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Coefficients of Bearings 9.2 Calculation of Dynamic Coefficients of Bearings Using a Method with Linear Calculation Algorithm 9.3 Calculation of Dynamic Coefficients of Bearings Using a Method with Non‐linear Calculation Algorithm 9.4 Verification of Results Obtained 9.5 Summary

      20  10 Comparison of Bearing Dynamic Coefficients Calculated with Different Methods

      21  11 Summary and Conclusions

      22  Appendix A A.1 Fast Fourier Transform Diagrams of Journal Displacement in Relation to Bearing Housings A.2 Journal Vibration Trajectories in Relation to Bearing Housings A.3 Acceleration of Vibrations of Bearing Supports during Start‐up A.4 Rotor Axial Alignment Report

      23  Appendix B B.1 Fragments of Code of the Program Used for Processing the Signal from Experimental Tests B.2 Fragments of Code of the Program Used for Calculation of Dynamic Coefficients of Bearings on the Basis of Experimental Tests

      24  Appendix C C.1 Journal Vibration Trajectories Calculated in KINWIR and LDW Software C.2 Journal Vibration Trajectories Calculated in NLDW Software

      25  Research Funding

      26  References

      27  Index

      28  End User License Agreement

      List of Tables

      1 Chapter 3Table 3.1 Successive eigenfrequencies and the corresponding damping values ca...

      2 Chapter 5Table 5.1 Parameters of the numerical model.Table 5.2 Stiffness coefficients.Table 5.3 Damping coefficients.Table 5.4 Mass coefficients.

      3 Chapter 7Table 7.1 Summary of the real and calculated stiffness, damping and mass coef...Table 7.2 Summary of the real and calculated stiffness, damping, and mass coe...Table 7.3 Summary of the real and calculated stiffness, damping and mass coef...Table 7.4 Summary of the real and calculated stiffness, damping and mass coef...

      4 Chapter 8Table 8.1 Stiffness, damping and mass coefficients of the rotor–bearing syste...Table 8.2 Standard deviation of stiffness, damping and mass coefficients of t...

      5 Chapter 9Table 9.1 Parameters of the numerical model in the KINWIR program.Table 9.2 Stiffness and damping coefficients obtained from linear calculation...Table 9.3 Minimum and maximum values of stiffness coefficients (N/m) calculat...Table 9.4 Minimum and maximum values of damping coefficients (N·s/m) calculat...

      6 Chapter 10Table 10.1 Comparison of the calculated stiffness and damping coefficients fo...

      List of Illustrations

      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) cxx = cyy = 6...Figure 2.19 Combination of oscillation in two directions taking into account...Figure 2.20 Trajectory changes: (a) cxy and cyx = 0 N·s/m; (b) cxy = 0 N·s/m...Figure 2.21 Trajectory changes: (a) kxy and kyx = 0 N/m; (b) kxy = 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

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