Improving the design of multivariable milling tools combining machine learning techniques

Abstract

Chatter in milling operations degrades surface quality, compromises dimensional accuracy, accelerates tool wear and may damage spindle components. One effective strategy to mitigate chatter while maintaining high productivity is the use of specialized milling tools, such as multivariable milling cutting tools (MMCT), designed with variable geometry in their pitch (𝜙􀯣) and helix (β) angles. However, identifying the combination of these angles remains challenging because of the absence of analytics models that link MMCT geometrical parameters with dynamic stability limits. This study proposes a novel approach that integrates analytical lobes calculation with machine learning to enhance tool design efficiency. We find optimal tool geometry (pitch and helix angles) and cutting conditions (spindle speed and axial depth) to maximize the Material Removal Rate (MRR) in milling of a single degree of freedom. Our approach employs a genetic algorithm (GA) combined with a pattern recognition neural network (NN) to predict whether specific parameter combinations will yield stable or unstable behavior. The Multilayer Feedforward Neural Network is trained using a database generated from simulation of a SDOF mathematical model of milling, a non-autonomous Delay Differential Equation. The solution to the DDE is approximated through the Enhanced Multistage Homotopy Perturbation Method (EMHPM). The database includes 23,606,700 observations, covering a catalog of 36,318 MMCT configurations and 650 cutting conditions (axial depth of cut and spindle speed) for each tool configuration. The NN training database uses an approach for handling variable cutting coefficients based on exponential fitting model to describe their variation. These coefficients were characterized at small radial immersion of 1.86 mm using cutting forces of five MMCTs with a diameter of 0.5 in. This approach accurately predicts cutting forces, achieving an NRMSE below 10% when compared with experimental signals. The trained NN estimates the stability of the milling process with an error of 3.3%. Additionally, the combined use of the NN and GA reduces computation time by 98% compared to the GA with EMHPM. The selection of five combinations of geometric parameters that maximize MRR in a range between 26% and 120%, compared to the MRR of a regular tool, which is 190,493 mm³/min, has been performed. The rate of increase in MRR depends on each of the five selected geometries (see Chapter 5). Moreover, without the proposed approach, identifying the improved geometry would require up to 25 days using an exhaustive search scheme, where a SLD is generated for 10,000 cutting conditions for every tool configuration.