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The normal operation of gear systems ensures the power transmission in coal cutters. Due to harsh work environment, the gears in coal cutters are prone to crack. By analyzing the gear dynamic response, useful crack detection indicators could be obtained. The literature review indicates that most of the gear dynamic models have been built with singlefrequency excitation, but very limited work has considered multi-frequency excitations. The coal cutter gear systems are always subjected to multi-frequency excitations. Hence, a nonlinear gear dynamic model taking multi-frequency excitations into account was established in this work. A meshing stiffness coefficient was defined to model the crack fault influence on the gear model. The amplitude-frequency of the model main resonance was analyzed by means of multi-scale method, and the model dynamic response was calculated by the incremental harmonic balance method. Numerical simulation results show that the dynamic response of the presented gear model provided strong chaotic characteristics and the chaotic degree of the gear dynamics increased with the deterioration of the crack level. Experimental validation was carried out on a real gearbox, and the analysis results were consistent with the simulations. Hence, the simulation and experimental analysis demonstrates that the multi-frequency excitation-based gear dynamic model was more correct than the single-frequency excitation-based model in representing the system dynamics.

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