Modeling And Transmission Accuracy Analysis Of Helical Cylindrical Gear Drive With Elasticity And Errors

Gear transmission system is one of the most important parts of mechanical products,with the development of products,high requirements are set in gear transmission performance.Helical gear transmission is widely used in various fields because of its superior performance.Take helical transmission system as the research object,transmission accuracy analysis model is established to analyse the effect of errors and elasticity of bearing,shafts and gears on transmission error,the contents of this paper are as follows:Firstly,the model of gear shafting with elasticity and errors is established,a cam mechanism supported by multiple followers with spring reset is used to express the gear shafting,in which cam profiles represent the geometric errors of bearings,spring stiffness represents the structure stiffness of bearings in corresponding directions.Vectors closed and forces balance equations are established,through which the error motion parameters of the cams are solved,and then the motion of any position on the shaft could be obtained.Furthermore,the contact analysis model of helical gear with load is established,the helical are divided into a series of thin spur gear slices,the stiffness of every spur gear slice can be obtained by the variable cross-section beam model,the tilting error of shaft is transformed to the position error of every spur gear slice,through which the complex problem of the helical gear spacial contact is translated into a series of planar contact problems of spur gears,by analysing the clearance and the deformation compatibility of every slices,transmission error and mesh stiffness are obtained.Thirdly,on the basis of the above two models,analytical model of helical gear transmission system is established,in low speed and high load condition,the effects of bearing raceway error`s magnitude,order,phase and the gear`s installation error,load,the shaft elasticity on transmission error and mesh stiffness are analysed.Finally,the contact finite element model of helical gear and the equivalent finite element model considering the elastic support of gear shafting are established respectively.The import error of the model is avoided by the bottom-up modeling method.Multi-dimensional spring element is adopted to equivalent stiffness of shaft and bearing,which greatly simplifies the complexity of the model and improves the calculation efficiency.The meshing stiffness of the ideal gear and different support forms are calculated respectively,and compared with the theoretical model,the correctness of the analytical model established in this paper is proved.Compared with the finite element calculation,the analytical model has higher efficiency.The errors and elasticity of bearings,shafts and gears are considered in the analytical model in this paper,so that the error motion of the gears can be simulated validly,compared with finite element method,it is more efficient,fast prediction of the design results is feasible,it can also lay the foundation for other research on the performance of helical gear transmission drive.