Stability of Milling Process with Variable Spindle Speed Using Runge–Kutta-Based Complete Method

The variable-spindle-speed (VSS) technique is effective in preventing regenerative chatter in milling processes. However, spindle-speed-modulation parameters should be deliberately selected to augment the material removal rate. Stability-prediction algorithms of stability predicting play an important role in this respect, as they allow the prediction of stability for all ranges of a given spindle speed. The increase in calculation time in variable-spindle-speed milling, which is caused by the modulation frequency, hinders its practical use in the workshop. In this paper, a Runge–Kutta-based complete discretization method (RKCDM) is presented to predict the stability of milling with variable spindle speeds, which is described by a set of delay differential equations (DDEs) with time-periodic coefficients and time-varying delay. The convergence and calculation efficiency are compared with those of the semidiscretization method (SDM) under different testing configurations and milling conditions. Results show that RKCDM is more accurate and saves at least 50% of the calculation time of SDM. The effects of modulation parameters on the stability of VSS milling are explored through stability lobe diagrams produced from RKCDM