In this paper,the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system.A simplified model of the dual-rotor syst...In this paper,the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system.A simplified model of the dual-rotor system is proposed by considering that there is a local defect on the inner ring of inter-shaft bearing.The local defect is modelled as an inverted isosceles trapezoidal groove,which can make great influence on the inter-shaft bearing force due to the change of radial clearance of the inter-shaft bearing.The motion equations of the dual-rotor system are formulated by using the Lagrange equation.The Runge-Kutta method is employed to solve the motion equation.The amplitude-frequency response curve of the dual-rotor system is obtained,the abnormal resonance characteristics are analyzed.In addition,the influence of defect parameters,rotors and support parameters and inter-shaft bearing parameters on the amplitude-frequency characteristics of the system are discussed.The results show that there are two main resonance peaks and four abnormal resonance peaks on the amplitude-frequency response curve of the dual-rotor with a local defect on the inner ring of the inter-shaft bearing.Through analyzing the vibration response of the abnormal resonance peaks,it is found that the first two abnormal resonances are caused by the combined resonance,which are related to the inner ring fault and the rotational speed of high or low pressure rotors,and the last two resonances are caused by the induced resonance of the inner ring fault.At the same time,when the parameters of defect,rotors and support and inter-shaft bearing change,the resonance of the system also shows the corresponding change law.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
The studies on dynamics of a fault bearing system are prevalent in recent years, however, we are studying a completely different frequency range than the one where the bearing faults are best seen. Considering a local...The studies on dynamics of a fault bearing system are prevalent in recent years, however, we are studying a completely different frequency range than the one where the bearing faults are best seen. Considering a local defect on outer raceway,a two-degree-of-freedom analytical model of a rigid-rotor ball bearing system is established. Three pulse force models are introduced to simulate the local defect. The frequency domain method—harmonic balance method with alternating frequency/time domain technique (HB-AFT) is used to calculate the response in a large frequency range. By comparing the performance at different frequencies, the fault systems with different defect models and parameters reveal the super-harmonic resonances,and the reasons for this phenomenon are uncovered as well. Finally, the theoretical calculation is verified qualitatively by the experimental results, through comparing the frequency spectrums of the defective bearing rotor system to the fault-free one.Therefore, the super-harmonic resonances can be regarded as a dynamic feature. Besides, the obvious super-harmonic resonances indicate the magnification of the harmonics of the "characteristic defect frequency" for outer race in the corresponding speed regions, which may be helpful for the diagnosis of a rotor ball bearing system with a local defect.展开更多
The isothermal local loading forming technology provides a feasible way to form Ti-alloy large-scale rib-web components in aerospace and aviation fields.However,the local loading process forming limit is restricted by...The isothermal local loading forming technology provides a feasible way to form Ti-alloy large-scale rib-web components in aerospace and aviation fields.However,the local loading process forming limit is restricted by forming defects in the transitional region.In this work,the feasibility of controlling forming defects and improving the process forming limit by adjusting die parameters is explored through finite element（FE） simulation.It is found that the common cavum and folding defects in the transitional region are significantly influenced by the fillet radii of left rib and middle rib,respectively.The cavum and folding defects can be effectively controlled by increasing the fillet radii of left rib and middle rib,respectively.The process forming limits considering forming defects in the transitional region are determined by the stepwise searching method under various die parameters.Moreover,the relationship between the process forming limit and die parameters is developed through the response surface methodology（RSM）.The developed RSM models suggest that increasing the fillet radii of left and middle ribs is effective to improve the process forming limit during local loading forming of rib-web components.The results will provide technical basis for the design of die parameters and the reduction amount,which is of great importance to control forming defects and improve the process forming limit in local loading forming of Ti-alloy large-scale rib-web components.展开更多
A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity.By introducing the local thickness defects function of the micro-beam,the variable coeffici...A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity.By introducing the local thickness defects function of the micro-beam,the variable coefficient differential equations of the buckling problem are obtained with the variational principle.Combining the eigensolution series of the complete micro-beam with the Galerkin method,we obtain the critical load and buckling modes of the micro-beam with defects.The results show that the depth and location of the defect are the main factors affecting the critical load,and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam.The effect of defect location on buckling is related to the axial gradient of the rotation angle,and defects should be avoided at the maximum axial gradient of the rotation angle.The model and method are also applicable to the static deformation and vibration of the micro-beam.展开更多
In this paper, we present a tire defect detection algorithm based on sparse representation. The dictionary learned from reference images can efficiently represent the test image. As the representation coefficients of ...In this paper, we present a tire defect detection algorithm based on sparse representation. The dictionary learned from reference images can efficiently represent the test image. As the representation coefficients of normal images have a specific distribution, the local feature can be estimate by comparing representation coefficient distribution. Meanwhile, a coding length is used to measure the global features of representation coefficients. The tire defect is located by both these local and global features. Experimental results demonstrate that the proposed method can accurately detect and locate the tire defects.展开更多
基金supported by the National Natural Science Foundation of China(No.11972129)the National Science and Technology Major Project,China(No.2017-Ⅳ-00080045)。
文摘In this paper,the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system.A simplified model of the dual-rotor system is proposed by considering that there is a local defect on the inner ring of inter-shaft bearing.The local defect is modelled as an inverted isosceles trapezoidal groove,which can make great influence on the inter-shaft bearing force due to the change of radial clearance of the inter-shaft bearing.The motion equations of the dual-rotor system are formulated by using the Lagrange equation.The Runge-Kutta method is employed to solve the motion equation.The amplitude-frequency response curve of the dual-rotor system is obtained,the abnormal resonance characteristics are analyzed.In addition,the influence of defect parameters,rotors and support parameters and inter-shaft bearing parameters on the amplitude-frequency characteristics of the system are discussed.The results show that there are two main resonance peaks and four abnormal resonance peaks on the amplitude-frequency response curve of the dual-rotor with a local defect on the inner ring of the inter-shaft bearing.Through analyzing the vibration response of the abnormal resonance peaks,it is found that the first two abnormal resonances are caused by the combined resonance,which are related to the inner ring fault and the rotational speed of high or low pressure rotors,and the last two resonances are caused by the induced resonance of the inner ring fault.At the same time,when the parameters of defect,rotors and support and inter-shaft bearing change,the resonance of the system also shows the corresponding change law.
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.
基金supported by the National Key Basic Research Program of China (Grant No. 2015CB057400)the National Natural Science Foundation of China (Grant No. 11602070)China Postdoctoral Science Foundation(Grant No. 2016M590277).
文摘The studies on dynamics of a fault bearing system are prevalent in recent years, however, we are studying a completely different frequency range than the one where the bearing faults are best seen. Considering a local defect on outer raceway,a two-degree-of-freedom analytical model of a rigid-rotor ball bearing system is established. Three pulse force models are introduced to simulate the local defect. The frequency domain method—harmonic balance method with alternating frequency/time domain technique (HB-AFT) is used to calculate the response in a large frequency range. By comparing the performance at different frequencies, the fault systems with different defect models and parameters reveal the super-harmonic resonances,and the reasons for this phenomenon are uncovered as well. Finally, the theoretical calculation is verified qualitatively by the experimental results, through comparing the frequency spectrums of the defective bearing rotor system to the fault-free one.Therefore, the super-harmonic resonances can be regarded as a dynamic feature. Besides, the obvious super-harmonic resonances indicate the magnification of the harmonics of the "characteristic defect frequency" for outer race in the corresponding speed regions, which may be helpful for the diagnosis of a rotor ball bearing system with a local defect.
基金the support of the National Natural Science Foundation of China(Nos.51605388,51675433)111 Project(B08040)+2 种基金the Research Fund of the State Key Laboratory of Solidification Processing(NWPU)in China(Grant No.131-QP-2015)the Fundamental Research Funds for the Central Universitiesthe Open Research Fund of State Key Laboratory of Materials Processing and Die&Mold Technology at Huazhong University of Science and Technology
文摘The isothermal local loading forming technology provides a feasible way to form Ti-alloy large-scale rib-web components in aerospace and aviation fields.However,the local loading process forming limit is restricted by forming defects in the transitional region.In this work,the feasibility of controlling forming defects and improving the process forming limit by adjusting die parameters is explored through finite element（FE） simulation.It is found that the common cavum and folding defects in the transitional region are significantly influenced by the fillet radii of left rib and middle rib,respectively.The cavum and folding defects can be effectively controlled by increasing the fillet radii of left rib and middle rib,respectively.The process forming limits considering forming defects in the transitional region are determined by the stepwise searching method under various die parameters.Moreover,the relationship between the process forming limit and die parameters is developed through the response surface methodology（RSM）.The developed RSM models suggest that increasing the fillet radii of left and middle ribs is effective to improve the process forming limit during local loading forming of rib-web components.The results will provide technical basis for the design of die parameters and the reduction amount,which is of great importance to control forming defects and improve the process forming limit in local loading forming of Ti-alloy large-scale rib-web components.
基金Project supported by the Young Core Instructor and Domestic Visitor Foundation from the Education Commission of Hunan Province(No.21B0315)。
文摘A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity.By introducing the local thickness defects function of the micro-beam,the variable coefficient differential equations of the buckling problem are obtained with the variational principle.Combining the eigensolution series of the complete micro-beam with the Galerkin method,we obtain the critical load and buckling modes of the micro-beam with defects.The results show that the depth and location of the defect are the main factors affecting the critical load,and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam.The effect of defect location on buckling is related to the axial gradient of the rotation angle,and defects should be avoided at the maximum axial gradient of the rotation angle.The model and method are also applicable to the static deformation and vibration of the micro-beam.
基金Supported by Project of Shandong Province Higher Educational Science and Technology Program(No.J11LG77)
文摘In this paper, we present a tire defect detection algorithm based on sparse representation. The dictionary learned from reference images can efficiently represent the test image. As the representation coefficients of normal images have a specific distribution, the local feature can be estimate by comparing representation coefficient distribution. Meanwhile, a coding length is used to measure the global features of representation coefficients. The tire defect is located by both these local and global features. Experimental results demonstrate that the proposed method can accurately detect and locate the tire defects.
