A planetary gear set (PGS) is a common component in transmissions. The rapid progress in the demand for high power density has led to an increased risk of fatigue cracks at the gear tooth roots, potentially causing malfunctions in transmission devices. Intelligent fault diagnosis is crucial for PGS. However, the traditional data-driven method requires a large amount of experimental data, is costly, and is poorly adaptable to variable operating conditions as it cannot cover all potential operating scenarios. The mechanism model is relatively slow in computation and not suitable for real-time applications. As a result, the digital twin approach has been proposed as an alternative. This study develops a digital twin model of PGS under crack faults to provide a substantial amount of high-fidelity data. Firstly, the formation of tooth root cracks is analyzed in terms of stress. On this basis, the time-varying mesh stiffness considering tooth root cracks is calculated. The dynamics of PGS is modeled using the lumped parameter method. The model can simulate the vibration response under various operational conditions, with different crack angles and depths, and provide data to the intelligent fault diagnosis system. The intelligent fault diagnosis system developed in this paper shows an accuracy of 97.5% in diagnosing cracks with different fault levels.