Research on the meshing stiffness and vibration response of cracked gears based on the universal equation of gear profile

• The universal gear profile equation was applied to gear dynamics.
• Both the mesh stiffness and fault indicators intersect at a special point.
• A double pulse appeared in the residual signal and was investigated.
• The parabolic affecting line is the right method for calculating tooth thickness.

To achieve the expected purpose monitoring the gearbox condition and preventing the occurrence of dangerous situations, it is important to improve the accuracy of the vibration response, which is primarily caused by the time-varying mesh stiffness. Thus, a universal gear profile equation that references the actual manufacturing process was applied to calculate the meshing stiffness. Based on the universal gear profile equation, two methods of calculating tooth thickness decrements (method 1: straight-affecting line; method 2: parabolic-affecting line) in cracked gears were compared, and their different effects on the vibration response were investigated with fault detection indicators, including RMS and kurtosis. The results revealed that the fault detection indicators of two affecting lines intersect when the crack size reaches a special point at which the two affecting lines overlap, and this result contrasts with those of previous research. The double pulse observed in the residual signals was analyzed, and the results revealed that the double pulse was generated by the two step-points of the residual stiffness. The behaviors of the fault detection indicators of the two affecting lines were investigated, and the results revealed that the parabolic-affecting method was appropriate for the calculating the decrement in tooth thickness.