Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional mo...Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional motions of each axis in the higher-order topology modification technique and how to accurately add the different movements expressed in the form of higher-order polynomials to the corresponding motion axes of the machine tool,a flexible higher-order gear topology modification technique based on an electronic gearbox is proposed.Firstly,a two-parameter topology gear surface equation and a grinding model of wheel grinding gears are established,and the axial feed and tangential feed are expressed in a fifth-order polynomial formula.Secondly,the polynomial coefficients are solved according to the characteristics of the point contact when grinding gears.Finally,an improved electronic gearbox model is constructed by combining the polynomial interpolation function to achieve gear topology modification.The validity and feasibility of the modification method based on the electronic gearbox are verified by experimental examples,which is of great significance for the machining of modification gears based on the continuous generative grinding method of the worm grinding wheel.展开更多
This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Op...This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Optimization(SFO)algorithm.The primary objective is to address multi-objective optimization challenges within mechanical engineering,with a specific emphasis on planetary gearbox optimization.The algorithm is equipped with the ability to dynamically select the optimal mutation operator,contingent upon an adaptive normalized population spacing parameter.The efficacy of HMODESFO has been substantiated through rigorous validation against estab-lished industry benchmarks,including a suite of Zitzler-Deb-Thiele(ZDT)and Zeb-Thiele-Laumanns-Zitzler(DTLZ)problems,where it exhibited superior performance.The outcomes underscore the algorithm’s markedly enhanced optimization capabilities relative to existing methods,particularly in tackling highly intricate multi-objective planetary gearbox optimization problems.Additionally,the performance of HMODESFO is evaluated against selected well-known mechanical engineering test problems,further accentuating its adeptness in resolving complex optimization challenges within this domain.展开更多
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...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.展开更多
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 th...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.展开更多
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 ...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.展开更多
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...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.展开更多
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 s...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.展开更多
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. ...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.展开更多
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...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.展开更多
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 p...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.展开更多
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 proble...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.展开更多
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 o...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.展开更多
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...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.展开更多
China manned space station is designed to operate for over ten years. Long-term and sustainable research on space science and technology will be conducted during its operation. The application payloads must meet the ...China manned space station is designed to operate for over ten years. Long-term and sustainable research on space science and technology will be conducted during its operation. The application payloads must meet the ‘‘long life and high reliability" mission requirement. Gearbox machinery is one of the essential devices in an aerospace utilization system, failure of which may lead to downtime loss even during some disastrous catastrophes. A fault diagnosis of gearbox has attracted attentions for its significance in preventing catastrophic accidents and guaranteeing sufficient maintenance. A novel fault diagnosis method based on the Ensemble Multi-Fault Features Indexing(EMFFI) approach is proposed for the condition monitoring of gearboxes. Different from traditional methods of signal analysis in the one-dimensional space, this study employs a supervised learning method to determine the faults of a gearbox in a two-dimensional space using the classification model established by training the features extracted automatically from diagnostic vibration signals captured. The proposed method mainly includes the following steps. First, the vibration signals are transformed into a bi-spectrum contour map utilizing bi-spectrum technology,which provides a basis for the following image-based feature extraction. Then, Speeded-Up Robustness Feature(SURF) is applied to automatically extract the image feature points of the bi-spectrum contour map using a multi-fault features indexing theory, and the feature dimension is reduced by Linear Discriminant Analysis(LDA). Finally, Random Forest(RF) is introduced to identify the fault types of the gearbox. The test results verify that the proposed method based on the multi-fault features indexing approach achieves the target of high diagnostic accuracy and can serve as a highly effective technique to discover faults in a gearbox machinery such as a two-stage one.展开更多
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 parti...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.展开更多
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...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.展开更多
For the fatigue failure and tribological property of a rolling element bearing,the contact load variation plays a significant role while the most loaded position of the bearing outer raceway takes the greatest risk of...For the fatigue failure and tribological property of a rolling element bearing,the contact load variation plays a significant role while the most loaded position of the bearing outer raceway takes the greatest risk of failure.This paper focuses on the variation in contact load on the most loaded position of the outer raceway of a gearbox bearing in high-speed train.Under operation conditions of different input speeds and torques,the dynamic contact load distribution in a gearbox bearing of high-speed train was measured by instrumenting the bearing with strain gauges.The most loaded position was identified accordingly and the features and reasons of the variation in contact load on this position were suggested.Three factors were found to have varying degrees of impact on the contact load variation under different gear meshing conditions:modal vibration of the cage or shaft,radial geometrical differences among the rollers and vibration of the gearbox housing.展开更多
Considerable studies have been carried out on fault diagnosis of gears, with most of them concentrated on conventional vibration analysis. However, besides the complexity of gear dynamics, the diagnosis results in ter...Considerable studies have been carried out on fault diagnosis of gears, with most of them concentrated on conventional vibration analysis. However, besides the complexity of gear dynamics, the diagnosis results in terms of vibration signal are easily misjudged owing to the interference of sensor position or other components. In this paper, an alternative gearbox fault detection method based on the instantaneous rotational speed is proposed because of its advantages over vibration analysis. Depending on the timer/counter-based method for the pulse signal of the optical encoder, the varying rotational speed can be obtained e ectively. Owing to the coupling and meshing of gears in transmission, the excitations are the same for the instantaneous rotational speed of the input and output shafts. Thus, the di erential signal of instantaneous rotational speeds can be adopted to eliminate the e ect of the interference excitations and extract the associated feature of the localized fault e ectively. With the experiments on multistage gearbox test system, the di erential signal of instantaneous speeds is compared with other signals. It is proved that localized faults in the gearbox generate small angular speed fluctuations, which are measurable with an optical encoder. Using the di erential signal of instantaneous speeds, the fault characteristics are extracted in the spectrum where the deterministic frequency component and its harmonics corresponding to crack fault characteristics are displayed clearly.展开更多
On the basis of each gear's failure correlation, the reliability Copula model of a wind turbine gearbox is established and a 1.5 MW wind turbine gearbox is taken as the research object. Firstly, based on the dynam...On the basis of each gear's failure correlation, the reliability Copula model of a wind turbine gearbox is established and a 1.5 MW wind turbine gearbox is taken as the research object. Firstly, based on the dynamic reliability model of mechanical parts, each gear's life distribution function of a wind turbine gearbox is obtained.The life distribution function can be used as the marginal distributions of the system's joint distribution. Secondly,Copula function is introduced to describe the failure correlation between parts, and the appropriate Copula function is selected according to the shape characters of Copula probability density function. Finally, the wind turbine gearbox system is divided into three parts according to the failure correlation of each gear. The Sklar theorem and the thought of step by step analysis are used to obtain the reliability Copula model for a wind turbine gearbox based on failure correlation.展开更多
基金Projects(52275483,52075142,U22B2084)supported by the National Natural Science Foundation of ChinaProject(JZ2023HGPA0292)supported by the Fundamental Research Funds for the Central Universities of China。
文摘Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional motions of each axis in the higher-order topology modification technique and how to accurately add the different movements expressed in the form of higher-order polynomials to the corresponding motion axes of the machine tool,a flexible higher-order gear topology modification technique based on an electronic gearbox is proposed.Firstly,a two-parameter topology gear surface equation and a grinding model of wheel grinding gears are established,and the axial feed and tangential feed are expressed in a fifth-order polynomial formula.Secondly,the polynomial coefficients are solved according to the characteristics of the point contact when grinding gears.Finally,an improved electronic gearbox model is constructed by combining the polynomial interpolation function to achieve gear topology modification.The validity and feasibility of the modification method based on the electronic gearbox are verified by experimental examples,which is of great significance for the machining of modification gears based on the continuous generative grinding method of the worm grinding wheel.
基金supported by the Serbian Ministry of Education and Science under Grant No.TR35006 and COST Action:CA23155—A Pan-European Network of Ocean Tribology(OTC)The research of B.Rosic and M.Rosic was supported by the Serbian Ministry of Education and Science under Grant TR35029.
文摘This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Optimization(SFO)algorithm.The primary objective is to address multi-objective optimization challenges within mechanical engineering,with a specific emphasis on planetary gearbox optimization.The algorithm is equipped with the ability to dynamically select the optimal mutation operator,contingent upon an adaptive normalized population spacing parameter.The efficacy of HMODESFO has been substantiated through rigorous validation against estab-lished industry benchmarks,including a suite of Zitzler-Deb-Thiele(ZDT)and Zeb-Thiele-Laumanns-Zitzler(DTLZ)problems,where it exhibited superior performance.The outcomes underscore the algorithm’s markedly enhanced optimization capabilities relative to existing methods,particularly in tackling highly intricate multi-objective planetary gearbox optimization problems.Additionally,the performance of HMODESFO is evaluated against selected well-known mechanical engineering test problems,further accentuating its adeptness in resolving complex optimization challenges within this domain.
文摘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.
文摘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.
基金supported by National Key R&D Program of China (No.2022YFB3303600)the Fundamental Research Funds for the Central Universities (No.2022CDJKYJH048).
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 71271078)National Hi-tech Research and Development Program of China (863 Program, Grant No. 2009AA04Z414)Integration of Industry, Education and Research of Guangdong Province, and Ministry of Education of China (Grant No. 2009B090300312)
文摘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.
基金Supported by National Natural Science Foundation of China(Grant No.51475053)
文摘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.
基金supported by Chinese Academy of Sciences(CAS)Pioneer Hundred Talents Program(No.2017-112)
文摘China manned space station is designed to operate for over ten years. Long-term and sustainable research on space science and technology will be conducted during its operation. The application payloads must meet the ‘‘long life and high reliability" mission requirement. Gearbox machinery is one of the essential devices in an aerospace utilization system, failure of which may lead to downtime loss even during some disastrous catastrophes. A fault diagnosis of gearbox has attracted attentions for its significance in preventing catastrophic accidents and guaranteeing sufficient maintenance. A novel fault diagnosis method based on the Ensemble Multi-Fault Features Indexing(EMFFI) approach is proposed for the condition monitoring of gearboxes. Different from traditional methods of signal analysis in the one-dimensional space, this study employs a supervised learning method to determine the faults of a gearbox in a two-dimensional space using the classification model established by training the features extracted automatically from diagnostic vibration signals captured. The proposed method mainly includes the following steps. First, the vibration signals are transformed into a bi-spectrum contour map utilizing bi-spectrum technology,which provides a basis for the following image-based feature extraction. Then, Speeded-Up Robustness Feature(SURF) is applied to automatically extract the image feature points of the bi-spectrum contour map using a multi-fault features indexing theory, and the feature dimension is reduced by Linear Discriminant Analysis(LDA). Finally, Random Forest(RF) is introduced to identify the fault types of the gearbox. The test results verify that the proposed method based on the multi-fault features indexing approach achieves the target of high diagnostic accuracy and can serve as a highly effective technique to discover faults in a gearbox machinery such as a two-stage one.
基金Project(50875247) supported by the National Natural Science Foundation of ChinaProject(2007011070) supported by the Natural Science Foundation of Shanxi Province, China
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 50675232)Key Project of Ministry of Education of ChinaChongqing Municipal Natural Science Key Foundation of China (Grant No. 2007BA6021)
文摘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.
基金This research was supported by the Joint Funds of the National Natural Science Foundation of China(Grant U1834202).
文摘For the fatigue failure and tribological property of a rolling element bearing,the contact load variation plays a significant role while the most loaded position of the bearing outer raceway takes the greatest risk of failure.This paper focuses on the variation in contact load on the most loaded position of the outer raceway of a gearbox bearing in high-speed train.Under operation conditions of different input speeds and torques,the dynamic contact load distribution in a gearbox bearing of high-speed train was measured by instrumenting the bearing with strain gauges.The most loaded position was identified accordingly and the features and reasons of the variation in contact load on this position were suggested.Three factors were found to have varying degrees of impact on the contact load variation under different gear meshing conditions:modal vibration of the cage or shaft,radial geometrical differences among the rollers and vibration of the gearbox housing.
基金Supported by National Natural Science Foundation of China(Grant No.51575438)China Postdoctoral Science Foundation(Grant Nos.2017M623159,2018T111046)Shaanxi Provincial Postdoctoral Science Foundation of China(Grant No.2017BSHEDZZ68)
文摘Considerable studies have been carried out on fault diagnosis of gears, with most of them concentrated on conventional vibration analysis. However, besides the complexity of gear dynamics, the diagnosis results in terms of vibration signal are easily misjudged owing to the interference of sensor position or other components. In this paper, an alternative gearbox fault detection method based on the instantaneous rotational speed is proposed because of its advantages over vibration analysis. Depending on the timer/counter-based method for the pulse signal of the optical encoder, the varying rotational speed can be obtained e ectively. Owing to the coupling and meshing of gears in transmission, the excitations are the same for the instantaneous rotational speed of the input and output shafts. Thus, the di erential signal of instantaneous rotational speeds can be adopted to eliminate the e ect of the interference excitations and extract the associated feature of the localized fault e ectively. With the experiments on multistage gearbox test system, the di erential signal of instantaneous speeds is compared with other signals. It is proved that localized faults in the gearbox generate small angular speed fluctuations, which are measurable with an optical encoder. Using the di erential signal of instantaneous speeds, the fault characteristics are extracted in the spectrum where the deterministic frequency component and its harmonics corresponding to crack fault characteristics are displayed clearly.
基金the National Natural Science Foundation of China(No.51265025)
文摘On the basis of each gear's failure correlation, the reliability Copula model of a wind turbine gearbox is established and a 1.5 MW wind turbine gearbox is taken as the research object. Firstly, based on the dynamic reliability model of mechanical parts, each gear's life distribution function of a wind turbine gearbox is obtained.The life distribution function can be used as the marginal distributions of the system's joint distribution. Secondly,Copula function is introduced to describe the failure correlation between parts, and the appropriate Copula function is selected according to the shape characters of Copula probability density function. Finally, the wind turbine gearbox system is divided into three parts according to the failure correlation of each gear. The Sklar theorem and the thought of step by step analysis are used to obtain the reliability Copula model for a wind turbine gearbox based on failure correlation.
