ROTORDYNAMICS OF TURBOMACHINERY Alfa-Tranzit Co., Ltd offers the new DYNAMICS R4. program system for analysis and design of rotor systems of high complexity Copyright Alfa-Tranzit Co., Ltd 2-25 e-mail lemk@alfatran.com
Unbalanced response 3D rotor model with unbalance Response curves in different sections of rotor model Unbalance response.25 4 4 5 6 6.2.15 1 2 3 4 5 6 7 8 9 1 [t-pr] Amplitude and phase response curves 3D unbalance response plot Phase[ ] 1 14 13 12 11 8 7 6 4 3 2.4.35.3.25.2.15.1 5 Unbalance response Subset 2 2 3 4 6 7 8 1 [t-pr]
Synchronous and nonsynchronous response Twin-shaft rotor model n1= 2 rpm n2= rpm Unbalances of LP and HP rotors
25 (linear rotor models) (Time behavior plot due to impulse excitation 8 7 6 4 3 2 - -2-3 -4 - -6-7 -8 Amplitude response versus rotor spin (acceleration and deceleration) 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 External harmonic excitation (post processing results examples) Orbit () 196..125 18 5.1.15.2.75.25 4 3 2 1 27 75
(nonlinear rotor systems) Response curves of linear rotor system with a retainer bearing Cascade plot (run-up and run-down) 25 2 Retainer bearing fixed No retainer bearing 15 1 5 1 2 2 3 3 4 4 with a retainer bearing 2 Peak-to-peak curves 15 1 5-5 -1-15 -2 5 1 15 2 25 3 35 4
Point mass model with damper Point mass model Transient orbits for rotor model with weight (n = Const): a) unbalance =153 gsm) Orbit () Time response for rotor without weight (n=const );.15 18.1.2.3.4.6.7.8..11.12.13.14.1.16.17.18 ) unbalance =153 gsm) Orbit () - Orbit () 27 - -.15.1.2.3.4.6.7.8.9.11 18.25.75 18.25.75.125.1 27 27
Rotor model with damper supports Rotor model 185. 1. 4.75 3 [1/min]..25 2 1..5. 25 75 -.5-1. 1 2 2 3 3 4 4 [1/min] Peak-to peak ( EXEL) Mean value 14 12 with dampers no dampers 2. 1 8 1.5 Y, mm 6 1. 4.5. 1 2 2 3 3 4 4 [1/min] 2 2 3 4 6-2 RPM
Point mass rotor with journal bearing Point mass rotor (n=const).15 Time response - - -.15 Harmonic analysis 146..1.2.3.4.6.7.8.9 Orbit Orbit ().125.75.15 1.25 2 18.2.7.12.1.175 27
Instability of point mass rotor with journal bearing Point mass rotor model Time response (n= rpm); 2D-orbits Orbit ().2.15 - - 18.2.7.12.1.17.2 -.15 -.2 Cascade plot 2 3 4 6 7 8 [1/min] 153. 3D-orbits 27.15 1. 7.5 5. 2 RMS.15.14.13 Mean value 1.11.12.9.8.7.6. 1 2 3 4 5 6 7 8 9 1
Dynamic response of rotor with journal bearing Twin-mass case-rotor model (n=const).1 - -.1 -.2 Time response of rotor -1-2 -3-4 Time response of case -.3-5 -.4 - -6-7 -.6-8 -.7-9 -.8 -.1 -.9 -.11 Rotor 3D-orbits -.1 -..1.2.3.4.5.6.7.8.9 Rotor 2D-orbits Orbit () -.1..1.2.3.4.5.6.7.8.9 1. Case orbits Orbit () 18.1.2.3.4.6.7.8.9 18 1 2 3 4 5 6 7 8 9.1.11 27 27
Instability of rotor with journal bearing (1) Twin mass case-rotor model Rotor (YOZ) Rotor (XOZ) - - - - - 2 3 4 6 7 [1/min] 2 3 4 6 7 [1/min] Case (YOZ) Case (XOZ).1-5 5 -.1 -.15 - -5 -.2 -.25 -.1 1 2 3 4 5 6 7 1 2 3 4 5 6 7
Instability of rotor with journal bearing (2) Twin-mass case-rotor model Rotor orbits Orbit () Case orbits Orbit () 18.25.75.125 18 5.1.15.2.25 n cr ~32 34 rpm Cascade plot 27 27 Response analysis: 1. Rotor instability threshold n ~ 68 rpm (~ 2*n cr ) 2-d 3-d harmonics 7.5..25 [e-2] 5. 3 2.
Elastic Damping Lateral Restraint (Clearance) Clearance element Modeling effects: rubs between rotor and stators; rubs between rotors; full and partial rubbings; external and internal damping; dry friction in contact point; slip response; weight; circumferential irregularity of clearance; etc
Elastic Damping Lateral Restraint (Clearance) Reverse (backward or dry) whirl due to rotor/stator interaction (impulse force on 7-th second) 2D-orbits Orbit () 2. 1.5 1..5 -. -.5 18.5 1. 1.5 2. -1. -1.5-2. - -1 1 2 3 4 5 6 7 8 Cascade plot 27 148. 3D orbits of rotor 2. 1.5 1. 7.5 5. 75 1..5. 25.
. 5. 5. 1. Rotor instability due to internal damping Thresholds of instability Analytical solution (Jeffcott rotor, E.J. Gunter) Points for simulation ω = ω 2 R (1 + ) D 1 1+ R C D = C r b R = k k r b Stable motion (point 1) Unstable motion (point 2) 2. 5 1.5 4 3 1. 2.5 1. 1. 195. -.5-1 -1. 1.25-2 4 1. -3-1.5.75 3. -4-2. 1 2 3 4 6 7 8 75.25 1. -5 2 1 1 2 3 4 6 7 8 75 7.5 25. 25 7.5