Active design of tooth profiles using parabolic curve as the line of action

• A design method of profiles using a parabola as the line of action is proposed.
• The mathematical models of gears using a parabola as the line of action are built.
• The stresses of the proposed gear are lower than those of the involute gear.
• The contact ratio can be calculated directly from the equation of the parabola.
• The profile can be controlled flexibly by changing the parameters of parabola.

This paper proposes a method for the design of gear tooth profiles using parabolic curve as its line of action. A mathematical model, including the equation of the line of action, the equation of the tooth profile, and the equation of the conjugate tooth profile, is developed based on the meshing theory. The equation of undercutting condition is derived from the model. The influences of the two design parameters, that present the size (or shape) of the parabolic curve relative to the gear size, on the shape of tooth profiles and on the contact ratio are also studied through the design of an example drive. The strength, including the contact and the bending stresses, of the gear drive designed by using the proposed method is analyzed by an FEA simulation. A comparison of the above characteristics of the gear drive designed with the involute gear drive is also carried out in this work. The results confirm that the proposed design method is more flexible to control the shape of the tooth profile by changing the parameters of the parabola.