Crack breathing as a function of crack location under the effect of unbalance force

In this work, an analytical model was developed to investigate the dependence of crack breathing behavior on the crack location 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 behaviours. 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 utilised to obtain the time-varying stiffness matrix of the cracked shaft element under the influence of unbalance force.