The　early　fault　of　tooth　crack　in　a　planetary　gearbox　is　difficult　to　be　detected　duo　to　its　weak　yet　complex　effects　on　the　system＇s　vibration　signals.　In　order　to　identify　fault　signals　aroused　from　small　tooth　crack　of　the　sun　gear　in　a　planetary　gear　train,　a　lateral-rotational-coupled　nonlinear　dynamic　model　that　incorporates　the　tooth-crack-induced　time-varying　mesh　stiffness　is　proposed.　A　three-dimensional　finite　element　model　of　gear　pair　is　established　to　formulate　the　mesh　stiffness　of　the　gear　pair　with　and　without　tooth　crack.　Based　on　the　proposed　nonlinear　dynamic　model,　the　vibration　signals　of　a　planetary　gear　system　in　both　healthy　and　tooth-cracked　conditions　are　predicted.　Though　a　distinct　reduction　in　the　time-varying　mesh　stiffness　of　the　sun-planet　gear　pair　can　be　observed　after　introducing　the　effects　of　tooth　crack,　the　time-domain　vibration　signals　for　both　healthy　and　fault　conditions　are　almost　the　same.　However,　the　vibration　signals　in　frequency-domain　under　two　conditions　are　quite　different　in　that　multiplicities　of　sidebands　spaced　by　characteristic　frequency　of　the　sun　gear　around　the　harmonics　of　mesh　frequencies　can　be　observed　in　the　fault　condition.　Hence,　from　the　perspective　of　fault　diagnosis,　the　dynamic-model-based　frequency　spectra　can　be　used　to　detect　the　early　fault　of　tooth　crack　in　a　planetary　gear　train.　(C)　2017　The　Authors.　Published　by　Elsevier　B.V.