Gear Vibration Research Articles

Investigation of Gear Meshing Vibration and Meshing Impact Resonance Intensity Assessment

Abstract Gear drive is one of the most widely used transmission forms. Its vibration analysis plays an important role in design and operation. Considering the gear meshing resonance phenomenon (MRP), the paper analyzes the influences of rotating speed and load on meshing resonance intensity (MRI). Based on the gear meshing impact mechanism, meshing force variation during the engagement process were obtained. It was considered as meshing impacts exerted on the gear system. By comparing the maximum meshing force under different circumstances, it was found that rotating speeds and loads were positively related to meshing forces. The vibration signals with different load torques and rotating speeds obtained from the gear pair were analyzed. The experiment results showed that the intensity of meshing impact increased with the increases of both rotating speed and load. It was also observed that due to the MRP, the gear meshing frequency was modulated to the resonance frequency band as meshing impacts. Consequently, the resonance frequency band contained most of the energy of the meshing impact. An indicator called resonance energy ratio (RER) was defined to represent the proportion of resonance energy due to meshing impact. The simulation and experiment result show that the proposed RER indicator can well assess the intensity of the vibration. By comparing the RER values of 20 sets of gear vibration data, the influences of rotating speed and load on MRI were discussed. The result shows that the proposed method is helpful to the vibration assessment and condition monitoring in different operational states.

A novel gearbox local fault feature extraction method based on quality coefficient and dictionary learning

The performance of sparse decomposition is directly determined by the similarity between impact atoms and the actual fault impact waveform. The shift-invariant K-singular value decomposition (K-SVD) dictionary learning algorithm is capable of training impact patterns from vibration signals collected by sensors to construct impact atoms, thereby extracting fault impact components from the vibration signals. However, the impact pattern training using the shift-invariant K-SVD algorithm is influenced by the presence of harmonics and white noise in the gear transmission system vibration signals. To solve the above problems, a novel gearbox local fault feature extraction method based on the quality coefficient and dictionary learning is proposed in this paper. Firstly, the original signal is decomposed into a series of intrinsic mode functions (IMFs) by empirical mode decomposition. Then, a new quality coefficient is proposed by comprehensively considering the intensity of the impact, harmonics and noise components in each IMF, as well as the degree of correlation with the original signal. The IMF with the largest quality coefficient is used to train the impact pattern and solve the sparse coefficients. Finally, the orthogonal matching pursuit algorithm is adopted to solve the sparse coefficients, which are used to reconstruct the fault impact response signal from the dictionary. Simulation and experimental analysis demonstrate the superior performance of the proposed method compared to other state-of-the-art methods.

Brake-Induced Landing Gear Walk Vibration Analysis and Suppression Method Research

During aircraft braking, brake-induced frequent wheel slippage may cause coupling vibration between the antiskid brake system and landing gear. Brake-induced longitudinal coupled vibration is also known as “gear walk” vibration. Gear walk vibration not only reduces the structural life of the landing gear but also impairs the efficiency of the aircraft braking system. This paper focuses on the landing gear walk vibration mechanism and suppresses the method by modifying the antiskid brake control law. Firstly, a comprehensive multiwheel landing gear walk vibration model is developed. This model describes not only the longitudinal and vertically coupled vibration characteristics of the landing gear but also the dynamics of the aircraft braking system and the fuselage. Secondly, by simplifying the landing gear walk to the transverse vibration of a cantilever beam with a tip mass, the landing gear walk vibration mechanism is revealed in the frequency domain. Finally, a method to suppress landing gear walk vibration by modifying the pressure-bias-modulated (PBM) antiskid braking control law is proposed, which can solve the serious landing gear walk vibration problem caused by the conventional PBM control law. Simulation and experimental results show that the proposed method can suppress the landing gear walk vibration while improving braking efficiency.

A novel method for helical gear modeling with an experimental validation

Dynamic models are important for developing gear diagnostics methods since they allow physical phenomena occurring during operation to be studied in a relatively simple environment. The main challenge in gear modeling is the calculation of the time-variant gear mesh stiffness, and this challenge is even greater in helical gears. The mechanism of helical gears is more complex than in spur gears; the helix angle both adds an axial component to the contact force and also makes the contact line three-dimensional. This study suggests a novel dynamic model for helical gear vibrations that combines an existing validated dynamic model for spur gears with a unique extension for helical gears. The extension is based on a common method called “multi-slice”, according to which the helical tooth width is divided into infinitesimal slices, and each slice is treated as spur tooth. The suggested model introduces a novel implementation of the multi-slice method that overcomes the aforementioned challenges with only few parameters and calculations, depends on the tooth geometry. Furthermore, for the first time in helical gear modeling, the manufacturing profile errors are integrated to the model to generate scatter in the data that can better reflect the reality. The model is validated experimentally and for two different test-rigs by a qualitative comparison of the RMS of the vibration signal. The simulations and the measured data show similar behavior at different ranges of rotational speed and applied load, emphasizing the potential inherent in the model for future work on gear fault diagnosis.

Failure analysis of gear using continuous wavelet transform applied in the context of wind turbines

One of the main reasons for failure in the wind turbine is the wear between the gear teeth during the power conversion and changes in the rotation speed, which is also generally associated with changes in the lubrication regimes. In this sense, vibration and signal analysis are frequently used in predictive maintenance as they usually permit the identification of deviations in the proper functioning of the equipment. Thus, this work aims to apply the continuous wavelet transform (CWT) to correlate gear wear and vibration signals, using visual and straightforward analysis. An experimental setup of a gear system was used to analyze vibration signals from different tooth gear damages. Gears with different levels and modes of damage were used in order to evaluate the sensitivity of vibration signals to them. The features from vibration signals were extracted by Morlet wavelet analysis. Results demonstrate that the proposed method accurately detected the early failure by visualization in frequency–time maps.

Gear fault diagnosis based on complex network theory and error-correcting output codes: Multi class support vector machine

Gearbox failures have a detrimental effect on the machine performance that affects the production capacity and economic benefits of a manufacturing industry in an adverse manner. Early detection of faults in gears helps to prevent sudden machine failures. Previously, many signal processing and artificial intelligence techniques have been successfully applied to diagnose gear faults by analyzing the machine vibrations. These techniques have repeatedly emphasized on the need to extract quality features from gear vibration signals and using artificial intelligence techniques that can identify multiple types of faults simultaneously. As such, in this article, new features called as visibility graph features based on complex network theory have been proposed to extract fault information from vibration signals. In addition, a new artificial intelligence framework for multifault classification known as error-correcting output codes-multiclass support vector machine is proposed to detect gear faults. To the best of authors’ knowledge, these features along with the error-correcting output codes-artificial intelligence framework have been rarely utilized for fault diagnosis purpose. The proposed approach has been applied on experimental gear vibration data to validate its effectiveness. First, the vibration signals are transformed to graphs, and various graph properties are computed to serve as fault features. Then, the fault features are supplied to train the error-correcting output codes-multiclass support vector machine model and learn the fault patterns. Finally, the gear fault classification accuracies are determined for various gear test conditions and compared with those of existing methods. It is observed that the proposed approach provides an average improvement of 4.22%, 9.93% and 11.8% over the time-domain features, time–frequency domain features and voting-based multiclass support vector machine classifier, respectively, for different operating conditions. Furthermore, the suggested technique augments the classification accuracies by 10%, 7.5% and 6.7%, respectively, as compared with the deep-learning models, namely standard stacked sparse autoencoder, deep neural network and convolution neural network.

A novel gear RUL prediction method by diffusion model generation health index and attention guided multi-hierarchy LSTM

Gears, as indispensable components of machinery, demand accurate prediction of their Remaining Useful Life (RUL). To enhance the utilization of ordered information within time series data and elevate RUL prediction precision, this study introduces the attention-guided multi-hierarchy LSTM (AGMLSTM). This innovative approach leverages attention mechanisms to capture the intricate interplay between high and low hierarchical features of the input data, marking the first application of such a technique in gear RUL prediction. Additionally, a refined health indicator (HI) is introduced, constructed through a diffusion model, to precisely reflect the gears' health condition. The proposed RUL prediction method unfolds as follows: firstly, HIs are computed from gear vibration data. Subsequently, leveraging the known HIs, AGMLSTM predicts future HIs, and the RUL of the gear is determined upon surpassing the failure threshold. Quantitative analysis of experimental results conclusively demonstrates the superiority of the proposed RUL prediction method over existing approaches for gear RUL estimation.

Experimental analysis of vibration and noise characteristics of helical gears with nano-lubricant additives

PurposeThe purpose of this study is to investigate the effects of nanoadditive lubricants on the vibration and noise characteristics of helical gears compared with conventional lubricants. The experiment aims to analyze whether nanoadditive lubricants can effectively reduce gear vibration and noise under different speeds and loads. It also analyzes the sensitivity of the vibration reduction to load and speed changes. In addition, it compares the axial and radial vibration reduction effects. The goal is to explore the application of nanolubricants for vibration damping and noise reduction in gear transmissions. The results provide a basis for further research on nanolubricant effects under high-speed conditions.Design/methodology/approachHelical gears of 20CrMnTi were lubricated with conventional oil and nanoadditive oils. An open helical gearbox with spray lubrication was tested under different speeds (200–500 rpm) and loads (20–100 N·m). Gear noise was measured by a sound level meter. Axial and radial vibrations were detected using an M+P VibRunner system and fast Fourier transform analysis. Vibration spectrums under conventional and nanolubrication were compared. Gear tooth surfaces were observed after testing. The experiment aimed to analyze the noise and vibration reduction effects of nanoadditive lubricants on helical gears and the sensitivity to load and speed.FindingsThe key findings are that nanoadditive lubricants significantly reduce the axial and radial vibrations of helical gears under low-speed conditions compared with conventional lubricants, with a more pronounced effect on axial vibrations. The vibration reduction is more sensitive to rotational speed than load. At the same load and speed, nanolubrication reduces noise by 2%–5% versus conventional lubrication. Nanoparticles change the friction from sliding to rolling and compensate for meshing errors, leading to smoother vibrations. The nanolubricants alter the gear tooth surfaces and optimize the microtopography. The results provide a basis for exploring nanolubricant effects under high speeds.Originality/valueThe originality and value of this work is the experimental analysis of the effects of nanoadditive lubricants on the vibration and noise characteristics of hard tooth surface helical gears, which has rarely been studied before. The comparative results under different speeds and loads provide new insights into the vibration damping capabilities of nanolubricants in gear transmissions. The findings reveal the higher sensitivity to rotational speed versus load and the differences in axial and radial vibration reduction. The exploration of nanolubricant effects on gear tribological performance and surface interactions provides a valuable reference for further research, especially under higher speed conditions closer to real applications.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2023-0220/

Dynamics model and vibrational response analysis of helical gear-rotor-bearing transmission system

As a core component of wind turbines, wind power gear speed increasers often work in harsh environments, so it is necessary to study the vibration characteristics of gear transmission systems. Taking a wind turbine gearbox high-speed stage helical gear transmission system as the research object, the dynamics model of multi-degree-of-freedom helical gear-rotor-bearing transmission system is established by the lumped parameter method and solved by Runge-Kutta method, taking into account the tooth side clearance of the gear, transmission error, eccentricity and support force of the nonlinear bearing. The effects of input torque, transmission error and tooth side clearance on the vibration characteristic response of the helical gear train were analyzed. The relationship between the trend of amplitude change in each direction of the gear and the trend of change in the major frequency components was analyzed under the conditions of changing internal and external excitation. The results show that torsional vibration dominates in the system. As the input torque increases, the vibration amplitude of the driving and driven gears decreases, and the frequency amplitude decreases significantly at multiple locations. Gear transmission errors and changes in tooth side clearance have significant effects on gear vibration amplitudes, but are sensitive only to the meshing frequency. The trend of gear vibration amplitude caused by the change of external excitation of the gear set is synchronized with the trend of main frequency amplitude in the corresponding direction, while the change of vibration amplitude caused by internal excitation is consistent with the trend of mesh frequency amplitude in the corresponding direction. The results of this paper can pave a certain foundation for the design and fault diagnosis of wind power gearbox transmission system.

A novel method for ring-planet gear mesh force identification via SVD-based Kalman filter

Dynamic mesh forces are the primary vibration excitations of the planetary gear transmission systems. However, they are difficult to measure directly, and conventional indirect measurement methods are typically only applicable to specific planetary gear sets with special measuring equipment. This study proposes a more widely applicable method for identifying the mesh forces of ring-planet gear pairs by utilizing vibration signals. To this end, a ring gear dynamic model is established based on the elastic theory of the thick ring in the form of a space state system. The state vector of the model is constructed from parameters of ring gear vibration responses, while the input state vector is derived from parameters of dynamic mesh forces. A singular value decomposition (SVD)-based Kalman filter is employed to provide a stable solution for the estimation of state vector and input vector simultaneously. A mesh force indirect measurement method based on tooth fillet strain signals collected by strain gauges is adopted to evaluate the accuracy of identification results. Results of dynamic experiments conducted in a planetary gear set test rig demonstrate that compared with measured results, the proposed method can obtain acceptable estimated mesh forces of ring-planet gear pairs by using vibration signals.

Static transmission error measurement of various gear-shaft systems by finite element analysis

Transmission error (TE) is a significant parameter related to gears vibration widely investigated by many authors using different approaches. However, in previous studies, spur and helical gears were mainly examined. There is a lack of studies addressed to double helical and herringbone gears and a comparison among several types of gearing with parallel axes. In this paper, spur, helical, double helical, and herringbone gears are analyzed in terms of static transmission error (STE), contact pressure and tooth root stress. Static contact analyses were conducted using the finite element method (FEM) which is often considered a tool for validating other methods and approaches. Moreover, three variants of boundary conditions of each gear type are introduced, including flexible shafts and the effect of a tip relief modification at sole gears, without shafts, was analyzed. In addition, a concept of a compact test rig intended for STE measurements at low loads was presented. The results have shown, among other things, significant influence of the shaft stiffness and boundary conditions on meshing characteristics.

Study on the Dynamic Characteristics of Gears Considering Surface Topography in a Mixed Lubrication State

Based on mixed lubrication analysis, considering the influence of rough interface contact stiffness, contact damping, and interface friction on the gear transmission system, the relationship between interface contact and the overall performance of the gear transmission system has been established. First, the surface topography is characterized using statistical parameters of rough surfaces, and the contact stiffness and damping for tooth surfaces with different roughnesses are calculated. Subsequently, a six degree of freedom gear tribo-dynamics coupling model is developed. Finally, the established tribo-dynamics model is employed to investigate the relationship between surface roughness and the overall performance of the gear transmission system. This study provides a more intimate connection between the contact interface and the general behavior of the gear transmission system, enabling a better representation of real-world engineering problems. The research findings reveal that contact stiffness and damping decrease with increasing surface roughness. Higher roughness leads to greater gear vibration amplitude. Moreover, elevated surface roughness results in intensified meshing force and more significant energy loss. Surprisingly, when the roughness is appropriate, gears with rough surfaces lose less energy than those with smooth surfaces.

Traveling-wave vibration modelling for thin-walled gear with ring damper

The harmful resonances of the thin-walled gears for aviation high-speed gear transmission systems, especially the traveling-wave vibration (TWV), frequently occur under complex excitations. The ring damper is an excellent and widely used damping technology for TWV reduction. However, lacking the TWV predictive method, there are few theoretical bases for the damper optimization. In this paper, firstly, assuming that the external input energy, the gear damping energy dissipation, and the ring damper energy dissipation form an energy balance, a novel model of TWV response based on energy dissipation (TRED) is proposed for the thin-walled gear with ring damper. Secondly, to solve the complex nonlinear TRED model, using the Rayleigh damping theory, the discrete expression of TRED model is innovatively given instead of traditional equation solving methods. Considering that the TRED model is established based on the vibrational displacement, a method for the conversion of gear vibration strain and displacement is given under different TWV directions and vibration strain measurements, and the solving method is proposed for the TRED model based on the above established theories. Finally, to validate the TRED model and its solutions, the speed-up experiments are conducted, and the experimental results are compared with the TRED prediction. Results show that the experimental and theoretical results are consistent, and the maximum predictive error is 8.7 %, which validates the feasibility of the proposed theories and methods.

Effect of teeth modifications and gear-paired materials on vibration and acoustic characteristics of polymer gears

Effect of teeth modifications and gear-paired materials on vibration and acoustic characteristics of polymer gears

Investigation of Effect of the Tooth Profile Modification on the Engagement Characteristics of the Gear Pair

As a vital component in the electric vehicle, the higher requirements for the gear precision are urgently needed in the service environment with high speed and heavy load. The tooth profile modification can greatly improve the accuracy and strength of the gear transmissions. Therefore, accurately obtaining the optimum modification parameters of the gear system under the action of specific loads is the premise of the research of gear vibration and noise reduction. The time-varying mesh stiffness calculation model is established in this paper considering the coupling effect of the tooth profile errors and structural coupling effect. The minimum variations of the loaded static transmission error are selected as the objective function to obtain the optimum modification parameters of gear pair. In addition, the effect of torque, modification amount and modification length on the engagement characteristics of the gear pair are studied. The research can provide some references for the design and optimization for the gear transmission system in the electric vehicle.

Research on Nonlinear Vibration Characteristics of Internal Beveloid Gear Transmission System

The internal beveloid gear has good scientific research value and a broad application field. However, there is a lack of research on the nonlinear vibration characteristics of internal beveloid gears. The present study establishes a nonlinear vibration model that takes into account axial vibration, gear torsional vibration, and radial support vibration. The effects of various excitation parameters on the vibration characteristics of the gear transmission system are analyzed and computed using the Runge–Kutta method. After analyzing the dynamic model of the gear pair using numerical methods, the harmonic balance method is employed to obtain the theoretical analytical solution for a single−stage gear. The obtained results are compared with the velocity and acceleration time−domain response curves obtained from the numerical method, and they show excellent agreement.

Vibration optimization of spur gear based on GSA-SA algorithm.

To determine the optimal design parameters of spur gear under a specific condition, based on the basic theories of gear dynamics theory, gear meshing principle, tooth contact analysis and load tooth contact analysis, a six-degree-of-freedom vibration analysis model of spur gear pair is established, and a gravitational search-simulated annealing hybrid algorithm (GSA-SA) is used to optimize the gear addendum modification coefficient and profile modification parameters. The vibration response of the spur gear pair is evaluated through the optimization objective function established by the combination of the G1 method and variation coefficient method. The study shows that the optimized design parameters effectively reduce the level of the vibration, which proves the effectiveness of the optimization method, and the simultaneous optimization of the addendum modification coefficient and profile modification parameters of the gear has a better result than only optimizing the addendum modification coefficient or profile modification parameters. This method can be used for gear transmission system vibration optimization design in the automotive industry and shipbuilding.

Impact-meshing vibration characteristics of high-speed gear systems with Backlash

The meshing process includes high-speed impact between the teeth. The vibration and noise in the gear transmission become prominent owing to the backlash between gears. Currently, the concentrated mass model is primarily used to analyse the vibration and noise mechanism of gear transmission, and it is difficult to effectively explain high-speed gear collision. In this study, an improved impact vibration model was applied to the meshing state of a high-speed gear. The gear transmission was simplified as a collision vibration system with absolute and traversable boundaries, and the piecewise-smooth dynamics model of the gear system is established. A mapping dynamic analysis method was then used to describe the impact and meshing boundary of gears. The impact-meshing situation of the gear system was observed, and the vibration response of the system under different speeds and loads was analysed using numerical simulation. The results revealed that the main source of the gear vibration was the meshing frequency of a gear pair. The resonance generated by the modulation of the rotation and meshing is the main reason for the long-term impact-meshing phenomenon of the gear transmission system. The results of this study are of great significance as they reveal the vibration characteristics of a high-speed gear transmission system.

Research on Gearbox Fault Diagnosis Method Based on VMD and Optimized LSTM

The reliability of gearboxes is extremely important for the normal operation of mechanical equipment. This paper proposes an optimized long short-term memory (LSTM) neural network fault diagnosis method. Additionally, a feature extraction method is employed, utilizing variational mode decomposition (VMD) and permutation entropy (PE). Firstly, the gear vibration signal is subjected to feature decomposition using VMD. Secondly, PE is calculated as a feature quantity output. Next, it is input into the improved LSTM fault diagnosis model, and the LSTM parameters are iteratively optimized using the chameleon search algorithm (CSA). Finally, the output of the fault diagnosis results is obtained. The experimental results show that the accuracy of the method exceeds 97.8%.

A novel resonance attractor evaluation method for traveling wave vibration of thin-walled gears: Modeling and experiments

Thin-walled gears have high power density and are the main gear type in aeronautical applications, but threatened by the traveling wave vibration (TWV). In this paper, a novel resonance attractor evaluation (RAE) method is proposed to describe this dynamics characteristic for the complex thin-walled gear drivetrain. The unsteady responses of the drivetrain are discretized into different time-series subsets, and each subset is reconstructed into a high-dimensional mapping phase space based on the average mutual information and the false nearest neighbor theory. Finally, the TWV is identified from the evolution of attractor features—which are quantified by indicators: the boundary radius and the phase point expansion rate. To verify the proposed method, a high-speed transmission experiment involving thin-walled bevel gears is designed, and the RAE model is established based on the proposed methodology and compared with the experimental results. Results show that this model accurately identifies resonance frequencies and describes rotation speed bands that excite the TWV. The proposed methodology provides a theoretical basis for introducing the phase space reconstruction method into the TWV study and for the safe operation of aero-engine gears.