Machine tool spindles must be periodically monitored to ensure the accuracy and productivity of machining operations. This paper presents a spindle fault detection model that is based on the combination of physics-based simulation and a machine learning network. The spindle imbalance and the wear of the race and ball are incorporated into the digital model of spindle dynamics, and the resulting vibrations at sensor locations are predicted at different speeds. A Gated Recurrent Unit Network (GRU) is trained to recognize the faults using the simulated and a few experimental vibration spectrum data. The model gave 97.6% fault detection accuracy when it is tested on faulty spindles.