Before occurrence of self-excited chatter, initial resonance has to be grown in turning. In this study, despite external forced vibration, we explain occurrence and growth of SDoF tool oscillation from the trajectory of the tool nose contacting with wavy cylindrical workpiece. By regarding the deviation of the workpiece as a simple sinusoidal function and local contact of the tool with finite radius, we showed the trajectory excites the oscillator under high-order harmonic resonance conditions. The amplitude of the resonance is affected from local contact radius against that of workpiece. From damping effect these resonance conditions are expanded. The growth of the initial resonance would cause either forced or self-excited chatters in afterwards. The occurrence of chatter during wear and the existence of ultra-precision machining are explained from these properties.

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