The rise of automobile industry in the 20th century has promoted the development of gear technology. The rise of navigation, aviation and aerospace industries and the use of modern large complete sets of industrial equipment put forward higher requirements for the quality, strength and reliability of bevel gear transmission. Some of these requirements can only be met by developing new bevel gear tooth surfaces. In the research and development of domestic high-grade bevel gear transmission products, there are still some problems, such as long scientific research cycle, high scientific research cost and difficult industrialization. It is mainly reflected in the fact that one or more requirements in the properties of high efficiency, high precision, high bearing capacity, high power density, long life, low noise and small volume required in the design process of bevel gear box are difficult to be met. These indexes are closely related to the sliding rate, contact strength and bending strength of bevel gear pair in transmission mechanism.
There is always relative sliding between meshing tooth profiles of conjugate surface bevel gears which are widely used now. For bevel gear transmission, the relative sliding between tooth surfaces will generally have a negative impact on the performance of the transmission mechanism. For example, the sliding friction between the tooth surfaces will bring friction loss and aggravate the wear of the tooth surface. In addition, the sliding contact will increase the contact stress of the tooth surface, resulting in the failure of the tooth surface. When the conjugate curve meshing theory is applied to design the tooth surface of bevel gear, because the conjugate curve is actually the contact line on the tooth surface of bevel gear during meshing, the contact line can be easily controlled. When the contact point is always controlled on the pitch line, there is no relative sliding between the two tooth surfaces, which can effectively avoid the problems caused by sliding friction to bevel gear transmission. In the previous article, the basic theory of conjugate curve meshing has been discussed. Therefore, how to use the conjugate curve meshing theory to establish the pure rolling contact conjugate curve bevel gear model is discussed.
According to differential geometry and finite element method, the kinematic geometry and mechanical properties of pure rolling contact conjugate curve bevel gear are discussed. The conjugate curve solution method and the properties of curve and surface of pure rolling contact conjugate curve bevel gear are discussed, On this basis, the tooth surface design method and forming theory of pure rolling contact conjugate curve bevel gear based on spatial conjugate curve meshing theory and curvature free interference condition are developed. The main work and conclusions are as follows:
① According to the conjugate curve meshing principle, the conjugate curve equation of pure rolling contact bevel gear is deduced. For this bevel gear, the conjugate curve is on the pitch cone, that is, the contact point is always on the pitch cone. At the same time, according to the two conjugate curve equations, Γ 1 and Γ 2 has the same expression, that is, they are the same type of conical curve.
② When deriving the pressure angle of conjugate curve bevel gear with pure rolling contact, it can be seen that the pressure angle and θ 1 there is a connection. This means that despite being right θ There are no clear restrictions, but in fact, θ The choice of 1 is still not arbitrary. For example, in practice, the general pressure angle is 20 degrees, which has actually been determined θ The value of 1.
③ According to differential geometry, the necessary condition of no local interference in the meshing process of equiangular helical gear pair is deduced. This condition is an important basis for the construction of solid tooth profile based on the basic principle of conjugate curve meshing. Because the final inequality to judge whether there is interference or not is only based on the two conditions of no local interference and pure rolling contact, the final inequality is actually applicable to all pure rolling contact gears.
④ Based on the theoretical model of pure rolling contact conjugate curve bevel gear, the models of pure rolling contact equiangular spiral bevel gear, equidistant spiral bevel gear and long epicycloid bevel gear are deduced, and the solid model is established.
⑤ The finite element analysis of the models of equiangular spiral bevel gear, equidistant spiral bevel gear and long epicycloid bevel gear with pure rolling contact is completed. The results of finite element analysis show that the actual contact area is still near the pure rolling contact point, so as to maintain the approximate pure rolling contact.
⑥ The maximum contact stress of pure rolling contact conjugate curve bevel gear in finite element analysis can be lower than 1290mpa, which shows that it has the potential to be applied to power transmission.