In curved surface machining, parametric surface representation is normally used for computer aided design (CAD). Parametric surfaces are often machined using a flat end mill for roughing and ball end mill for finishing. The core of this work is to propose and implement a model that is able to estimate the cutting force in milling parametric surfaces with HSS ball end cutter of different diameters. For this purpose, a mechanistic model has been developed to calculate the cutting forces by dividing the cutting edge into small discrete
elements and applying simple mathematical expressions for the cutting force estimation, once the force of each discrete element is calculated, these elements summed up along the cutting edge to obtain the resulting cutting force. The slope (inclination angle α) of the surface was included to the model to estimate the influence of ifferent conditions of the slope ( - 90o ⟨ a ⟨ +90o ) which most parametric surfaces included. The results showed that the predicted results deviate
from experimental by (0.6-11 %) for Fx, by (2-10 %) for Fy and by (0.18-14 %) for Fz