Analytical Model of Spur Gear Tooth Crack for Evaluating the Effect of Crack Propagation Angle on Vibration Response

Vibration-based health monitoring is considered as an important tool since any anomaly present in the system is manifested through its own vibration signature. This vibration signature is unique in nature. This uniqueness is very well established and being utilized in industry effectively for obtaining vibration response of industrial gear boxes and this forms the basis of diagnosis of the extent to which the gears are working at the intended level of accuracy. In this study, the mathematical model is developed and based on eight degrees of freedom governing differential equations are formed consisting time varying meshing force. Further, this time varying mesh force is diffused in terms of time varying mesh stiffness. The eight degrees of freedom are four rotational and four translational. During mesh in spur gear pair, the load sharing is variable with respect to time along the line of contact and it also depends upon the number of teeth pair in contact. Different faults in gear can be enlisted as crack, spalling, pitting, etc., each contributing adversely on the system characteristics, mesh stiffness being one of those. A cracked gear tooth is attributed by many features such as crack depth, crack length, initiation zone of crack and crack propagation angle. Amidst these, the study associated with the influence of crack propagation angle on gear tooth vibrations has been undertaken and the results are presented in this paper. Time varying mesh stiffness equations are formulated based on potential energy theory and it is solved by using a MATLAB code. TVMS plot is generated to investigate the influence of propagation angle on TVMS.