One-Dimensional Chatter Stability Analysis and Simplified FRF Measurement for Three-Dimensional Cutting

Chatter vibration is one of the huge obstacles in the cutting process since it often results in poor cut surface, severe tool wear, and low productivity. For improvement of the cutting process in the manufacturing field, chatter stability analysis can be conducted to predict the chatter-free conditions. In order to conduct it, the frequency response function (FRF) must be measured. However, this measurement requires specialized knowledge and long measurement/analysis time. In particular, to perform accurate chatter stability analysis for three-dimensional cutting such as the turning process, it was necessary to measure 2 × 3 = 6 components of the dynamic compliance between three-directional cutting forces and two-directional vibration displacements. In this study, a one-dimensional chatter stability analysis model for three-dimensional cutting is proposed. In addition, a simplified FRF-measurement is proposed based on this model. Specifically, through the examination of the growth mechanism of chatter vibration in the three-dimensional turning process, it is found that the chatter stability analysis can be reduced to a one-dimensional analysis by considering the dynamic compliance between the resultant cutting force and the vibration displacement in the uncut chip thickness direction (named as dimension-reduced dynamic compliance). Since this dimension-reduced dynamic compliance can be identified by applying the force in one direction and measuring the vibration in one direction, it is possible to reduce the dimension of the dynamic compliances from three to one and also the measurement time. Therefore, it makes possible to conduct accurate chatter stability analysis both quickly and practically by using the proposed FRF-measurement method. To verify the effectiveness of the method, the equivalent dynamic compliances obtained by the conventional and proposed methods are compared.