Research On Some Key Technologies Of Computer Aided Engineering For Logarithmic Spiral Bevel Gear

The spiral angle of the conventional spiral bevel gear at a point on tooth trace curve varies with different positions.In order to ensure the spiral angles of meshing contact point at a point are equal,several parameters of the cutters and machine tools need to be adjusted for the manufacture which increasing the difficulty for the manufacture of conventional spiral bevel gear.Logarithmic spiral bevel gear is a novel kind of spiral bevel gear which using the conical logarithmic spiral curve as tooth trace curve and using the involutes as tooth profile curve.The spiral angle at a point defined between the tooth trace curve tangent direction and the cone generatrix line direction is a constant.The logarithmic spiral bevel gear has better transmission characteristics than conventional spiral bevel gear.Based on the logarithmic spiral bevel gear,the system researches focus on three-dimensional parametric modeling,meshing angular velocity and tangential contact force simulation,free modal analysis,meshing numerical simulation and five-axis NC machining experiment are carried out in this dissertation.The main research work can be summarized as follows:(1)Research on three-dimensional parametric modeling of logarithmic spiral bevel gear based on Boolean subtraction operation.A novel modeling method based on Boolean subtraction operation is put forward in this paper.A pair of logarithmic spiral bevel gears whose number of teeth is 37:7,with modules being 4.5 mm,normal pressure angle being 20 degree and spiral angle being 35 degree are taken as an example for the accurate modeling.The interfaces of parametric modeling are designed,and the three-dimensional parametric modeling of logarithmic spiral bevel gear is realized by using the UG/OPEN GRIP as the second development tool.(2)Simulation research on the meshing angular velocity and tangential contact force of the logarithmic spiral bevel gear based on the Hertz contact theory.The theoretical calculation formula for the meshing angular velocity and tangential contact force simulation are established.The meshing angular velocity and tangential contact force simulation of the working condition for a pair of logarithmic spiral bevel gears and conventional spiral bevel gears have been done.The simulation results show that the transmission stability of the logarithmic spiral bevel gear are superior to the conventional spiral bevel gear in meshing angular velocity and tangential contact force.(3)Free modal analysis of spiral bevel gear based on the Lanczos numerical iterative calculation method and experimental verification based on PolyMax method.The free modal analysis of logarithmic spiral bevel gear pinion,logarithmic spiral bevel gear wheel,logarithmic spiral bevel gear assembly and conventional spiral bevel gear wheel are established based on the Lanczos numerical iterative calculation method.The experimental platform of free modal analysis for spiral bevel gear wheel is constructed by using LMS modal analysis module.The modal parameters are extracted by using the least squares complex frequency domain PolyMax method.The experimental modal test results are in good consistence with the results of finite element free modal analysis.(4)Numerical simulation of a pair of logarithmic spiral bevel gears meshing(Tooth Contact Analysis)based on penalty function method.According to the principle of penalty function method,the additional constraint conditions are introduced into the solution of functional minimum value,and the penalty function equation is established to solve the contact problem of a pair of logarithmic spiral bevel gears meshing by the finite element method.The numerical simulations of meshing tooth contact stress and tooth root bending stress for a pair of conventional spiral bevel gears and logarithmic spiral bevel gears have been done.The simulation results are compared with the theoretical analytical calculation results based on ISO10300-2001.The contact patch results by using numerical meshing simulation are consistent with the contact patch results by experiment.(5)Machining research and milling parameter optimization for the prototype of a pair of logarithmic spiral bevel gears on general five-axis vertical machining center.The blanks of a pair of logarithmic spiral bevel gears are processed on conventional horizontal lathe C6140A1.The tool path and path interval are determined according to the relations between the ball-end cutter and tooth surface of a pair of logarithmic spiral bevel gears.The tool path of numerical control machining for a pair of logarithmic spiral bevel gears are generated.A pair of tapered depth prototype of logarithmic spiral bevel gears are processed on DMG DMU 40 monoBLOCK general five-axis vertical machining center.