Simulation results

To show crack influence on dynamic rotor behavior, rotor acceleration was calculated in the range from 0 to

4000 rpm. Only weight force has outer influence. The first critical speed of such rotor accounts for wcr =2643,6 rpm (44,06 Hz). Figure 4 shows the obtained amplitudefrequency characteristics. 

Figure 4. Amplitude-frequency characteristics in crack section

At 1/3 and 1/2 from critical speed, parametrical resonances being the result of cyclic change in moment stiffness appear. Cascade diagram shows 1x, 2x and 3x rotor harmonics, Figure 5. 

Figure 5. Cascade diagram of vibration speed while rotor accelerating up to 4000 rpm

   Dynamic rotor characteristics (spectra and orbits) are given below at regimes w =1/3wcr , w =1/ 2wcr ,w = wcr . Only rotor weight represents outer loads. 

Figure 6 Signal spectrum at 1/3 wcr regime in logarithmical coordinates

Figure 7 Signal spectra at 1/3 wcr regime in linear coordinates

Figure 8 Orbits of rotor center in crack section at 1/3 wcr regime

Figure 9 Signal spectra at 1/2 wcr regime in logarithmic coordinates

Figure 10 Signal spectrum at 1/2 wcr regime in linear coordinates

Figure 11 Orbits of rotor center in crack section at 1/2 wcr regime

Figure 12 Signal spectra at wcr regime in logarithmic coordinates

Figure 13 Signal spectra at wcr regime in linear coordinates

Figure 14 Orbits of rotor center in crack section at wcr regime

    Obtained results show that appearance of subharmonic resonances may be a diagnostic sign of crack appearance. The best diagnostic regime to detect multiple rotor harmonics is the regime of 1/3 from the first critical speed. Three harmonics of rotor frequency close in amplitudes value are seen at it. 

Conclusion

Use of the developed crack model in the algorithms of analysis of dynamic characteristics of rotors with crack lowers significantly time needed for their modeling and analysis. Calculation results show that crack in the shaft of the investigated rotor causes parametric resonances at regimes 1/3 wcr , 1/3 wcr , wcr being the result of rotor harmonics with frequencies 1x, 2x, 3x, 4x, etc. In actual tests there is an opportunity to highlight two or three rotor

harmonics. Presence of subharmonic resonances, multiple harmonics and change in the motion orbit of the shaft  sections may be signs of crack appearance. At the same time it should be taken into account that probability to detect crack in actual practice depends on its geometry and depth, sensitivity of the used equipment, presence of orbits sensors, etc. So the proposed model should be considered mainly as an instrument to train engineers in the area of vibrational diagnostics, and to obtain limiting values of diagnostic signs of crack.