Causal inference dynamic modeling for real-time surface roughness monitoring in the milling process

Surface roughness plays a crucial role in maintaining the productivity and quality of milling operations. Cutting force signals have direct relationships with the surface roughness; however, they are difficult to measure in the practical milling process. Spindle vibration signals are much more easily accessible during milling and widely utilized for force and surface roughness monitoring. However, some vibration frequency contents related to surface roughness are distorted due to the dynamic characteristics of the machine tool, which results in poor monitoring performance. Meanwhile, the mechanism of existing studies that compensate for these distortions remains unclear, and most existing studies apply multi-sensor technology, which makes the monitoring system costly. To bridge these gaps, this paper proposes a causal inference model that learns the dynamic behavior of the spindle system to mitigate signal distortions, alongside developing lightweight models for roughness monitoring. First, a novel causal inference neural network model was proposed to analyze the dynamic behavior of spindle system components during vibration transmission, and a wide-bandwidth force reconstruction model based on single-channel vibration signals was established. Second, to reduce the complexity of the roughness monitoring model, this study investigated the relationship between the surface profile and cutting force, proposing an adaptive method called improved decorrelation EMD (IDEMD) to extract surface roughness-related force components automatically. To enhance the algorithm's efficiency for real-time component extraction, a cutting force component extraction neural network (FCENN) is proposed to learn the IDEMD process. Third, lightweight surface roughness models were established using a small number of features extracted from the extracted force components. Experimental results under variable cutting conditions demonstrated that the force reconstruction accuracy could reach 0.989, and the surface roughness monitoring accuracy could reach 0.994 in the test set. The proposed method improved the interpretability of data-driven methods by incorporating domain knowledge from signal transmission, surface formation, and signal decomposition, met real-time monitoring requirements, reduced the monitoring model's complexity, and was less costly and suitable for industrial applications.