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Crack characteristic analysis of multi-fault rotor system based on whirl orbits

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Abstract

In this paper, the nonlinear crack characteristics of different multi-fault rotor system are analyzed for crack detection based on whirl orbits. The nonlinear crack response can bring instability of the rotating shaft. The identification of the nonlinear characteristics is very important in the crack detection. Considering the interaction of rub-impact forces, time-varying stiffness and nonlinear oil-film forces, the nonlinear dynamic models are established. The numerical simulations put emphasis on the evolution of whirl orbits by studying orbit morphological characteristics near subcritical speed for a rotor system with crack. The bifurcation diagrams, time series and frequency spectra are used to analyze the nonlinear coupled behaviors of the multi-fault rotor system. The typical features and rules of whirl orbits are found in the rotor system with crack. The morphological characteristics of whirl orbit present the number and orientation changes of inner loops during the subcritical speed region, even though multi-fault exist in the rotor system with crack. The experimental whirl orbits of a rotor system with crack during passage through the 1/2 subcritical speeds agree with the theoretical analysis. The orbit morphological characteristics will offer a method for crack detection in multi-fault rotor system.

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Abbreviations

\(o^{{\prime }}\) :

The center of the rotating shaft

\(\phi _o \) :

The initial phase angle of the shaft

\(\omega ,t,\theta \) :

The rotation speed, rotating time and rotating angle of the rotor

\(\phi \) :

The angle of difference between rotation and whirl

\(\beta \) :

The angle between the eccentricity and the crack direction

\(\alpha ,\psi \) :

The half of the crack angle and the whirl angle

a, A :

The crack depth and the dimensionless crack depth

\(R_1 \) :

The radius of the shaft

\(\mathbf{K},k_{ij} (i,j=x,y)\) :

The stiffness matrix and the stiffness of the cracked shaft

\(k,\Delta k\) :

The stiffness of the rotating shaft and the stiffness variable with shaft crack

\(P_i (i=N,T)\) :

The striking force and the frictional force

\(r,\delta ,f\) :

The radial displacement of the shaft center, initial clearance and friction factor of rotor–stator

\(k_c \) :

The stiffness of stator

\(p_{i}=(i=x,y)\) :

The component of rub-impact forces in X direction and Y direction

\(F_{i}=(i=x,y)\) :

The oil-film forces acting on the shaft

\(f_i (i=x,y)\) :

The non-dimensional components of nonlinear oil-film forces

\(\sigma ,\mu \) :

The Sommerfeld correction number and the viscosity of lubricating oil

\(R,L,c^{\prime }\) :

The bearing radius, length and the radial clearance

\(O_1 ,O_2 \) :

The geometric center and centroid of rotor

\(O_1^{\prime }\) :

The geometric center of the oil-film journal bearing

\(O_2^{\prime },O_3 \) :

The geometric center and centroid of the rotor in rotor-bearing system

m, c :

The mass of disk and the damping in Jeffcott rotor

e :

The disk eccentricity

\(x_s \) :

The static deformation of the shaft

U :

The dimensionless eccentricity

\(\omega _{{n}} \) :

The natural frequency

\(\xi ^{\prime }\) :

The damping ratio of Jeffcott rotor system

\(\varOmega \) :

The ratio of rotating speed

K :

The ratio of the stiffness change

\(m_i (i=1,2)\) :

The lumped mass of the shaft and the disk

\(c_i (i=1,2)\) :

The damping of the shaft and the disk

\(k_0 \) :

The stiffness of the shaft in rotor-bearing system

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Acknowledgements

This research work is funded by the National Natural Science Foundation of China (No. 51675178).

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Authors and Affiliations

  1. Department of Mechanical Engineering, North China Electric Power University, Baoding, 071003, Hebei Province, China

    Ling Xiang, Yue Zhang & Aijun Hu

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  1. Ling Xiang
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  2. Yue Zhang
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Correspondence to Ling Xiang.

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Xiang, L., Zhang, Y. & Hu, A. Crack characteristic analysis of multi-fault rotor system based on whirl orbits. Nonlinear Dyn 95, 2675–2690 (2019). https://doi.org/10.1007/s11071-018-4715-y

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