Reliable quality control and fault diagnosis are essential for ensuring machine reliability and preventing unexpected failures. One of the critical machine components for which such a diagnosis enables failure-free, long-term exploitation is gearboxes. Conventional vibration-based monitoring often depends on expert interpretation of signal patterns and gear-mesh behaviour, which limits scalability and consistency. In this work, physics-informed machine-learning framework for binary gearbox health classification using engineered vibration features. Time and frequency domain descriptors capturing impulsiveness, gear-mesh spectral characteristics, and modulation effects were extracted from tri-axial acceleration signals. To account for direction-dependent dynamics, separate models were developed for left (RPM0) and right (RPM1) rotational conditions. We employ a unsupervised Isolation Forest trained exclusively on healthy data for anomaly detection, and a supervised Logistic Regression classifier trained on both healthy and faulty samples. Predefined decision thresholds were applied to ensure methodological transparency and minimize overfitting. Evaluation on independent test cases demonstrates that direction-specific modelling combined with physically interpretable features enables robust gearbox fault detection. The proposed framework provides a reproducible and industrially applicable strategy for automated condition monitoring. Such an approach will provide precise solutions for early fault detection, predictive maintenance scheduling, and real-time performance optimization of gearboxes and machinery systems.