Research On The Transmission Stability And Near-periodic Motion Of Spur Gear Pairs Considering Pitch Deviatio

Gear transmission system is most widely used to transmit the power and motion in mechanical field.Higher precision and stability of gear transmission system are required by the high precision mechanical equipment.The short-period errors,such as pitch deviation,which induced by machining and abrasion,are key factors affecting transmission stationarity.The influence of teeth difference caused by pitch deviation on the time-varying parameters and dynamics characteristics of gear transmission system is studied.The influence mechanism of pitch deviation on transmission stationarity is revealed.It provides a theoretical basis for the parameters optimization design of the high-precision gear transmission system.The research object is the basic spur gear pair in the dissertation,and the main research contents are shown as follows.Firstly,the meshing characteristics of the spur gear pair with pitch deviation are analyzed based on its meshing principle.The calculation models of time-varying parameters of the spur gear pair with pitch deviation are established and analyzed.There are nine meshing conditions for the spur gear pair considering pitch deviation.The time-varying backlash affected by the pitch deviation shows sinusoidal variation trend.The pitch deviation results in the decrease of the time-varying meshing stiffness.The corner contact caused by pitch deviation leads to increase vibration of teeth and decrease the transmission stationarity of the gear.Secondly,the characterization method of pitch deviation in nonlinear dynamics equations is established.The nonlinear dynamics model of spur gear pair considering pitch deviation under multi-state meshing is proposed.The meshing states of the dynamics model include mesh-in at corner contact,mesh-out at corner contact,single and double pair drive-side teeth mesh,single and double pair back-side teeth contact and tooth disengagement.This dynamics model is closer to the actual meshing state.The nonlinear dynamics characteristics and transmission stationarity of the spur gear pair are studied.The number of mutations of dynamic meshing force increases when the drive-side teeth mesh,tooth disengagement and back-side teeth contact all appears in spur gear pair which leads to nonstationary transmission.The possibility of the tooth disengagement,back-side teeth contact and chaotic motion of system increases with the increase of complexity of pitch deviation values.A reasonable range of system and operating parameters can improve the gear transmission stationarity.Finally,a special kind of complex periodic motion is found in the study of the nonlinear dynamics of system which is defined as neighboring periodic motion,and its identification method is established.The dynamics characteristics of the system in different time scales are analyzed.The integrity of motion for the system with variation of parameters is studied.The actual motion period of system is the number of mapping points obtained in long time scale.The pitch deviation affects the range of parameters of coexisting motion for spur gear pair,and affects its transition process.The attractors of the system considering pitch deviation show points clusters.The investigation of the neighboring periodic motion provides a theoretical basis for the dynamics analysis of gear transmission systems considering other short-period errors.