How Can a Neural Network Predict Cutting Forces of Corner Radius End Mills?

Corner radius end mills (CREM) are stars in machining labs: their special shape yields smoother surfaces and tighter tolerances. Yet, cutting forces can fluctuate unpredictably, causing vibrations, noise, and loss of precision. To tame these effects, engineers created a hybrid model that merges the Separate‑Edge‑Forecast (SEF) method with a BP (Back‑Propagation) neural network. The key is accounting for "runout," the slight wobble of the tool around its ideal axis, which changes force coefficients. SEF breaks down each edge's contribution, while the neural network learns the non‑linear relationships introduced by runout. The model was tested by milling a 7075 aluminum block with a corner‑radius cutter, measuring real forces with a dynamometer. The outcome? A maximum error of just 9.43% between predicted and measured forces, showing the new approach is both accurate and faster than traditional element‑force models that need complex formulas and long computation times. In practice, this blend of physics and AI lets manufacturers anticipate vibrations, cut waste, and fine‑tune CNC programs, paving the way for more efficient and sustainable production.

The proposed model operates on two abstraction layers. The Separate‑Edge‑Forecast (SEF) method starts by decomposing the cutter into individual edges, each linked to a specific force coefficient (Kc). These coefficients depend on geometric parameters (radius, tooth count) and cutting conditions (feed rate, depth of cut). Runout, typically measured in micrometers, introduces an angular variation θ that changes the radial distance of each edge from the theoretical center, thus altering the local load. This effect is modeled through a correction function ΔKc(θ) inserted into the base coefficients.

The BP neural network, with three layers (input, hidden, output), receives as input the process parameters (v, f, d), the corrected Kc coefficients, and the runout value. During training, the network minimizes the mean squared error between measured forces (Fx, Fy, Fz) and predicted ones, updating weights via back‑propagation. Thanks to its ability to learn non‑linear relationships, the network captures complex interaction effects, such as the combined influence of cutting speed and runout on high‑frequency vibrations.

Experimental comparison was performed on 7075 aluminum, a material known for high strength and light weight, using a 6 mm diameter cutter with a 0.5 mm corner radius. Force data were acquired at 10 kHz, providing sufficient temporal resolution to distinguish dynamic components. The hybrid model showed an average absolute error below 5 % and a maximum error of 9.43 %, far surpassing traditional element models that typically exhibit errors above 15 % under significant runout conditions.

Computationally, the prediction phase requires less than 0.2 ms per cutting cycle, making the model suitable for real‑time implementation on CNC controllers. This enables adaptive control systems where the neural network updates its weights online in response to tool wear or material changes, ensuring consistent surface quality.