Coupled longitudinal and bending vibrations of a rotating shaft with an open crack

Rigid finite element model of a cracked rotor

“…10c). It can be noticed that the crack breathes in a completely different manner than this suggested by Papadopoulos and Dimarogonas [19], Darpe et al [10], and others. The line delimiting the closed part of the crack from the uncracked one is not all time perpendicular to the crack edge.…”

“…First finite element models of the rotating shaft cracks were introduced by fundamental works of Dimarogonas and Paipetis [18], who starting from the fracture mechanics, obtained a full 6 � 6 flexibility matrix for a transverse open surface crack on a shaft. Papadopoulos and Dimarogonas [19] derived the flexibility matrix for the finite shaft element with an open crack. Ostachowicz and Krawczuk [9] used the finite element model with a modified stiffness matrix of a beam accounting for the effect of crack and considering all but axial degree of freedom.…”

“…The characteristic feature of the cracked shaft finite element, modeled using fracture mechanics approach [9,10,18,19] is the presence of additional components that appear beyond the main diagonal of the stiffness matrix. This may lead to the couplings between torsional, bending and longitudinal modes of vibration.…”

“…The appearance of the coupled vibrations may be used for shaft crack detection. Ostachowicz and Krawczuk [9], Papadopoulos and Dimarogonas [19] reported the possibility to use the torsional-bending, while Darpe et al [22] reported using bending-longitudinal coupled vibrations for such purposes. Unfortunately, these methods have not been widely employed due to very low amplitudes of the induced, coupled vibrations.…”

Quasi-static numerical study of the breathing mechanism of an elliptical crack in an unbalanced rotating shaft

“…The opening and closing of the crack has been modeled in different ways. The simplest one is to consider that the crack is always open (Papadopoulos and Dimarogonas (1987), Zhou et al (2005) and Papadopoulos (2008), among others), or that the crack is open or closed, so that the crack is half the rotation in the open state and the other half in the closed one. This model, commonly called "switching" model has been used quite often i.e by Gasch (1976), Muller et al (1994), Pu et al (2002), Qin et al (2003), Qin et al (2004), Gasch (2008) due to its simplicity.…”