# Dynamics of rotors with crack in shafts

### Аuthors

Degtiarev S. A.1*, Kutakov M. N.2**, Leontiev M. K.2***

1. Scientific and technical centre of rotor dynamic «Alfa-Tranzit», 1, Leningradskaya str., Khimky, Moscow region, 141400, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: degs@alfatran.com
**e-mail: maxim.kutakov@alfatran.com
***e-mail: lemk@alfatran.com

### Abstract

Crack in the shaft influences the rotor system during operation. Crack is a reason for parametric oscillations due to presence of local variable stiffness. The aim of the work is to develop the algorithm of consideration of transverse crack influence at mathematical simulation of dynamic behavior of the rotor system.

The article gives the methodology and algorithm of consideration of transverse crack when modeling dynamic rotors behaviour. In the rotor system model crack is substituted for the elastic link dividing the shaft into two sections and described by the stiffness matrix with variable factors. When describing crack, only rotation along lateral axes is taken into account. Displacements at other freedom degrees are neglected. Law of change in stiffness coefficients is obtained by the authors on the basis of the existed crack models and considers opening and closing of crack under external forces.

Calculation results of dynamics behavior of the two-support rotor with crack obtained for the crack’s depth of 30% of the shaft diameter at the acceleration regime from 0 to 4000 rpm and at the stationary regimes1/3х, 1/2х, 1х of the first critical speed are presented. Calculation is hold in the program Dynamics R4 designed to calculate rotordynamic tasks; the algorithm of crack consideration was included there. The obtained results show appearance of parametric resonances at 1/3х, 1/2х and 1х of critical speed; the cascade diagram shows excitation frequencies multiple of 1х, 2х, 3х of the rotor frequency, etc. Orbits of the rotor centre in the crack section are given. Calculation of flexibility of the beam with crack done in Dynamics R4 using the presented crack model showed convergence with similar calculation in the finite-element system with error of less than 1%.

The proposed methodology and the algorithm should be mainly considered as an instrument to train the engineers in the vibrational diagnostics area and to obtain limiting values of diagnostics signs of crack.

### Keywords:

rotor dynamics, crack, nonlinear model, Dynamics R4

### References

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