Dynamic response and time-frequency analysis for gear tooth crack detection Omar D. Mohammed a,b,n , Matti Rantatalo a a Division of Operation, Maintenance and Acoustics, Lulea University of Technology, Sweden b Mechanical Engineering Department, College of Engineering, University of Mosul, Iraq article info Article history: Received 3 May 2014 Received in revised form 12 May 2015 Accepted 17 May 2015 Keywords: Gear tooth crack Gear mesh stiffness Gear dynamic modelling Vibration analysis Short-time Fourier transform abstract 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. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction Cracks in gear teeth can occur due to an excessive load or operation under improper conditions, or simply because the end of the fatigue life has been reached. When a crack is propagating, the mesh stiffness and then the vibration characteristics will change. Various techniques for vibration analysis and signal processing have been applied for improving gear teeth fault detection in an early stage. In this field, dynamic modelling of a gear system with simulated faults has an important role in fault detection analysis. By modelling the gear system, different kinds of faults can be studied and the dynamic response can be simulated. The meshing action is the main source of vibration in gearing systems, and the mesh stiffness is one of the basic parameters in gear dynamic modelling. Moreover, any reduction in the gear mesh stiffness due to the presence of a fault will affect the dynamic behaviour and the vibration characteristics of the system. Mode shapes and natural frequencies were investigated in [1,2] for different mesh stiffness values over a wide range of time-averaged mesh stiffness. However, fault modelling was not considered. The quantification of wear in a gear tooth based on stiffness reduction was presented in [3]. Analytical calculations and experimental modal analysis were conducted to investigate the change in the vibration characteristics when the tooth damage is propagating. The dynamic response and frequency response functions (FRFs) were investigated for a gear dynamic model with different crack sizes in [4]. The conclusion in this study was that a change in the FRF could be detected with increasing crack size. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ymssp Mechanical Systems and Signal Processing http://dx.doi.org/10.1016/j.ymssp.2015.05.015 0888-3270/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: omar.mohammed@ltu.se, omar.mohammed@uomosul.edu.iq (O.D. Mohammed). Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]] Please cite this article as: O.D. Mohammed, M. Rantatalo, Dynamic response and time-frequency analysis for gear tooth crack detection, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.05.015i