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Gears are one of the most important power transmission elements in every area of the industry. Because of its importance, the gear design must be carefully performed. Unfortunately, due to the changing of the boundary conditions, gears are exposed to failures such as cracks, pitting, tooth missing etc. during the operation. Thus the gear diagnostic and monitoring become a very critical phenomenon for the gearboxes. A dynamic transmission error (DTE) based numerical fault detection model is proposed. Firstly, numerical finite element model is created to calculate single tooth stiffness with different crack levels. Furthermore, the model is used for the asymmetric gear profile which has a great importance nowadays for different areas. After that, the time-varying mesh stiffness is calculated by using single tooth stiffness with different crack levels for both symmetric and asymmetric types of the gears. To understand the effects of the gear cracks along the tooth thickness on dynamic transmission error of the gear system and to detect the gear crack faults for symmetric and asymmetric gear profiles, a four-degree of freedom dynamic model is created. The results show that with the increment of the crack level, the mesh stiffness of the gears is decreased.

Planetary gear trains equipped in wind turbine often run under slow speed and non-stationary load condition. The incipient gear faults in a wind turbine gearbox can hardly be detected yet might cause tremendous loss. In order to detect the incipient faults, a resultant vibration signal model is proposed to characterize the faulty features of a single stage planetary gear train working under non-stationary load conditions. For this purpose, an analytical dynamic model is developed. By introducing the crack-induced mesh stiffness and varying load into the dynamic model, the vibration responses of the system are predicted. Based on this, a resultant vibration signal model is developed in the form of weighted summation of mesh vibration signals. With the resultant model, the vibration signals of an example system are simulated and analyzed. The simulation results indicate that varying load and tooth crack make the system's vibration signals become extremely complicated in both time and frequency domains. The incipient tooth crack induced impulse vibration signals are too weak to be identified in the time domain but can be detected from the order spectrum. The simulation results from the resultant signal model are verified by the test rig experimental measurements.

Gear tooth crack is likely to happen when a gear transmission train is working under excessive and/or long-term dynamic loads. Its appearance will reduce the effective tooth thickness for load carrying, and thus cause a reduction in mesh stiffness and influence the dynamic responses of the gear transmission system, which enables the possibility for gear fault detection from variations of the dynamic features. Accurate mesh stiffness calculation is required for improving the prediction accuracy of the dynamic features with respect to the tooth crack fault. In this paper, an analytical mesh stiffness calculation model for non-uniformly distributed tooth root crack along tooth width is proposed based on previous studies. It enables a good prediction on the mesh stiffness for a spur gear pair with both incipient and larger tooth cracks. This method is verified by comparisons with other analytical models and finite element model (FEM) in previous papers. Finally, a dynamic model of a gear transmission train is developed to simulate the dynamic responses when cracks with different dimensions are seeded in a gear tooth, which could reveal the effect of the tooth root crack on the dynamic responses of the gear transmission system. The results indicate that both the mesh stiffness and the dynamic response results show that the proposed analytical model is an alternative method for mesh stiffness calculation of cracked spur gear pairs with a good accuracy for both small and large cracks.

As one of the most important dynamic excitation sources, the gear time-varying mesh stiffness is the key parameter of gear system dynamic model. So how to calculate the gear mesh stiffness accurately is of great importance. In this paper, an accumulated integral potential energy method is proposed to calculate the mesh stiffness of helical gears. Compared with the finite element model (FEM) and the ISO standard, the proposed analytical method is verified as its results agree well with the others'. Meanwhile the effects of different helical gears parameters (e.g., helix angle, normal module) on mesh stiffness are studied. The results show that the fluctuation degree of mesh stiffness becomes smaller as helix angle or face width increases, by contrast the influence of normal module on the mesh stiffness shows an opposite trend. Furthermore, the mesh stiffness reduction of helical gears due to the tooth crack is quantified. Finally, a dynamic model of helical gear transmission is established to study the vibration characteristics of helical gears. The results show that the mesh stiffness plays a vital role in controlling the vibration of helical gears and has a significant effect on the vibration characteristic of helical gears with tooth crack.

In this paper, the effects of tooth crack on the vibration response of a one-stage gearbox with spur gears are studied. The growth in a tooth crack is reflected in the total mesh stiffness of the gear system. A lumped parameter model is used to simulate the vibration response of the pair of meshing gears. Several statistical indicators reported in the literature are used to reflect the change in the vibration response caused by the tooth crack. The performance of these indicators are compared. Their pros and cons are outlined.

Vibration analysis is widely used in machinery diagnostics and the wavelet transform has also been implemented in many applications in the condition monitoring of machinery. In contrast to previous applications, this paper examines whether acoustic signal can be used effectively along vibration signal to detect the various local faults in gearboxes using the wavelet transform. Two commonly encountered local faults, tooth breakage and tooth crack, were simulated. The results from acoustic signals were compared with vibration signals. The results suggest that acoustic signals are very affective for the early detection of faults and may provide a powerful tool to indicate the various types of progressing faults in gearboxes.