Due to cutting forces and the flexibility of the tool and its holder, the tool (or end-mill) deflects when it is engaging with the workpiece; unfortunately, large deflections can cost part accuracy, even break the tool. To produce high-precision parts, it is important to predict the deflections with high fidelity and then greatly reduce them through compensation in CNC tool paths. For this purpose, many research works have been successfully conducted on cutting forces prediction; however, another critical factor, the area moment of inertia of the tool, is always approximated, significantly reducing the accuracy of estimated deflections. The main reason for this is that the 3-D geometric model of end-mills is difficult to construct. To find the moment of inertia, in this work, first, a parametric model of APT cutters has been established and implemented in the CATIA CAD/CAM system by using its API. Then, a system of calculating the area moment of inertia for end-mills is built. Finally, a detailed discussion on the moment of inertia of end-mills is provided, along with comparison of this work with the existing methods. The major contributions of this work include the parametric end-mill modeling, which can automatically render the 3-D geometric model of an end-mill in seconds, and accurate calculation of the moments of inertia of end-mills. This work can be used, together with an existing cutting force calculation method, to accurately predict cutter deflections during milling in order to compensate them in CNC tool paths. It can also provide more precise 3-D solid models of end-mills for machining simulation by using finite element analysis
