Deep learning models have created great opportunities for data-driven fault diagnosis but they require large amount of labeled failure data for training. In this paper, we propose to use a digital twin to support developing data-driven fault diagnosis model to reduce the amount of failure data used in the training process. The developed fault diagnosis models are also able to diagnose component-level failures based on system-level condition-monitoring data. The proposed framework is evaluated on a real-world robot system. The results showed that the deep learning model trained by digital twins is able to diagnose the locations and modes of 9 faults/failure from $4$ different motors. However, the performance of the model trained by a digital twin can still be improved, especially when the digital twin model has some discrepancy with the real system.