Forced vibration analysis of the milling process with structural nonlinearity, internal resonance, tool wear and process damping effects

• Primary & super-harmonic resonance of the milling process with internal resonance.
• Extended model with chatter, structural nonlinearity, tool wear and process damping.
• Using multiple-scales approach to construct analytical approximate responses.
• Parametric study on the frequency response functions of the dynamic system.
• Existence of multiple solutions, jump and energy transfer between vibration modes.

In this paper, forced vibration analysis of an extended dynamic model of the milling process is investigated, in the presence of internal resonance. Regenerative chatter, structural nonlinearity, tool wear and process damping effects are included in the proposed model. Taking into account the average and first order expansion of Fourier series for cutting force components; their closed form expressions are derived. Moreover, in the presence of large vibration amplitudes, the loss of contact effect is included in this model. Analytical approximate response of the nonlinear system is constructed through the multiple-scales approach. Dynamics of the system is studied for two cases of primary and super-harmonic resonance, associated with the internal resonance. Under steady state motion, the effects of structural nonlinearity, cutting force coefficients, tool wear length and process damping are investigated on the frequency response functions of the system. In addition, existence of multiple solutions, jump phenomenon and energy transfer between vibration modes are presented and compared for tow cases of primary and super-harmonic resonances.