Calculation of the Cutting Forces and Torque when Milling with End Mills

This paper presents a computational sequence for calculating the components of the cutting force and torque when milling with carbide end mills. The calculation algorithm includes the transition from the tangential and radial components of the force to the force components in the machine coordinate system. On the helical cutting edge, two parts are highlighted: one on the cylindrical (peripheral) surface and the other one on the arc of the rounded tip of the tooth. These parts of the cutting edge are divided into sections where the calculation is performed, followed by summation of the force components along the axes of the machine co-ordinate system and the moment relative to the axis of the cutter. An analysis of the components of the force and torque depending on the depth of cutting, feed, number of teeth of the cutter, blade wear and radius of the tip rounding is performed. The ratio of forces and moments for various milling conditions of structural carbon steel and aluminum alloys is shown. The developed algorithm is applied in a computational program that can be used to perform operational calculations of forces and torque for various milling conditions. The calculated parameters can be used as technological limiters in optimization problems, as well as for strength calculations of tools, milling equipment, and the selection of components of milling machine drives.

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