Analytical Modeling of Process Damping in Machining

The machining process induced damping caused by the indentation of the cutting edge into the wavy cut surface greatly affects the process stability in low-speed machining of thermally resistant alloys and hardened steel, which have high-frequency vibration marks packed with short wavelengths. This paper presents an analytical model to predict the process damping forces and chatter stability in low-speed machining operations. The indentation boundaries are evaluated using the cutting edge geometry and the undulated surface waveform. Contact pressure due to the interference of the rounded and straight sections of the rigid cutting edge with the elastic-plastic work material is analytically estimated at discrete positions along the wavy surface. The overall contact pressure is obtained as a function of the cutting edge geometry, vibration frequency and amplitude, and the material properties of the workpiece. The resulting specific indentation force is evaluated by integrating the overall pressure along the contact length. Then, the process damping force is linearized by an equivalent specific viscous damping, which is used in the frequency domain chatter stability analysis. The newly proposed analytical process damping model is experimentally validated by predicting the chatter stability in orthogonal turning, end milling, and five-axis milling of flexible blades. It is shown that the proposed model can replace currently used empirical models, which require extensive experimental calibration approach or computationally prohibitive finite elements based numerical simulation methods.