Torque effect on vibration behavior of high-speed train gearbox under internal and external excitations

The high-speed train transmission system,experiencing both the internal excitation originating from gear meshing and the external excitation originating from the wheel-rail interaction,exhibits complex dynamic behavior in the actual service environment.This paper focuses on the gearbox in the high-speed train to carry out the bench test,in which various operat-ing conditions(torques and rotation speeds)were set up and the excitation condition covering both internal and external was created.Acceleration responses on multiple positions of the gearbox were acquired in the test and the vibration behavior of the gearbox was studied.Meanwhile,a stochastic excitation modal test was also carried out on the test bench under different torques,and the modal parameter of the gearbox was identified.Finally,the sweep frequency response of the gearbox under gear meshing excitation was analyzed through dynamic modeling.The results showed that the torque has an attenuating effect on the amplitude of gear meshing frequency on the gearbox,and the effect of external excitation on the gearbox vibration cannot be ignored,especially under the rated operating condition.It was also found that the torque affects the modal param-eter of the gearbox significantly.The torque has a great effect on both the gear meshing stiffness and the bearing stiffness in the transmission system,which is the inherent reason for the changed modal characteristics observed in the modal test and affects the vibration behavior of the gearbox consequently.

Dynamics and Fault Diagnosis of Railway Vehicle Gearboxes:A Review

The railway vehicle gearbox is an important part of the railway vehicle traction transmission system which ensures the smooth running of railway vehicles.However,as the running speed of railway vehicles continues to increase,the railway vehicle gearbox is exposed to a more demanding operating environment.Under both internal and external excitations,the gearbox is prone to faults such as fatigue cracks,and broken teeth.It is crucial to detect these faults before they result in severe failures and accidents.Therefore,understanding the dynamics and fault diagnosis of railway vehicle gearbox is needed.At present,there is a lack of systematic review of railway vehicle gearbox dynamics and fault diagnosis.So,this paper systematically summarizes the research progress on railway vehicle gearbox dynamics and fault diagnosis.To this end,this paper first summarizes the latest research progress on the dynamics of railway vehicle gearboxes.The dynamics and vibration characteristics of the gearbox are summarized under internal and external excitations,as well as faulty conditions.Then,the stateof-the-art signal processing and artificial intelligence methods for fault diagnosis of railway vehicle gearboxes are reviewed.In the end,future research prospects are given.

Multi-objective Optimization of a Two-Stage Helical Gearbox to Improve Efficiency and Reduce Height

The goal of this research is to look at multi-target optimization of a two-stage helical gearbox in order to determine the best key design elements for reducing gearbox height and enhancing gearbox efficiency.To do this,the method known as Taguchi and GRA(Grey Relation Analysis)were used in two stages to address the problem.The single-objective optimization problem was addressed first to close the gap between variable levels,and then the multi-objective optimization problem was solved to determine the best primary design variables.The first and second stage CWFWs(Coefficients of Wheel Face Width),ACS(Permissible Contact Stresses),and first stage gear ratio were also calculated.The study’s findings were utilized to identify the best values for five critical design aspects of a two-stage helical gearbox.

An Improved Coupled Dynamic Modelling for Exploring Gearbox Vibrations Considering Local Defects

Gearbox is a key part in machinery,in which gear,shaft and bearing operate together to transmit motion and power.The wide usage and high failure rate of gearbox make it attract much attention on its health monitoring and fault diagnosis.Dynamic modelling can study the mechanism under different faults and provide theoretical foundation for fault detection.However,current commonly used gear dynamic model usually neglects the influence of bearing and shaft,resulting in incomplete understanding of gearbox fault diagnosis especially under the effect of local defects on gear and shaft.To address this problem,an improved gear-shaft-bearing-housing dynamic model is proposed to reveal the vibration mechanism and responses considering shaft whirling and gear local defects.Firstly,an eighteen degree-of-freedom gearbox dynamic model is proposed,taking into account the interaction among gear,bearing and shaft.Secondly,the dynamic model is iteratively solved.Then,vibration responses are expounded and analysed considering gear spalling and shaft crack.Numerical results show that the gear mesh frequency and its harmonics have higher amplitude through the spectrum.Vibration RMS and the shaft rotating frequency increase with the spalling size and shaft crack angle in general.An experiment is designed to verify the rationality of the proposed gearbox model.Lastly,comprehensive analysis under different spalling size and shaft crack angle are analysed.Results show that when spalling size and crack angle are larger,RMS and the amplitude of shaft rotating frequency will not increase linearly.The dynamic model can accurately simulate the vibration of gear transmission system,which is helpful for gearbox fault diagnosis.

Measured load spectra of the bearing in high-speed train gearbox under different gear meshing conditions

The load spectrum is a crucial factor for assess-ing the fatigue reliability of in-service rolling element bear-ings in transmission systems.For a bearing in a high-speed train gearbox,a measurement technique based on strain detection of bearing outer ring was used to instrument the bearing and determine the time histories of the distributed load in the bearing under different gear meshing conditions.Accordingly,the load spectrum of the total radial load car-ried by the bearing was compiled.The mean value and class interval of the obtained load spectrum were found to vary non-monotonously with the speed and torque of gear mesh-ing,which was considered to be caused by the vibration of the shaft and the bearing cage.As the realistic service load input of bearing life assessment,the measured load spectrum under different gear meshing conditions can be used to pre-dict gearbox bearing life realistically based on the damage-equivalent principle and actual operating conditions.

Intelligent Fault Diagnosis for Planetary Gearbox Using Transferable Deep Q Network Under Variable Conditions with Small Training Data

Effective fault diagnosis of planetary gearboxes is critical for ensuring the safety and dependability of mechanical drive systems.Nevertheless,variable conditions and inadequate fault data bring huge challenges to its practical fault diagnosis.Taking this into account,this study presents a new intelligent fault diagnosis(IFD)approach for planetary gearbox using a transferable deep Q network(TDQN)that merges deep reinforcement learning(DRL)and transfer learning(TL).First,a DRL environment simulation is designed by a predefined classification Markov decision process.Then,leveraging varied-size convolutions and residual learning,a multiscale residual convolutional neural network agent for TDQN is created to automatically learn meaningful features directly from vibration signals while avoiding model degradation.Next,a large source dataset is obtained from complex conditions,and this agent learns an IFD policy via autonomous interaction with the data environment.Finally,a parameter-based TL strategy is adopted to retrain the model on target datasets with variable conditions and small training data,which is conducted by fine-tuning the model parameters gained from the source task to accomplish target tasks.The results show that this TDQN outperforms not only state-of-the-art methods in a source task with an accuracy of 98.53%but also in two target tasks with 99.63%and 98.37%,respectively.

Numerical Visualization of Grease Flow in a Gearbox

Lubricating greases are widely used in e.g.open gear drives and gearboxes with difficult sealing conditions.The efficiency and heat balance of grease-lubricated gearboxes depend strongly on the lubrication mechanisms channeling and circulating,for which the grease flow is causal.The computational fluid dynamics opens up the possibility to visualize and understand the grease flow in gearboxes in more detail.In this study,a single-stage gearbox lubricated with an NLGI 1-2 grease was modeled by the finite-volume method to numerically investigate the fluid flow.Results show that the rotating gears influence the grease sump only locally around the gears.For a low grease fill volume,the rotation of the gears is widely separated from the grease sump.For a high grease fill volume,a pronounced geargrease interaction results in a circulating grease flow around the gears.The simulated grease distributions show good accordance with high-speed camera recordings.

Characterization,identification and life prediction of acoustic emission signals of tensile damage for HSR gearbox housing material

Purpose-This study aims to ensure the operation safety of high speed trains,it is necessary to carry out nondestructive monitoring of the tensile damage of the gearbox housing material in rail time,yet the traditional tests of mechanical property can hardly meet this requirement.Design/methodology/approach-In this study the acoustic emission(AE)technology is applied in the tensile tests of the gearbox housing material of an high-speed rail(HSR)train,during which the acoustic signatures are acquired for parameter analysis.Afterward,the support vector machine(SVM)classifier is introduced to identify and classify the characteristic parameters extracted,on which basis the SVM is improved and the weighted support vector machine(WSVM)method is applied to effectively reduce the misidentification of the SVM classifier.Through the study of the law of relations between the characteristic values and the tensile life,a degradation model of the gearbox housing material amid tensile is built.Findings-The results show that the growth rate of the logarithmic hit count of AE signals and that of logarithmic amplitude can well characterize the stage of the material tensile process,and the WSVM method can improve the classification accuracy of the imbalanced data to above 94%.The degradation model built can identify the damage occurred to the HSR gearbox housing material amid the tensile process and predict the service life remains.Originality/value-The results of this study provide new concepts for the life prediction of tensile samples,and more further tests should be conducted to verify the conclusion of this research.

Wind Turbine Planetary Gearbox Fault Diagnosis via Proportion-Extracting Synchrosqueezing Chirplet Transform

Wind turbine planetary gearboxes usually work under time-varying conditions,leading to nonstationary vibration signals.These signals often consist of multiple time-varying components with close instantaneous frequencies.Therefore,high-quality time-frequency analysis(TFA)is needed to extract the time-frequency feature from such nonstationary signals for fault diagnosis.However,it is difficult to obtain high-quality timefrequency representations(TFRs)through conventional TFA methods due to low resolution and time-frequency blurs.To address this issue,we propose a new TFA method termed the proportion-extracting synchrosqueezing chirplet transform(PESCT).Firstly,the proportion-extracting chirplet transform is employed to generate highresolution underlying TFRs.Then,the energy concentration of the underlying TFRs is enhanced via the synchrosqueezing transform.Finally,wind turbine planetary gearbox fault can be diagnosed by analysis of the dominant time-varying components revealed by the concentrated TFRs with high resolution.The proposed PESCT is suitable for achieving high-quality TFRs for complicated nonstationary signals.Numerical and experimental analyses validate the effectiveness of the PESCT in characterizing the nonstationary signals from wind turbine planetary gearboxes.

Valuable Impulses and Successful Models of Gearbox Development from Practice

Gears play an important role in mechanical engineering because of their moment and speed transmission possibilities. Design and optimization of a complete gearbox provide many requirements to the designer. The complex gearbox model consists of many machine elements （shafts, gears, bearings, housing, seals, and shaft-hub connections）. The gearbox must be understood as a system with interactive parts. Next to the calculation of kinematics, load capacities and life times of single elements, aspects of load distribution and efficiency and noise excitation of gearboxes become important. The wide range of knowhow needed mostly cannot be covered by a small number of engineers. The development of automated calculation routines with understandable and comprehensive results is the goal for these research projects that lead to sottware-realizing solutions for engineers to efficiently design, calculate, optimize and verify gearboxes with minimal resources in terms of calculation experts and time.

Optimum Determination of Partial Transmission Ratios of Mechanical Driven Systems Using a Chain Drive and a Two-step Helical Gearbox

This paper presents a study on optimum determination of partial ratios of mechanical drive systems using a chain drive and two-step helical gearbox for getting minimum size of the system. The chosen objective function was the cross section dimension of the system. In solving the optimization problem, the design equation for pitting resistance of a gear set was investigated and equations on moment equilibrium condition of a mechanic system including a chain drive and two helical gear units and their regular resistance condition were analyses. From the results of the study, effective formulas for determination of the partial ratios of the chain drive and two-step helical gearboxes were introduced. As the formulas are explicit, the partial ratios can be calculated accurately and simply.

Optimum Determination of Partial Transmission Ratios of Mechanical Driven Systems Using a V-belt and a Helical Gearbox with Second-Step Double Gear-Sets

This paper presents a study on the optimum determination of partial transmission ratios of a mechanical drive system using a V-belt and a helical gearbox with second-step double gear-sets in order to get the minimum size of the system. The chosen objective function was the cross section dimension of the system. In the optimization problem, the design equation for pitting resistance of a gear set was investigated and equations on moment equilibrium condition of a mechanic system including a V-belt and a helical gearbox with second-step double gear-sets and their regular resistance condition were analysed. Based on the results of the study, effective formulas for calculation of the partial ratios of the V-belt and a helical gearbox with second-step double gear-sets were proposed. By using explicit models, the partial ratios can be determined accurately and simply.

Optimum Determination of Partial Transmission Ratios of Mechanical Driven Systems Using a V-belt and a Three-Step Helical Gearbox

This paper introduces a new study on the optimum calculation of partial transmission ratios of a mechanical drive system using a V-belt and a three-step helical gearbox in order to get the minimum size of the system. The chosen objective function was the cross section dimension of the system. In solving the optimization problem, the design equation for pitting resistance of a gear set was investigated and equations on moment equilibrium condition of a mechanic system including a V-belt and three helical gear units and their regular resistance condition were analysed. From the results of the study, effective formulas for determination of the partial ratios of the V-belt and three-step helical gearboxes were introduced. As using explicit models, the partial ratios can be determined accurately and simply.

Optimum Calculation of Partial Transmission Ratios of Mechanical Driven Systems Using a V-belt and a Two-Step Bevel Helical Gearbox

This paper introduces a new study on the optimum calculation of partial transmission ratios of mechanical drive system using a V-belt and two-step bevel helical gearbox for getting minimum size of the system. In the paper, based on moment equilibrium condition of a mechanic system including V-belt and a two-gear-unit of the gearbox, models for optimum calculation of the partial ratios of the V-belt and the gearbox were proposed. As the models are explicit, the partial ratios can be calculated accurately and simply.

Optimum Determination of Partial Transmission Ratios of Coupled Planetary Gearboxes

This paper presents a new study on optimum determination of the partial ratios of coupled planetary gear sets for getting minimum radial size of the gear sets. In this paper, based on moment equilibrium condition of a mechanic system including two-row planetary gear sets and their regular resistance conditions, an explicit model for calculating the partial ratios of coupled planetary gear sets was proposed. In addition, by giving this effective model, the partial ratios can be calculated simply and accurately.

Optimum Determination of Partial Transmission Ratios of Three-Step Helical Gearboxes for Getting Minimum Cross Section Dimension

This paper presents a new study on optimum calculation of partial ratios of three-step helical gearboxes. The chosen objective function is the cross section dimension of the gearbox. In solving the optimization problem, the design equation for pitting resistance of a gear set was investigated and equations on moment equilibrium condition of a mechanic system including three gear units and their regular resistance condition are analyses. From the results of the study, effective formula for determination of the partial ratios of three-step helical gearboxes is introduced. As the formulas are explicit, the partial ratios can be calculated accurately and simply.

Gearbox Fault Diagnosis using Adaptive Zero Phase Time-varying Filter Based on Multi-scale Chirplet Sparse Signal Decomposition

When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To overcome this drawback, the zero phase filter is introduced to the mentioned filter, and a fault diagnosis method for speed-changing gearbox is proposed. Firstly, the gear meshing frequency of each gearbox is estimated by chirplet path pursuit. Then, according to the estimated gear meshing frequencies, an adaptive zero phase time-varying filter(AZPTF) is designed to filter the original signal. Finally, the basis for fault diagnosis is acquired by the envelope order analysis to the filtered signal. The signal consisting of two time-varying amplitude modulation and frequency modulation(AM-FM) signals is respectively analyzed by ATF and AZPTF based on MCSSD. The simulation results show the variances between the original signals and the filtered signals yielded by AZPTF based on MCSSD are 13.67 and 41.14, which are far less than variances (323.45 and 482.86) between the original signals and the filtered signals obtained by ATF based on MCSSD. The experiment results on the vibration signals of gearboxes indicate that the vibration signals of the two speed-changing gearboxes installed on one foundation bed can be separated by AZPTF effectively. Based on the demodulation information of the vibration signal of each gearbox, the fault diagnosis can be implemented. Both simulation and experiment examples prove that the proposed filter can extract a mono-component time-varying AM-FM signal from the multi-component time-varying AM-FM signal without distortion.

Crack Fault Classification for Planetary Gearbox Based on Feature Selection Technique and K-means Clustering Method

During the condition monitoring of a planetary gearbox, features are extracted from raw data for a fault diagnosis.However, different features have different sensitivity for identifying different fault types, and thus, the selection of a sensitive feature subset from an entire feature set and retaining as much of the class discriminatory information as possible has a directly effect on the accuracy of the classification results. In this paper, an improved hybrid feature selection technique(IHFST) that combines a distance evaluation technique(DET), Pearson’s correlation analysis, and an ad hoc technique is proposed. In IHFST, a temporary feature subset without irrelevant features is first selected according to the distance evaluation criterion of DET, and the Pearson’s correlation analysis and ad hoc technique are then employed to find and remove redundant features in the temporary feature subset, respectively, and hence,a sensitive feature subset without irrelevant or redundant features is selected from the entire feature set. Further, the k-means clustering method is applied to classify the different kinds of health conditions. The effectiveness of the proposed method was validated through several experiments carried out on a planetary gearbox with incipient cracks seeded in the tooth root of the sun gear, planet gear, and ring gear. The results show that the proposed method can successfully distinguish the different health conditions of a planetary gearbox, and achieves a better classification performance than other methods. This study proposes a sensitive feature subset selection method that achieves an obvious improvement in terms of the accuracy of the fault classification.

Application of particle swarm optimization blind source separation technology in fault diagnosis of gearbox

Blind source separation (BBS) technology was applied to vibration signal processing of gearbox for separating different fault vibration sources and enhancing fault information. An improved BSS algorithm based on particle swarm optimization (PSO) was proposed. It can change the traditional fault-enhancing thought based on de-noising. And it can also solve the practical difficult problem of fault location and low fault diagnosis rate in early stage. It was applied to the vibration signal of gearbox under three working states. The result proves that the BSS greatly enhances fault information and supplies technological method for diagnosis of weak fault.

Gearbox Deterioration Detection under Steady State,Variable Load, and Variable Speed Conditions

Multiple dominant gear meshing frequencies are present in the vibration signals collected from gearboxes and the conventional spiky features that represent initial gear fault conditions are usually difficult to detect. In order to solve this problem, we propose a new gearbox deterioration detection technique based on autoregressive modeling and hypothesis testing in this paper. A stationary autoregressive model was built by using a normal vibration signal from each shaft. The established autoregressive model was then applied to process fault signals from each shaft of a two-stage gearbox. What this paper investigated is a combined technique which unites a time-varying autoregressive model and a two sample Kolmogorov-Smimov goodness-of-fit test, to detect the deterioration of gearing system with simultaneously variable shaft speed and variable load. The time-varying autoregressive model residuals representing both healthy and faulty gear conditions were compared with the original healthy time-synchronous average signals. Compared with the traditional kurtosis statistic, this technique for gearbox deterioration detection has shown significant advantages in highlighting the presence of incipient gear fault in all different speed shafts involved in the meshing motion under variable conditions.