| Hypoid gear transmission has a series of advantages such as large coincidence degree,strong bearing capacity,high transmission efficiency,stable transmission,low noise and large reduction ratio.It can be used to transmit the motion and power between the two crossed-axis.Because of the existence of the offset,it is widely used in mechanical transmission devices that have special requirements on space such as automobiles.The time-varying of the gear pair stiffness causes periodic vibration of the transmission system.Therefore,it is an important research direction to develop the accurate calculation of the time-varying mesh stiffness of the hypoid gear pair and to improve the hypoid gear transmission,it has important theoretical significance and engineering practical value on dynamic performance.In this paper,for Gleason modified roll method(HGM)hypoid gears,gear pair solid modeling,contact analysis(TCA)and loaded contact analysis(LTCA),time-varying mesh stiffness calculation,and pionion machine tool settings’ influence on time-varying mesh stiffness and dynamic performance are studied.The main research work of the paper is as follows:(1)Based on the principle of gear meshing,the mathematical expression of the tooth surface equation of the wheel and pinion is derived from the equation of the machining tool.The tooth surface contact equation is established according to the conjugate condition,the contact trajectory and the contact ellipse is gotten by solving.Then the tooth surface equation is solved based on Matlab programming to obtain the coordinate of the tooth surface discrete points.The imageware software is used to fit the tooth surface and the Ug software is used to establish the 3D model of the gear pair.(2)The finite element model of the hypoid gear pair is established.The substructure method is used to solve the normal compliance matrix of the contact tooth surface.Then the mathematical model of the loaded contact analysis for the hypoid gear is established.The iterative algorithm is used to solve the loaded contact equation and obtain the tooth surface contact force and contact deformation,and then the time-varying mesh stiffness of the gear pair is calculated,which is in good agreement with the finite element calculation result.(3)Based on the LTCA time-varying mesh stiffness calculation method,the influence of HGM pinion machine tool settings on the gear tooth single tooth mesh stiffness and the comprehensive mesh stiffness is studied.As the shaped wheel cone pitch and tooth height curvature correction coefficient increase,the mesh stiffness shows an increasing trend.As the vertical and radial tool positions,the mesh stiffness shows a decreasing trend.(4)Considering the internal excitations such as time-varying mesh stiffness,transmission error and flank clearance,the model analysis of the bending-torsional-axis coupling vibration of the hypoid gear transmission is established based on the lumped parameter method.the influence of different pinion machine tool settings on the vibration acceleration of the gear pair,dynamic transmission error and dynamic meshing force are studied,it is concluded that the increase of the tooth curvature correction coefficient and the production cone pitch is beneficial to improve the dynamic performance of the gear pair,while the increase of the vertical wheel position and the radial tool position will degrade the gear pair dynamic performance. |
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