Unified and Efficient Analysis of Machining Chatter and Surface Location Error

Although machining chatter can be suppressed by the choice of stable cutting parameters through means of stability lobe diagram (SLD), surface roughness still remains due to the forced vibration, which limits surface quality, especially in the surface finish. Better cutting parameters can be achieved considering surface location error (SLE) together with SLD. This paper proposes an innovative modeling framework of the machining dynamic system that enables efficient computation of the chatter stability and SLE. The framework mainly embodies two techniques, namely semi-discretization method (SDM) and lifting method. The machining dynamics system is mathematically expressed as an angle-varying delay differential equation (DDE). The SDM approximates the angle-varying and delayed terms to ordinary terms using zero-phase interpolations and governs the discrete angle-varying dynamics system. Then, the system is merged over the tooth passing angle using the lifted approach to establish an explicit dynamic system in the compact state-space form. Based on the compact state-space model, the chatter stability and SLE prediction are easily and efficiently conducted. Simulation results show the improved efficiency of the proposed method over other well-known methods.