An effective time domain model for milling stability prediction simultaneously considering multiple modes and cross-frequency response function effect

The dynamic properties of the machine tool structure usually contain multiple modes and significant cross-frequency response functions whose vibration in one direction is caused by a force in the orthogonal direction. To simplify the stability prediction model, the stability of a milling process has been traditionally predicted in the time domain by selecting only the most flexible mode and neglecting the cross-frequency response functions. This paper proposes an effective stability prediction model simultaneously considering multiple modes and the cross-frequency response functions in the time domain. When introducing the cross-frequency response functions, mechanical mobility and impedance transformation method dealing with measured frequency response functions is proposed to establish the dynamic matrix equation. In considering the multiple modes, the approaches of multiple modal parameter normalization on the tool tip and reducing the vibration variable number in modal space are described in detail. The comparisons of numerical simulation results between the proposed method and the frequency domain method demonstrate the effectiveness of the proposed model. A cutting experiment produces results in agreement with the theoretical prediction. The analysis of the numerical simulation and the experimental data indicates that the multiple modes have great effect on stability boundary. Additionally, it also shows that the cross-frequency response functions influence the stability boundary increasingly along with the increasing amplitude ratio of the cross-frequency response functions and direct frequency response functions.