Research On Coupled Dynamic Characteristics Of Hypoid Gear Transmission System Considering Bearing Defects

Hypoid gears are suitable for large shaft angle transmission due to offset.Compared with other gears,Hypoid gear have the advantages of smooth transmission,large coincidence,high load capacity and low noise and is one of the most complicated gear transmission system.Bearings are important supporting components of hypoid gear transmission systems,and their performance has an important impact on system dynamics.With the development of high-speed and integrated machinery and equipment,the operating conditions of bearings have become more severe,and failure rate is higher.As an important cause of failure,bearing defects have received widespread attention from scholars.The existence of bearing defects will cause abnormal vibration of the bearing,and the vibration transmission through the shaft will further affect the gear system,and worsen the dynamic characteristics of the system and shorten its service life.Therefore,investigating the impacts of bearing waviness on the dynamics of a geared rotor system is of great importance,which is helpful for engineers to understand the system dynamic response characteristics and vibration laws induced by bearing defects and improve the design quality of gear systems.In this paper,a dynamic model of a hypoid gear-shaftbearing coupled system considering bearing defects is established.The effects of off-sized rollers,race surface waviness and race surface spall defects on the dynamic behavior of the gear system are studied,and the vibration characteristics of the gear system caused by the bearing defects are revealed,which helps to improve the reliability of the gear system.The major research work of this dissertation are as follows:(1)Based on the process and mesh principles of hypoid gears,a mathematical model of the tooth surface was established,and a quasi-static tooth surface loaded contact model was generated by finite element analysis software.The time-varying mesh point position and time-varying direction of mesh force action line,time-varying transmission error,and time-varying mesh stiffness are calculated and analyzed,which provide input parameters for studying the dynamic characteristics of hypoid gear systems.The results show that the change of the equivalent mesh point along the tooth length direction is greater than that along the tooth height direction,and the first-order harmonics of mesh stiffness and transmission error dominate.(2)The finite element method is used to couple the lumped parameter models of gears,shafts,and bearings to establish a hypoid gear-shaft-bearing coupled system dynamics model.The model comprehensively considered nonlinear bearing forces,flexible shafts,time-varying transmission errors and time-varying meshing stiffness were considered and laid the foundation for subsequent dynamic analysis.Based on this model,modification and deformation were carried out,and dynamic models considering off-sized rollers,dynamic model considering raceway surface waviness,and dynamic model considering raceway surface spall defects were established.(3)The effects of a series of dynamic parameters on the dynamic mesh force,dynamic transmission error and dynamic bearing force of the system under defect-free conditions were studied,including the rotational speed,bearing radial clearance,and the harmonic order of mesh stiffness and transmission error.The results show that the vibration of the No.2 bearing closest to pinion is the most intense in the range of 300～12000r/min.As the bearing radial clearance gradually increases from 0μm to 60μm,the peak-to-peak value of dynamic mesh force increases by 7.38%,10.41%,17.35%,and 22.74%,respectively.The peak-to-peak values of dynamic transmission error increases by 5.40%,7.61%,12.56%and 16.48%,respectively.As the harmonic order of meshing stiffness and transmission error excitation increases from 1st order to 3rd order,the peak-to-peak value of dynamic transmission error,dynamic mesh force and dynamic bearing force increases.(4)The effects of off-sized rollers,race surface waviness and spall defects on the hypoid gear-shaft-bearing coupled system’s vibration are analyzed.The influences of offsized rollers amplitude,the number of off-sized rollers,the position distribution of the off-sized rollers,the number of surface waviness,the amplitude of waviness,and the width of spall defects on the vibration characteristics were investigated respectively.The results show that the error absolute value of off-sized roller is increased from 0μm to 6μm,the number of off-sized rollers is increased from 0 to 3,and the angle between off-sized rollers is reduced from 120° to 24° will increased the amplitude corresponding to bearing cage rotation frequency.The number of waviness and the amplitude of waviness have a significant effect on the dynamic transmission error and dynamic mesh force,including changing the characteristic frequency and vibration amplitude.When the number of waviness is 15,30 and 45,that is,when the number of waviness is equal to the number of bearing rollers or its multiple,the dynamic transmission error and dynamic mesh force response peak.The dynamic transmission error and dynamic mesh force contain highfrequency components due to the excitation of spall defects on the raceway surface,and the root mean square value and peak-to-peak value increase with the increase of spall width.