| The gear is an essential transmission part of the modern mechanical equipment,the working performance of gear directly affects the quality of the mechanical transmission system.The cylindrical gear is widely used in the helicopter gear split torque transmission because of easy fabrication and installation.With the fast-developing of aviation industry,more and more higher transmission performance requirements are put forward to the mechanical drive system.Therefore,it is significant to establish more refined gear dynamic model to predict the vibration characteristics of gear transmission accurately and propose method to reduce the noise and vibration.In consideration of the reliability and efficiency of the analytical model,based on the theory of gear meshing principle,the elastohydrodynamic lubrication principle,the lumped mass method and the optimization design theory,the gear dynamic model which can reflect the actual transmission state of the system is established fully considering the dynamic excitation and tooth surface modification.Then,combining the actual service conditions of gear transmission,the optimal design method of gear tooth surface modification is formed on the basis of the vibration analysis.On the basis of the principle of gear tooth surface generation,the tooth surface equation with parabola modification using worm wheel is deduced.Considering the typical installation errors and tooth surface modification,the tooth contact analysis model is developed to study the influence of the installation error and modification on the gears contact path and the transmission error.The changing of tooth contact path with different combination of second-order parabolic modification and fourth-order parabolic modification is discussed to provide a basic for modification.Considering the backlash and tooth surface modification,the efficient loaded tooth contact analysis(ELTCA)model of cylindrical gear is established combining the finite element method,the analytical method and the nonlinear programming method.The ELTCA model gives adequate consideration in the computational accuracy and efficiency.The finite element method is used to calculate the bending-shear macroscopic deformation of the teeth,and the nonlinear contact deformation is analyzed by the elastic contact theory.The integration of finite element method and analytic method not only improves the efficiency of gear tooth contact analysis but also lays the foundation for the calculation of the dynamic excitation and the design of tooth surface modification.The accuracy and efficiency of the ELTCA model are further verified by the calculation of gear meshing stiffness.To include the lubrication effect in dynamic analysis,the multi-grid method is used to solve the non-Newtonian thermal elastohydrodynamic lubrication model on the basis of the efficient loaded tooth contact analysis(ELTCA)model of gears.Then according to the principle of friction coefficient combination under the mixed elastohydrodynamic lubrication(MEHL)condition,the friction coefficient of gear tooth surface under MEHL is calculated.The calculation model of friction force and friction torque coefficient of tooth surface is proposed with consideration of the actual meshing position obtained from tooth surface point contact analysis model.Considering the effect of oil film transient extrusion,the stiffness of the gear system is regarded as the series of the unlubrication stiffness and the oil film stiffness.Considering the application background of cylindrical gear in the main gear reducer of helicopter,a fast and simple method for modeling the dynamics of cylindrical gear system is proposed.Fully considering the influence of gear mesh stiffness,impact excitation,and tooth surface friction excitation,the bending-torsion-axial coupled dynamic model of the helical gear transmission system are established by Lagrange method.The influences of dynamic excitations and the modification parameters on the vibration characteristics of gears are analyzed which lay the foundation for dynamics modeling and analysis for gear split torque transmission system of helicopter main reduce.The dynamic model of the herringbone gear pair is established considering the axial floating of the herringbone gear used in aviation.The effects of axial angle error,helix angle error and phase angle error on the vibration characteristics of the herringbone gear system are analyzed.It is found that the tooth profile modification can reduce the vibration in the direction of the gear action line,and the tooth lead modification can reduce the axial vibration of the gears effectively.Based on the dynamic model of tooth modification cylindrical gear,a multi-objective optimization process considering the actual working conditions of gear transmission is established to define the optimal ease-off shape of gear surface.With special attention given to computational efficiency,a novel fitness predicted adaptive genetic algorithm(FPAGA)is developed.The algorithm adaptively adjusts the frequency of prediction according to the accuracy of prediction,greatly improves the computational efficiency while guaranteeing the optimization accuracy.An application of FPAGA to design the tooth surface modification of helical gear is presented.The results show that when compared with the traditional genetic algorithm,the average calculation ratio of the real fitness is significantly reduced.Two kinds of design variables(different modifications for the two ends pinion,same modifications for the two ends pinion)of herringbone gear are considered in the paper.The vibration reduction effect and computational efficiency of herringbone gear with the two different modification design parameters are analysed to provide the basis for the selection of the herringbone gear tooth surface modification.Finally,the vibration test system of the cylindrical gear transmission system is constructed.The transmission error and vibration performance of the helical gear and the herringbone gear are measured.It further verify the validity of the theory of vibration analysis and the method of optimum tooth surface modification design of the cylindrical gear. |
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