Study on spatial curve meshing and its application for logarithmic spiral bevel gears

• We propose a method to build any shape of tooth surfaces of space curve meshing.
• We demonstrate this method for gear meshing correctly in math.
• We propose the model of pure-rolling contact logarithmic spiral bevel gears.
• The loaded contact analysis of these bevel gears agrees with the method and model.
• These bevel gears could bear heavier loads.

The goal of the paper is to develop the theory of curving meshing and apply it in high performance gear transmission. With this aim, this study investigates the gear geometry and kinematics of space curve meshing in gear design field. Here, definition of conjugate curves and the method of obtaining them are described. What's more, an extended method to get tooth surfaces from a space curve and its conjugate curve is proposed and the meshing characteristics of these tooth surfaces are argued. Then, based on arguments for conjugate curve theorem, this paper proposes the mathematical model of conical-helix bevel gears from the idea of logarithmic spiral bevel gears. To validate this model and investigate the tooth contact characteristics of conical-helix bevel gears, the numerical example of a pair of these gears with specific profiles is represented by applying the general computer program, ANSYS 14.0. Results show that the main characteristics of these gears include loads in the same direction, pure rolling contact and low bending stresses. The results also agree with the theoretical derivations for conjugate curves and conical-helix bevel gears.