<p>Dynamic behaviors critically influence the reliability and service life of split-torque transmissions. Previous studies have mainly focused on fault-free systems, with limited attention given to fault conditions. This work presents a comprehensive analysis of a dual-branch split-torque transmission with a tooth crack fault, from the perspectives of dynamic modeling and fault diagnosis. Firstly, an improved analytical method is developed to calculate time-varying mesh stiffness (TVMS) under both healthy and cracked conditions. The method accounts for several complex factors, including deformation compatibility, extended tooth contact, and gear body structure coupling. The accuracy of the proposed TVMS calculation approach is validated through finite element analysis. A nonlinear dynamic model of the dual-branch split-torque transmission is then established, incorporating key system parameters such as gear rotation directions and installation angles. The model is verified using experimental data obtained from a real split-torque gearbox. Numerical simulations are conducted to reveal how tooth crack propagation affects vibration characteristics and load sharing performances. Finally, frequency responses, bifurcation diagrams, phase diagrams and Poincaré maps are evaluated under different health conditions, to evaluate the sensitivity of nonlinear dynamic behaviors to the tooth crack fault. The developed modeling framework and analytical results may provide valuable insights for vibration-based monitoring and condition assessment in split-torque transmission systems.</p> Graphical abstract <p></p>