Vibration-based gear diagnosis is crucial for ensuring the reliability of rotating machinery, making the monitoring of gear health essential for preventing costly downtime and optimizing performance. This study proposes a multidisciplinary framework to enhance gear diagnosis, that aligns with the new era of digital twins by integrating experiments, dynamic modeling, physical preprocessing, and machine learning. Within this framework, we focus on three core procedures: domain adaptation to reduce discrepancies between measured data and synthetic data generated by dynamic models; physical preprocessing, grounded in in-depth investigations dictating signal processing and feature engineering techniques; and learning algorithms, encompassing the process of training AI-based models. We demonstrate this framework through a comprehensive case study of localized tooth fault diagnosis, using controlled-degradation tests and realistic simulations. First, we detect faults using unsupervised learning algorithms; then, we use zero-shot-learning for classifying between localized and distributed faults; finally, we adopt a one-shot-learning strategy for severity estimation. Above all, this hybrid framework bridges the gaps between physical-based and AI-based approaches by combining physical knowledge and advanced algorithmics with machine learning. This contributes to the PHM field by offering valuable insights into integrating different aspects of research, thereby enhancing performance in gear diagnosis tasks.