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Prediction of machining chatter is very significant to ensure stable operation by reasonably selecting cutting parameters. Based on holistic-discretization technique, this paper presents a holistic approach for milling operations using piecewise cubic Hermite interpolation. According to vibration mode analysis of the milling dynamic system, the one tooth period of system is carved up into two sub-periods. After separating the forced vibration duration into a limited number of equally sized intervals, piecewise Hermite interpolation is employed to estimate the integral nonhomogeneous term, including delay term, state term and time-periodic parameter matrix. Subsequently, the transition matrix is acquired directly for prediction of chatter stability according to Floquet theory. Two classic benchmark examples are provided for validating the calculation speed and precision of the presented approach. Compared with other two existing methods, the presented approach obtains significantly better precision and efficiency under the identical parameters. Finally, the availability and reliability of the presented approach are further validated via cutting experimental data. The stability limits predicted by using piecewise cubic Hermite interpolation method exhibit a high coincidence with experimental results.
Inspec keywords: delays; mechanical stability; cutting; milling; vibrations; Hermitian matrices; machining chatter; interpolation
Subjects: Production equipment; Machining; Algebra; Vibrations and shock waves (mechanical engineering); Buckling and instability (mechanical engineering)