Research On The Meshing And Dynamic Characteristics Of Gear Systems Considering Tooth Profile Errors

Gear transmission systems are widely applied in the power transmission,speed conversion and other occasions in industry.In practice,the gear tooth surface usually deviates from the theoretical tooth profile,leading to tooth profile error.The tooth profile error mainly comes from tooth modifications(profile relief and lead modification,etc.),tooth surface damage(pitting,spalling,wear and scuff,etc.),manufacturing error and assembly error(parallel misalignment and angular misalignment).Tooth profile errors change the contact status and meshing characteristics.The changes of meshing characteristics will further affect the dynamic characteristics of gear systems.The aim of this study is to establish a dynamic model to analyze the meshing characteristics and dynamic characteristics of the gear pairs with tooth profile errors.The relationships between tooth profile error and the meshing/dynamic characteristics are further discussed.The research topics of this study include:(1)Based on the loaded tooth contact analysis(LTCA)method,an evaluation model for the meshing characteristics of gear pairs with tooth modifications is established.The finite element method is used to verify the accuracy(the error for mesh stiffness calculation is less than 5%)and efficiency of the proposed method.The effects of the profile relief and lead crown on the mesh stiffness,tooth root stress and contact stress are analyzed.The results show that the profile relief can avoid the sudden change of the stiffness and stress between the single tooth contact and double tooth contact;the lead crown can compensate the misalignment and relieve the stress concentration caused by partial load.(2)The two-dimensional(2D)and three-dimensional(3D)LTCA methods are used to acquire the load distribution under the condition of even load and partial load,respectively.Based on the obtained contact stress and Archard’s wear theory,the wear prediction model of gear pairs is established.In order to demonstrate the validity of the proposed model,the wear depth obtained from the proposed model is compared with that obtained from a published literature.The effects of the wear,profile relief,lead crown and misalignment on the meshing characteristics are analyzed.The results show that the tooth modification can relieve the stress concentration caused by the misalignment,reducing the severe wear at the tooth root and the end face of the face width.(3)For the realistic spalling morphology obtained by fatigue experiment,based on the 3D LTCA method,an evaluation model for the meshing characteristics of gear pairs with realistic spalling morphology is established.The meshing characteristics(meshing stiffness and contact stress)of spalled gear pairs are analyzed by using the proposed method,the traditional equivalent method of contact line length and the finite element method.The results show that the proposed method can accurately calculate the mesh stiffness and contact stress of the gear pairs with complex spalling morphology.(4)Based on the Timoshenko beam theory and shell theory,a flexible geared rotor dynamic model is established.The interaction between the wear and gear dynamics is studied.The excitation mechanism of wear and partial load on the vibration of flexible gear foundation is analyzed.The results show that the accuracy of quasi-static wear prediction model is similar as the dynamic wear prediction model in non-resonant speed regions.The time-varying meshing moment caused by the wear and partial load provides the exciting force components in the axial direction,leading to the nodal diameter vibration of the thin-rimmed gears.(5)Considering the realistic spalling morphology,a geared rotor dynamic model is established.The proposed model is verified by comparing with the experimental results in time domain,frequency domain and statistical indicators.The effects of the spalling morphology and spalling position on the vibration characteristics and fault characteristics are analyzed.The effects of the meshing moment caused by spalling on the vibration of flexible gear body are discussed.The results show that the impact of the time domain signal and the sideband frequency will become more obvious with the increase of fault degree.The vibration of gear foundation caused by spalling-induced impact excitation is the superposition of various nodal diameter vibrations.