A correction method for milling stability analysis based on local truncation error

The appearance of chatter vibration can severely affect the product quality and machining productivity. Hence, prediction of chatter stability is becoming increasingly significant to achieve stable milling operations. Based on local truncation error, this study develops a correction Milne-Simpson method (CMM) for chatter stability analysis by using two linear multistep methods. The dynamic model of milling operations embracing the self-excited vibration is represented by delay differential equations (DDEs). With the period of milling system being carved up into two different subintervals, two kinds of linear multistep methods are combined together by using local truncation error to estimate the state terms. Subsequently, two benchmark dynamic models and two typical discretization methods are employed to demonstrate the characteristics of CMM. The convergence rates and stability boundaries are analyzed in detail, and the contrastive results show that the CMM exhibits better prediction accuracy and provides more satisfactory calculation speed than the others under the same discrete parameters. Finally, for the purpose of verifying the validity and operability of CMM, modal impact experiment and actual cutting tests are performed on a CNC machine tool (EMV650). It is apparent that the predicted stability lobes show better coincidence with experimental results, which indicates that the CMM is of practicability and feasibility.