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Overview

Overview. Introduction and Motivation Mathematical Model Numerical solution method Results Conclusions. Introduction and Motivation. Introduction and Motivation. Vibratory system. Introduction and Motivation. Introduction and Motivation. Vibro-impact system. Disk. Stator.

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Overview

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  1. Overview • Introduction and Motivation • Mathematical Model • Numerical solution method • Results • Conclusions 1st International Conference on Vibro-Impact Systems

  2. Introduction and Motivation Introduction and Motivation Vibratory system 1st International Conference on Vibro-Impact Systems

  3. Introduction and Motivation Introduction and Motivation Vibro-impact system 1st International Conference on Vibro-Impact Systems

  4. Disk Stator Introduction and Motivation Introduction and Motivation Actual background – vertical rotor test rig 1st International Conference on Vibro-Impact Systems

  5. 4 DOF system Rotor: xr ,yr Stator: xs ,ys w= const 2 Imperfections Rotor unbalance Center offset Mathematical model Rotor and elastically suspended stator Mathematical model 1st International Conference on Vibro-Impact Systems

  6. Mathematical model Rotor and elastically suspended stator Mathematical model Contact system 1st International Conference on Vibro-Impact Systems

  7. Rotor Stator Radial intrusion depth Mathematical model Equations of motion Mathematical model 1st International Conference on Vibro-Impact Systems

  8. yoff xoff rrs vt d Mathematical model Coordinates Contact forces Mathematical model 1st International Conference on Vibro-Impact Systems

  9. Rotor Stator Mathematical model Dimensionless system equations Mathematical model 1st International Conference on Vibro-Impact Systems

  10. Mass ratio Stiffness ratio Physical damping ratio Ratio of damping ratios Dimensionless rotor speed Mathematical model Mathematical model 1st International Conference on Vibro-Impact Systems

  11. Numerical solution method Numerically stiff problem Gear‘s algorithm Numerical solution method Detection of state events (contacts) Start of contact phase Geometric condition End of contact phase D>0 Force condition 1st International Conference on Vibro-Impact Systems

  12. rotor stator Results – Rotor and Stator Orbits Rotor orbit and stator motion for a 2p/2c-Orbit Results 2p/2c-Orbit … 2 periods and 2 contacts 1st International Conference on Vibro-Impact Systems

  13. Parameters M = 0.01 K = 3 C = 66.667 Z = 384.9 Lossless Contact Last 100points Last 1000points Ch=0, m=0 Results – Bifurcation Diagram for h Results 1st International Conference on Vibro-Impact Systems

  14. Parameters Parameters M = 0.01 M = 0.01 K = 3 K = 3 C = 66.667 C = 66.667 Z = 384.9 Z = 384.9 h= 0.774 h= 0.82 Results – Rotor Orbits and Poincare-Maps Results 1st International Conference on Vibro-Impact Systems

  15. Parameters M = 10-2÷103 K = 3 C = 66.6 Z = 384.9 ÷ 1.217 Last 100points Last 1000points Results – Bifurcation Diagram for M Results Lossless Contact Ch=0, m=0 h= 0.799 1st International Conference on Vibro-Impact Systems

  16. Parameters M = 10÷100 K = 3 C = 12.550 ÷ 39.686 Z = 2.291 Lossless Contact Last 100points Last 1000points Ch=0, m=0 Results - Bifurcation Diagram for M Results h= 0.799 1st International Conference on Vibro-Impact Systems

  17. Parameters M = 10÷100 K = 3 C = 25.100 ÷ 79.373 Z = 4.583 Lossless Contact Last 100points Last 1000points Ch=0, m=0 Results - Bifurcation Diagram for M Results h= 0.799 1st International Conference on Vibro-Impact Systems

  18. Parameters M = 10÷100 K = 3 C = 41.833 ÷ 132.288 Z = 7.638 Lossless Contact Last 100points Last 1000points Ch=0, m=0 Results - Bifurcation Diagram for M Results h= 0.799 1st International Conference on Vibro-Impact Systems

  19. Conclusion • Flexible rotor contacting an elastically suspended stator was investigated • System exhibits rich dynamic behavior (periodic, quasi-periodic and chaotic solutions) • Damping ratio has a large influence on the occurance of periodic and non-periodic solutions • Still a basic system but already high dimension of the parameter space Conclusion 1st International Conference on Vibro-Impact Systems

  20. Thanks for Your Attention Deflection Xr Rotor speed h Mass ratio M 1st International Conference on Vibro-Impact Systems

  21. Vertical Rotor Test Rig - Results Simulation results Measurements 1st International Conference on Vibro-Impact Systems

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