Multiple　vibration　signal　models　for　planetary　gearboxes　have　been　built,　but　details　in　the　signals　are　often　ignored　when　verifying　their　correctness.　The　main　reason　is　that　the　vibration　mechanism　of　the　gearbox　is　not　well　studied.　To　overcome　this　problem,　the　stiffness　model　of　the　faulty　external　gear　pair　is　firstly　developed　and　the　end　meshing　time　of　the　broken　tooth　under　different　fault　sizes　is　explored.　Based　on　this,　an　improved　phenomenological　model　is　established,　and　the　assisted　phases　for　verifying　its　correctness　are　proposed.　Subsequently,　the　simulated　signal　is　decomposed　into　two　components,　which　mainly　contain　meshing　impacts　and　fault　impacts,　respectively.　Based　on　the　time　difference　between　these　two　types　of　impacts,　the　mapping　relationship　between　the　assisted　phases　and　the　fault　size　is　verified.　Finally,　the　correctness　of　the　vibration　mechanism　of　the　gearbox　and　the　improved　phenomenological　model　are　verified　by　simulation　and　experiments.　©　2021