Identification of System Parameters for Ball End Milling

Abstract

In this paper, the system parameters including the cutting force coefficients and the equivalent parameters (mass, damping and stiffness) are identified. The cutting force coefficients including the shear force coefficients and the edge force coefficients are identified from the end milling by using the recursive least square method (RLS) and the average cutting force method (ACF). The cutting parameters including the shear stress, friction angle, and chip ratio are thus derived from the identified shear force coefficients. Then the cutting forces in the end milling and the ball end milling are predicted from the cutting parameters and the edge force coefficients. The equivalent mass, damping and stiffness parameters of the rotor system are identified by using Fourier transform filter (FTF), the extended Kalman filter (EKF), and the direct Kalman filter (DKF) through the predicted cutting forces and the measured displacements of the tool tip. The cutting forces and the tool tip displacements measured from the experiment are also carried out and compared graphically with those from the identification estimation to verify the reliability of the proposed identification methods. About the experiment, the cutting forces are measured with the dynamometer, and the tool tip displacements are derived from the measured data using two laser displacement sensors. The identified shear force coefficients decrease and the identified edge force coefficients increase as the feed per flute increases for AL6061-T6. The derived cutting parameters show that the shear stress decreases and the friction angle and the chip ratio remain almost constant as the feed per flute increases. Using these edge force coefficients and cutting parameters, the cutting forces in ball end milling and end milling can be successfully predicted. The predicted cutting forces by using the RLS are almost coincident with the experimental results. The equivalent mass, damping and stiffness parameters can be effectively identified by using the FTF and the EKF, which predict the tool tip displacements similar to the experimental measurements.