The deflections of screw rotors under machining forces cause mismatch between the male and female rotors and, consequently, accelerated wear and suboptimal efficiency in their performance. Optimizing the machining process to minimize the generated forces and accounting for the resulting mismatch in the design of the rotor profile requires accurately computing the machining forces in computer simulations. Virtual machining systems combine graphics-based computation of the Cutter-Workpiece Engagement (CWE) with the physics-based models of machining mechanics to simulate the forces during complex machining processes. However, because of the high computational load of graphical simulations, virtual machining is not suitable for the repetitive force simulations that are required for optimizing the design and manufacturing of rotors. In this work, we present a new method that simulates screw milling forces based on the process kinematics instead of graphical simulations.

Utilizing mathematical equations that describe the process kinematics, the theoretical rotor profile is determined for feasible combinations of cutting tool profile, setup angle, and centre distance. Subsequently, to find the milling forces, the cutting edge is discretized into multiple small edge segments and a mechanistic cutting force model is used to determine the local cutting forces at each segment. After geometric and kinematic transformations of these local forces, the screw milling forces are obtained for each roughing and finishing pass. Instead of graphics-based methods, the engagement conditions between the cutter and workpiece are determined by the ensemble of 2D rotor and tool profiles;​ as a result, the computational efficiency is increased substantially.

The semi-analytical nature of the presented method allows for computing the forces with arbitrary resolution within a reasonable time. The accuracy and efficiency of the presented method is verified by comparing the simulated forces against a dexelbased virtual machining system.