Effect of unbalance force on the crack breathing mechanism

The dependence of crack breathing behavior on the crack location was investigated under the effect of unbalance force. A parameter known as the effectual bending angle is introduced to describe the non-linear relationship between crack direction and bending direction for balanced and unbalanced shaft along the shaft length. Breathing behavior of crack was visualized by examining the duration of each crack status (open, closed and partially open/closed) during a full shaft rotation. It is shown that a crack in an unbalanced shaft has more breathing patterns than a crack in a balanced shaft, including single status (fully open/never closed or fully closed/never open) and dual statuses. Two pairs of interesting locations along the shaft length were identified, where the crack shows specific breathing behaviors. Further, the angular range during which a crack remains fully closed, partially open/closed or fully open, changes significantly with the crack location. The analytical model developed in this work can be further utilized to obtain the time-varying stiffness matrix of the cracked shaft element under the influence of unbalance force.