# Study on general conjugate curve bevel gear

According to differential geometry and finite element method, the kinematic geometry and mechanical properties of conjugate curve bevel gear under general contact state are analyzed, and the tooth surface design method and surface properties of conjugate curve bevel gear under general contact state are discussed, On this basis, a general method for tooth surface design of general conjugate curve bevel gear based on spatial conjugate curve meshing theory and curvature free interference condition is developed. The main work and conclusions are as follows:

① According to the conjugate curve meshing principle, the conjugate curve equation of non pure rolling contact conjugate curve bevel gear is deduced. For non pure rolling conjugate curve bevel gear, because the contact point is not limited to the pitch line, the contact line can be taken arbitrarily, which has greater flexibility for the tooth surface design of bevel gear.

② For the general conjugate curve bevel gear, the relative sliding speed between tooth surfaces is not set to zero, which makes it in the first derivative of R2, so that φ Derivative expression of and R2

The formula can not be transformed into a simple form, and finally the condition for judging curvature interference is also composed of a series of formulas, but can not be transformed into a simple inequality.

③ According to differential geometry and gear meshing principle, the necessary condition of no local interference in the meshing process of equiangular helix 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. Since the formula in this chapter no longer requires pure rolling contact, the final set of inequality conditions to judge whether there is interference or not are applicable to all conjugate curve bevel gears.

④ The formula for judging curvature interference is also applicable to pure rolling contact bevel gears, but from the point of view of simplicity of calculation, the formula in Chapter 3 is more practical for pure rolling contact conjugate curve bevel gears.

⑤ The design and finite element analysis of non pure rolling contact equiangular spiral bevel gear are completed. The results of finite element analysis show that the contact stress will not be greatly affected when there is a small displacement at the design contact point under load.

⑥ The maximum contact stress point of tooth surface in finite element analysis is near the theoretical contact point. Therefore, in practical application, it can be considered that the maximum contact stress point of tooth surface is on the theoretical contact point.

Scroll to Top