Gear Vibration Research Articles

Investigating bearing and gear vibrations with a Micro-Electro-Mechanical Systems (MEMS) and machine learning approach

Bearings and gears are the pivotal components of mechanical systems and are prone to faults that can impact the system's overall performance. These components' condition monitoring and fault diagnosis are vital for maintaining system reliability and efficiency. In this research, a MEMS setup is initially developed, comprising a Raspberry Pi 4B+ CPU module, a NucleoF401RET6 MCU, an OLED screen, and an Adxl1002z accelerometer for acquiring vibration signals at the desired sampling frequency stored in the CPU memory. Further, an RF model is also developed to classify different types of faults based on features extracted from the acquired vibration data. The model evaluates the precision and reliability of the MEMS setup in capturing and classifying vibration signals. A detailed signal analysis is also conducted to determine the performance of the developed MEMS setup and to investigate the effect of bearing vibration signature due to gear fault and vice versa. The results indicate that bearing faults cause irregularities in the shaft's rotational speed, leading to modulation of the gear mesh frequency (gmf) of gears mounted on the affected shaft. Conversely, gear faults disrupt the shaft's rotational motion, imposing excessive loads on shaft-supported bearings. These disruptions result in distinct vibration patterns characterised by increased harmonics and side bands within the bearing frequency range. The RF model effectively identifies and classifies faults with high accuracy by leveraging its ability to prioritise the most significant vibrational features, resulting in improved predictive performance and robustness.

Modeling Method of Meshing Stiffness of High Speed Spur Gears

As one of the most important dynamic excitation sources, the gear time-varying mesh stiffness is the key parameter of gear system dynamic model. So how to calculate the gear mesh stiffness accurately is of great importance. Based on Euler beam theory, this paper proposes a primitive calculation algorithm (PCA) to calculate the time-varying mesh stiffness of spur gears. A simplified gear model is developed based on nonlinear strain-displacement relationships, and a finite element program is used to simulate the gear's meshing stiffness. The rationality of this method was verified through finite element analysis. The results indicate that mesh stiffness plays a crucial role in controlling mesh deformation. In view of this, this study lays a theoretical foundation for further analysis of the vibration and noise of gears.

Simulation and experimental analysis of traveling wave resonance of flexible spiral bevel gear system

Considering the traveling wave resonance (TWR) phenomenon of the spiral bevel gear system in the aero engine accessory casing, the flexible spiral bevel gear model is established by three-dimensional (3D) shell element and beam element. The dynamic model of flexible bevel gear system considering the change of meshing teeth pairs in the operating process is established by component mode synthesis (CMS) method and rotational modal projection method. The proposed model is verified by finite element (FE) solid model and experiment test results. On this basis, the TWR phenomenon of the bevel gear system is studied in combination with dynamic response and vibration stress experimental test. The results show that the bevel gear system has 3 nodal diameter resonance speeds within the actual operating speed range, which are one 1st nodal diameter resonance of pinion and two 1st nodal diameter resonance of gear. When the bevel gear system operates at TWR state, the amplitude corresponding to fm ± m·fr (fm is meshing frequency, m is nodal diameter number, fr is shaft rotational frequency) is larger than that corresponding to fm in the Fast Fourier transform (FFT) spectrum of the of the gear foundation vibration stress, and the vibration stress cloud map of the gear foundation shows the corresponding nodal diameter vibration shape. The research results provide a theoretical basis for feature recognition and influence law evaluation of TWR of bevel gear system.

New Multi-Channel VSMFxLMS Algorithm for Vibration Reduction of Gear Systems

At present, the active control of gear vibration mostly relies on existing algorithms. In order to achieve effective vibration reduction of the gear system, particularly during the vibration process, this paper proposes a multi-channel VSMFxLMS algorithm based on the FxLMS algorithm. This novel approach takes into account the time-varying nature of the vibration signal during gear vibration. Adaptive filter power coefficients are updated in a skip-tongue variable-step manner using momentum factors. Firstly, the paper establishes the dynamics model of the gear system and analyzes the nonlinear dynamic characteristics of the system. It then examines the vibration damping effect of the FxLMS algorithm and analyzes its performance under different gear system motion states, considering different step lengths and momentum factors. Lastly, the proposed VSMFxLMS algorithm is compared with the FxLMS algorithm, highlighting the superiority of the former. Overall, this research highlights the potential of a multi-channel VSMFxLMS algorithm in reducing vibrations in gear systems. The study optimizes the performance of gear systems while using advanced control strategies.

Evaluation of Scuffing Load Capacity of Helical Gear Based on the Tribo‐Dynamic Model

ABSTRACTThe scuffing load capacity of gear is closely related to the meshing temperature rise of tooth surface. The key to predict the temperature rise is to establish an accurate meshing temperature rise model. In the paper, a tribo‐dynamic model of helical gear is established through coupling of tooth surface lubrication parameters, and the influence of temperature rise on ambient temperature during meshing process is considered. Then, the effects of oil supply temperature, input speed and torque on tooth surface temperature rise, film thickness, friction excitation and gear dynamic characteristics are discussed. The results show that the temperature rise of the gear is higher during the engaging‐in and engaging‐out regions. Meanwhile, there is local high temperature at the end of the contact line due to the end effect. The vibration of gear along the off‐line‐of‐action direction is mainly determined by friction excitation. With the increase of oil supply temperature, input speed and torque, the risk of scuffing failure increases and the influence of oil supply temperature and input load is more significant. The conclusions of this paper may provide some valuable suggestions for the anti‐gluing failure design of gear in engineering.

Structural design and dynamic analysis of a metal rubber composite gear pair

This paper introduces a metal rubber composite gear for gear vibration reduction. A comprehensive structural design calculation program is developed for the metal rubber composite gear pair. The design incorporates a gap between the tooth ring and the hub to accommodate thermal expansion and contraction, ensuring smooth transmission without jamming or seizing. The design process takes into consideration the compression and damping properties of the metal rubber material. A significant variable in the design process is the relative density of the metal rubber material. It is utilized to calculate the torsional stiffness, starting friction torque, and dynamic performance of the composite gear pair. To guide and optimize the design process, a nine-degree-of-freedom dynamic model is employed for dynamic analysis. The vibration reduction effect of the metal rubber composite gear is validated through numerical simulations and experimental testing. The results confirm the efficacy of the gear in reducing vibrations. This paper provides valuable insights and guidance for future designs focused on gear vibration reduction, paving the way for further advancements in this field.

Unified gear tribo-dynamic of transient mixed lubrication and nonlinear dynamics and its experimental validation

The rapid development of electric drives technology presents new challenges in the domain of vibration and noise suppression within gear trains. Dynamics modeling serves as a crucial method for studying vibration and noise; however, a deficiency exists in adequately considering the interaction between tribology and the dynamics of gear drives in current research endeavors. This article proposes a unified tribo-dynamic approach to facilitate a more realistic and accurate linkage analysis of transient mixed lubrication, friction, flash temperature, stiffness, backlash, and dynamics in gear drives. The TPMD approach is proposed to reduce convergence elapsed time. The meshing stiffness and backlash under transient mixed lubrication are developed and used as additional crucial bridges for the interactions in tribo-dynamic, supplementing the traditional consideration of friction. Gear vibration tests are carried out in both LOA and OLOA directions to validate the accuracy of the proposed model. Comparative analyses with conventional models highlight the advancements of the proposed model. The lubricated meshing stiffness, influenced by the combined effects of dynamics and tribology, exhibits characteristic fluctuations and is significantly lower than the Hertzian meshing stiffness. Tribological characteristics in tribo-dynamic differ notably from quasi-static conditions due to gear vibrations. The proposed tribo-dynamic model reveals higher DTE and vibration in the LOA direction compared to traditional dynamics. The intricate effects of friction, meshing stiffness, and backlash on vibration depend on factors like surface roughness, torque, and rotational speed.

Nonlinear dynamic characteristics analysis method of planetary gear train torsional vibration considering meshing oil film force

Planetary gear train is an important part of automatic transmission. The oil film between teeth is one of the key factors affecting the torsional vibration of planetary gear train. Selecting the appropriate oil film stiffness is of great significance for analyzing the nonlinear dynamic characteristics of planetary gear train. A method for analyzing the nonlinear dynamic characteristics of planetary gear system torsional vibration considering the oil film force between teeth is proposed in this paper. A 3-DOF torsional vibration model of planetary gear train considering oil film is established. In this model, the oil film between teeth is equivalent to a time-varying nonlinear spring-damper element, and nonlinear factors such as backlash and meshing error are also considered. The effects of meshing oil film thickness on oil film stiffness and damping are analyzed, and the torsional vibration characteristics of planetary gear train under different meshing stiffness, meshing damping ratio, and rotational speed are analyzed based on bifurcation diagrams. The results show that in one meshing cycle, the meshing oil film thickness first becomes larger and then becomes smaller. When the meshing oil film thickness increases, the meshing oil film stiffness and the equivalent meshing oil film damping become smaller. The torsional vibration of planetary gear train can be effectively reduced by increasing meshing stiffness, damping ratio, rotational speed within a certain range. This method provides technical support for reducing torsional vibration of planetary gear train and realizing stable transmission of planetary gear train.

Modelling of electromechanical coupling dynamics for high-speed EHT system used in HEV and characteristics analysis

As the development of hybrid electric vehicle (HEV) to high-speed, heavy-load, the electromechanical coupling vibration becomes the bottleneck in high-speed electromechanical hybrid transmission (EHT) system. To explore the dynamics characteristics and optimization direction for high-speed EHT system, an electromechanical coupling dynamics model under multi-source excitations is established with lumped-distributed parameter method and verified with experiment data. The dynamics model shows higher accuracy in both time and frequency domain analysis. On this basis, firstly, the comparison between lumped-shaft and distributed-shaft model is studied under time and frequency domain. Comparing with the lumped-shaft model, the distributed-shaft model shows higher accuracy, and can better reflect the coupling vibration of multi-stage planetary gears (PGs). Secondly, the inherent vibration model is derived, and the effect of electromechanical coupling and high-speed working conditions on inherent vibration characteristics are studied. Thirdly, a new method called ‘machine-electricity-magnet coupling interface’ is proposed to reveal the coupling vibration phenomenon. In addition, the signal of stator current and electromagnetic torque includes the frequency of PGs, which is a basis on the fault diagnosis and state monitor of EHT system. Last but not the least, the vibration acceleration of EHT system is analysed under variable speed and load working conditions. Rotation speed and gear meshing force is found as the main influencing factor of series EHT system, and the specific optimization direction is also given.

Support vector machine-based optimisation of traction gear modifications for multiple-condition electric multiple unit

The traction gear train is subjected to various internal excitations under different traction conditions, such as stiffness excitation, error excitation, meshing shock excitation, and tooth side clearance. The optimal modification scheme is different for each state, and the optimal modification plan based on a single working condition may not be applicable to every working condition. In this paper, we investigate the vibration response characteristics of electric multiple unit gearing under multiple conditions and propose a multi-condition modification scheme. Under different traction conditions, the mapping between gear modification parameters and vibration acceleration in gear transmissions is investigated using support vector machines. Genetic algorithms are used to solve the gear-modifying parameters to minimise the maximum vibration acceleration. A weight assignment principle is proposed to calculate the electric multiple unit traction gear transmission under different conditions, with the operating time and the amount of vibration in each condition as the measurement index. The results of the simulation show that the vibration acceleration under continuous conditions is reduced by 3.55 m/s2, a decrease of 69.88%; the vibration acceleration under high-speed conditions is reduced by 3.301 m/s2, a reduction of 58.74%, and the results show that the overall index of the electric multiple unit traction gear transmission system under different conditions has been improved after the optimisation of the multi-conditions modification, the gear transmission system's vibration is significantly reduced.

Effect of tooth surface wear on dynamic characteristics of spur gear transmission system

The meshing stiffness and system dynamic characteristics caused by gear wear fault are studied. Firstly, potential energy method was used to model and solve the meshing stiffness of gears and the effect of wear on the meshing stiffness and static transfer error was analyzed. A 6-dof spur gear dynamics model was established considering various nonlinear factors, and the dynamic responses of the spur gear system under various wear degrees were analyzed by using time domain, spectrum, phase plane, and Poincare mapping. Finally, the visual test platform of the gear box is built, and the wear condition and dynamic response of the gear box under different wear cycles are analyzed. Results show that the meshing stiffness of gear decreases due to wear, and the meshing stiffness of double tooth decreases more than that of single tooth. In addition, the static transmission errors caused by wear changes periodically with meshing frequency. Wear causes the vibration response of gear system to become complex gradually, and the nonlinear of the system is enhanced, which changes from single period motion to quasi period motion. Results can provide theoretical support for gear wear reduction, life extension, vibration reduction, and noise reduction and lubrication improvement.

Anomaly Detection and Remaining Useful Life Estimation for the Health and Usage Monitoring Systems 2023 Data Challenge.

Gear fault detection and remaining useful life estimation are important tasks for monitoring the health of rotating machinery. In this study, a new benchmark for endurance gear vibration signals is presented and made publicly available. The new dataset was used in the HUMS 2023 conference data challenge to test anomaly detection algorithms. A survey of the suggested techniques is provided, demonstrating that traditional signal processing techniques interestingly outperform deep learning algorithms in this case. Of the 11 participating groups, only those that used traditional approaches achieved good results on most of the channels. Additionally, we introduce a signal processing anomaly detection algorithm and meticulously compare it to a standard deep learning anomaly detection algorithm using data from the HUMS 2023 challenge and simulated signals. The signal processing algorithm surpasses the deep learning algorithm on all tested channels and also on simulated data where there is an abundance of training data. Finally, we present a new digital twin that enables the estimation of the remaining useful life of the tested gear from the HUMS 2023 challenge.

A distinguished deep learning method for gear fault classification using time–frequency representation

Fault diagnosis of gearboxes has attracted increasing interest in recent decades due to their ubiquity and importance in the industry. Modern research trends focus on developing a diagnosis system that works automatically with the application of artificial intelligence. These previous studies have used the Deep Learning (DL) network without adequately addressing noise of the input data, requiring more data to achieve effective training. Thus, this work proposes a novel Transfer Learning method using the time–frequency representation of gear vibration signals, which enables more accurate classification in complex working conditions and reduces necessary input data to train. Using fine-tuning techniques proposed in this paper requires only a limited data set while ensuring acceptable classification results. An experiment test rig within different gear faults and load conditions was set up to evaluate the algorithm’s effectiveness.

Evaluation of vibration behavior at different sensing positions on gearboxes

Monitoring systems for rolling contacts in machinery are widespread. There are multiple solutions in various applications like Health Usage Monitoring Systems (HUMS) for Helicopters and smart bearings from different manufacturers. The number of solutions and possibilities is rising. This paper outlines how the vibrational behavior depends on the measuring position outside and inside the gearbox. The effect of the sensor location is evaluated by examining different locations close to the main excitation of gearboxes—the loaded tooth contact—as well as positions on the gearbox housing. Based on the results, recommendations for an optimal sensor position for gear vibration monitoring are given by considering the efforts of sensor integration. The results can be used to select sensors with the lowest cost to support the widespread gear vibration monitoring.Important locations for health monitoring are the gear meshes inside the gearbox. Due to the requirement of high power density, a compact design is mandatory. This does not allow for sensor application close to the gear meshes but only on the outside of the gearbox. An impediment of signal quality and less chance of early damage detection is the consequence. Hence, efforts have been made to directly integrate multiple sensors inside the gear body without negatively impacting the package.For the investigation of the vibration transmission behavior, an FZG gear test rig is selected. These standardized test rigs are approved and established all around the world for the creation and evaluation of various gear failure data. The presented test rig has been modified to be able to sense vibration in the gear wheel, at the gear wheel, and on the gearbox housing to evaluate different sensor positions and vibration sensors for their suitability on vibration measurement.

A high-speed gear reshaping method for electric vehicles combining the effects of input torque and speed variation.

In this study, we introduce an optimization method for high-speed gear trimming in electric vehicles, focusing on variations in input torque and speed. This approach is designed to aid in vibration suppression in electric vehicle gears. We initially use Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA) to investigate meshing point localization, considering changes in gear tooth surface and deformations due to load. Based on impact mechanics theory, we then derive a formula for the maximum impact force. A 12-degree-of-freedom bending-torsion-axis coupled dynamic model for the helical gear drive in the gearbox's input stage is developed using the centralized mass method, allowing for an extensive examination of high-speed gear vibration characteristics. Through a genetic algorithm, we optimize the tooth profile and tooth flank parabolic modification coefficients, resulting in optimal vibration-suppressing tooth surfaces. Experimental results under various input torques and speeds demonstrate that the overall vibration amplitude is stable and lower than that of conventional gear shaping methods. Specifically, the root mean square of vibration acceleration along the meshing line under different conditions is 58.02 m/s2 and 20.33 m/s2, respectively. The vibration acceleration in the direction of the meshing line is 20.33 m/s2 and 20.02 m/s2 under varying torques and speeds, with 20.33 m/s2 being the lowest. Furthermore, the average magnitude of the meshing impact force is significantly reduced to 5015.2. This high-speed gear reshaping method not only enhances gear dynamics and reliability by considering changes in input torque and speed but also effectively reduces vibration in electric vehicle gear systems. The study provides valuable insights and methodologies for the design and optimization of electric vehicle gears, focusing on comprehensive improvement in dynamic performance.

Research on a Wind Turbine Gearbox Fault Diagnosis Method Using Singular Value Decomposition and Graph Fourier Transform.

Gearboxes operate in challenging environments, which leads to a heightened incidence of failures, and ambient noise further compromises the accuracy of fault diagnosis. To address this issue, we introduce a fault diagnosis method that employs singular value decomposition (SVD) and graph Fourier transform (GFT). Singular values, commonly employed in feature extraction and fault diagnosis, effectively encapsulate various fault states of mechanical equipment. However, prior methods neglect the inter-relationships among singular values, resulting in the loss of subtle fault information concealed within. To precisely and effectively extract subtle fault information from gear vibration signals, this study incorporates graph signal processing (GSP) technology. Following SVD of the original vibration signal, the method constructs a graph signal using singular values as inputs, enabling the capture of topological relationships among these values and the extraction of concealed fault information. Subsequently, the graph signal undergoes a transformation via GFT, facilitating the extraction of fault features from the graph spectral domain. Ultimately, by assessing the Mahalanobis distance between training and testing samples, distinct defect states are discerned and diagnosed. Experimental results on bearing and gear faults demonstrate that the proposed method exhibits enhanced robustness to noise, enabling accurate and effective diagnosis of gearbox faults in environments with substantial noise.

Mathematical Complexities in Modelling Damage in Spur Gears

Analytical modelling is an effective approach to obtaining a gear dynamic response or vibration pattern for health monitoring and useful life prediction. Many researchers have modelled this response with various fault conditions commonly observed in gears. The outcome of such models provides a good idea about the changes in the dynamic response available between different gear health states. Hence, a catalogue of the responses is currently available, which ought to aid predictions of the health of actual gears by their vibration patterns. However, these analytical models are limited in providing solutions to useful life prediction. This may be because a majority of these models used single fault conditions for modelling and are not valid to predict the remaining life of gears undergoing more than one fault condition. Existing reviews related to gear faults and dynamic modelling can provide an overview of fault modes, methods for modelling and health prediction. However, these reviews are unable to provide the critical similarities and differences in the single-fault dynamic models to ascertain the possibility of developing models under combined fault modes. In this paper, existing analytical models of spur gears are reviewed with their associated challenges to predict the gear health state. Recommendations for establishing more realistic models are made especially in the context of modelling combined faults and their possible impact on gear dynamic response and health prediction.

Study on the contact performance of the variable hyperbolic circular arc tooth trace cylindrical gear with installation errors

Abstract. Installation errors are important factor for the contact performance of the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear; the study of the relationship between installation errors and contact performances is beneficial for gear vibration and noise reduction. Firstly, based on the meshing theory, the tooth surface equation and contact ellipse of the VH-CATT cylindrical gear were deduced, and the tooth surface imprinting experiment was realized. Next, the tooth contact analysis model of the VH-CATT cylindrical gear was developed to investigate the influence of the installation errors on the elliptical contact area. Then, the calculation formulas of the tooth surface gap and contact point flexibility matrix were carried out to develop the load tooth contact analysis model of the VH-CATT cylindrical gear. Finally, the influence of the installation errors on the load distribution was investigated. Research shows that the elliptical contact area of the VH-CATT cylindrical gear is a line contact within a certain range and is located in the middle section of the tooth width. The elliptical contact area of the VH-CATT cylindrical gear increases or decreases rapidly when meshing in and out, and all the installation errors have a certain influence on the elliptical contact area, except for the center distance error. The single-tooth meshing area with the installation errors is greater than that of the ideal gear pair. The load distribution area with the installation errors deviates from the middle section, except for the center distance error. The installation rotation errors around the x and y axis have a certain influence on the maximum load of the single-tooth meshing area. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimizing the design.

Influence of gear modification on dynamic characteristics of star gearing system in geared turbofan (GTF) gearbox based on a closed-loop dynamic analysis method

The star gearing transmission system is a key component of a geared turbofan (GTF) aero-engine. Accurate prediction of the dynamic characteristics of the star gearing transmission system, especially after gear modification, is important for the design of high-performance engines. Firstly, this paper establishes a dynamic time-varying mesh stiffness (TVMS) and a comprehensive transmission error (TE) calculation model for herringbone gear pair considering changes in the meshing state. Then, the dynamic internal excitation calculation model is combined with the lumped parameter dynamic model of the system to form the “excitation–response–feedback” closed-loop coupling dynamic analysis method of the GTF star gearing system. Compared with traditional analysis methods, this method takes into account the effect of contact state changes on internal excitation during the calculation process and corrects internal excitation in real time. Finally, the effect of different topology modification schemes on the system's dynamic characteristics is investigated based on this method. The results show that the closed-loop coupled dynamics analysis method is able to capture contact state changes of the same gear pair at different moments and between different gear pairs at the same moment. Modified #2 is only to modify the planet gear. This scheme can effectively reduce the vibration displacement of the ring gear, and reduce the peak-to-peak value of the ring gear's vibration displacement in all directions by more than 70%. At the same time, the scheme also reduces the load-sharing coefficient of the internal and external meshing pairs of the system by 1.92% and 2.01%, respectively, and the peak-to-peak value of the dynamic factor of the internal and external meshing pairs can be reduced by 57.91% at most.

Stochastic Optimization-Based Comparative Study of New Energy Vehicles’ Noise Characteristics

The gearbox gearbox transmission system, which is the foundation of a new energy vehicle, is responsible for the crucial duty of power transmission. In reality, the reducer gearbox system is the primary source of noise inside cars because of the design of the system, mistakes made during manufacturing and assembly, and gear engagement impulses. The research target is the second-stage retarder gearbox system of a new energy vehicle. A three-dimensional model of the retarder gearbox system is created using the Romax software.Static and dynamic analyses were carried out in Romax software based on the five typical conditions of start, acceleration, equal speed, deceleration, and stop in order to derive performance data such as maximum contact and bending stresses of the gears, single-position length load distribution, gearbox error, etc. In the NVH analysis, the system’s vibration acceleration was ascertained using the findings of the gearbox error analysis. In order to provide comparative data for vibration and noise reduction of gear modification, the comparative study analyses the data output results under various working conditions and analyses the relationship between gear engagement force and gear vibration.