Читать книгу Bearing Dynamic Coefficients in Rotordynamics - Lukasz Brenkacz - Страница 4

1 Chapter 1Figure 1.1 Lubrication film model for small journal displacement.Figure 1.2 Methods of analysis for (a) small and (b) large displacement of t...

2 Chapter 2Figure 2.1 Bearing as part of a rotating system. Question marks indicate the...Figure 2.2 Different bearing models: (a) oscillating mass with one degree of...Figure 2.3 Displacement of the mass attached to a fixed support by means of ...Figure 2.4 The effect of a change in the damping coefficients on the displac...Figure 2.5 The effect of a change in the stiffness coefficients on the displ...Figure 2.6 A single degree of freedom system with harmonic excitation.Figure 2.7 The effect of a change in the damping coefficients on the displac...Figure 2.8 The effect of a change in the stiffness coefficients on the displ...Figure 2.9 Excitation force of constant value and of variable value changing...Figure 2.10 The relationship between the excitation force frequency and the ...Figure 2.11 The relationship between the excitation force frequency and the ...Figure 2.12 Impact of damping coefficients.Figure 2.13 Impact of stiffness coefficients.Figure 2.14 Impact of mass coefficients.Figure 2.15 Areas of influence of different types of coefficients for variab...Figure 2.16 Areas of influence of different types of coefficients for the co...Figure 2.17 Combination of oscillation in two directions taking into account...Figure 2.18 Two‐directional displacement and trajectories: (a) c_xx = c_yy = 6...Figure 2.19 Combination of oscillation in two directions taking into account...Figure 2.20 Trajectory changes: (a) c_xy and c_yx = 0 N·s/m; (b) c_xy = 0 N·s/m...Figure 2.21 Trajectory changes: (a) k_xy and k_yx = 0 N/m; (b) k_xy = 6 630 000...

3 Chapter 3Figure 3.1 Photograph of the laboratory test rig.Figure 3.2 Diagram of the laboratory test rig.Figure 3.3 (a) Hydrodynamic bearing and (b) bearing diagram.Figure 3.4 Run‐up of the laboratory test rig; during 66.4 seconds the speed ...Figure 3.5 Maximum displacement of the rotor journals.Figure 3.6 Stable operation of bearings no. 1 (a and b) and no. 2 (c and d) ...Figure 3.7 Stable operation of bearings no. 1 (a and b) and no. 2 (c and d) ...Figure 3.8 FFT analysis of the stable operation signal from eddy current sen...Figure 3.9 Trajectory of bearing journal movement no. 2 during stable operat...Figure 3.10 Combination of the vibration trajectories of a second bearing op...Figure 3.11 Cascade diagram based on the accelerometer signal placed on supp...Figure 3.12 The first form of natural vibrations of the laboratory test rig....

4 Chapter 4Figure 4.1 SCADAS mobile analyzer.Figure 4.2 (a) Eddy current sensors placed at a 90° angle to each other and ...Figure 4.3 (a) Accelerometer used to measure accelerations of vibrations of ...Figure 4.4 Impact hammer.Figure 4.5 (a) Speed measurement using a laser sensor and (b) fiber optic sw...Figure 4.6 The Vision Research Phantom v2512 camera (right), the LED lamps u...Figure 4.7 (a) MBJ Diamond 401 measuring device used for balancing the rotor...Figure 4.8 Interface of the Test.Lab 11B software.Figure 4.9 Interface of the Samcef Rotors software.Figure 4.10 Interface of the Matlab software.Figure 4.11 Interface of GRAFMESWIR – a graphical processor of the NLDW soft...Figure 4.12 Interface of the Abaqus/CAE software 6.14‐2.

5 Chapter 5Figure 5.1 (a) Rotor model in the Samcef Rotors software and (b) bearing mod...Figure 5.2 Diagram for the calculation of dynamic bearing coefficients.Figure 5.3 (a) Force in direction X as a function of time and (b) displaceme...Figure 5.4 (a) Frequency distribution of force and (b) amplitude of node no....Figure 5.5 Bearing no. 1: (a) flexibility amplitude and (b) flexibility phas...Figure 5.6 The first form of natural vibrations of the rotor at 46 Hz.

6 Chapter 6Figure 6.1 Calculation scheme of dynamic coefficients of bearings including ...Figure 6.2 (a) Stable operation of the rotor – reference signal in the beari...Figure 6.3 (a) Amplitude of vibrations after subtracting the reference signa...Figure 6.4 The fast Fourier transform displacement signal in bearings for ro...Figure 6.5 Dynamic flexibility of bearings: (a) amplitude course and (b) pha...

7 Chapter 7Figure 7.1 Diagram showing the sensitivity analysis scheme.Figure 7.2 (a) Rotor model on which the method of force displacement is mark...Figure 7.3 (a) Model showing how the force is applied at an angle and (b) th...Figure 7.4 Model on which the place of bearing displacement measurement was ...Figure 7.5 Diagram of an asymmetrical rotor.Figure 7.6 Response of an asymmetrical rotor system.

8 Chapter 8Figure 8.1 Program window for signal preparation; the diagrams presented the...Figure 8.2 Window of the software used for calculations of dynamic coefficie...Figure 8.3 Photograph showing the test stand during the shaft alignment.Figure 8.4 Photograph showing the tested rotor.Figure 8.5 Phantom Camera Control, a program window for operating a high‐spe...Figure 8.6 Calculation scheme of dynamic coefficients of bearings.Figure 8.7 Signal measured near bearing no. 2 in the Y direction at 4500 rpm...Figure 8.8 Excitation force curve in the Y direction over 20 seconds; signal...Figure 8.9 Excitation force in the X and Y directions over 0.4 ms; excitatio...Figure 8.10 Stable bearing operation no. 2 (a and b) at 4500 rpm and signal ...Figure 8.11 Amplitude of rotor vibrations after excitation in the X and Y di...Figure 8.12 Changes in the stiffness coefficients of bearing no. 2 for the e...Figure 8.13 Changes in the damping coefficients of bearing no. 2 for the ent...Figure 8.14 Changes in the mass coefficients of bearing no. 2 for the entire...Figure 8.15 Increasing vibration amplitude recorded in bearing no. 2 during ...Figure 8.16 Schematic model of mass, damping, and stiffness.Figure 8.17 Comparison of the dynamic response of the real rotor and the num...

9 Chapter 9Figure 9.1 Coordinate system at a selected point in the lubrication gap.Figure 9.2 Algorithm of calculation of a radial hydrodynamic bearing.Figure 9.3 Numerical rotor model in the KINWIR program.Figure 9.4 Numerical model of hydrodynamic bearing.Figure 9.5 Presentation of the pressure distribution calculated for the stat...Figure 9.6 Bearing no. 2 stiffness coefficients calculated using a linear al...Figure 9.7 Bearing no. 2 damping coefficients calculated using a linear algo...Figure 9.8 Numerical model of the rotor, bearing and disk in the NLDW progra...Figure 9.9 Pressure distribution calculated using the NLDW program for (a–d)...Figure 9.10 Stiffness coefficients calculated in the NLDW program for 3 roto...Figure 9.11 Damping coefficients calculated in the NLDW program for 3 rotor ...Figure 9.12 Stiffness coefficients calculated in the NLDW program for 3 roto...Figure 9.13 Damping coefficients calculated in the NLDW program for 3 rotor ...Figure 9.14 Stiffness coefficients calculated in the NLDW program for 3 roto...Figure 9.15 Damping coefficients calculated in the NLDW program for 3 rotor ...Figure 9.16 Bearing journal displacements calculated using the method with a...Figure 9.17 Bearing journal displacements calculated using the NLDW program....Figure 9.18 Vibration trajectories of the journal of bearing no. 2: (a) meas...Figure 9.19 The FFT analysis of the signal for a speed of 5750 rpm based on ...

10 Chapter 10Figure 10.1 (a) Change in journal vibration trajectory due to e.g. increased...

11 Chapter 11Figure 11.1 A diagram of the work carried out. The division into experimenta...

12 Appendix 1Figure A.1 Fast Fourier transform (FFT) diagrams of the first and second bea...Figure A.2 FFT diagrams of the first and second bearings in the X and Y dire...Figure A.3 FFT diagrams of the first and second bearings in the X and Y dire...Figure A.4 FFT diagrams of the first and second bearings in the X and Y dire...Figure A.5 Vibration trajectory of the first bearing for 16 rotational speed...Figure A.6 Vibration trajectory of the second bearing for 16 rotational spee...Figure A.7 Cascade diagram of an accelerometer placed on support no. 1 in th...Figure A.8 Cascade diagram of an accelerometer placed on support no. 1 in th...Figure A.9 Cascade diagram of an accelerometer placed on support no. 2 in th...Figure A.10 Cascade diagram of an accelerometer placed on support no. 2 in t...Figure A.11 Shaft alignment report – part one.Figure A.12 Shaft alignment report – part two.

13 Appendix 3Figure C.1 Vibration trajectories calculated for the second bearing using a ...Figure C.2 Vibration trajectories calculated for the second bearing using a ...