing diagnosis under variable speed conditions. However, FCF-extracted methods have poor adaptability to amplitude attenuation and noise interference due to local distortions or even transitions in the estimated instantaneous frequency ridges. Consequently, this paper proposes an improved FCF tracking method for variable speed bearing diagnosis. A strategy for locating distortion intervals is first developed using exponential smoothing and residual distribution. Subsequently, an advanced fast path optimization method, including peak map renewal and curve search optimization, is proposed to extract the ridges of interest. Finally, the probability density function of curve-to-curve ratios is designed to accurately identifying bearing faults. Simulation and experimental results demonstrate the effectiveness of the proposed method.

SEACKgram: a targeted method of optimal demodulation-band selection for compound faults diagnosis of rolling bearing

Rolling bearing plays an important role in carrying and transmitting power in rotating machinery, and the bearing fault is easy to lead to mechanical accidents, resulting in huge losses and casualties. Therefore, the condition monitoring and diagnosis of rolling bearings are very important to improve the safety of equipment. Compound fault is a common fault evolved from the initial defect, which is characterized by randomness, coupling, concealment, and secondary. The existence of these characteristics brings great challenges to the accurate diagnosis of compound faults. In the diagnosis of compound faults, the traditional methods that select the single optimal demodulation frequency band for analysis and identification sometimes cannot completely extract multiple fault components, which are prone to miss diagnosis and misdiagnosis. In order to solve this problem, the SEACKgram method is proposed by constructing a Square Envelope Unbiased Autocorrelation Correlation Kurtosis (SEACK) index. The frequency band of the original signal is divided by the Maximal Overlap Discrete Wavelet Packet Transform, and the SEACK index is used to quantitatively describe the fault signals of different frequency bands. According to the different fault periods, the resonant frequency bands of the maximum SEACK value are selected, then the resonance band signal is analyzed by square envelope spectrum, and the fault type is identified according to the fault characteristic frequency. The simulated and experimental vibration signals of rolling bearings with compound faults are used to verify the feasibility of the proposed method. The results show that the proposed SEACKgram can improve the accuracy of compound faults identification and would be applied in engineering practice to a certain extent.

Dynamic modeling and analysis of rolling bearing faults under time-varying excitations considering defect deformation

Fault mechanism analysis is one of the methods in fault diagnosis, and the dynamic modeling of rolling bearing faults plays a crucial role in studying fault mechanisms. Existing dynamic fault models only consider the impact of fault size and bearing speed on the impact force, providing an incomplete description of the impact force. In order to more accurately describe the dynamic fault model of impact forces, this paper focuses on the deep groove ball bearing with outer race faults. Factors such as defect deformation, speed, and fault size are considered, and an instantaneous impact force excitation function is proposed. Based on this proposed excitation function, a dynamic model for the outer race fault of deep groove ball bearings is established. Finally, through simulation and experimental comparison, the results indicate that the fault characteristic frequencies and their harmonics of the model in this paper are closer to the actual fault characteristic frequencies, reducing the error by 1 to 2 Hz. Therefore, the model proposed in this paper is more effective and accurate, providing a more precise rolling bearing fault model for the study of fault mechanisms.

Nonlinear weight learning model for incipient fault detection and degradation modelling and its interpretability for fault diagnosis

Optimization-based weight learning approaches that incorporate multiple sensor signals or vibration spectral components have demonstrated their effectiveness in monitoring mechanical systems. However, the current weight learning methods are limited by their reliance on linear fusion functions. The exploration of nonlinear link functions, particularly in the context of fusing spectral components in vibration spectra for health indices (HIs) construction, remains largely unexplored. Additionally, the development of formulas for interpreting HIs constructed using nonlinear fusion functions poses significant theoretical challenges. To address these limitations, this study proposes a novel nonlinear optimization-based weight learning model for constructing an HI that captures the nonlinear relationships among spectral components. This HI is designed to pinpoint fault characteristic frequencies while also highlighting other spectral lines associated with bearing degradation modelling. Furthermore, we derive formulas that enable the calculation of the contributions of frequency components to nonlinearly constructed HIs, thereby enhancing the interpretability of the model. By selecting an appropriate kernel function, subtle changes resulting from incipient faults and the underlying degradation process can be effectively captured. The effectiveness of the proposed model in detecting incipient faults, modelling degradation, and identifying fault types is validated through two run-to-failure case studies and a gearbox bearing experiment.

A Novel Wind Turbine Rolling Element Bearing Fault Diagnosis Method Based on CEEMDAN and Improved TFR Demodulation Analysis

Among renewable energy sources, wind energy is regarded as one of the fastest-growing segments, which plays a key role in enhancing environmental quality. Wind turbines are generally located in remote and harsh environments. Bearings are a crucial component in wind turbines, and their failure is one of the most frequent reasons for system breakdown. Wind turbine bearing faults are usually very localized during their early stages which is precisely when they need to be detected. Hence, the early diagnosis of bearing faults holds paramount practical significance. In order to solve the problem of weak pulses being masked by noise in early failure signals of rolling element bearings, a novel fault diagnosis method is proposed based on the combination of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and an improved TFR demodulation method. Initially, the decomposition of vibration signals using CEEMDAN is carried out to obtain several intrinsic mode functions (IMFs). Subsequently, a novel KC indicator that combines kurtosis and the correlation function is designed to select the effective components for signal reconstruction. Finally, an innovative approach based on the continuous wavelet transform (CWT) for multi-scale demodulation analysis in the domain of time–frequency representation (TFR) is also introduced to extract the envelope spectrum. Further fault diagnosis can be achieved by the identification of the fault characteristic frequency (FCF). This study focuses on the theoretical exploration of bearing faults diagnosis algorithms, employing modeling and simulation techniques. The effectiveness and feasibility of the proposed method are validated through the analysis of simulated signals and experimental signals provided by the Center for Intelligent Maintenance Systems (IMS) of the University of Cincinnati and the Case Western Reserve University (CWRU) Bearing Data Center. The method demonstrates the capability to identify various types of bearing faults, including outer race and inner race faults, with a high degree of computational efficiency. Comparative analysis indicates a significant enhancement in fault diagnostic performance when compared to existing methods. This research contributes to the advancement of effective bearing fault diagnosis methodologies for wind turbines, thereby ensuring their reliable operation.

Attention on the key modes: Machinery fault diagnosis transformers through variational mode decomposition

Machinery signals typically consist of multiple sub-signals in different frequency bands, while existing Transformer-based fault diagnosis methods often lack attention to key fault frequencies, causing interference in fault diagnosis. Therefore, an innovative Transformer structure for fault diagnosis based on variational mode decomposition (VMD) is proposed. First, to address the difficulty in identifying signal features arising from coupling of multiple frequency bands, a mode encoder based on VMD is proposed to decompose the coupled modes and calculate the key modes. Second, a position encoding method based on central frequency is proposed to address the lack of attention to signal’s frequency in existing position encoding methods. Third, fault characteristic frequency is used to verify the frequency band attention scores, improving the interpretability and reliability of the network in response to the lack of internal interpretability in fault diagnosis methods based on deep learning. Finally, the proposed method was validated on bearing vibration dataset and motor sound dataset. The results showed that the method has high diagnostic accuracy, and could capture the intrinsic modes of different faults.

Sparse Bayesian Learning Approach for Compound Bearing Fault Diagnosis

Compound bearing fault diagnosis is an essentially challenging task due to the mutual interference among multiple fault components. The state-of-the-art methods usually take the potential fault characteristic frequencies as the prior knowledge and then try to recover every fault component by exploiting the impulse signal sparsity. However, they inevitably suffer from algorithmic degradation caused by energy leakage, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -norm approximation, and/or improper parameter selection. To handle these shortcomings, in this paper, we propose a novel sparse Bayesian learning (SBL)-based method for the compound bearing fault diagnosis. We first present a new categorical probabilistic model to efficiently capture the truly-occurred fault components with a truncated feasible domain, which can greatly reduce the energy leakage effect. Then, we devise a more general SBL framework to recover the compound sparse impulse signal under the new categorical probabilistic model. The newly proposed method successfully avoids the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -norm approximation and manual parameter selection, thus it can yield much higher accuracy and robustness. Both simulations and experiments demonstrate the superiority of the developed method.

Fault diagnosis for rolling bearings based on generalised dispersive mode decomposition and accugram

Bearing fault diagnosis helps to ensure the safe operation of electromechanical equipment and reduce unnecessary losses due to downtime. The interference of noise in the signal poses a challenge in the effective identification of rolling bearing faults. To address the above problems, this paper proposes a rolling bearing fault diagnosis (RBFD) method based on generalised dispersive mode decomposition (GDMD) and an accugram. Firstly, the bearing signal is decomposed using GDMD and the optimal number of decomposition modes is chosen using a new index based on the correlation coefficient and accuracy. According to the number of determined decomposition modes, the fault signal is reconstructed. Then, the centre frequency and bandwidth of the resonant frequency are determined using an accugram. Finally, the fault signal is filtered and analysed using a square envelope spectrum to achieve rolling bearing fault diagnosis. Experimental signal analysis verifies the effectiveness and feasibility of the method. The method is applied to the early fault diagnosis of rolling bearings and compared with kurtogram and accugram results. The results show that the approach can not only effectively avoid the interference of external impacts but it can also correctly recognise the fault characteristic frequency band.

Bearing fault damage degree identification method based on SSA-VMD and Shannon entropy–exponential entropy decision

Aiming at the problem that the weak fault signal of rolling bearing is affected by background noise and the weak fault signal itself leads to the difficulty in extracting fault features, a weak fault diagnosis method of rolling bearing based on sparrow search algorithm-variational mode decomposition (SSA-VMD) and Shannon entropy–exponential entropy decision is proposed. Firstly, the failure energy ratio of the original signal is acquired to judge the bearing failure. Secondly, the original time-domain signal is decomposed by the VMD optimized by SSA-VMD to obtain the Intrinsic Mode Function (IMF) component, and the kurtosis and correlation coefficient are normalized and fused. The fusion parameter ratio ( RV) is used to filter the IMF component, and the filtered component is reconstructed to achieve the noise reduction effect. The reconstructed signal is subjected to Hilbert transform to obtain the envelope spectrum of the vibration signal, and the fault type of the bearing can be judged. Finally, the entropy of the reconstructed signal is input into the model based on entropy-multilayer forward neural network (MFNN) to identify the degree of bearing fault damage. The effectiveness of the method is verified by using the experimental data of different fault types of intermediate shaft bearings in Shenyang Aerospace University and the self-built experimental data of outer ring fault detachment evolution. The results show that the fault energy ratio of the original signal is more conducive to judging whether the bearing has a fault than the reconstructed signal. The bearing fault type diagnosis method based on SSA-VMD and parameter fusion screening can effectively identify fault characteristic frequency and its frequency doubling of the inner and outer rings of rolling bearings. The entropy values of different bearing damage signals have different distribution regions, which verify the effectiveness of the bearing fault damage identification method based on entropy–MLP judgement.

Simulation method and spectrum modulation characteristic analysis of typical fault signals of inter-shaft bearing

In order to study the frequency spectrum characteristics of the vibration signal of the inter-shaft bearing defect fault in the aero-engine dual-rotor system, a vibration signal mathematical model is established based on the fault characteristic frequency of the inner and outer ring defects of the inter-shaft bearing, and the mutual modulation law of the signals during transmission is analyzed. A test bench for signal transmission path analysis is built to verify the calculation results. The results indicate that the fault signal of the inter-shaft bearing defect significantly attenuates during transmission, and the characteristic frequency of the inter-shaft bearing fault is modulated with the rotor rotation frequency. There are corresponding characteristic frequencies and modulation frequency components in the envelope spectrum of the inter-shaft bearing. The error between the experimental and simulation results is less than 1%, which verifies the accuracy of the simulation calculation results. After being transmitted to the rotor through the inter-shaft bearing, the rotor frequency includes the modulation frequency of bearing varying compliance frequency and rotation frequency, as well as the fault characteristic frequency of the inter-shaft bearing.