Tooth Surface Optimization Design And Contact Strength Analysis Of Internal Line Gear

The contradiction between the complex profile and structure miniaturization restricts the application of gear mechanism in micro device.The line gear fundamentally avoids undercut and minimizes the space usage,which promotes the development of the gear mechanism in the micro/nano field.At present,some breakthroughs have been made in the fields of design theory,manufacturing,failure analysis and engineering application of line gear.However,the existing research mainly focuses on the external-meshing line gear mechanism,and less on the internal meshing line gear.This paper mainly studies internal line gear mechanism.Based on the spatial curve meshing theory,an internal meshing line gear pair is designed for arbitrary intersecting shaft transmission,and the sliding ratio is used as the constraint parameter to optimize the tooth surface design.The optimal sliding ratio is taken as the parameter constraint condition to optimize the tooth surface structure.The bearing capacity of tooth surfaces is low because of point-contact meshing happen on surfaces.This paper discusses the numerical calculation method for contact stress of internal line gear on tooth surface,and determines the relation between design parameters and contact stress,so as to provide a theoretical basis for designing tooth surface with higher contact strength.Specifically,the main work of this article includes the following aspects:1.The tooth surface forming principle of internal meshing line gear is studied.Based on the space curve meshing theory,the gear meshing equation and the conjugate contact line parameter equation for the intersecting shaft with a transmission angle from 0 to 90° are solved.And the circular arc profile of the cross section along the direction of any contact angle is established.The tooth surface forming method of internal meshing line gear is studied.According to the contact curves and section tooth profile curves,the tooth surface mathematical models of convex-convex,convex-concave and convex-flat contact are established,and the bearing capacity of tooth surface with three contact forms is analyzed.2.The tooth surface optimization and motion simulation of internal meshing line gear are studied.According to the space curve meshing principle,the calculating formula of instantaneous sliding rate of internal meshing line gear is deduced.And the optimal meshing conditions for different transmission occasions are determined.By determining the design parameter selection criteria under the optimal meshing state,the tooth profiles optimization design are achieved to reduce the relative sliding,and the internal meshing line gear pairs with small sliding or pure-rolling are constructed.The solid model of internal meshing line gear pairs are established according to mathematical models,and the kinematics simulation are carried out by UG software to verify the transmission stability of gear pairs and the correctness of tooth surface construction.3.The contact strength of tooth surface of internal meshing line gear is studied.Based on Hertz contact theory,the contact model of internal meshing line gear is established.The theoretical numerical calculation method of contact stress for line gear is deduced,and the relationship between contact stress of tooth surface and design parameters is determined.According to finite element simulation,the variation trend of contact stress in meshing period is studied,and the feasibility of theoretical calculation method is verified,which provides a theoretical basis for designing internal line gear pairs with high contact strength tooth surfaces.