| Spiral bevel gear has the advantages of high loading capacity,changing torque transmission direction and smooth transmission.It is widely used in aviation,automobile,ship and other engineering fields and its working transmission performance directly affects the smooth operation of transmission system.Since the tooth surface of spiral bevel gear is a complex three-dimensional curved surface,it becomes very difficult to accurately calculate the time-varying meshing stiffness of spiral bevel gear.But the time-varying meshing stiffness of gears is the basis of dynamic research.So it is one of the urgent problems to establish a general and more accurate calculation method for the meshing stiffness of spiral bevel gear.With the development of aerospace transmission technology in the direction of high speed,heavy load and light weight,the requirements for dynamic characteristics of spiral bevel gear are also rapidly increasing.In this paper,an aviation spiral bevel gear transmission is taken as the research object.The traditional method of calculating time-varying meshing stiffness of spiral bevel gears is improved.The bending-torsion-axis-pendulum coupling dynamic model of spiral bevel gears transmission system considering flexibility of shaft segment is established by node finite element method.The effects of load torque,contact ellipse long axis length and contact path direction on the dynamic vibration characteristics of transmission system are studied.The main contents are as follows:(1)Based on the tooth surface active design method,the tooth surface of spiral bevel gear is designed.The three dimensional solid model of spiral bevel gear is established by calculating the machining parameters of gear and pinion.And the influence of contact ellipse long axis length and contact path direction on tooth surface contact mark is studied.(2)The traditional method of calculating time-varying meshing stiffness of spiral bevel gears is improved.A single node meshing stiffness is introduced.The meshing stiffness of each node on the tooth surface is superimposed to calculate single tooth meshing stiffness.The node contact force and node elastic deformation solved by explicit dynamic finite element analysis are more accurate.Based on the established meshing stiffness calculation model and the dynamic meshing angle of gear and pinion obtained by explicit dynamic analysis,the time-varying meshing stiffness and transmission error of the spiral bevel gear are obtained.Furthermore,the influence of load torque,contact ellipse long axis length and contact path direction on the time-varying meshing stiffness and transmission error of gear pair were studied.(3)According to the structural characteristics of spiral bevel gear transmission system,the dynamic differential equations of constant section shaft element,variable section shaft element,spiral bevel gear meshing element and bearing support element are analyzed and derived.Based on the node finite element method,the bending-torsion-axis-pendulum coupling dynamic model of spiral bevel gear transmission system considering the flexibility of shaft segment is established.The internal excitations such as time-varying meshing stiffness,meshing error and backlash are considered in the model.The variation of natural frequencies of transmission system under different meshing stiffness of gears and bearing support stiffness is also studied.(4)The precise integration method is used to solve the dynamic differential equation of spiral bevel gear transmission system,and the steady-state vibration response of each element node of the transmission system is obtained.The effects of variable input speed,variable load torque,variable contact ellipse long axis length and variable contact path direction on the vibration characteristics of transmission system are studied,which provides a theoretical basis for the tooth surface design of spiral bevel gears and the reduction of transmission system vibration and noise. |
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