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
Planetary gear systems have been widely used in transportation, construction, metallurgy, petroleum, aviation and other industrial fields. Under the same condition of power transmission, they have a more compact struc...Planetary gear systems have been widely used in transportation, construction, metallurgy, petroleum, aviation and other industrial fields. Under the same condition of power transmission, they have a more compact structure than ordinary gear train. However, some critical parts, such as sun gear, planet gear and ring gear often suffer from fatigue and wear under the conditions of high speed and heavy load. For reliability research, in order to predict the fatigue probability life of planetary gear system, detailed kinematic and mechanical analysis for a planetary gear system is firstly completed. Meanwhile, a gear bending fatigue test is carried out at a stress level to obtain the strength information of specific gears. Then, a life distribution transformation model is established according to the order statistics theory. Transformation process is that, the life distribution of test gear is transformed to that of single tooth, and then the life distribution of single tooth can be effectively transformed to that of the planetary gear system. In addition, the effectiveness of the transformation model is finally verified by a processing method with random censoring data.展开更多
Considering the effect of planet's number on the dynamic characteristics of the planetary gear system, a translationtorsion lumped-parameter model of 2K-H spur planetary gear system was established. Through the an...Considering the effect of planet's number on the dynamic characteristics of the planetary gear system, a translationtorsion lumped-parameter model of 2K-H spur planetary gear system was established. Through the analysis of numerical solution, the results show that 1) When the planet's number is more than 3, the order of the natural frequency will become the same; 2) When the planet's number increases, the natural frequencies of planet mode remain invariant, but when it comes to rotational mode and translational mode, the higher order natural frequencies increase and the lower order natural frequencies decrease; 3) The planet's number has a great impact on the higher order natural frequencies and a little impact on the lower order natural frequencies; and 4) To avoid the resonance, we can appropriately increase or decrease the number of the planet.展开更多
Few studies were focused on the load-sharing characteristics of double-row planetary gear(DRPG)systems with bearings.Meanwhile,the supported bearing has an important influence on the transmission characteristics of th...Few studies were focused on the load-sharing characteristics of double-row planetary gear(DRPG)systems with bearings.Meanwhile,the supported bearing has an important influence on the transmission characteristics of the entire system.To overcome this problem,a multi-body dynamic(MBD)model of the DRPG system fully considering the influences of bearing parameters is established.Dynamic loads among contacting gear pairs have been obtained to calculate the load-sharing coefficient(LSC)of the system.The LSC of each gear tooth pair has been compared to study the effect of the supported bearing clearance on the load-sharing characteristics.These methods are based on Hertz contact theory.The liner stiffness and damping are used in the model.The results show that the supported bearing clearance has a greatly effect on the LSC of the DRPG system.Choosing appropriate clearance parameters of supported bearing can help suppress the uneven load distribution of the DRPG system.The results can provide some guidance to find new method to study the LSC and increase the service life of planetary gear systems.展开更多
To investigate the dynamical load sharing behaviors of multi-floating components in the heavy load planetary gear system,a multi-floating planetary gear system that includes a floating central component and a quasi-fl...To investigate the dynamical load sharing behaviors of multi-floating components in the heavy load planetary gear system,a multi-floating planetary gear system that includes a floating central component and a quasi-floating planet flexible supporting pin is employed.Then a 21 degree of freedom lumped parameters dynamical model of this system is presented to study the dynamical load sharing behaviors.Some influencing factors,such as supporting stiffness,positions error of sun or carrier,and external input load are analyzed on the dynamical load sharing of the planetary gear system with multi-floating components.The results demonstrate that the load sharing condition of the system is best when both the sun gear and planet gears are multi-floating at the same time.When the planet gear position errors remain constant,reducing the flexible pin stiffness of planet gear or increasing external input load can effectively improve the load sharing.These conclusions are verified by the relevant experiments.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
The metamaterial based on external meshing gears(MEG)is designed based on the principle of external meshing gear transmission.Based on the meshing transmission principle of external meshing gears and planetary gear tr...The metamaterial based on external meshing gears(MEG)is designed based on the principle of external meshing gear transmission.Based on the meshing transmission principle of external meshing gears and planetary gear trains,the internal and external gear rings are designed.Based on the internal and external gear rings,the metamaterial based on inner and outer planetary gear trains(MIP)is designed to study the shear modulus,Young's modulus,and amplitude-frequency characteristics of the metamaterial based on gears at different angles.The effects of the number of planetary gears on the physical characteristics of the MIP are studied.The results show that the MEG can be continuously adjusted by adjusting the shear modulus and Young's modulus due to its meshing characteristics.With the same number of gears,the adjustment range of the MIP is larger than the adjustment range of the MEG.When the number of planetary gears increases,the adjustment range of the MIP decreases.Moreover,when the metamaterial based on gears rotates,the harmonic response changes with the change of the angle.展开更多
Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random error...Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.展开更多
In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical syst...In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.展开更多
It has been challenging to design seedling pick-up mechanism based on given key points and trajectories,because it involves dimensional synthesis and rod length optimization.In this paper,the dimensional synthesis of ...It has been challenging to design seedling pick-up mechanism based on given key points and trajectories,because it involves dimensional synthesis and rod length optimization.In this paper,the dimensional synthesis of seedling pickup mechanism with planetary gear train was studied based on the data of given key points and the trajectory of the endpoint of seedling pick-up mechanism.Given the positions and orientations requirements of the five key points,the study first conducted a dimensional synthesis of the linkage size and center of rotation.The next steps were to select a reasonable solution and optimize the data values based on the ideal seedling trajectory.The link motion was driven by the planetary gear train of the two-stage gear.Four pitch curves of noncircular gears were obtained by calculating and distributing the transmission ratio according to the data.For the pitch curve with two convex points,the tooth profile design method of incomplete noncircular gear was applied.The seedling pick-up mechanism was tested by a virtual prototype and a physical prototype designed with the obtained parameter values.The results were consistent with the theoretical design requirements,confirming that the mechanism meets the expected requirements for picking seedlings up.This paper presents a new design method of vegetable pot seedling pick-up mechanism for an automatic vegetable transplanter.展开更多
Planetary gear set is the critical component in helicopter transmission train, and an important problem in condition monitoring and health management of planetary gear set is quantitative damage detection. In order to...Planetary gear set is the critical component in helicopter transmission train, and an important problem in condition monitoring and health management of planetary gear set is quantitative damage detection. In order to resolve this problem, an approach based on physical models is presented to detect damage quantitatively in planetary gear set. A particular emphasis is put on a feature generation and selection method, which is used for sun gear tooth breakage damage detection quantitatively in planetary gear box of helicopter transmission system. In this feature generation procedure, the pure torsional dynamical models of 2K-H planetary gear set is established for healthy case and sun gear tooth-breakage case. Then, a feature based on the spectrum of simulation signals of the dynamical models is generated. Aiming at selecting the best feature suitable for quantitative damage detection, a two-sample Z-test procedure is used to analyze the performance of features on damage evolution tracing. A feature named SR, which had better performance in tracking damage, is proposed to detect damage in planetary gear set. Meanwhile, the sun gear tooth-chipped seeded experiments with different severity are designed to validate the method above, and then the test vibration signal is picked up and used for damage detection. With the results of several experiments for quantitative damage detection, the feasibility and the effect of this approach are verified. The proposed method can supply an effective tool for degradation state identification in condition monitoring and health management of helicopter transmission system.展开更多
A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consi...A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.展开更多
Planetary gear train is a prominent component of helicopter transmission system and its health is of great significance for the flight safety of the helicopter.During health condition monitoring,the selection of a fau...Planetary gear train is a prominent component of helicopter transmission system and its health is of great significance for the flight safety of the helicopter.During health condition monitoring,the selection of a fault sensitive feature subset is meaningful for fault diagnosis of helicopter planetary gear train.According to actual situation,this paper proposed a multi-criteria fusion feature selection algorithm (MCFFSA) to identify an optimal feature subset from the highdimensional original feature space.In MCFFSA,a fault feature set of multiple domains,including time domain,frequency domain and wavelet domain,is first extracted from the raw vibration dataset.Four targeted criteria are then fused by multi-objective evolutionary algorithm based on decomposition (MOEA/D) to find Proto-efficient subsets,wherein two criteria for measuring diagnostic performance are assessed by sparse Bayesian extreme learning machine (SBELM).Further,Fmeasure is adopted to identify the optimal feature subset,which was employed for subsequent fault diagnosis.The effectiveness of MCFFSA is validated through six fault recognition datasets from a real helicopter transmission platform.The experimental results illustrate the superiority of combination of MOEA/D and SBELM in MCFFSA,and comparative analysis demonstrates that the optimal feature subset provided by MCFFSA can achieve a better diagnosis performance than other algorithms.展开更多
A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet...A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.展开更多
The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced li...The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase. The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis (FEA), the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.展开更多
The hybrid tracked vehicles(HTV)usually adopt series hybrid powertrain with extra steering mechanism,which has relatively low transmission efficiency and reduces the flexibility of structural arrangement.To overcome t...The hybrid tracked vehicles(HTV)usually adopt series hybrid powertrain with extra steering mechanism,which has relatively low transmission efficiency and reduces the flexibility of structural arrangement.To overcome the disadvantages,a new kind of single-mode powertrain has been proposed.The power-split hybrid powertrain is composed of three planetary gear(PG)sets connected to one engine,left and right track outputs,and three motors.The proposed powertrain can realize steering while going forward by controlling the output torque on each side without extra steering mechanism or steering shaft.Due to the diversity of the connection way between components and planetary gear sets,a rapid configuration design approach is proposed for the design selection of HTV.The automated dynamic modelling method can show the one-to-one correspondence with the selected feasible groups by establishing two characteristic matrices,which is more simple than other researches.The analytically-based method is proposed to classify all possible connection designs into several groups to decrease the searching scope with improved design efficiency.Finally,the optimal control strategy is used to find the design with optimal fuel economy under typical condition of HTV.The case study is implemented by the proposed design approach which demonstrates better design performances compared with the existing series-hybrid HTV.展开更多
The current research of a balanced hydraulic motor focuses on the characteristics of the motor with three planet gears.References of a balanced hydraulic motor with more than three planet gears are hardly found.In ord...The current research of a balanced hydraulic motor focuses on the characteristics of the motor with three planet gears.References of a balanced hydraulic motor with more than three planet gears are hardly found.In order to study the characteristics of a balanced hydraulic motor with planetary gear train that includes more than three planet gears,on the basis of analysis of the structure and working principle of a balanced hydraulic motor with planetary gear train,formulas are deduced for calculating the hydraulic motor＇s primary performance indexes such as displacement,unit volume displacement,flowrate fluctuation ratio,etc.Influences of the gears＇ tooth number on displacement and flowrate characteristics are analyzed.In order to guarantee the reliability of sealing capability,the necessary conditions that tooth number of the sun gear and the planet gears should satisfy are discussed.Selecting large unit volume displacement and small displacement fluctuation ratio as designing objectives,a balanced hydraulic motor with three planet gears and a common gear motor are designed under the conditions of same displacement,tooth addendum coefficien and clearance coefficient.By comparing the unit volume displacement and fluctuation ratio of the two motors,it can be seen that the balanced hydraulic motor with planetary gear train has the advantages of smaller fluctuation ratio and larger unit volume displacement.The results provide theoretical basis for choosing gear tooth-number of this kind of hydraulic motor.展开更多
From the general formula for calculating the efficiency of planetary geartrains, the efficiency of the double crank ring-plate-type pin-cycloidal gear planetary drive isderived. To prove the theory, an experimental st...From the general formula for calculating the efficiency of planetary geartrains, the efficiency of the double crank ring-plate-type pin-cycloidal gear planetary drive isderived. To prove the theory, an experimental study has been conducted. The tested value of theefficiency of a sample set of the new-type drive in the experiment agrees with the calculated one.It shows that the new-type drive is of not merely high bearing capacity, but also quite highefficiency.展开更多
Fault diagnosis for helicopter's main gearbox based on vibration signals by experiments always requires high costs. To solve this problem,a helicopter's planetary gear system is taken as an example. Firstly,a ...Fault diagnosis for helicopter's main gearbox based on vibration signals by experiments always requires high costs. To solve this problem,a helicopter's planetary gear system is taken as an example. Firstly,a simulation model is established by McFadden,and analyzed under ideal condition. Then this model is developed and improved as the delay-time model of the vibration signal which determines the phase-change of sidebands when the system is running. The cause and change-rules of planetary gear system's vibration signal are analyzed to establish the fault diagnosis model.At the same time,the vibration signal of fault condition is simulated and analyzed. This simulation method can provide a reference for fault monitoring and diagnosis for planetary gear system.展开更多
A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation d...A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation diagram of the system's motion state with rotational speed of sun gear was conducted through four steps.As a bifurcation parameter,the effect of rotational speed on the bifurcation properties of the system was assessed.The study results reveal that periodic motion is the main motion state of planetary gear train in low speed region when ns<2 350 r/min,but chaos motion state is dominant in high speed region when ns>2 350 r/min,The way of periodic motion to chaos is doubling bifurcation.There are two kinds of unstable modes and nine unstable regions in the speed region when 1 000 r/min<ns<3 000 r/min.展开更多
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 National Key Technology Research and Development Program of China(Grant No.2014BAF08B01)Natural Science Foundation of China(Grant No.51335003)Collaborative Innovation Center of Major Machine Manufacturing in Liaoning Province of China
文摘Planetary gear systems have been widely used in transportation, construction, metallurgy, petroleum, aviation and other industrial fields. Under the same condition of power transmission, they have a more compact structure than ordinary gear train. However, some critical parts, such as sun gear, planet gear and ring gear often suffer from fatigue and wear under the conditions of high speed and heavy load. For reliability research, in order to predict the fatigue probability life of planetary gear system, detailed kinematic and mechanical analysis for a planetary gear system is firstly completed. Meanwhile, a gear bending fatigue test is carried out at a stress level to obtain the strength information of specific gears. Then, a life distribution transformation model is established according to the order statistics theory. Transformation process is that, the life distribution of test gear is transformed to that of single tooth, and then the life distribution of single tooth can be effectively transformed to that of the planetary gear system. In addition, the effectiveness of the transformation model is finally verified by a processing method with random censoring data.
基金Funded by the Key Research and Development Project in Henan Province(No.142102210067)
文摘Considering the effect of planet's number on the dynamic characteristics of the planetary gear system, a translationtorsion lumped-parameter model of 2K-H spur planetary gear system was established. Through the analysis of numerical solution, the results show that 1) When the planet's number is more than 3, the order of the natural frequency will become the same; 2) When the planet's number increases, the natural frequencies of planet mode remain invariant, but when it comes to rotational mode and translational mode, the higher order natural frequencies increase and the lower order natural frequencies decrease; 3) The planet's number has a great impact on the higher order natural frequencies and a little impact on the lower order natural frequencies; and 4) To avoid the resonance, we can appropriately increase or decrease the number of the planet.
基金National Natural Science Foundation of China(No.51975068)。
文摘Few studies were focused on the load-sharing characteristics of double-row planetary gear(DRPG)systems with bearings.Meanwhile,the supported bearing has an important influence on the transmission characteristics of the entire system.To overcome this problem,a multi-body dynamic(MBD)model of the DRPG system fully considering the influences of bearing parameters is established.Dynamic loads among contacting gear pairs have been obtained to calculate the load-sharing coefficient(LSC)of the system.The LSC of each gear tooth pair has been compared to study the effect of the supported bearing clearance on the load-sharing characteristics.These methods are based on Hertz contact theory.The liner stiffness and damping are used in the model.The results show that the supported bearing clearance has a greatly effect on the LSC of the DRPG system.Choosing appropriate clearance parameters of supported bearing can help suppress the uneven load distribution of the DRPG system.The results can provide some guidance to find new method to study the LSC and increase the service life of planetary gear systems.
基金support provided by the National Natural Science Foundation of China Nos.51405048 and 51375519the China Postdoctoral Science Foundation No.2016M590861+2 种基金the Chongqing Research Program of Frontier and Application Foundation No.cstc2014jcyjA70010the Foundation of Municipal Education Committee of Chongqing No.KJ1705129the CQJTU Program of Study Abroad for Young Scholar for their support of this research.
文摘To investigate the dynamical load sharing behaviors of multi-floating components in the heavy load planetary gear system,a multi-floating planetary gear system that includes a floating central component and a quasi-floating planet flexible supporting pin is employed.Then a 21 degree of freedom lumped parameters dynamical model of this system is presented to study the dynamical load sharing behaviors.Some influencing factors,such as supporting stiffness,positions error of sun or carrier,and external input load are analyzed on the dynamical load sharing of the planetary gear system with multi-floating components.The results demonstrate that the load sharing condition of the system is best when both the sun gear and planet gears are multi-floating at the same time.When the planet gear position errors remain constant,reducing the flexible pin stiffness of planet gear or increasing external input load can effectively improve the load sharing.These conclusions are verified by the relevant experiments.
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supported by the Guangxi Science and Technology Major Program of China(Nos.AA23073019 and AA24263074)the National Natural Science Foundation of China(No.52265004)+7 种基金the Guangxi Natural Science Fund for Distinguished Young Scholars of China(No.2024JJG160014)the Innovation Project of Guangxi Graduate Education of China(No.YCSW2024119)the Open Fund of State Key Laboratory of Intelligent Manufacturing Equipment and Technology of China(No.IMETKF2025021)the Open Research Fund of State Key Laboratory of Precision Manufacturing for Extreme Service Performance-Central South University of China(No.Kfkt2023-06)the Open Fund of High-end Basic Component Innovation Station of China(No.KY01080030124001)the Open Fund for Academician Mao Ming's Workstation of China(No.XSJSFW-QNKXJ-202404-007)the Technology Innovation Platform Project of China Aviation Engine Group Corporation(No.CXPT-2023-044)the Open Fund for Innovation Workstation in the National Defense Science and Technology Innovation Special Zone(Xi'an Jiaotong University).
文摘The metamaterial based on external meshing gears(MEG)is designed based on the principle of external meshing gear transmission.Based on the meshing transmission principle of external meshing gears and planetary gear trains,the internal and external gear rings are designed.Based on the internal and external gear rings,the metamaterial based on inner and outer planetary gear trains(MIP)is designed to study the shear modulus,Young's modulus,and amplitude-frequency characteristics of the metamaterial based on gears at different angles.The effects of the number of planetary gears on the physical characteristics of the MIP are studied.The results show that the MEG can be continuously adjusted by adjusting the shear modulus and Young's modulus due to its meshing characteristics.With the same number of gears,the adjustment range of the MIP is larger than the adjustment range of the MEG.When the number of planetary gears increases,the adjustment range of the MIP decreases.Moreover,when the metamaterial based on gears rotates,the harmonic response changes with the change of the angle.
基金Supported by National Natural Science Foundation of China(Grant No.51375013)Anhui Provincial Natural Science Foundation of China(Grant No.1208085ME64)
文摘Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.
基金Supported by the Project DPI2013-44860 funded by the Spanish Ministry of Science and Technology
文摘In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.
基金National Key Research and Development Program of China(Grant No.2017YFD0700800)National Science Foundation of China(Grant Nos.51775512,51575496)Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ16E050003).
文摘It has been challenging to design seedling pick-up mechanism based on given key points and trajectories,because it involves dimensional synthesis and rod length optimization.In this paper,the dimensional synthesis of seedling pickup mechanism with planetary gear train was studied based on the data of given key points and the trajectory of the endpoint of seedling pick-up mechanism.Given the positions and orientations requirements of the five key points,the study first conducted a dimensional synthesis of the linkage size and center of rotation.The next steps were to select a reasonable solution and optimize the data values based on the ideal seedling trajectory.The link motion was driven by the planetary gear train of the two-stage gear.Four pitch curves of noncircular gears were obtained by calculating and distributing the transmission ratio according to the data.For the pitch curve with two convex points,the tooth profile design method of incomplete noncircular gear was applied.The seedling pick-up mechanism was tested by a virtual prototype and a physical prototype designed with the obtained parameter values.The results were consistent with the theoretical design requirements,confirming that the mechanism meets the expected requirements for picking seedlings up.This paper presents a new design method of vegetable pot seedling pick-up mechanism for an automatic vegetable transplanter.
基金supported by National Natural Science Foundation of China (Grant No. 50905183)
文摘Planetary gear set is the critical component in helicopter transmission train, and an important problem in condition monitoring and health management of planetary gear set is quantitative damage detection. In order to resolve this problem, an approach based on physical models is presented to detect damage quantitatively in planetary gear set. A particular emphasis is put on a feature generation and selection method, which is used for sun gear tooth breakage damage detection quantitatively in planetary gear box of helicopter transmission system. In this feature generation procedure, the pure torsional dynamical models of 2K-H planetary gear set is established for healthy case and sun gear tooth-breakage case. Then, a feature based on the spectrum of simulation signals of the dynamical models is generated. Aiming at selecting the best feature suitable for quantitative damage detection, a two-sample Z-test procedure is used to analyze the performance of features on damage evolution tracing. A feature named SR, which had better performance in tracking damage, is proposed to detect damage in planetary gear set. Meanwhile, the sun gear tooth-chipped seeded experiments with different severity are designed to validate the method above, and then the test vibration signal is picked up and used for damage detection. With the results of several experiments for quantitative damage detection, the feasibility and the effect of this approach are verified. The proposed method can supply an effective tool for degradation state identification in condition monitoring and health management of helicopter transmission system.
基金Projects(NZ2013303,NZ2014201)supported by the National Natural Science Foundation of ChinaProjects(51375226,51305196,51475226)supported by the Fundamental Research Funds for the Central Universities,China
文摘A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.
基金co-supported by the Equipment Pre-research Foundation Project of China (No. JZX7Y20190243016301)Helicopter Transmission Technology Key Laboratory Foundation of China (No. KY-52-2018-0024)the Fundamental Research Funds for the Central Universities & Funding of Jiangsu Innovation Program for Graduate Education under Grant (No. KYLX16_0336)
文摘Planetary gear train is a prominent component of helicopter transmission system and its health is of great significance for the flight safety of the helicopter.During health condition monitoring,the selection of a fault sensitive feature subset is meaningful for fault diagnosis of helicopter planetary gear train.According to actual situation,this paper proposed a multi-criteria fusion feature selection algorithm (MCFFSA) to identify an optimal feature subset from the highdimensional original feature space.In MCFFSA,a fault feature set of multiple domains,including time domain,frequency domain and wavelet domain,is first extracted from the raw vibration dataset.Four targeted criteria are then fused by multi-objective evolutionary algorithm based on decomposition (MOEA/D) to find Proto-efficient subsets,wherein two criteria for measuring diagnostic performance are assessed by sparse Bayesian extreme learning machine (SBELM).Further,Fmeasure is adopted to identify the optimal feature subset,which was employed for subsequent fault diagnosis.The effectiveness of MCFFSA is validated through six fault recognition datasets from a real helicopter transmission platform.The experimental results illustrate the superiority of combination of MOEA/D and SBELM in MCFFSA,and comparative analysis demonstrates that the optimal feature subset provided by MCFFSA can achieve a better diagnosis performance than other algorithms.
基金Projects(51375226,51305196,51475226) supported by the National Natural Science Foundation of ChinaProjects(NZ2013303,NZ2014201) supported by the Fundamental Research Funds for the Central Universities,China
文摘A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.
基金Key Project of Ministry of Education of China (No.106050).
文摘The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase. The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis (FEA), the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.
基金Project(CIT&TCD20190304)supported by the Beijing Great Scholars Program,China。
文摘The hybrid tracked vehicles(HTV)usually adopt series hybrid powertrain with extra steering mechanism,which has relatively low transmission efficiency and reduces the flexibility of structural arrangement.To overcome the disadvantages,a new kind of single-mode powertrain has been proposed.The power-split hybrid powertrain is composed of three planetary gear(PG)sets connected to one engine,left and right track outputs,and three motors.The proposed powertrain can realize steering while going forward by controlling the output torque on each side without extra steering mechanism or steering shaft.Due to the diversity of the connection way between components and planetary gear sets,a rapid configuration design approach is proposed for the design selection of HTV.The automated dynamic modelling method can show the one-to-one correspondence with the selected feasible groups by establishing two characteristic matrices,which is more simple than other researches.The analytically-based method is proposed to classify all possible connection designs into several groups to decrease the searching scope with improved design efficiency.Finally,the optimal control strategy is used to find the design with optimal fuel economy under typical condition of HTV.The case study is implemented by the proposed design approach which demonstrates better design performances compared with the existing series-hybrid HTV.
文摘The current research of a balanced hydraulic motor focuses on the characteristics of the motor with three planet gears.References of a balanced hydraulic motor with more than three planet gears are hardly found.In order to study the characteristics of a balanced hydraulic motor with planetary gear train that includes more than three planet gears,on the basis of analysis of the structure and working principle of a balanced hydraulic motor with planetary gear train,formulas are deduced for calculating the hydraulic motor＇s primary performance indexes such as displacement,unit volume displacement,flowrate fluctuation ratio,etc.Influences of the gears＇ tooth number on displacement and flowrate characteristics are analyzed.In order to guarantee the reliability of sealing capability,the necessary conditions that tooth number of the sun gear and the planet gears should satisfy are discussed.Selecting large unit volume displacement and small displacement fluctuation ratio as designing objectives,a balanced hydraulic motor with three planet gears and a common gear motor are designed under the conditions of same displacement,tooth addendum coefficien and clearance coefficient.By comparing the unit volume displacement and fluctuation ratio of the two motors,it can be seen that the balanced hydraulic motor with planetary gear train has the advantages of smaller fluctuation ratio and larger unit volume displacement.The results provide theoretical basis for choosing gear tooth-number of this kind of hydraulic motor.
基金This project is supported by National Natural Science Foundation of China (No.50175011).
文摘From the general formula for calculating the efficiency of planetary geartrains, the efficiency of the double crank ring-plate-type pin-cycloidal gear planetary drive isderived. To prove the theory, an experimental study has been conducted. The tested value of theefficiency of a sample set of the new-type drive in the experiment agrees with the calculated one.It shows that the new-type drive is of not merely high bearing capacity, but also quite highefficiency.
文摘Fault diagnosis for helicopter's main gearbox based on vibration signals by experiments always requires high costs. To solve this problem,a helicopter's planetary gear system is taken as an example. Firstly,a simulation model is established by McFadden,and analyzed under ideal condition. Then this model is developed and improved as the delay-time model of the vibration signal which determines the phase-change of sidebands when the system is running. The cause and change-rules of planetary gear system's vibration signal are analyzed to establish the fault diagnosis model.At the same time,the vibration signal of fault condition is simulated and analyzed. This simulation method can provide a reference for fault monitoring and diagnosis for planetary gear system.
基金Project(50775108) supported by the National Natural Science Foundation of China
文摘A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation diagram of the system's motion state with rotational speed of sun gear was conducted through four steps.As a bifurcation parameter,the effect of rotational speed on the bifurcation properties of the system was assessed.The study results reveal that periodic motion is the main motion state of planetary gear train in low speed region when ns<2 350 r/min,but chaos motion state is dominant in high speed region when ns>2 350 r/min,The way of periodic motion to chaos is doubling bifurcation.There are two kinds of unstable modes and nine unstable regions in the speed region when 1 000 r/min<ns<3 000 r/min.
