Predictive method for turning nonlinear vibration responses of large length-to-diameter ratio tools with flexible boundary constraints

This paper proposes a predictive method for turning nonlinear vibration response of large length-to-diameter ratio turning tools with flexible boundary constraints, overcoming the inaccuracies in vibration prediction caused by the conventional rigid boundary assumption. First, a hybrid physics-data-driven framework is established for predicting instantaneous cutting forces. By employing an ensemble learning model with multi-feature parallel prediction, accurate end-to-end forecasting of the eigen-fluctuations of cutting forces from machining parameters is achieved. Meanwhile, the nonlinear influence of cutting speed on the mean cutting force is revealed. Subsequently, a flexible boundary constraint is introduced to quantify the clamping contact effect between the tool holder and the turning tool. Based on the Euler-Bernoulli beam theory, a cutting dynamics model for the large length-to-diameter ratio tool under instantaneous cutting forces is developed. The vibration responses, such as acceleration and displacement at the tool tip, are then numerically solved using the fourth-order Runge-Kutta algorithm. Furthermore, a precise parameter identification method for the dynamic model is proposed, enabling accurate characterization of key parameters. These include the nonlinear shear force coefficient, linear edge force coefficient, eigen-fluctuations of the cutting force, and the force-dependent boundary constraint stiffness. Finally, modal testing, cutting force measurement, and cutting experiments are conducted to comprehensively validate the proposed method for predicting the nonlinear cutting vibration response of the large length-to-diameter ratio tool under flexible boundary constraints. The results demonstrate that the predictions of the flexible boundary model, including the tool’s modal frequency, modal stiffness, acceleration, and vibration displacement, show significantly closer agreement with experimental measurements than those obtained from the conventional rigid boundary model.