| Gear transmission is the most widespread transmission way in the field of mechanical engineering.Gear system performance affect the reliability of machine,and gear modification has great influences on meshing characteristics and vibration characteristics of gear system,so it has great significance to investigate gear modification.Taking spur/helical gears as the research object,an analytical mesh stiffness calculation model is established considering fillet-foundation stiffness correction,nonlinear contact,effective elastic modulus,gear addendum modification and friction for calculating the time-varying meshing stiffness(TVMS)of standard gears and the gears with modification,and the optimization of modification parameters is carried out based on the stiffness calculation model.Time-varying meshing stiffness of the gear pair which including optimized modification parameters is introduced to the dynamic model of gear system,and the effects of modification parameters on vibration characteristics of the gear system are analyzed.The main contents include:(1)Considering extended tooth contact,fillet-foundation stiffness correction,nonlinear contact and other influential factors in actual meshing process,an analytical mesh stiffness calculation model is established under gear tip relief,lead crowning relief and mixed gear modification.Meshing characteristics are analyzed with different modification parameters,and the optimization of modification parameters are studied through first five amplitude of TVMS Fast Fourier transform(FFT)and gear deformation.Gear tip relief can only make TVMS more smooth under alternating area between single and double teeth meshing area.However,TVMS decreases of the overall cycle and the amplitude of the wave reduces with lead crowning relief which is different from tip relief.(2)Based on gear engagement principle,the helical gear is divided into independent slice spur gears along tooth width direction.An analytical model for helical gear stiffness calculation is proposed considering the effects of fillet-foundation stiffness correction,nonlinear contact,effective elastic modulus,gear addendum modification and friction.The validity of the proposed model is verified by comparing TVMS with finite-element(FE)method and references.In addition,the comparison of the computer efficiency and precision of TVMS are taken between empirical formula method,traditional analytical method,FE method,FE-analytical method and the improved analytical method in the paper,and the advantages and disadvantages of each model are evaluated.The results show that the improved analytical method can guarantee the computer efficiency and precision of TVMS at the same time.(3)An analytical model of helical gear pair is proposed considering different gear modification(such as gear tip relief,tooth lead crowning relief and mixed gear modification),and the proposed model is verified by comparing TVMS with FE-analytical method and references.Meshing characteristics of helical gear are analyzed under different modification parameters,and the optimization of gear modification parameters are discussed through first five amplitude of TVMS Fourier transform and gear deformation.The effects of gear tip relief on TVMS of the helical gear pair are different from spur gear pair,TVMS of helical gear pair decreases in the whole meshing cycle with gear tip relief and lead crowning relief.Besides,the volatility of TVMS reduces relative to the standard helical gear pair.(4)The excitation of mesh stiffness and transmission error are introduced into the gear rotor system dynamics model,and the effects of different modification parameters on the vibration response of system are studied.Results show that the choose of gear modification parameters should base on the gear basic parameters and vibration response of system with mesh stiffness excitation.Lead crowning relief amount can reduce when there is not edge contact,and tip relief amount should be suitable for vibration deduction and guarantee system stability. |
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