Local linearization modeling and coefficients identification of five-axis milling force considering size effect and radial runout

In the five-axis machining of complex curved surfaces, the cutter-workpiece engagement geometry fluctuates dramatically with the change of cutting parameters, making it difficult for traditional mechanical models to achieve a balance between the identification efficiency and the real-time prediction accuracy. To address this issue, a local linearized milling force model and its corresponding milling force coefficients identification method are proposed, while also taking into account the size effect and radial runout. By parameterizing the instantaneous undeformed chip thickness and the engagement state between the cutter and the workpiece, a five-axis milling force parametric model related to parameters such as the tool orientation, radial runout, and feed rate was established. By extending the size effect law of the single edge element to the entire cutting edge, and statistically describing the mapping relationship between the equivalent force coefficient of the cutting edge and the average undeformed chip thickness, a local linearized five-axis machining force model was further obtained. In this model, the milling force was explicitly expressed as a function of the cutting force coefficient, radial runout and geometric operator. The latter (geometric operator) is determined by the distribution of the cutting edge on the cutter surface and is modeled as a parameter of the tool rotation angle. The proposed method can achieve linear modeling of milling force under different rotation angles. With a small amount of monitoring data, the model could support online updates of force coefficients and radial runout parameters, effectively reducing the prediction errors caused by changes in cutting parameters and cutter wear. Milling experiments were conducted with different tool orientations, different rotational speeds, and different feed rates. The experimental results showed that the prediction error of the proposed method was less than 9.2 %, which was 6.6 % lower than that of the method without considering the time variation coefficient. This study lays the foundation for intelligent process optimization in aerospace manufacturing and online monitoring of advanced milling equipment based on digital twins.