A Generalized Algorithm and Simulation Verification of Non-circular Gear Tooth Surface Data Points

This paper presents a method to establish a mathematical model of non-circular gear tooth surface, which can avoid the issues of low accuracy and low efficiency in extracting tooth surface of previous non-circular gear tooth surface design methods. A new tooth envelope method is proposed, where the gear inserting knife rotates only on a fixed axis, while the non-circular gear rotates and translates in the horizontal plane. By utilizing the conjugate theory and coordinate transformation theory, the coordinate system, meshing equation, and tooth surface equation of the non-circular gear are obtained, and the 3D point cloud of the tooth surface is programmed. Finally, the mathematical model of the tooth surface proposed in this paper is used to establish multiple pairs of non-circular gears with different orders, and the correctness and generality of the method are verified by comparing the simulated and experimental transmission ratio with the theoretical transmission ratio in the test.