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This paper established the system dynamics model for two kinds of tooth cracks of different depths of the sun gear and inner gear ring to study the influence mechanism of crack failure on the tooth root strain of the planetary gear transmission system. Combined with the finite element model of the inner gear ring, the tooth root strain of the ring was solved. Experiments verified the correctness of the solution method. The root strain under the crack fault of the sun gear and the tooth crack fault of the inner gear ring is analyzed, and the following conclusions are drawn: Periodic fault impact occurs in the strain signal of the tooth root of the inner gear ring during the crack fault of the sun gear root. The fault can be extracted by the fast spectral kurtosis method (FSK), and the fault components are used to determine whether the sun gear cracks. The Lempel–Ziv index showed a tendency to increase gradually during the process of solar wheel crack deepening, which could be used as the damage index of crack depth. The results can provide a basis and reference for fault diagnosis. [ABSTRACT FROM AUTHOR]