Bending Moment Synthesis by Integrating Cutting Mechanics with Diffusion Model for Tool Wear Prediction​

Technical Summary: Bending Moment Synthesis by Integrating Cutting Mechanics with Diffusion Model for Tool Wear Prediction

Problem Statement
In smart manufacturing, accurate tool wear prediction is frequently hindered by data scarcity and the difficulty of adapting models across varying cutting conditions. While indirect monitoring methods using dynamic signals (e.g., cutting force, vibration) are common, data-driven approaches like Generative Adversarial Networks (GANs) often fail to synthesize high-frequency dynamic signals that adhere to physical laws. This lack of physical guidance can lead to frequency shifts and "negative transfer," where synthesized data degrades the performance of downstream prediction tasks. Furthermore, existing physics-informed methods often rely on loss functions to enforce physical constraints, which can be difficult to optimize for high-frequency machining signals, or require computationally expensive Finite Element Method (FEM) simulations. Additionally, the physical installation of force dynamometers is often constrained by machine space, limiting the availability of direct force measurements.

Methodology
To address these challenges, the authors propose a framework that synthesizes cutting bending moment signals by integrating a mechanistic cutting model with a conditional diffusion model. The methodology consists of three primary components:

1. Mechanistic Cutting Bending Moment Model:
   Instead of relying solely on data distributions, the framework utilizes an analytical cutting force model to generate "ideal" bending moment trajectories. These trajectories are derived from tangential, radial, and axial cutting force components, integrated along the tool's axial depth. These ideal signals serve as a deterministic physical prior, capturing the periodicity and geometric features dictated by spindle speed and tool geometry, though they do not account for wear-induced geometric variations.

2. Conditional Diffusion Architecture (1D-CNN U-Net with FiLM):
   The core generative model is a Denoising Diffusion Probabilistic Model (DDPM) built on a 1D-CNN U-Net backbone. Unlike traditional approaches that impose physical equations as soft constraints in the loss function, this framework injects physical knowledge directly into the network architecture:

   • Physical Input: The ideal bending moment generated by the mechanistic model is concatenated with the noisy signal at the input layer, providing a structural prior that ensures the generated signal follows the correct physical frequency.
   • Wear Conditioning: The tool wear state is injected via Feature-wise Linear Modulation (FiLM) blocks. The FiLM mechanism scales and shifts the feature channels within the U-Net based on the wear condition and diffusion timestep. This allows the network to learn and reconstruct the non-linear deformations and high-frequency variations caused by tool wear, which the ideal model cannot capture.

3. Downstream Prediction Task:
   The synthesized high-fidelity bending moment signals are combined with a small fraction of real experimental data to augment the training set. A standard 1D-CNN model is then trained on this augmented dataset to predict tool wear (flank wear, VB).

Key Contributions

• Novel Integration Strategy: The paper introduces a method where the ideal cutting bending moment acts as a physical input condition rather than a loss function penalty. This ensures the generated signals maintain the fundamental periodicity of the cutting process while learning wear dynamics from data.
• FiLM-Based Wear Modulation: The use of FiLM blocks allows the diffusion model to dynamically adjust its internal features according to the specific wear state, effectively modeling the transition from initial to severe wear stages.
• Bending Moment as a Feature: The study utilizes cutting bending moments, which can be derived from smart tool holders, as a monitoring feature, offering an alternative to direct force measurement which is often physically constrained.

Experimental Results
The framework was validated using cutting experiments on a five-axis CNC machine with S45C steel workpieces. Ten different cutting conditions were tested, with Tools 1–7 and 9 used for training and Tools 8 and 10 reserved as an unseen test set to evaluate cross-condition generalization.

• Signal Fidelity: The proposed diffusion model significantly outperformed both a standard WGAN and a physics-guided WGAN (PG-WGAN). In the final wear stage, the proposed method achieved a Resultant Moment Deviation (RMD) of approximately 2.95 Nm and an FFT Spectral Correlation of 0.9972, compared to an RMD of 47.53 Nm and correlation of 0.38 for the WGAN. The t-SNE analysis confirmed that the synthetic data effectively populated the feature space gaps between experimental clusters without introducing negative transfer.
• Prediction Performance: In a cross-condition prediction task using only 5% of real training data, the proposed method reduced the Root Mean Square Error (RMSE) by 60.45% compared to a baseline model trained solely on real data. The proposed method achieved an RMSE of 0.0155 mm, whereas the baseline (5% real data) had an RMSE of 0.0440 mm.
• Ablation Study: Removing the physical input or the FiLM mechanism resulted in significant performance degradation, confirming the necessity of both the mechanistic prior and the conditional modulation for high-fidelity synthesis.

Significance and Claims
The authors claim that this framework effectively addresses the data scarcity problem in tool wear monitoring by generating high-fidelity synthetic data that adheres to physical laws. The primary significance lies in the ability to support tool wear prediction under unseen cutting conditions using a minimal amount of real data. Specifically, the study asserts that for tools with the same number of flutes, this approach can reduce the need for exhaustive full-life tool wear experiments when operating conditions change, thereby lowering the cost and time associated with developing robust predictive maintenance models in smart manufacturing environments.