The two-dimensional chip shape is combined with the oblique cutting model to predict the cutting force at each time step. For each node related to chip shape, the force increment components ft, FF and fr generated in the tangential T, feed F and radial r directions can be expressed as:
Ft = Ktca + Kteb，Ff = Kfcafc + Kfeb，Fr = Krca + Kreb
Where: KTC, KFC, KRC, kte, KFE, kre – cutting force coefficient determined by test.
The vectors in tangential T, feed F and radial r directions must be analyzed in TCS in order to correctly locate their corresponding force components in the formula. This is achieved by considering the local geometry and cutting kinematics of each node, specifically following the detailed gear planning operation process. This method is suitable for strong gear scraping. The bevel cutting model for the blade is shown in Figure. The overall rake angle of the tool is considered in this process α c. The local blade shape (PI-1, PI, PI + 1) and the cutting speed vector VC at each node are also calculated α N and inclination I.
Combining the calculated cutting force direction vector with the force in the formula, the cutting force vector of each node can be obtained; The force vectors of all participating nodes from the current time step are combined to predict their instantaneous total cutting force.