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New crack breathing mechanism under the influence of unbalance force

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Abstract

In this paper, a new analytical model (unbalanced one), which considers the coupling effects of unbalance force, rotor weight, and rotor physical and dimensional properties, is developed to study the actual breathing mechanisms of the transverse fatigue crack in a cracked rotor system. The results are also compared with those of the existing balanced model, where only rotor weight is considered. It has been identified that a crack in the unbalanced model breathes differently from the one in the balanced model. A crack’s breathing mechanism in the unbalanced model depends strongly on its location along shaft length. At some special locations, a crack in the unbalanced model may remain fully closed or open during the shaft rotation, which will never occur in a balanced model. It may also behave completely like the one in the balanced shaft. Depending on the crack location, unbalance force magnitude and orientation, the unbalanced shaft may be stiffer or more flexible than the balanced counterpart. It is also demonstrated that the unbalanced model will progressively approach balanced one as unbalance force decreases. Further, different crack breathing mechanisms between two models lead to a large difference along shaft length in the second area moment of inertia, which forms the elements of local stiffness matrix at crack location. It is expected that more accurate prediction of the vibration response of a cracked rotor can be achieved when the effect of unbalance force and rotor properties on the crack breathing has been taken into account.

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Abbreviations

\(\varphi \) :

Effectual bending angle, bending direction of the shaft relative to the crack direction

\(\delta \) :

Bending direction of the shaft relative to the negative Y-axis

\(\beta \) :

The angular position of unbalance force relative to the crack direction

\(\theta \) :

Shaft rotation angle

\(\mu \) :

The ratio of crack depth

\(\eta \) :

The ratio of the total weight force to the unbalance force

\(\lambda \) :

The ratio of the crack position to the shaft length

\(\varLambda \) :

Percentage of opening of the crack

\(A_1 \) :

Area of the uncracked cross section at \(t = 0\)

\(A_2 \left( t \right) \) :

Area of the closed portion of the crack segment at time t

\(A_\mathrm{c} \) :

Area of the crack segment

\(F_\mathrm{un} \) :

Rotational unbalance force

L :

Total shaft length

\(l_0 \) :

Location of the crack

\(l_1 \) :

Location of the left disk

\(l_2 \) :

Location of the unbalance force disk

\(M_{m_\mathrm{d} g} \) :

Gravitational moment due to two disks

\(M_{m_\mathrm{S} g} \) :

Gravitational moment due to shaft self-weight

\(M_\mathrm{un} \) :

Dynamic moment due to the rotational unbalance force

\(M_X \) :

Summation of the moments in X-axis

\(M_Y \) :

Summation of the moments in Y-axis

\(M_\mathrm{R} \) :

Resultant moment

\(m_\mathrm{d} \) :

The mass of a disk

\(m_\mathrm{d} g\) :

Gravitational force of a disk

\(m_\mathrm{s} \) :

Mass of the shaft

\(m_\mathrm{s} g\) :

The gravitational force of the shaft

X, Y :

Fixed coordinate system

\(\bar{X}\bar{Y}\) :

Centroid coordinate system

\({X^{\prime }}{Y^{\prime }}\) :

The rotational coordinate system

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Acknowledgements

The authors would like to gratefully acknowledge the financial support given by the School of Computing, Engineering, and Mathematics, Western Sydney University, Australia, for the development of this research.

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  1. School of Computing, Engineering and Mathematics, Western Sydney University, Penrith, NSW, 2747, Australia

    H. M. Mobarak, Helen Wu, Joseph P. Spagnol & Keqin Xiao

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  1. H. M. Mobarak
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Mobarak, H.M., Wu, H., Spagnol, J.P. et al. New crack breathing mechanism under the influence of unbalance force. Arch Appl Mech 88, 341–372 (2018). https://doi.org/10.1007/s00419-017-1312-3

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