Analysis of the Formation Mechanism of Surface Waviness in Tooth Profile Cold Roll-Beating

Abstract

Cold roll-beating of tooth profiles is an efficient and environmentally sustainable metal forming process. Because cold roll-beating constitutes a discontinuous forming process, it inherently generates periodic waviness on the tooth surface and at the root. This paper first derives analytical equations to calculate the waviness curve at the tooth root based on the kinematics of the cold roll-beating process. Subsequently, FE simulations were performed to extract the resulting root waviness curve. The simulated wave height is significantly larger than the analytical prediction, with the wave trough measuring 0.02 mm higher than the nominal tooth root circle radius. To investigate material flow behavior, this research establishes a slip-line field model for the deformation zone and utilizes FE software to map the velocity vectors of the metal particles. The research demonstrates that the analytical method fails to accurately predict the waviness curve; metal bulging ahead of the roller constitutes the primary cause of tooth surface waviness; and the final waviness profile emerges from the continuous overlapping of these localized material bulges. These findings effectively explain why the minimum inter-roller distance in actual production must be slightly smaller than the diameter of the tooth root circle. Physical experiments conducted on a custom-built testing machine measure the sample’s root waviness, yielding results that align closely with the FE simulations. These experimental results subsequently validate the numerical analysis.