<p>As the core components of various power transmission systems, gear systems are often subjected to harsh external conditions that can lead to gear failures, potentially resulting in catastrophic consequences. Although numerous vibration signal models have been developed to guide fault diagnosis in gear systems, they typically address only local or distributed faults separately, failing to effectively analyze compound faults or the combined effects of different fault modes on vibration signals, compromising diagnostic accuracy. To address these limitations, this study proposes a universal AM-FM vibration model by improving the traditional vibration signal modeling methods at the gear meshing point. Based on this universal model, vibration signal models and their theoretical spectral structures are derived for distributed faults, local faults, and particularly multiple compound faults, with the model’s validity verified through simulations. Additionally, experimental validation confirms the accuracy of the prior spectral structures obtained from the vibration model, particularly the secondary modulation sidebands generated by the combined effects of different fault modes. The proposed model comprehensively explains the vibration characteristics in gear systems under various fault modes, offering new insights into vibration signal analysis and diagnosis for complex fault patterns.</p>