Effect of a Novel Tooth Pitting Model on Mesh Stiffness and Vibration Response of Spur Gears

Abstract

The existence of pitting failure has a direct influence on the time-varying mesh stiffness (TVMS) and thus changes the vibration properties of the gears. The shape of pitting on the tooth surface is characterized by randomness and geometric complexity. The overlapping pitting shape has rarely been investigated, especially when the misalignment of gear base circle and root circle was considered. In this paper, the pitting shape is considered as approximately the union of several ellipse cylinders, in which the gear tooth is treated as a cantilever beam starting from the root circle. Then, the TVMS of perfect gear and that of gear with different pitting severity levels are solved by the potential energy method. The effect of pitting size on TVMS is discussed in detail. In addition, the vibration response in the frequency domain for the gear system is analyzed, and the effectiveness is qualitatively verified by comparing with the vibration signals of the experimental gearbox. The results indicate that the new pitting model overcomes the problem of ignoring the overlap between different pits and is more consistent with the actual situation. The presence of tooth pitting reduces the TVMS, and the complex sidebands appear around the gear mesh frequency and its harmonics. The proposed model can be used to predict the fluctuation of gear mesh stiffness when tooth pitting occurs, and the corresponding dynamic characteristics can provide the theoretical basis for gear condition monitoring and fault diagnosis.

Mathematical Complexities in Modelling Damage in Spur Gears

“…The shape of pits has been modelled as several geometric shapes with the aim of providing a reasonably realistic model. Some researchers have modelled the surface area of a single pit as circular [45][46][47][48][49][50], spherical [51], part of a sphere [52], or part of an elliptic cylinder [53]. As the gear tooth under pitting is likely to have more than one pit, models were defined with pits having any of the defined geometric shapes but with a regular spread on the surface of the gear tooth; the number and sizes of pits were used to define the severity as slight, moderate, or severe [45,53].…”

“…Some researchers have modelled the surface area of a single pit as circular [45][46][47][48][49][50], spherical [51], part of a sphere [52], or part of an elliptic cylinder [53]. As the gear tooth under pitting is likely to have more than one pit, models were defined with pits having any of the defined geometric shapes but with a regular spread on the surface of the gear tooth; the number and sizes of pits were used to define the severity as slight, moderate, or severe [45,53]. It is not likely to have a regular spread of pits on an affected tooth flank in actual gears in operations, so other researchers defined the pitting degree as a defined number of pits randomly placed around the pitch line [52].…”

Dynamical modeling of spur gear with pitting based on image processing tooth surface

“…Furthermore, the analysis of geometric characteristics is essential in traditional calculation of mesh stiffness, 10,11 especially in different pitting shapes. 12–14…”

“…Furthermore, the analysis of geometric characteristics is essential in traditional calculation of mesh stiffness, 10,11 especially in different pitting shapes. [12][13][14] Several studies have examined the analytical model of dynamic response of spur gear with pitting. Yang 15 proposed a new dynamic model to simulate the vibration behaviors of a spur gear transmission with pitting and spalling defects, which considered the effect of gearbox and the experimental validation was performed.…”

Experimental study and comparative analysis of pitting fault in spur gear system

“…To determine the total stiffness brought on by circular pits and to further explain the circumstances of repeated tooth surface pitting, Chen et al [17] adopted a two-dimensional Gaussian model using a potential method. By utilizing the appropriate technology to provide qualitative information on the forces applied to the machine components, this method, when compared to time-domain and frequency-domain analysis methods [18], generates more accurate and illuminating results, enabling the diagnosis of potential malfunctions. In the context of gear dynamics, Li and Lee [19] proposed a four-degree-of-freedom concentrated mass model for gear systems to predict the fatigue life of cracked gears and verified the feasibility of the method through comparison with experiments.…”