Multi Frequency Solution of Chatter Stability for Low Immersion Milling

Finish milling is usually required in the peripheral milling of thin aircraft webs with long end mills, where the structures are flexible and radial depths of cut are small. The spindle speed and depth of cut must be selected optimally to avoid both forced and chatter vibrations, which in turn enables production of the parts within specified tolerances. Recent articles show that stability pockets differ at certain speeds when the radial immersion in milling is low and the machining process is highly intermittent. This paper presents a stability theory which predicts chatter stability lobes that are not covered by classical chatter theories in which the coupling between the spindle speed and process stability are neglected. The dynamics of low radial immersion milling are formulated as an eigenvalue problem, where harmonics of the tooth spacing angle and spread of the transfer function with the harmonics of the tooth passing frequencies are considered. It is shown that the stability lobes are accurately predicted with the presented method. This paper details the physics involved when the tooth passing frequencies alter the effective transfer function of the structure in the stability solution. The products of the harmonics of the directional coefficients and transfer functions of the structure are evaluated at the natural mode under the influence of tooth passing frequency harmonics in order to obtain the exact locations of chatter stability lobes.