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.
Highlights
As one of the key components of mechanical transmission, spur gears have the characteristics of simple structure, convenient manufacture, reliable operation, and long service life and play an extremely important role in the process of power transmission
The time-varying mesh stiffness (TVMS) of gear teeth is reduced, and the vibration of the transmission system is unstable, which directly affects the transmission precision and the running state of the whole mechanical equipment. It is of great theoretical significance and engineering value to study the mechanism of gear failure and its influence on the dynamic responses of gear systems for early fault diagnosis, gear design, and safety maintenance in mechanical equipment
Tooth pitting and tooth root crack are the most typical fatigue damages in gear transmission. They mainly lead to the abnormal vibration response of the system by changing the TVMS
Summary
As one of the key components of mechanical transmission, spur gears have the characteristics of simple structure, convenient manufacture, reliable operation, and long service life and play an extremely important role in the process of power transmission. In 1987, Yang [13] proposed the potential energy method for obtaining the TVMS He considered the gear tooth as a cantilever of variable cross-section staring from the base circle and derived the analytical expressions of the stiffness of Hertzian contact, bending, and axial compressive. When pittings with different severity are distributed over adjacent multiple teeth, Liang [30] obtained the TVMS of gear with cylindrical tooth pitting, including bending, axial compressive stiffness, Hertzian contact stiffness, and shear stiffness. In the analysis of the TVMS with pitting or spalling based on the potential energy method above, the gear tooth is treated as a cantilever of variable cross-section starting from the root circle.
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