Enhancing parametric and causal reasoning through a formula-augmented language model approach for belt grinding knowledge assistance

Abrasive belt grinding is a flexible surface finishing process in which precision machining of geometrically complex components often involves coupled parameters and contact mechanisms. Retrieval-augmented large language models (LLMs) have shown promise in domain-specific knowledge questioning. However, their capabilities in numerical computation and mechanism-oriented reasoning remain limited in scenarios involving coupled parameters. This study introduces a structural enhancement mechanism based on formula-group embedding. It integrates formula retrieval, task classification, structured prompting, and code execution into the conventional retrieval-augmented generation (RAG) pipeline. The approach addresses numerical computation and mechanistic reasoning in belt grinding and is validated through contact modeling, a representative core problem of the process. In numerical computation tasks, the proposed method achieved 100% accuracy in basic cases. In more challenging scenarios, it reached 90% accuracy with an average deviation within 5%. In contrast, for these complex tasks, general-purpose LLMs achieved only about a 10% pass rate. In mechanism-related reasoning tasks, utilizing a hybrid expert-LLM evaluation, the method demonstrated a 13.1% improvement over the second-best model and a 36.6% gain over the baseline without formula augmentation. These results indicate that the proposed mechanism provides value in improving the reliability of numerical computation and the coherence of mechanistic reasoning.