Meshing Vibration Research Articles

Effectiveness study of wire mesh vibration damper for sensitive equipment protection from seismic events

Wire Mesh Vibration Damper (WMVD) is proposed for the protection of vibration-sensitive equipment, such as Information Technology (IT) equipment, from seismic events. The mathematical model of the proposed isolator is primarily defined and then implemented to develop the Matlab Simscape MultibodyTM model of the WMVD isolated system subjected to earthquake induced floor motion. The latter is simultaneously generated for natural earthquake records and scaled to satisfy the GR-63-CORE (Zone 4) standard requirements via an artificial seismic time-history generation procedure, developed in the present work. In order to study the isolation effectiveness of the WMVD, comparative analysis with linear anti-seismic support is firstly provided. Results reveal that the WMVD isolated system can effectively attenuate seismic response more than 85%, whereas the seismic responses of the linearly isolated system increase by 160% as compared to the ground motion acceleration. Subsequently, an Incremental Dynamic Analysis (IDA) by specifying the operational vibration limit of the sensitive equipment mounted on the WMVD, is conducted to create the fragility curves. Considering the maximum acceleration response as engineering demand parameter, seismic fragility analysis eventually demonstrates the performance of the WMVD to protect the sensitive equipment from floor motion excitation.

Vibration mechanism and improved phenomenological model of the planetary gearbox with broken ring gear fault

Accurate modeling of the vibration signal model of planetary gearboxes is essential for the subsequent fault diagnosis. According to the existing improved phenomenological model based on the meshing vibration, this paper conducts further investigations on the vibration mechanism of the gearbox. The time delay phenomenon of faulty ring gear tooth participating in meshing is theoretically analyzed, and the assisted phases for experimental verification are proposed and deduced. Based on the improved model, the vibration signal under the fault condition is simulated and compared with the results of traditional methods. Subsequently, the paper proposes to divide and reconstruct this signal and use the maximum correlation kurtosis deconvolution (MCKD) to enhance its impact characteristics. The results show that the phase between the fault impact and its adjacent meshing impact is consistent with the proposed assisted phase. Finally, the correctness of the vibration mechanism and the improved phenomenological model are verified experimentally.

Signal Identification of Gear Vibration in Engine-Gearbox Systems Based on Auto-Regression and Optimized Resonance-Based Signal Sparse Decomposition

As an essential part of the transmission system, gearboxes are considered as a major source of vibration. Signal identification of gear vibration is necessary for online monitoring of the mechanical systems. However, in engine-gearbox systems, the ignition impact of the engine is strong, so that the gear vibration is generally submerged. To overcome this issue, the resonance-based signal sparse decomposition (RSSD) method is used in this paper based on different oscillatory behaviors of the gear meshing impact and the engine ignition impact. To improve the accuracy of RSSD under interferences, the meshing frequency energy ratio (MF–ER) index is introduced into RSSD to adaptively choose the decomposition parameters. Before applying the RSSD method, the auto-regression (AR) model is used as a pre-whitening step to eliminate the normal gear meshing vibration, which improves the decomposition performance of RSSD. The effectiveness of the proposed AR-ORSSD (AR-based optimized RSSD) algorithm is tested using both simulated signals and measured vibration signals from an engine-gearbox system in a forklift. Comparisons were made with the RSSD algorithm based on a genetic algorithm. Experimental results indicate that the AR-ORSSD algorithm is superior at identifying gear vibration signals especially when under strong interferences.

Linking the modulation of gear mesh vibration in planetary gearboxes to manufacturing deviations

The gear mesh vibration caused by planetary geartrains is modulated. Small planetary gearboxes, commonly used in servo drives, are examined experimentally and numerically. The goal is to link the modulation of the gearbox vibration to the deviations from the ideal geometry caused by manufacturing and assembly. Operational modal analysis shows that, while the dynamical behavior of nominally identical gearboxes is very similar, their modulation is not. The modulation also strongly depends on the operating conditions, such as speed and torque. Therefore, the modulation is aggregated to a vibration signature. In the vibration signature, distinct features are present. These can be linked to the eccentricity of the gears using numerical multi-body simulation and correlation analysis.

Relationship between meshing vibration frequency components and tooth leaning deformation estimated from tooth profile slope deviation of non-active tooth surface

Relationship between meshing vibration frequency components and tooth leaning deformation estimated from tooth profile slope deviation of non-active tooth surface

An improved phenomenological model of vibrations for planetary gearboxes

Interpreting and understanding vibration characteristics are the cornerstone for health condition monitoring schemes of a planetary gearbox. Phenomenological modeling provides a concise and efficient mathematical description of sensor-related vibration measurements, thus allowing prior guidance for spectrum analysis to be relied on. In this paper, some overlooked problems during the modeling process in previous researches are pointed out and analyzed. Some discoveries are consequently obtained: First, the asymmetry of spectrum structure should be attributed to the magnitude randomness of gear meshing vibration rather than different phase angles of multiple-planet gears; Second, the basic frequency component to constitute a model, namely a product of the rotational frequency of a planet carrier and the number of planet gears, is far from sufficient to describe the actual vibrations; Finally, improper function the phases of multiple-planet gears will lose some sidebands that should have been. For these reasons, we map the phase variation of multiple-planet gears into the time-varying propagating distance, therefore, solving the neutralization phenomena of the frequency components. With consideration of the attenuation effect and random gear meshing magnitudes, an improved model is proposed to provide a more reasonable representation of the vibration behaviors, both for the dominant frequency components and structure. Simulation and experimental studies both demonstrate the higher fidelity and descriptive capability than the traditional models.

Fault detection of planetary subassemblies in a wind turbine gearbox using TQWT based sparse representation

Planetary subassemblies in wind turbine gearbox are subject to compound faults due to harsh environment and complex structure. Disturbed by the meshing vibration from higher-speed transmission stage and intensive noise, fault diagnosis of planetary subassemblies with low rotational speed is challenging. In this paper, a tunable Q-factor wavelet transform based sparse representation method is proposed, which integrates the property of tunable Q wavelet transform, non-convex penalty and noise optimization into sparse decomposition. This method makes it possible to accurately decompose vibration signal from faulty planetary subassemblies into two resonance components and noise, relying less on the setting of regularization parameters due to the noise restriction. It is easier to detect potential fault information in decomposed low or high resonance component than in the original signal. Further, normalized multi-stage enveloping spectrogram is presented to reveal the fault characteristic frequencies of planetary gears and bearings even though they are weak. The effectiveness of the proposed methods is verified by the analysis of a simulated faulty signal and an on-site case from one 850 kW wind turbine gearbox.

Research on Meshing Stiffness and Vibration Response of Pitting Fault Gears with Different Degrees

In order to study the influence of pitting on meshing stiffness, the normal distribution function is used to simulate the pitting location of pitting gear, and the potential energy method is used to analyze the influence of pitting on meshing stiffness. At the same time, the meshing stiffness of pitting gears with different degrees is analyzed by finite element method, and the validity of the calculation results with potential energy method is verified. On the basis of meshing stiffness, the dynamic model of gear system is established, and the vibration response of pitting gear system with different degrees is analyzed. The results show that with the increase of pitting area, the meshing stiffness decreases; the closer the meshing area of the driving wheel is to the pitting line, the more the meshing stiffness decreases, resulting in the intensification of vibration response and periodic impact; and in the time history diagram, there is a small spurious frequencies near the meshing frequency; in the phase diagrams and the Poincare diagram, trajectory and discrete point aggregation area is gradually increased.

Cyclostationary modeling for local fault diagnosis of planetary gear vibration signals

Owing to the rotation and reciprocation of mechanical equipment, their vibration signals inherently exhibit cyclic stationary characteristics. This paper provides a phenomenological signal model of the planetary gear vibrations under the cyclostationarity paradigm. The model is helpful to give comprehensive demodulation information which is the limit of classic spectral analysis of deterministic signals, so that the diagnosis of local faults in planetary gear sets can be more explicit. First, the effects of rotating speed fluctuation on periodic gear meshing vibrations are analyzed. It is shown that the stationary speed fluctuation will turn the periodicity of signals into second-order cyclostationarity. Next, an impulsive oscillation sequence with interval timing jitter is used to describe the dynamic response of the meshing stiffness change caused by local defects. Meanwhile, the influence of a vibration transfer path is also considered in the model. Based on the above analysis, the following procedure is utilized to analyze planetary gearbox vibrations: remove the periodic components by the self-adaptive noise cancellation method and then, apply the second-order frequency descriptor to reveal fault features of the signals. Both the simulation and experiment are used to validate the correctness of model derivation and the superiority of the cyclostationary analysis.

An Improved Phenomenological Model of the Planetary Gearbox Based on Meshing Vibration Characteristics

With the construction of periodic functions relative to the meshing frequency, rotating frequency, and the faulty frequency, etc., the phenomenological model provides a simple and effective way of representing the vibration signal of the planetary gearbox. However, due to that the meshing vibration is simplified, the traditional model can only reflect the modulation characteristic of the signal, but not the impact characteristic. Therefore, an improved phenomenological model is proposed, which can satisfy these two characteristics of the vibration signal at the same time. To consider the meshing vibration correctly, two key points should be determined: occurring moment of impact signals, and their relative amplitudes. In order to calculate the occurring time, this paper proposes modifying the reference point of the meshing phase and using the modified phases to represent it. Then two experiments are designed to verify the correctness of the modified phases and the occurring moment. Fortunately, these experimental results also provide a factual basis for determining the relative amplitudes of these impact signals. Subsequently, signal model of the gearbox in the healthy state is established based on the meshing vibration characteristics. The simulation results show that the new model can satisfy the modulation and impact characteristics. In addition, combined with the time-varying meshing stiffness of the gear pair, the paper theoretically analyzes the influence of fault type, location, and size on the impact frequency in a fault meshing period. Finally, the correctness of the new phenomenological model is verified by experiments.

Dynamic characteristics for coal shearer cutting unit gearbox housing

Long wall mining is most widely used in coal mining of China, and coal shearer is the most important machine due to its direct role in cutting coal. Nevertheless, coal mining enterprises are suffering from faults of coal shearer, especially cutting unit gearbox housing (CUGH). Published dynamic studies on CUGH have not considered the excitation caused by gear meshing and complete machine vibration. Due to the apparent lack of experimental validation of these published papers, the dynamic response of CUGH is not convincing. In this study, dynamic behavior of CUGH is investigated both theoretically and experimentally for finding out failure mechanism and improving reliability. Complete machine vibration and gear meshing vibration are two excitation sources for CUGH, and vibration is transferred via articulated holes and bearing holes. Hence, complete machine dynamics model is established for obtaining force on articulated holes. Dynamics model of gear transmission system is established for obtaining force on bearing holes. Stochastic cutting forces model is established as external load of complete machine dynamics model. Dynamics response is calculated by finite element model established by ANSYS. A measurement system to capture three-dimensional vibratory motions under realistic working conditions of coal mines is implemented by National Energy Mining Equipment Laboratory of China. Direct comparisons between predicted and measured results are presented to demonstrate the accuracy of the proposed model in predicting three-dimensional vibrations of CUGH. Maximum deformation and stress positions of CUGH are determined, and the excitation sources are investigated.

Crack detection of plastic gears using a convolutional neural network pre-learned from images of meshing vibration data with transfer learning

In this paper, a crack detection method of plastic POM (Polyoxymethylene) gears using a deep convolutional neural network is proposed. The vibration signal is collected from an automatic data acquisition system for a gear operation test rig, with an accelerometer installed on the housing of bearings. The FFT (Fast-Fourier Transform) spectrums of the measured vibration signal are visualised as grayscale images for training input. Additionally, a high-speed camera observes cracks occurring at the root of the teeth which enable to label the visualised images for training data. A popular convolutional neural network, called VGG16 ConvNet, is employed for the classification of the crack or non-crack situation of gears. This VGG16 is pre-learned from image data of ImageNet and relearned from the created images of vibration data with the transfer learning technique. The weights of the last two layer are re-trained in the transfer learning process. The accuracy rate for learning from training data approached 99% by transfer learning. Additionally, the accuracy rate can reach 100% on classification tasks from testing data. Finally, four endurance tests of plastic gear were carried out. The proposed crack detection was carried out at the rate of 10 times per minute, and the errors of detection results are investigated by training data assessment. The experimental results show that the proposed method is sufficient to specify the crack or non-crack situation of gear during the operation test.

Gear misalignment diagnosis using statistical features of vibration and airborne sound spectrums

Failure in gears, transmission shafts and drivetrains is very critical in machineries such as aircrafts and helicopters. Real time condition monitoring of these components, using predictive maintenance techniques is hence a proactive task. For effective power transmission and maximum service life, gears are required to remain in prefect alignment but this task is just beyond the bounds of possibility. These components are flexible, thus even if perfect alignment is achieved, random dynamic forces can cause shafts to bend causing gear misalignments. This paper investigates the change in energy levels and statistical parameters including Kurtosis and Skewness of gear mesh vibration and airborne sound signals when subjected to lateral and angular shaft misalignments. Novel regression models are proposed after validation that can be used to predict the degree and type of shaft misalignment, provided the relative change in signal RMS from an aligned condition to any misaligned condition is known.

Dynamic Behaviors of Geared Rotor System in Integrally Centrifugal Compressor

In this paper, a five-shaft geared rotor system coming from a prototype of centrifugal compressor is taken to investigate the determination of its critical speeds and unbalance response analyses. And also its complicated dynamic characteristics due to the interaction of the multiple rotors in paralleled arrangement and coupled by different gears are studied. A finite element model of the geared rotor system is established, where the rotating beam elements (6 DOFs at each node) are used and the linear mesh stiffness of engaged helical gears is involved. Then, Campbell diagrams of the rotor system with different mesh stiffness are calculated using the image eigenvalues of the coefficient matrices based on the FE model. To improve the computational efficiency, an analytical model is derived to calculate the coupling dynamic response, and the effect of mesh coupling is analyzed. Finally, vibrations of shafts near the bearing are measured on test rig to verify the calculated vibration phenomena of the whole machine. Comparing with the results without the mesh effort, some new critical speed lines appear in the system’s Campbell diagram due to involving of gear mesh stiffness. In addition, significant coupling phenomenon shows in the Campbell diagram that the critical speed lines corresponding to different modes transform sharply from one to the other in some richly concentrated areas, where the lateral vibration, axial vibration, and the meshing vibration are mixed at the same time. The rotating frequency of any shaft can affect the vibration frequencies of any other shafts, and the proportions of the three frequencies are different at different input speed. The test signals from the test rig validated the theoretical model, which shows the modeling method in this paper can describe the dynamics of the geared rotor system well. The dynamic analysis and design strategy based on the separated single-shaft rotor systems may lose some important dynamic properties and might cause failures in the machine operation. And the geared rotor system of the integrally centrifugal compressor is more complex not only for its multi-shafts coupled by the helical gears, but also for all the output shafts always suffering changed loads in processing. So the interaction and restriction among all the paralleled shafts must be considered.

Deep convolutional neural network based planet bearing fault classification

Condition monitoring and fault diagnosis of the planet bearing is key to operational reliability of the planetary gearbox, and also have remained challenging due to complex modulation phenomenon and strong planetary gear noise. As such, a new fault diagnosis strategy based on the synchrosqueezing transform (SST) and the deep convolutional neural network (DCNN) is proposed in this paper. Specifically, the envelope time-frequency representations (TFRs) of the vibration signals of the planetary gearbox are firstly calculated using the Hilbert transform and the SST. Next, a DCNN is constructed to learn the underlying features from the TFRs and then the fault types can be determined automatically. As its main contribution, the proposed method automatically recognizes the planet bearing fault type, which is free from artificially capturing fault characteristic frequencies in spectrum or time-frequency spectrum that contain many interference items, and effectively avoid missed diagnosis and misdiagnosis. In addition, it is also free from considering frequency band selection, which is difficult duo to the strong interferences of the gear meshing vibration. The analysis results of the planetary gearbox data demonstrate effectiveness of the proposed approach with a classification accuracy better than 98.3%.

Compound faults diagnosis and analysis for a wind turbine gearbox via a novel vibration model and empirical wavelet transform

Fault diagnosis of a wind turbine gearbox can schedule maintenance strategy on a wind turbine and save operational cost for wind farms. Owing to low rotational speed and weak vibration energy, fault diagnosis for planetary stage is arduous in a wind turbine gearbox involving multi-stage transmissions. A novel modulation model is presented to support the fault diagnosis of the planetary stage of a wind turbine gearbox, which is described as the mesh frequency of intermediate stage, high speed stage, or mechanical natural frequency of the gearbox is a carrier wave modulated by the mesh frequency of planetary stage with distributed faults. Even possessing this presented vibration model, the fault feature of planetary stage with lower rotational speed is easily concealed by the meshing vibration energy of ordinary stages with higher speed, especially when faults simultaneously arise in the ordinary stages. Aiming at the diagnosis of the above compound faults in an industrial wind turbine gearbox, empirical wavelet transform is utilized to adaptively find weak fault frequency in planetary stage as well as evident fault characteristics in other ordinary stages.

Acquisition of meshing vibration data and image pictures of crack propagation at tooth root of plastic gears

Acquisition of meshing vibration data and image pictures of crack propagation at tooth root of plastic gears

Helicopter interior noise reduction using compounded periodic struts

This paper characterizes the performance of a novel compounded gearbox periodic strut on controlling the noise in a helicopter cabin through modelling, simulation and experimental research. The strut exhibits low transmissibility in the specified frequency ranges, called “stop bands”. Based on a certain helicopter model, a dynamic acoustic-structure coupled system is first built by using the finite element method and the transfer matrix method. Subsequently, according to the gear mesh vibration transmission path, analyses of the vibration and noise reduction characteristics are conducted. Compared with the plain strut, attenuations of both vibration and noise in excess of 60 dB are obtained in the simulations. On a specially designed helicopter platform, experimental research is conducted simultaneously on the two aspects of fuselage vibration and cabin noise. The effectiveness of the novel strut used for helicopter cabin broadband noise reduction is demonstrated by the agreement between the simulation and experimentation results, where the attenuations of measured fuselage vibration and cabin noise exceed the levels of 40 dB and 30 dB, respectively, in the frequency range from 300 to 2000 Hz.

A leakage-free resonance sparse decomposition technique for bearing fault detection in gearboxes

Most of rotating machinery deficiencies are related to defects in rolling element bearings. Reliable bearing fault detection still remains a challenging task, especially for bearings in gearboxes as bearing-defect-related features are nonstationary and modulated by gear mesh vibration. A new leakage-free resonance sparse decomposition (LRSD) technique is proposed in this paper for early bearing fault detection of gearboxes. In the proposed LRSD technique, a leakage-free filter is suggested to remove strong gear mesh and shaft running signatures. A kurtosis and cosine distance measure is suggested to select appropriate redundancy r and quality factor Q. The signal residual is processed by signal sparse decomposition for highpass and lowpass resonance analysis to extract representative features for bearing fault detection. The effectiveness of the proposed technique is verified by a succession of experimental tests corresponding to different gearbox and bearing conditions.

Resultant vibration signal model based fault diagnosis of a single stage planetary gear train with an incipient tooth crack on the sun gear

Abstract Planetary gear trains equipped in wind turbine often run under slow speed and non-stationary load condition. The incipient gear faults in a wind turbine gearbox can hardly be detected yet might cause tremendous loss. In order to detect the incipient faults, a resultant vibration signal model is proposed to characterize the faulty features of a single stage planetary gear train working under non-stationary load conditions. For this purpose, an analytical dynamic model is developed. By introducing the crack-induced mesh stiffness and varying load into the dynamic model, the vibration responses of the system are predicted. Based on this, a resultant vibration signal model is developed in the form of weighted summation of mesh vibration signals. With the resultant model, the vibration signals of an example system are simulated and analyzed. The simulation results indicate that varying load and tooth crack make the system's vibration signals become extremely complicated in both time and frequency domains. The incipient tooth crack induced impulse vibration signals are too weak to be identified in the time domain but can be detected from the order spectrum. The simulation results from the resultant signal model are verified by the test rig experimental measurements.