Accurate Modeling And Contact Performance Analysis For Spiral Bevel And Hypoid Gears

Spiral bevel and hypoid gears are used as a power transmission component for intersecting or staggered shaft drives.They are widely used in aviation,aerospace,navigation,automotive,machine tools,construction machinery and mining machinery,and many other important fields because of their large transmission ratio,smooth transmission,carrying capacity and other advantages.Obtaining high performance,such as low vibration and low noise,is its important development direction.Firstly,the structure of spiral bevel and hypoid gears is extremely complex,the design of its 3D model is difficult;Secondly,many uncertain factors such as cutting force changes,gear thermal deformation result in the machining of the tooth surface geometry will deviate from the precise standard tooth surface or theoretical design of the tooth surface in the actual process of the spiral bevel and hypoid gears;And Finally,the strengths and weaknesses of spiral bevel and hypoid gears will directly affect the performance of machine.Therefore,the accurate designing of 3D model,high quality and efficient tooth surface machining error correction,precise contact performance analysis are always the hot spots,focuses and difficulties in research of the spiral bevel and hypoid gears by experts and scholars in recent years.This paper investigates 3D modeling,tooth surface machining error correction,meshing performance based on achievements and shortcomings in terms of spiral bevel and hypoid gears in recent years.The main contents of this research can be summarized as the follows:I)Construction of 3D solid model of the spiral bevel and hypoid gears.Firstly,this paper points out the shortcomings of spiral bevel and hypoid gears which are designed and processed on the basis of the conjugate surface principle as the design of the tooth profile curve for the approximate spherical involute;Then,the theory of spherical involute correlation is analyzed and the design scheme of gear model is summarized;And finally,the detailed solution of the tooth surface mathematical model is completed,and the 3D solid model of the spiral bevel and hypoid gears are constructed applying 3D model design software.II)A modification method of spiral bevel and hypoid gears based on ease-off general machining parameters is proposed.Firstly,based on the universal generation model,the universal machine tool settings are represented by using the mathematical high-order polynomial functions and completed the definition of the theoretical tooth surface with those parameters;Then,the ease-off value of the real tooth surface is obtained by the 3D coordinate measurement and the objective function is established;And finally,the error sensitivity coefficient matrix and an improved Levenberg-Marquardat(L-M)algorithm with a trust-region strategy is utilized to obtain accurate and stable solution,the tooth surface processing error of the modification is completed,a high precision,high efficiency of the design and manufacturing of gear tooth is achieved.III)The static and dynamic meshing performance of spiral bevel and hypoid gears are studied applying finite element method based on the high quality finite element mesh model and the reasonable finite element analysis of the pre-processing related settings.Firstly,the contact stress,bending stress of tooth root,shape of tooth contact area and its trajectory are simulated;Then,the calculation method of gear transmission error is analyzed and summarized and the influence law of different load conditions is investigated;And finally,taking the speed and acceleration time of the small wheel and the load as factors,establishing the contrast data curve to study the dynamic meshing performance of spiral bevel and hypoid gears.The research rules and conclusions provide important reference value for the design,manufacture,vibration and noise reduction of spiral bevel and hypoid gears.