Machine Tool Chatter and Surface Location Error in Milling Processes

A two degree of freedom model of the milling process is investigated. The governing equation of motion is decomposed into two parts: an ordinary differential equation describing the periodic chatter-free motion of the tool and a delay-differential equation describing chatter. The stability chart is derived by using the semi-discretization method for the delay-differential equation corresponding to the chatter motion. The periodic chatter-free motion of the tool and the associated surface location error (SLE) are obtained by a conventional solution technique of ordinary differential equations. It is shown that the SLE is large at the spindle speeds where the ratio of the dominant frequency of the tool and the tooth passing frequency is an integer. This phenomenon is explained by the large amplitude of the periodic chatter-free motion of the tool at these resonant spindle speeds. It is shown that large stable depths of cut with a small SLE can still be attained close to the resonant spindle speeds by using the SLE diagrams associated with stability charts. The results are confirmed experimentally on a high-speed milling center.