Identification of transfer function by inverse analysis of self-excited chatter vibration in milling operations

Analysis of the stability limits in self-excited chatter vibration requires the transfer function of the mechanical structure, and thus the accuracy of the analytical prediction strongly depends upon the accuracy of the transfer function, which is generally measured by the impulse response method. However, it is often difficult to measure the transfer function accurately, especially in a case where a small-diameter tool or a workpiece is flexible, or when the transfer function changes as a result of spindle rotation. This paper presents a novel method of identifying the transfer function by utilizing inverse analysis of the self-excited chatter vibration measured during an end milling experiment. In the proposed method, the transfer function can be identified to minimize errors between chatter analysis and experimental results. A basic end milling test verified that the transfer function identified by the developed method is similar to that measured by the impulse response method, and that it yields a more accurate prediction of the stability limits. Further applications using a small-diameter end mill were conducted, and the feasibility of identifying the transfer function by using the proposed method was investigated.