Dynamic response and time-frequency analysis for gear tooth crack detection

• Time-varying gear mesh stiffness was investigated for different crack cases.
• The frequency response functions of the gear model were derived for healthy and faulty cases.
• Dynamic simulation was performed to study the dynamic response for all studied cases.
• A new approach involving a short-time Fourier transform was applied for gear fault detection.
• The proposed method shows promising results for gear crack detection and size estimation.

Vibration health monitoring is a non-destructive technique which can be applied to detect cracks propagating in gear teeth. This paper studies gear tooth crack detection by investigating the natural frequencies and by performing time-frequency analysis of a 6 DOF dynamic gear model. The gear mesh stiffness used in the model was calculated analytically for different cases of crack sizes. The frequency response functions (FRFs) of the model were derived for healthy and faulty cases and dynamic simulation was performed to obtain the time signal responses. A new approach involving a short-time Fourier transform (STFT) was applied where a fast Fourier transform (FFT) was calculated for successive blocks with different sizes corresponding to the time segments of the varying gear mesh stiffness. The relationship between the different crack sizes and the mesh-stiffness-dependent eigenfrequencies was studied in order to detect the tooth crack and to estimate its size.