Stochastic Cutting Force Modeling and Prediction in Machining

Abstract

As the cutting force plays an important role in machining, the modeling of cutting force has drawn considerable interests in recent years. However, most of current methods were focused on the deterministic modeling of cutting force, while the inherent stochasticity of cutting force is rarely considered for general metal cutting machining. Thus, a stochastic model is proposed in this paper to predict the stochastic cutting force by considering realistic cutting conditions, including the inhomogeneity of cutting material and the multi-mode machining system. Specifically, we transform the constant cutting coefficient in previous models into a stationary Gaussian process in the proposed stochastic model. As for the tool vibration, the uncut chip thickness is also modeled in a stochastic manner. Moreover, it is found that the random cutting coefficients can be estimated conveniently through experiments and effectively simulated by stochastic differential equations at any timescale. Then, the stochastic cutting force can be predicted numerically by combining the stochastic model and the multi-mode dynamic equations. For verification, a three-mode machining system was set up, and workpieces with different metal alloys were tested. It is found that the random cutting coefficients estimated are insensitive to cutting parameters, and the prediction results show satisfactory agreement with experimental results in both time and statistical domains. The proposed method can provide rich statistical information of cutting forces, which can facilitate related applications like tool condition monitoring when the on-line measurement of cutting force is not preferred or even impossible.