Machine Learning-based Online Stability Lobe Diagram Estimation and Chatter Suppression Control in Milling Process

TL;DR

This work tackles milling chatter caused by regenerative delay by replacing fixed offline SLDS with an online, ML-enabled estimation framework. It uses semi-discretization to convert the DDE governing milling dynamics into a linear time-varying system and evaluates stability via the period-transition matrix, with chatter predicted when $\\lambda_{\\max}(\\bm\\Phi_i) > 1$. A physics-informed neural network $\\mathcal{N}$ learns evolving process parameters (e.g., $\\zeta(t)$, $\\omega_n(t)$, $K_t(t)$, $K_r(t)$) from sensor data to compute the online SLD, while a multi-network roughness predictor forecasts surface finish for chatter detection. A stability–roughness focused loss is used to optimally adjust the spindle speed $\\omega_{sp}$ in real time, balancing robust stability (via $\\lambda_{\\max}(\\bm \\\Phi_i)$) against surface quality. Numerical simulations and benchtop experiments demonstrate that online SLD estimation and adaptive control achieve superior chatter suppression and significant surface roughness reduction (e.g., from $r=6.10\\,\\mu$m to $r=3.14\\,\\mu$m), without requiring offline identification of the milling system coefficients.

Abstract

Chatter is a self-excited vibration in milling that degrades surface quality and accelerates tool wear. This paper presents an adaptive process controller that suppresses chatter by leveraging machine learning-based online estimation of the Stability Lobe Diagram (SLD) and surface roughness in the process. Stability analysis is conducted using the semi-discretization method for milling dynamics modeled by delay differential equations. An integrated machine learning framework estimates the SLD from sensor data and predicts surface roughness for chatter detection in real time. These estimates are integrated into an optimal controller that adaptively adjusts spindle speed to maintain process stability and improve surface finish. Simulations and experiments are performed to demonstrate the superior performance compared to the existing approaches.

Figures (9)

• Figure 1: Experimental setup and schematics of the milling process. Left: Milling machine used in experiments. Right: Modeling schematic.
• Figure 2: Overview of the proposed chatter suppression control strategy.
• Figure 3: Flowchart of the machine learning-based approach for real-time SLD estimations.
• Figure 4: Flowchart of the machine learning-based roughness estimation.
• Figure 5: Adaptive spindle speed with SLD-guided stability and surface finish quality improvement.