The application of Carbon Fiber-Reinforced Polymers (CFRP) has been recently increasing in a wide range of industries such as automotive and aerospace due to their excellent mechanical properties and high strength-to-weight ratio. Machining of CFRPs is required at the finishing stage of the manufacturing process before assembly. The occurrence of failure types including fiber pull-out, fiber breakage, and delamination causes rejection of the high-value-added composite part. This work is motivated by the need to better understand the fundamental machining processes for CFRP parts.

Since delamination is correlated with the level of cutting forces, it is required to develop mechanistic force models for the prediction of milling forces under different machining parameters to avoid damage. In isotropic (e.g. metallic) materials, parameters of the mechanistic model are treated as constants that are identified using well-established experimental procedures. However, the mechanics of chip formation in milling CFRP varies continuously depending on the fiber cutting angle.

To address this variation, a mechanistic model with parameters depending on the fiber cutting angle is proposed, and a new experimental method is presented to identify the parameters of the proposed model. The model parameters, also known as specific force coefficients (SFC), are assumed to be periodic functions of the fiber cutting angle, where the Fourier coefficients of the periodic function are identified from the milling forces measured during a set of milling operations at various feedrate and fiber orientations. The experimental analysis confirms the accuracy of this approach to predict cutting forces in CFRP milling.

Unexpected changes in cutting conditions and tool wear during the cutting process add to the uncertainty of the conventional offline calibration approaches, causing the need for online identification methods to adaptively recalibrate the model parameters. In this work, two identification methods based on recursive least squares (RLS) and Kalman filter (KF) algorithms are presented. In the RLS method, the model parameters are identified by the recursive regression of the forces measured at discrete time steps. Runout parameters are measured accurately and modeled properly in the RLS algorithm in order to improve the performance of RLS. The initial immersion angle of the tool is also estimated in the first stage of the identification process before the algorithm starts recursively updating the unknown parameters of the force model in the second stage.

In the KF approach, a state-space model and observer with constant stochastic dynamics are constructed. In addition to SFC, the runout forces could be also identified as harmonic functions in the state variables vector without prior knowledge of their values, which is one advantage of KF over RLS. The initial immersion angle is considered as an additional state variable in an extended Kalman filter (EKF) by linearization of the observation matrix in a one-stage identification process. Numerical simulations and experimental studies on milling UD-CFRP and MD-CFRP validate the performance of the presented methods. As a result, the identified model accurately predicts the machining forces, and therefore, can be used for process monitoring and optimization in the machining of metals and composite materials.