Transmission components in a gearbox are prone to premature fatigue damage due to high and intermittent loading cycles. Early fault diagnostics of these components is essential to avoid sudden failures during operation. Recently, several vibration-based diagnostics approaches using Machine Learning (ML) and Deep Learning (DL) algorithms have been proposed to identify gearboxes faults. However, most of them rely on a large amount of training data collection from physical experiments, which is often associated with high costs in test-rig building and instrumentation. Numerical simulations using realistic gearbox dynamic models have been considered a promising alternative to generating training data for existing classification algorithms. Thus, four studies were offered in this dissertation. First, crack faults in simple gear-pair were analyzed with various ML and DL algorithms as a benchmark to determine the best performing algorithm. Then, condition monitoring of a planetary gear set was performed. Thirdly, hydrodynamic journal bearings with wear and ovalization faults were investigated. In the first three approaches, mathematical models were used to obtain the datasets to use for ML and DL algorithms. In the last study, in order to demonstrate the significance of the simulated vibration data for DL training, a hybrid framework was proposed by using a Finite Element (FE) model and experimental setup of a cantilever beam with several crack conditions. The generated datasets from the FE model and the collected datasets from the experimental setup were fed to the convolutional neural network algorithm for training and testing respectively. The results showed that training DL algorithms with simulated vibration data are a great alternative to costly test rig building and collection of experimental data. This approach provides a significant improvement in diagnostics at the circumstances of a big experimental dataset shortage. This research contributes to the prevention of catastrophic failures in gearbox components by early fault detection and maintenance schedule optimization using simulation vibration data.