Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment.In this study,an accurate and efficient loaded tooth contact analysis(LTCA)model is developed to predict the contact behavior ...Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment.In this study,an accurate and efficient loaded tooth contact analysis(LTCA)model is developed to predict the contact behavior and time-varying meshing stiffness(TVMS)of spiral bevel gear pair with cracked tooth.The tooth is sliced,and the contact points on slices are computed using roll angle surfaces.Considering the geometric complexity of crack surface,a set of procedures is formulated to generate spatial crack and determine crack parameters for contact points.According to the positional relationship between contact point and crack path,each sliced tooth is modeled as a non-uniform cantilever beam with varying reduced effective load-bearing tooth thickness.Then the compliance model of the cracked tooth is established to perform contact analysis,along with TVMS calculations utilizing three different models.By employing spiral bevel gear pairs with distinct types of cracks as examples,the accuracy and efficiency of the developed approach are validated via comparative analyses with finite element analysis(FEA)outcomes.Furthermore,the investigation on effects of cracks shows that tooth cracks can induce alterations in meshing performance of both entire gear pair and individual tooth pairs,including not only cracked tooth pair but also adjacent non-cracked tooth pairs.Hence,the proposed model can serve as a useful tool for analyzing the variations in contact behavior and meshing stiffness of spiral bevel gears due to different cracks.展开更多
According to the relationship between the meshing stiffness and the inherent characteristics of a seven-speed three-row coupled planetary transmission mechanism,a equivalent concentrated mass dynamics model of the pla...According to the relationship between the meshing stiffness and the inherent characteristics of a seven-speed three-row coupled planetary transmission mechanism,a equivalent concentrated mass dynamics model of the planetary transmission mechanism is established.The natural frequency of the planetary gear train at a specific gear is calculated and extracted.The relationship between the meshing stiffness of each row and the natural frequency of the system is analyzed,thereby avoiding possible resonance behavior by changing the meshing stiffness.These results show that the meshing stiffness,in its range of possible values,has nearly no effect on the low order natural frequency(<4.000.Hz),and that the time-varying meshing stiffness mainly affects the natural frequencies of the higher-and middle-order parts of the system.Changes of the natural frequencies lead to the change of the system's corresponding vibration mode,which will change the vibration situation of the system.展开更多
Simulation study on the cylindrical gear meshing with the evolution gear meshing stiffness is being done for better understanding the dynamic characteristics of the kinematics.With consideration of damping,bearing cle...Simulation study on the cylindrical gear meshing with the evolution gear meshing stiffness is being done for better understanding the dynamic characteristics of the kinematics.With consideration of damping,bearing clearance and gear backlash nonlinearity,the dynamic model is set up and computed in MATLAB.The analysis about the relationship between the kinematic responses and the meshing stiffness are carried out.And the results showed that as the gear mesh stiffness is changed from small to large,the performance of the system is changed from the harmonic stable periodic motion to with one times,two times,four times,ending chaos of the stability of the bifurcation.The research results would have theoretical guidance value for the fault diagnosis in engineering.展开更多
The contact characteristics of the rough tooth surface during the meshing process are significantly affected by the lubrication state.The coupling effect of tooth surface roughness and lubrication on meshing character...The contact characteristics of the rough tooth surface during the meshing process are significantly affected by the lubrication state.The coupling effect of tooth surface roughness and lubrication on meshing characteristics of planetary gear is studied.An improved three-dimensional(3 D)anisotropic tooth surface roughness fractal model is proposed based on the experimental parameters.Considering asperity contact and elastohydrodynamic lubrication(EHL),the contact load and flexibility deformation of the tooth surface are derived,and the deformation compatibility equation of the 3 D loaded tooth contact analysis(3 D-LTCA)method is improved.The asperity of the tooth surface changes the system from EHL to mixed lubrication and reduces the stiffness of the oil film.Compared with the sun planet gear,the asperity has a greater effect on the meshing characteristics of the ring-planet gear.Compared with the proposed method,the comprehensive stiffness obtained by the traditional calculation method considering the lubrication effect is smaller,especially for the ring-planet gear.Compared with roughness,speed and viscosity,the meshing characteristics of planetary gears are most sensitive to torque.展开更多
Gearbox fault diagnosis based on vibration sensing has drawn much attention for a long time.For highly integrated complicated mechanical systems,the intercoupling of structure transfer paths results in a great reducti...Gearbox fault diagnosis based on vibration sensing has drawn much attention for a long time.For highly integrated complicated mechanical systems,the intercoupling of structure transfer paths results in a great reduction or even change of signal characteristics during the process of original vibration transmission.Therefore,using gearbox housing vibration signal to identify gear meshing excitation signal is of great significance to eliminate the influence of structure transfer paths,but accompanied by huge scientific challenges.This paper establishes an analytical mathematical description of the whole transfer process from gear meshing excitation to housing vibration.The gear meshing stiffness(GMS)identification approach is proposed by using housing vibration signals for two stages of inversion based on the mathematical description.Specifically,the linear system equations of transfer path analysis are first inverted to identify the bearing dynamic forces.Then the dynamic differential equations are inverted to identify the GMS.Numerical simulation and experimental results demonstrate the proposed method can realize gear fault diagnosis better than the original housing vibration signal and has the potential to be generalized to other speeds and loads.Some interesting properties are discovered in the identified GMS spectra,and the results also validate the rationality of using meshing stiffness to describe the actual gear meshing process.The identified GMS has a clear physical meaning and is thus very useful for fault diagnosis of the complicated equipment.展开更多
Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteris...Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.展开更多
Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic m...Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic model was established using the lumped-mass method.Time-varying meshing stiffness was calculated by the energy method.The model consumes the backlash,bearing clearance,time-varying meshing stiffness,time-varying bearing stiffness,and time-varying friction coefficient.The time-varying bearing stiffness was calculated according to the Hertz contact theory.The load distribution among the gears was computed,and the time-varying friction coefficient was calculated according to elastohydrodynamic lubrication(EHL)theory.The dynamical equations were solved via numerical integration.The global bifurcation characteristics caused by the input speed,backlash,bearing clearance,and damping were analyzed.The system was in a chaotic state at natural frequencies or frequency multiplication.The system transitioned from a single-period state to a chaotic state with the increase of the backlash.The bearing clearance of the sun gear had little influence on the bifurcation characteristics.The amplitude was restrained in the chaotic state as the damping ratio increased.展开更多
A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, appli...A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.展开更多
Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh sti...Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.展开更多
Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gea...Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.展开更多
Tooth breakage is a common issue in geared systems. The high-contact-ratio spur gear system (HCRSG) maintains continuoustransmission despite tooth breakage, but experiences increased impact vibration. In aviation, eve...Tooth breakage is a common issue in geared systems. The high-contact-ratio spur gear system (HCRSG) maintains continuoustransmission despite tooth breakage, but experiences increased impact vibration. In aviation, even if the gear teeth break, the gear'stransmission cannot be stopped immediately. Therefore, studying gear system dynamics with tooth breakage is crucial for assessing thereliability of mechanical equipment. This study treats the tooth-back contact induced by backlash as the tooth-back collision andpresents the multi-state meshing-collision pattern of HCRSG with one tooth breakage (OTB), including triple-tooth, double-tooth,single-tooth meshes, disengagement, and tooth-back collision. Time-varying meshing stiffness and load distribution coefficients ofHCRSG with OTB are calculated. Then a multi-state meshing-collision nonlinear dynamic model of HCRSG with OTB is established.The meshing forces of HCRSG with OTB and without OTB are calculated and compared to examine the effect of tooth breakage. Themulti-state meshing-collision nonlinear dynamics of HCRSG with OTB are studied via bifurcation diagram, phase portraits, andPoincaré maps by changing the transmission error amplitude. The results show that 3-2-3-2-3 meshing pattern of HCRSG is shifted to2-1-2-1-2 meshing pattern due to tooth breakage. The effect of tooth breakage on the meshing force and dynamic behavior significantlydepends on teeth disengagement or tooth-back collision. Tooth breakage greatly affects the bifurcation and chaos characteristics ofmultistate meshing-collision behavior of HCRSG. This study creates a framework to predict and assess the dynamics of gear transmissionsystems with tooth breakage in extreme aviation and aerospace environments.展开更多
In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a ...In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.展开更多
Tooth pitting is a common failure mode of a gearbox. Many researchers investigated dynamic properties of a gearbox with localized pitting damage on a single gear tooth. The dynamic properties of a gearbox with pitting...Tooth pitting is a common failure mode of a gearbox. Many researchers investigated dynamic properties of a gearbox with localized pitting damage on a single gear tooth. The dynamic properties of a gearbox with pitting distributed over multiple teeth have rarely been investi- gated. In this paper, gear tooth pitting propagation to neighboring teeth is modeled and investigated for a pair of spur gears. Tooth pitting propagation effect on time-vary- ing mesh stiffness, gearbox dynamics and vibration char- acteristics is studied and then fault symptoms are revealed. In addition, the influence of gear mesh damping and environmental noise on gearbox vibration properties is investigated. In the end, 114 statistical features are tested to estimate tooth pitting growth. Statistical features that are insensitive to gear mesh damping and environmental noise are recommended.展开更多
Time?varying mesh stiffness(TVMS) and gear errors include short?term and long?term components are the two main internal dynamic excitations for gear transmission. The coupling relationship between the two factors is u...Time?varying mesh stiffness(TVMS) and gear errors include short?term and long?term components are the two main internal dynamic excitations for gear transmission. The coupling relationship between the two factors is usually neglected in the traditional quasi-static and dynamic behaviors analysis of gear system. This paper investigates the influence of short?term and long?term components of manufacturing errors on quasi?static and dynamic behaviors of helical gear system considering the coupling relationship between TVMS and gear errors. The TVMS, loaded static transmission error(LSTE) and loaded composite mesh error(LCMS) are determined using an improved loaded tooth contact analysis(LTCA) model. Considering the structure of shaft, as well as the direction of power flow and bearing location, a precise generalized finite element dynamic model of helical gear system is developed, and the dynamic responses of the system are obtained by numerical integration method. The results suggest that lighter loading conditions result in smaller mesh stiffness and stronger vibration, and the corresponding resonance speeds of the system become lower. Long?term components of manufacturing errors lead to the appearance of sideband frequency components in frequency spectrum of dynamic responses. The sideband frequency components are predominant under light loading conditions. With the increase of output torque, the mesh frequency and its harmonics components tend to be enhanced relative to sideband frequency components. This study can provide effective reference for low noise design of gear transmission.展开更多
The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points o...The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points of contact were also obtained.Meanwhile, an involute slope modification method considering the effects of static transmission errors was proposed based on the meshing properties. The characteristic of the involute slope modification was analyzed by changing different modification parameters.The mesh stiffness and synthetic mesh stiffness of unmodified and modified asymmetric spur gears were investigated. Furthermore,the spectrums of synthetic mesh stiffness under different modification parameters were compared. Research results showed that the modification parameters influence the meshing performance of gear pairs, and the proposed modification method was feasible to improve the transmission performance of gear pairs with appropriate modification parameters.展开更多
In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis （TCA）...In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis （TCA） and loaded tooth contact analysis （LTCA）, the actual meshing process of each gear pairs is simulated, and the time-varying mesh stiffness excitations are obtained, which can improve the numerical precision. Second- ly, by using the lumped mass method, the bending-torsional coupling three dimensional dynamic model of the dual power-split transmission is established, and the identical dimensionless equations are deduced by elimina- ting the effect of rigid displacement and the method of dimensional normalization. Finally, by the method of the fourth order Runge-Kutta algorithm with variable step lengths, the responses of this system in a frequency domain and time domain are obtained, and the dynamic load change characteristics of each gear pairs are analyzed. The results show that the establishment, solution and analysis of the system dynamics model could provide a basis for the dynamic design, and have an important significance for the dynamic efficiency analysis and dynamic perform- ance optimization design of the dual power-split transmission.展开更多
Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analyti...Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analytical mesh stiffness calculation model for an internal gear pair in mesh considering the tooth profile shift is developed based on the potential energy principle. Geometrical representations of the tooth profile shift are firstly derived, and then fitted into the analytical tooth stiffness model of gears. This model could supply a convenient way for mesh stiffness calculation of profile shifted spur gears. Then, simulation studies are conducted based on the developed model to demonstrate the effects of tooth profile shift coefficient on the tooth compliances and the mesh stiffness of the internal spur gear pair. The results show that tooth profile shift has an obvious influence on the mean value, amplitude variation and phase of the mesh stiffness, from which it can be predicted that the dynamic response of an internal gear transmission system will be affected by the tooth profile shift.展开更多
As one of the most typical fault forms of the helical gear,the crack will change the dynamic excitation and further affect the dynamic behaviors of the transmission systems.Due to the complicated structure of the heli...As one of the most typical fault forms of the helical gear,the crack will change the dynamic excitation and further affect the dynamic behaviors of the transmission systems.Due to the complicated structure of the helical gears,the coupling effect between the neighboring loaded teeth is usually ignored in the mesh stiffness calculation,making it considerably overestimated especially in the case of the crack fault.An improved mesh stiffness calculation method of helical gear with spatial crack is proposed to make up this gap.The interactions between the loaded neighboring teeth induced by the gear body flexibility were considered to improve the calculation accuracy and applicability.Besides,the load distribution law for the engaged cracked tooth along the tooth width and profile can be obtained.The results indicated that the mesh stiffness of the multi-tooth engagement calculation using this model could be further improved compared with the traditional methods.Finally,the effects of the helix angle,crack depth,and crack propagation length on the mesh stiffness and load distribution were investigated using the proposed method.展开更多
An improved variable cross‐section cantilever beam model for evaluating the time‐varying mesh stiffness(TVMS)of the perfect gear tooth is developed in which the tooth number of driving gear is less than 42 and that ...An improved variable cross‐section cantilever beam model for evaluating the time‐varying mesh stiffness(TVMS)of the perfect gear tooth is developed in which the tooth number of driving gear is less than 42 and that of driven is more than 42.The TVMS obtained by the proposed method is compared with the result without considering the misalignment between the base circle and gear root.Four types of root crack models and changes inTVMS of 13‐crack levels are presented.The fault vibration characteristic of a single‐stage spur gear reducer with root crack is ana-lyzed and the correctness is qualitatively verified by the vibration signals of an experimental gearbox with crack or missing failure.The results presented in this paper are of great significance for a deep understanding of the possible causes of vibration and noise of gears and provide a theoretical foundation for the fault diagnosis of the gearbox.展开更多
Gear mesh excitations are widely concerned in the dynamic studies of the gear transmission system.Meanwhile,intentional and unintentional tooth profile deviations often occur in gears.At present,the established calcul...Gear mesh excitations are widely concerned in the dynamic studies of the gear transmission system.Meanwhile,intentional and unintentional tooth profile deviations often occur in gears.At present,the established calculation models of gear mesh excitations consider tooth profile deviations as displacement excitation.However,gear mesh excitations calculated by such models have reduced stability compared with the actual situation.Therefore,in this study,an improved analytical model of gear mesh excitations with tooth profile deviations is established.This established model considers tooth profile deviations,extended tooth contact,and the structure coupling effect of the gear body simultaneously.More importantly,the model considers the strong correlation among tooth contact parameters,contact force,and tooth profile deviations to better reflect the actual gear mesh.A calculation flowchart with a simple calculation method of contact forces is also proposed to calculate the gear mesh excitations.Finally,the effects of tooth profile deviations on gear mesh excitations are studied.The results show that the effects of tooth profile deviations on tooth contact position,the direction of contact force,and equivalent basic circle radii should be considered in the calculation of gear mesh excitations because of smaller system transmission errors,larger double-teeth meshing area,and slighter extended tooth contact.Tooth profile deviations also cause jumps in tooth contact position and time-varying mesh stiffness.Thus,our findings show that the proposed model can be used to calculate the gear mesh excitations more accurately when the tooth profile deviates greatly.展开更多
基金co-supported by the National Natural Science Foundation of China (No. 52175104)the Postdoctoral Fellowship Program of CPSF (No. GZC20233008)
文摘Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment.In this study,an accurate and efficient loaded tooth contact analysis(LTCA)model is developed to predict the contact behavior and time-varying meshing stiffness(TVMS)of spiral bevel gear pair with cracked tooth.The tooth is sliced,and the contact points on slices are computed using roll angle surfaces.Considering the geometric complexity of crack surface,a set of procedures is formulated to generate spatial crack and determine crack parameters for contact points.According to the positional relationship between contact point and crack path,each sliced tooth is modeled as a non-uniform cantilever beam with varying reduced effective load-bearing tooth thickness.Then the compliance model of the cracked tooth is established to perform contact analysis,along with TVMS calculations utilizing three different models.By employing spiral bevel gear pairs with distinct types of cracks as examples,the accuracy and efficiency of the developed approach are validated via comparative analyses with finite element analysis(FEA)outcomes.Furthermore,the investigation on effects of cracks shows that tooth cracks can induce alterations in meshing performance of both entire gear pair and individual tooth pairs,including not only cracked tooth pair but also adjacent non-cracked tooth pairs.Hence,the proposed model can serve as a useful tool for analyzing the variations in contact behavior and meshing stiffness of spiral bevel gears due to different cracks.
基金National Natural Science Foundation of China(51375043)。
文摘According to the relationship between the meshing stiffness and the inherent characteristics of a seven-speed three-row coupled planetary transmission mechanism,a equivalent concentrated mass dynamics model of the planetary transmission mechanism is established.The natural frequency of the planetary gear train at a specific gear is calculated and extracted.The relationship between the meshing stiffness of each row and the natural frequency of the system is analyzed,thereby avoiding possible resonance behavior by changing the meshing stiffness.These results show that the meshing stiffness,in its range of possible values,has nearly no effect on the low order natural frequency(<4.000.Hz),and that the time-varying meshing stiffness mainly affects the natural frequencies of the higher-and middle-order parts of the system.Changes of the natural frequencies lead to the change of the system's corresponding vibration mode,which will change the vibration situation of the system.
基金supported by the National Natural Science Foundation-supported Program(51275052&51575055)
文摘Simulation study on the cylindrical gear meshing with the evolution gear meshing stiffness is being done for better understanding the dynamic characteristics of the kinematics.With consideration of damping,bearing clearance and gear backlash nonlinearity,the dynamic model is set up and computed in MATLAB.The analysis about the relationship between the kinematic responses and the meshing stiffness are carried out.And the results showed that as the gear mesh stiffness is changed from small to large,the performance of the system is changed from the harmonic stable periodic motion to with one times,two times,four times,ending chaos of the stability of the bifurcation.The research results would have theoretical guidance value for the fault diagnosis in engineering.
基金Project(2024A1515240020)supported by the Guangdong Basic and Applied Basic Research Foundation,China。
文摘The contact characteristics of the rough tooth surface during the meshing process are significantly affected by the lubrication state.The coupling effect of tooth surface roughness and lubrication on meshing characteristics of planetary gear is studied.An improved three-dimensional(3 D)anisotropic tooth surface roughness fractal model is proposed based on the experimental parameters.Considering asperity contact and elastohydrodynamic lubrication(EHL),the contact load and flexibility deformation of the tooth surface are derived,and the deformation compatibility equation of the 3 D loaded tooth contact analysis(3 D-LTCA)method is improved.The asperity of the tooth surface changes the system from EHL to mixed lubrication and reduces the stiffness of the oil film.Compared with the sun planet gear,the asperity has a greater effect on the meshing characteristics of the ring-planet gear.Compared with the proposed method,the comprehensive stiffness obtained by the traditional calculation method considering the lubrication effect is smaller,especially for the ring-planet gear.Compared with roughness,speed and viscosity,the meshing characteristics of planetary gears are most sensitive to torque.
基金supported by the Basic Research Foundation,China(Grant No.MKF20210013).
文摘Gearbox fault diagnosis based on vibration sensing has drawn much attention for a long time.For highly integrated complicated mechanical systems,the intercoupling of structure transfer paths results in a great reduction or even change of signal characteristics during the process of original vibration transmission.Therefore,using gearbox housing vibration signal to identify gear meshing excitation signal is of great significance to eliminate the influence of structure transfer paths,but accompanied by huge scientific challenges.This paper establishes an analytical mathematical description of the whole transfer process from gear meshing excitation to housing vibration.The gear meshing stiffness(GMS)identification approach is proposed by using housing vibration signals for two stages of inversion based on the mathematical description.Specifically,the linear system equations of transfer path analysis are first inverted to identify the bearing dynamic forces.Then the dynamic differential equations are inverted to identify the GMS.Numerical simulation and experimental results demonstrate the proposed method can realize gear fault diagnosis better than the original housing vibration signal and has the potential to be generalized to other speeds and loads.Some interesting properties are discovered in the identified GMS spectra,and the results also validate the rationality of using meshing stiffness to describe the actual gear meshing process.The identified GMS has a clear physical meaning and is thus very useful for fault diagnosis of the complicated equipment.
基金supported by the National Natural Science Foundation of China(grant no.52075414).
文摘Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.
基金supported by the National Natural Science Foundation of China(No. 51975274)National Key Laboratory of Science and Technology on Helicopter Transmission(Nanjing University of Aeronautics and Astronautics)(No. HTL-A-19K03)
文摘Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic model was established using the lumped-mass method.Time-varying meshing stiffness was calculated by the energy method.The model consumes the backlash,bearing clearance,time-varying meshing stiffness,time-varying bearing stiffness,and time-varying friction coefficient.The time-varying bearing stiffness was calculated according to the Hertz contact theory.The load distribution among the gears was computed,and the time-varying friction coefficient was calculated according to elastohydrodynamic lubrication(EHL)theory.The dynamical equations were solved via numerical integration.The global bifurcation characteristics caused by the input speed,backlash,bearing clearance,and damping were analyzed.The system was in a chaotic state at natural frequencies or frequency multiplication.The system transitioned from a single-period state to a chaotic state with the increase of the backlash.The bearing clearance of the sun gear had little influence on the bifurcation characteristics.The amplitude was restrained in the chaotic state as the damping ratio increased.
基金Project(51175505)supported by the National Natural Science Foundation of China
文摘A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.
基金Project(51575062)supported by the National Natural Science Foundation of ChinaProject(51605049)supported by the National Natural Science Foundation for Young Scholar of ChinaProject(BA2015177)supported by the Science and Technology Achievements Transformation Program of Jiangsu Province of China
文摘Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.
基金supported by the National Natural Science Foundations of China(Nos.51105194,51375226)the Fundamental Research Funds for the Central Universities(No.NS2015049)
文摘Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.
基金supported by the National Natural Science Foundation of China(Grant Nos.12102159,12462003)the Lanzhou Youth Science and Technology Talent Innovation Project(2023-QN-39)the postgraduate research exploration project(222080201023).
文摘Tooth breakage is a common issue in geared systems. The high-contact-ratio spur gear system (HCRSG) maintains continuoustransmission despite tooth breakage, but experiences increased impact vibration. In aviation, even if the gear teeth break, the gear'stransmission cannot be stopped immediately. Therefore, studying gear system dynamics with tooth breakage is crucial for assessing thereliability of mechanical equipment. This study treats the tooth-back contact induced by backlash as the tooth-back collision andpresents the multi-state meshing-collision pattern of HCRSG with one tooth breakage (OTB), including triple-tooth, double-tooth,single-tooth meshes, disengagement, and tooth-back collision. Time-varying meshing stiffness and load distribution coefficients ofHCRSG with OTB are calculated. Then a multi-state meshing-collision nonlinear dynamic model of HCRSG with OTB is established.The meshing forces of HCRSG with OTB and without OTB are calculated and compared to examine the effect of tooth breakage. Themulti-state meshing-collision nonlinear dynamics of HCRSG with OTB are studied via bifurcation diagram, phase portraits, andPoincaré maps by changing the transmission error amplitude. The results show that 3-2-3-2-3 meshing pattern of HCRSG is shifted to2-1-2-1-2 meshing pattern due to tooth breakage. The effect of tooth breakage on the meshing force and dynamic behavior significantlydepends on teeth disengagement or tooth-back collision. Tooth breakage greatly affects the bifurcation and chaos characteristics ofmultistate meshing-collision behavior of HCRSG. This study creates a framework to predict and assess the dynamics of gear transmissionsystems with tooth breakage in extreme aviation and aerospace environments.
基金Project supported by the National Natural Science Foundation of China(Grant No.61104040)the Natural Science Foundation of Hebei Province,China(Grant No.E2012203090)the University Innovation Team of Hebei Province Leading Talent Cultivation Project,China(Grant No.LJRC013)
文摘In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.
基金Supported by Natural Science and Engineering Research Council of Canada(Grant No.RGPIN-2015-04897)International S&T Cooperation Program of China(Grant No.2015DFA71400)+1 种基金National Key Research and Development Program of China(Grant No.2016YFB1200401)National Natural Science Foundation of China(Grant No.51375078,51505066)
文摘Tooth pitting is a common failure mode of a gearbox. Many researchers investigated dynamic properties of a gearbox with localized pitting damage on a single gear tooth. The dynamic properties of a gearbox with pitting distributed over multiple teeth have rarely been investi- gated. In this paper, gear tooth pitting propagation to neighboring teeth is modeled and investigated for a pair of spur gears. Tooth pitting propagation effect on time-vary- ing mesh stiffness, gearbox dynamics and vibration char- acteristics is studied and then fault symptoms are revealed. In addition, the influence of gear mesh damping and environmental noise on gearbox vibration properties is investigated. In the end, 114 statistical features are tested to estimate tooth pitting growth. Statistical features that are insensitive to gear mesh damping and environmental noise are recommended.
基金Supported by Key Project of National Natural Science Foundation of China(Grant No.51535009)111 Project(Grant No.B13044)
文摘Time?varying mesh stiffness(TVMS) and gear errors include short?term and long?term components are the two main internal dynamic excitations for gear transmission. The coupling relationship between the two factors is usually neglected in the traditional quasi-static and dynamic behaviors analysis of gear system. This paper investigates the influence of short?term and long?term components of manufacturing errors on quasi?static and dynamic behaviors of helical gear system considering the coupling relationship between TVMS and gear errors. The TVMS, loaded static transmission error(LSTE) and loaded composite mesh error(LCMS) are determined using an improved loaded tooth contact analysis(LTCA) model. Considering the structure of shaft, as well as the direction of power flow and bearing location, a precise generalized finite element dynamic model of helical gear system is developed, and the dynamic responses of the system are obtained by numerical integration method. The results suggest that lighter loading conditions result in smaller mesh stiffness and stronger vibration, and the corresponding resonance speeds of the system become lower. Long?term components of manufacturing errors lead to the appearance of sideband frequency components in frequency spectrum of dynamic responses. The sideband frequency components are predominant under light loading conditions. With the increase of output torque, the mesh frequency and its harmonics components tend to be enhanced relative to sideband frequency components. This study can provide effective reference for low noise design of gear transmission.
基金Project(51105287)supported by the National Natural Science Foundation of ChinaProject(2012BAA08003)supported by the Key Research and Development Project of New Product and New Technology of Hubei Province,ChinaProject(IRT13087)supported by the Progress for Innovative Research Team in University of Ministry of Education of China
文摘The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points of contact were also obtained.Meanwhile, an involute slope modification method considering the effects of static transmission errors was proposed based on the meshing properties. The characteristic of the involute slope modification was analyzed by changing different modification parameters.The mesh stiffness and synthetic mesh stiffness of unmodified and modified asymmetric spur gears were investigated. Furthermore,the spectrums of synthetic mesh stiffness under different modification parameters were compared. Research results showed that the modification parameters influence the meshing performance of gear pairs, and the proposed modification method was feasible to improve the transmission performance of gear pairs with appropriate modification parameters.
基金supported by the Natural Science Foundation of China under Grant No.51175423
文摘In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis （TCA） and loaded tooth contact analysis （LTCA）, the actual meshing process of each gear pairs is simulated, and the time-varying mesh stiffness excitations are obtained, which can improve the numerical precision. Second- ly, by using the lumped mass method, the bending-torsional coupling three dimensional dynamic model of the dual power-split transmission is established, and the identical dimensionless equations are deduced by elimina- ting the effect of rigid displacement and the method of dimensional normalization. Finally, by the method of the fourth order Runge-Kutta algorithm with variable step lengths, the responses of this system in a frequency domain and time domain are obtained, and the dynamic load change characteristics of each gear pairs are analyzed. The results show that the establishment, solution and analysis of the system dynamics model could provide a basis for the dynamic design, and have an important significance for the dynamic efficiency analysis and dynamic perform- ance optimization design of the dual power-split transmission.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51405400 & 51375403)the Fundamental Research Funds for the Central Universities (Grant Nos. 2682015ZD12 & 2682016CX125)the Fundamental Research Funds for State Key Laboratory of Traction Power (Grant Nos. 2015TPL_T14 & 2014TPL_T10)
文摘Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analytical mesh stiffness calculation model for an internal gear pair in mesh considering the tooth profile shift is developed based on the potential energy principle. Geometrical representations of the tooth profile shift are firstly derived, and then fitted into the analytical tooth stiffness model of gears. This model could supply a convenient way for mesh stiffness calculation of profile shifted spur gears. Then, simulation studies are conducted based on the developed model to demonstrate the effects of tooth profile shift coefficient on the tooth compliances and the mesh stiffness of the internal spur gear pair. The results show that tooth profile shift has an obvious influence on the mean value, amplitude variation and phase of the mesh stiffness, from which it can be predicted that the dynamic response of an internal gear transmission system will be affected by the tooth profile shift.
基金supported by the National Natural Science Foundation of China(Grant Nos.52022083,52275132 and 51735012)。
文摘As one of the most typical fault forms of the helical gear,the crack will change the dynamic excitation and further affect the dynamic behaviors of the transmission systems.Due to the complicated structure of the helical gears,the coupling effect between the neighboring loaded teeth is usually ignored in the mesh stiffness calculation,making it considerably overestimated especially in the case of the crack fault.An improved mesh stiffness calculation method of helical gear with spatial crack is proposed to make up this gap.The interactions between the loaded neighboring teeth induced by the gear body flexibility were considered to improve the calculation accuracy and applicability.Besides,the load distribution law for the engaged cracked tooth along the tooth width and profile can be obtained.The results indicated that the mesh stiffness of the multi-tooth engagement calculation using this model could be further improved compared with the traditional methods.Finally,the effects of the helix angle,crack depth,and crack propagation length on the mesh stiffness and load distribution were investigated using the proposed method.
基金National Natural Science Foundation of China,Grant/Award Numbers:11790282,12032017,11802184,11902205,12002221S&T Program of Hebei,Grant/Award Number:20310803DNatural Science Foundation of Hebei Province,Grant/Award Number:A2020210028。
文摘An improved variable cross‐section cantilever beam model for evaluating the time‐varying mesh stiffness(TVMS)of the perfect gear tooth is developed in which the tooth number of driving gear is less than 42 and that of driven is more than 42.The TVMS obtained by the proposed method is compared with the result without considering the misalignment between the base circle and gear root.Four types of root crack models and changes inTVMS of 13‐crack levels are presented.The fault vibration characteristic of a single‐stage spur gear reducer with root crack is ana-lyzed and the correctness is qualitatively verified by the vibration signals of an experimental gearbox with crack or missing failure.The results presented in this paper are of great significance for a deep understanding of the possible causes of vibration and noise of gears and provide a theoretical foundation for the fault diagnosis of the gearbox.
基金supported by the National Key Rrsearch and Development Program of China(Grant No.2022YFB3402100)the National Natural Science Foundation of China(Grant Nos.52022083 and 52275132)。
文摘Gear mesh excitations are widely concerned in the dynamic studies of the gear transmission system.Meanwhile,intentional and unintentional tooth profile deviations often occur in gears.At present,the established calculation models of gear mesh excitations consider tooth profile deviations as displacement excitation.However,gear mesh excitations calculated by such models have reduced stability compared with the actual situation.Therefore,in this study,an improved analytical model of gear mesh excitations with tooth profile deviations is established.This established model considers tooth profile deviations,extended tooth contact,and the structure coupling effect of the gear body simultaneously.More importantly,the model considers the strong correlation among tooth contact parameters,contact force,and tooth profile deviations to better reflect the actual gear mesh.A calculation flowchart with a simple calculation method of contact forces is also proposed to calculate the gear mesh excitations.Finally,the effects of tooth profile deviations on gear mesh excitations are studied.The results show that the effects of tooth profile deviations on tooth contact position,the direction of contact force,and equivalent basic circle radii should be considered in the calculation of gear mesh excitations because of smaller system transmission errors,larger double-teeth meshing area,and slighter extended tooth contact.Tooth profile deviations also cause jumps in tooth contact position and time-varying mesh stiffness.Thus,our findings show that the proposed model can be used to calculate the gear mesh excitations more accurately when the tooth profile deviates greatly.
