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The gear transmission system is a vital component of the locomotive bogie. During locomotive operation, the damage to the gear transmission system spreads rapidly and affects the locomotive’s operational safety. In this paper, a method is proposed to detect the degree of tooth root crack damage. First, a dynamic locomotive model with a gear transmission is built, and the vertical acceleration of the locomotive subsystem (car body, bogie frame, wheelset, and motor) vibrations is obtained under various degrees of tooth root crack damage on the gear transmission system. By comparing the characteristics of those signals, the subsystem that is more sensitive to the effect of the tooth root crack is found. The characteristic parameters of the sensitive subsystem are calculated, and a multidimensional characteristic parameter matrix is established. The multidimensional characteristic parameter matrix is optimized and reduced by principal component analysis (PCA). Using the Grey relational analysis method, the degree of tooth root crack damage is detected. The proposed method demonstrates the ability to recognize the degree of tooth root crack damage. [ABSTRACT FROM AUTHOR]