Study On Meshing Characteristics Of Elliptic Gear Transmission System

Gear is one of the basic components of mechanical equipment,and it is the most widely used key basic component.Elliptic gear is derived from cylindrical gear,cam mechanism and connecting rod mechanism in order to meet the requirements of variable ratio transmission.Elliptic gear has the advantages of compact structure,smooth transmission and can adapt to specific motion function,which is mainly suitable for low speed and high torque applications.With the expansion of the special application of elliptic gear and its key role in the transmission process,it has certain guiding significance and practical value to analyze the meshing characteristics of elliptic gear transmission system.This thesis takes elliptic gear as the research object,through a combination of theoretical analysis,finite element simulation and transmission test,and focuses on several key issues in its engineering application process: In-depth research has been carried out on several key issues such as non-linear transmission characteristics,meshing characteristics,transmission errors and transmission tests of the elliptic gear transmission system in the engineering application process.The meshing characteristics of the elliptic gear transmission system are systematically analyzed.The main contents of the study are as follows:(1)The parameter model of elliptic gear pair is established,and the influence of structural parameters on inherent characteristics is analyzed.The transmission ratio,driven wheel angle,angular velocity,angular acceleration,pressure angle,and coincidence degree of the elliptic gear pair all show an increasing trend with the increase of eccentricity.The tooth profile angle of the elliptic gear presents a periodic change trend with the position distribution of the gear teeth on the pitch curve,which further verifies the inconsistency of the elliptic gear profile.The analysis of torque fluctuation shows that the transmission characteristics of the variable ratio of the elliptic gear pair cause a certain difference in the torque on the driving and driven wheels.(2)A nonlinear dynamic model of the elliptic gear pair is established to analyze the nonlinear response of the system under parametric excitation.The mathematical expressions of the model parameters are deduced,and the nonlinear dynamic model of the elliptic gear pair is established after considering the factors of time-varying tooth backlash,time-varying meshing stiffness,meshing damping,static transmission error and dynamic excitation.The analysis results show that reducing the excitation frequency within a certain range is beneficial to improve the stability of the system,and the increase of the damping coefficient can reduce the time interval for the system to enter the chaotic state.The increase of the time-varying meshing stiffness coefficient will make the system gradually transition from the quasi-periodic motion to the chaotic motion state,and increasing the load can make the system quickly enter the steady-state motion.(3)The finite element model of the loaded tooth contact of the elliptic gear pair is proposed and established to study the distribution law of the meshing characteristics of the elliptic gear pair.Based on the loaded tooth contact theory,a finite element model of the full-tooth loaded tooth contact of an elliptic gear is established.The dynamic matching relationship of the effective plastic strain,effective stress and tooth surface pressure on the tooth surface of the elliptic gear with the position of the tooth in the tooth width direction,the tooth height direction and the pitch curve is analyzed and obtained.On this basis,based on the elliptic gear loaded tooth contact model,the meshing impact distribution law of the elliptic gear pair is obtained.The impact stress and the resultant force of the impact show a gradually increasing distribution trend from both ends of the major axis of the elliptic pitch curve to both ends of the minor axis.The impact time showed an increasing trend from the near focal point to the far focal point of the elliptic pitch curve.(4)The transmission error model of the elliptic gear pair is established,and the influence of the transmission error on the meshing characteristics of the system is analyzed.On the basis of considering the eccentricity error,a model of the transmission ratio error and transmission error of the elliptic gear pair is established,and the influence of the eccentricity error,eccentricity and initial phase angle on the system transmission ratio error and transmission error is obtained.With the increase of eccentricity,the transmission ratio error and transmission error of the elliptic gear show an increasing trend,and optimizing the initial phase can reduce the transmission error.Based on the bearing contact model of the elliptic gear,the concept of meshing error is proposed.With the different positions of the gear teeth on the pitch curve,the meshing error presents a distribution law that gradually decreases from both ends of the long axis of the elliptic pitch curve to the ends of the short axis.(5)An elliptic gear transmission test bench was built to analyze the influence of working condition parameters on the meshing characteristics of the gear system.Combined with theoretical analysis,the elliptic gear transmission system has been tested and analyzed for transmission error,dynamic lost motion,friction torque and transmission efficiency.The analysis results show that the dynamic transmission error presents a decreasing trend with the increase of speed,and presents an increasing relationship with the increase of load torque.The test results are consistent with the theoretical analysis.The dynamic lost motion shows an increasing trend with the increase of speed and load torque.The friction torque shows an increasing trend with the increase of speed.The instantaneous transmission efficiency shows a decreasing trend with the increase of the speed,and an increasing trend with the increase of the load torque.This is consistent with the theoretical analysis and verifies that the elliptic gear pair is indeed suitable for low-speed and high-torque occasions.In this thesis,through the combination of theoretical analysis,finite element simulation and transmission test,the meshing characteristics of the elliptic gear transmission system are systematically studied,which provides certain theoretical guidance for the engineering application and related product development of elliptic gear.