Research On Design And Optimization Of Line-Contact Spiral Bevel Gears

In order to solve the problems that the design and optimization of spiral bevel gears could only realize local contact based on point-contact,which led to small contact area and poor contact performance of tooth surface,this thesis proposed a design and optimization method of line-contact spiral bevel gears,aiming at expanding contact area and improving contact performance of tooth surface by changing tooth profile in the theoretical design stage.The design method of line-contact spiral bevel gear was based on the method of adjustment parameters compensation of machine tool,in which the gear was processed by format method,and the pinion was processed by generated method with machine tool parameters compensated,completing the design of line-contact spiral bevel gear under the working conditions.To satisfy high contact performance of tooth surface,the comprehensive design method including two meshing limit lines,addendum becoming sharp,lubrication performance and bearing performance of line-contact spiral bevel gear was studied.The optimal design of tooth contact performance was realized.The main contents of thesis are as follows:(1)According to the principle of crown generating gear,the essence of line-contact tooth surface of bevel gear was expounded.Based on the principle of differential geometry and gear meshing,the meshing coordinate system of bevel gear was established,and the general meshing equation and the general parameterized expression equation of line-contact tooth surface were derived,which provided a general mathematical formula of line-contact tooth surface under different coordinate systems in a fast way.(2)By comparing the theoretical design of spiral bevel gear with the actual machining method,the reason why the traditional machining method could not process line-contact tooth surface was analyzed.Combined with the theory of geometric topological error of tooth surface,the compensation method of adjustment parameters of machine tool and the least square optimization mathematical model of tooth surface deviation,a design method was proposed to make the tooth surface of pinion processed by compensating the adjustment parameters of machine approach the tooth surface which theoretically conjugate with gear,so that the line-contact spiral bevel gear could be obtained by a certain processing method.A group of tooth blank parameters were introduced to verify the method.(3)To meet the requirements of high contact performance of the tooth surface,an optimization design method for the tooth profile parameters of line-contact spiral bevel gears was proposed.Taking the tooth profile parameters as the optimization variables,eliminating two kinds of boundary lines and preventing the addendum becoming sharp as the constraint conditions,a multi-objective optimization mathematical model was established with the comprehensive parameters of lubrication performance and the length of the instantaneous contact line as objectives,and a bare-bones multi-objective particle swarm optimization algorithm was introduced and improved to obtain the optimal tooth profile parameters.A pair of spiral bevel gears with specific parameters were taken as the research object,and the numerical simulation results of the tooth surface showed that the contact area was expanded and the contact performance were improved,which provided a reference for the optimal design of spiral bevel gear.(4)In order to verify the theoretical design and optimization method,a 3D model of line-contact spiral bevel gear was established and the finite element simulation was carried out.The simulation results showed that the working tooth surface had no interference and was in full tooth surface contacted after optimization,which proved the above method and provided theoretical guarantee for the application of line-contact spiral bevel gear.