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
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
The thermal elasto-hydrodynamic lubrication characteristics of the internal meshing gears in a planetary gear train under vibrations were examined considering the influence of the modification coefficient and time-var...The thermal elasto-hydrodynamic lubrication characteristics of the internal meshing gears in a planetary gear train under vibrations were examined considering the influence of the modification coefficient and time-varying meshing stiffness.Based on dynamic theory of the gear system,a dynamic model of the planetary gear train was established.The lubrication performances of modified gear systems under vibrations and static loads were analyzed.Compared with other transmission types,the best lubrication effect could be produced by the positive transmission.A thicker lubricating oil film could be formed,and the friction coefficient and oil film flash temperature are the smallest.Increasing modification coefficient improves the lubrication performance continuously but intensifies the engage-in and tooth-change impact.For the planetary and inner gears,the increase in the modification coefficient also leads a decrease in the oil film stiffness.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
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
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
A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time...A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.展开更多
Planet gear systems(PGSs)are key components of transmission mechanisms.Structural and material characteristics of gearbox and shaft can affect the support stiffness and vibrations of PGSs.The ring gear flexibility sho...Planet gear systems(PGSs)are key components of transmission mechanisms.Structural and material characteristics of gearbox and shaft can affect the support stiffness and vibrations of PGSs.The ring gear flexibility should affect the vibrations of PGSs too.However,most previous work did not completely consider the effects of the ring gear flexibility on the vibrations of PGSs and flexible supports of ring and sun gears.Thus,this paper presents a flexible-rigid coupling multi-body dynamic(FMBD)model for a PGS with the flexible supports and ring gear flexibility.A finite element model of ring gear is established to formulate the ring gear flexibility.The influences of clearance and damping of planet bearings on the vibrations of PGS are considered.The effects of flexible supports and ring gear flexibility on the vibrations of PGS under different moment and speed conditions are studied.The statistical parameters and peak frequencies of PGS from the proposed FMBD and previous rigid multi-body dynamic(RMBD)models are compared.The results denote that the flexible support has a great effect on the vibrations of PGS.This paper can provide some guidance for the support structure design and vibration control for PGSs.展开更多
This paper presents a new study on optimum determination of the partial ratios of coupled planetary gear sets for getting minimum radial size of the gear sets. In this paper, based on moment equilibrium condition of a...This paper presents a new study on optimum determination of the partial ratios of coupled planetary gear sets for getting minimum radial size of the gear sets. In this paper, based on moment equilibrium condition of a mechanic system including two-row planetary gear sets and their regular resistance conditions, an explicit model for calculating the partial ratios of coupled planetary gear sets was proposed. In addition, by giving this effective model, the partial ratios can be calculated simply and accurately.展开更多
Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-...Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference.The kinematic calculation was conducted based on the analysis of structural composition and working principle.Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time.Then,main factors that affect the systematic backlash were introduced and the effects of manufacture error,misaligments and roller bearing parameters on the distribution of backlash were presented.The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed.The results show that the backlash is a little large,of which the backlash of bearing takes a greater part than two gearing stages.So we presented some practical methods to reduce the systematic backlash.展开更多
This paper presents the design method of hybrid drive system for the minibus with some limited conditions. The approach of design hybrid drive system is based on the dynamic modeling and simulation of the hybrid minib...This paper presents the design method of hybrid drive system for the minibus with some limited conditions. The approach of design hybrid drive system is based on the dynamic modeling and simulation of the hybrid minibus with planetary gear system. The main target of the design is to obtain the optimal design with the proper hybrid drive configuration and control for a given set of design constraints. In oder to meet the design target, it's necessary to adjust some parameters such as mechanical ratios and parameters of battery pack as well as control by simulation. During simulation the transient operating process can be studied in details with the dynamic model in Matlab/Simulink. The control strategy can be optimized by running the simulation and monitoring the operation of each components: the operating area of internal combustion engine (ICE), fuel consumption (energy consumption), the power distribution, the torque and rotary speed of ICE and motor, the operating efficiency of motor, the aheration of battery state of charge (SOC), current and voltage.展开更多
A CAD/CAE system of the ring-type planetary reducer with small tooth number difference is presented. It is a parameterized CAD/CAE system adopting the object-oriented technique and comprising in itself the geometric f...A CAD/CAE system of the ring-type planetary reducer with small tooth number difference is presented. It is a parameterized CAD/CAE system adopting the object-oriented technique and comprising in itself the geometric feature database (including the modules of ring-plates with inner teeth, eccentric shaft modules and output shaft modules), standard component database and material database. In comparison with design by handwork , this computer aided design and analysis system has the advantages of improved quality, shortened design period and reduced cost. The reliability of the system has been verified by a illustrative example.展开更多
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Projects(51575289,51705270)supported by the National Natural Science Foundation of China。
文摘The thermal elasto-hydrodynamic lubrication characteristics of the internal meshing gears in a planetary gear train under vibrations were examined considering the influence of the modification coefficient and time-varying meshing stiffness.Based on dynamic theory of the gear system,a dynamic model of the planetary gear train was established.The lubrication performances of modified gear systems under vibrations and static loads were analyzed.Compared with other transmission types,the best lubrication effect could be produced by the positive transmission.A thicker lubricating oil film could be formed,and the friction coefficient and oil film flash temperature are the smallest.Increasing modification coefficient improves the lubrication performance continuously but intensifies the engage-in and tooth-change impact.For the planetary and inner gears,the increase in the modification coefficient also leads a decrease in the oil film stiffness.
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.
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.
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Project(51105194)supported by the National Natural Science Foundation of ChinaProject(20113218110017)supported by the Doctoral Program Foundation of Institutions of Higher Education of China+2 种基金Project supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions,ChinaProject(CXZZ11_0199)supported by the Funding of Jiangsu Innovation Program for Graduate Education,ChinaProjects(NZ2013303,NZ2014201)supported by the Fundamental Research Funds for the Central Universities,China
文摘A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.
基金Projects(51605051,51975068)supported by the National Natural Science Foundation of China。
文摘Planet gear systems(PGSs)are key components of transmission mechanisms.Structural and material characteristics of gearbox and shaft can affect the support stiffness and vibrations of PGSs.The ring gear flexibility should affect the vibrations of PGSs too.However,most previous work did not completely consider the effects of the ring gear flexibility on the vibrations of PGSs and flexible supports of ring and sun gears.Thus,this paper presents a flexible-rigid coupling multi-body dynamic(FMBD)model for a PGS with the flexible supports and ring gear flexibility.A finite element model of ring gear is established to formulate the ring gear flexibility.The influences of clearance and damping of planet bearings on the vibrations of PGS are considered.The effects of flexible supports and ring gear flexibility on the vibrations of PGS under different moment and speed conditions are studied.The statistical parameters and peak frequencies of PGS from the proposed FMBD and previous rigid multi-body dynamic(RMBD)models are compared.The results denote that the flexible support has a great effect on the vibrations of PGS.This paper can provide some guidance for the support structure design and vibration control for PGSs.
文摘This paper presents a new study on optimum determination of the partial ratios of coupled planetary gear sets for getting minimum radial size of the gear sets. In this paper, based on moment equilibrium condition of a mechanic system including two-row planetary gear sets and their regular resistance conditions, an explicit model for calculating the partial ratios of coupled planetary gear sets was proposed. In addition, by giving this effective model, the partial ratios can be calculated simply and accurately.
基金Funded by Key Technology R&D Program of Chongqing(No. 2008AC3087)Science & Technology Project of Chongqing Education Committee(No. KJ091414)
文摘Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference.The kinematic calculation was conducted based on the analysis of structural composition and working principle.Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time.Then,main factors that affect the systematic backlash were introduced and the effects of manufacture error,misaligments and roller bearing parameters on the distribution of backlash were presented.The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed.The results show that the backlash is a little large,of which the backlash of bearing takes a greater part than two gearing stages.So we presented some practical methods to reduce the systematic backlash.
文摘This paper presents the design method of hybrid drive system for the minibus with some limited conditions. The approach of design hybrid drive system is based on the dynamic modeling and simulation of the hybrid minibus with planetary gear system. The main target of the design is to obtain the optimal design with the proper hybrid drive configuration and control for a given set of design constraints. In oder to meet the design target, it's necessary to adjust some parameters such as mechanical ratios and parameters of battery pack as well as control by simulation. During simulation the transient operating process can be studied in details with the dynamic model in Matlab/Simulink. The control strategy can be optimized by running the simulation and monitoring the operation of each components: the operating area of internal combustion engine (ICE), fuel consumption (energy consumption), the power distribution, the torque and rotary speed of ICE and motor, the operating efficiency of motor, the aheration of battery state of charge (SOC), current and voltage.
基金Funded by National Natural Science Foundation of China (50005025).
文摘A CAD/CAE system of the ring-type planetary reducer with small tooth number difference is presented. It is a parameterized CAD/CAE system adopting the object-oriented technique and comprising in itself the geometric feature database (including the modules of ring-plates with inner teeth, eccentric shaft modules and output shaft modules), standard component database and material database. In comparison with design by handwork , this computer aided design and analysis system has the advantages of improved quality, shortened design period and reduced cost. The reliability of the system has been verified by a illustrative example.