SAMCEF For ROTORS. Chapter 1 : Physical Aspects of rotor dynamics. This document is the property of SAMTECH S.A. MEF A, Page 1

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1 SAMCEF For ROTORS Chapter 1 : Physical Aspects of rotor dynamics This document is the property of SAMTECH S.A. MEF A, Page 1

2 Table of Contents rotor dynamics Introduction Rotating parts Gyroscopic effect Whirling modes Centrifugal Stiffening Internal Damping Asymmetry Temperature effect Initial stress Cracked rotors Coupling between lateral and torsional Vibrations Multi-rotors systems Fixed parts effects This document is the property of SAMTECH S.A. MEF A, Page 2

3 Table of Contents rotor dynamics Interaction elements Rolling element bearings Magnetic bearings Journal bearings Seals Dry friction rubs Alford s effect: tip clearance excitation Loads Unbalances Maneuvers loads Overall acceleration Vibrations Vibrations vocabulary Bistable vibrations This document is the property of SAMTECH S.A. MEF A, Page 3

4 Introduction SYSTEM BREAKDOWN Rotating parts - One or several (flexible) rotors - Different rotation speeds - Linking devices : Bearings : Interaction elements Seals rolling element bearings journal bearings Magnetic bearings Fixed parts Dampers : Gears Squeeze film dampers Solid-state damper - Casing - Stator - Foundation - Interaction forces Fluid forces Rubbing This document is the property of SAMTECH S.A. MEF A, Page 4

5 Rotating Parts Gyroscopic Effect Cause : -Modification of the orientation of the axis of rotation due to shaft deformation or to bearing deformation Effects : -Induced torque proportional to : -The rotational speed Ω -The polar moment of inertia -Elastic rotation velocity This torque originates a coupling between lateral vibrations Significant : -If high rotational speed -If large polar moment of inertia Examples : -Fan disk of aircraft engine -High-speed turbo pump This document is the property of SAMTECH S.A. MEF A, Page 5

6 Rotating Parts Gyroscopic Effect Example : Overhung disk: Campbell diagram and 4th bending mode (inertial frame) This document is the property of SAMTECH S.A. MEF A, Page 6

7 Rotating Parts Gyroscopic Effect Example : Mid span disk: Campbell diagram and 4th bending mode (inertial frame) This document is the property of SAMTECH S.A. MEF A, Page 7

8 Rotating Parts Whirling modes Forward whirl or co-rotating modes : - With gyroscopic stiffening - As seen in a fixed frame - Sensitive to unbalance - Static mode in a rotating frame Backward whirl or counter-rotating modes : - With gyroscopic softening - As seen in a fixed frame - Sensitive to rubbing - 2Ω t mode in a rotating frame This document is the property of SAMTECH S.A. MEF A, Page 8

9 Rotating Parts Whirling modes Examples : This document is the property of SAMTECH S.A. MEF A, Page 9

10 Rotating Parts Centrifugal Stiffening Second order effect Increase of eigenfrequencies Affects blades dynamic behavior Has to be taken into account for : -If high rotational velocity -If flexible components Example: overhung disk with large flexible blades (Rotating reference frame centrifugal stiffening and Coriolis effect cyclic symmetry : 2 diameters modes) Basic sector Campbell diagram Recombined mode Centrifugal effect => bending modes Coriolis effect => membranes modes This document is the property of SAMTECH S.A. MEF A, Page 10

11 Rotating Parts Internal Damping Origin : - Damping within the material - Damping associated with joints of assembled elements of the rotating parts Effects : - Generation of a damping force in phase with the velocity of the whirling motion - In the fixed frame: circulatory force (tangential) - Increases forward whirling - Instability at rotational speeds above the first forward critical speed Avoidance : - The external damping has to be increased - Limitation of the number of assembled elements This document is the property of SAMTECH S.A. MEF A, Page 11

12 Rotating Parts Internal Damping Example : Rotor with internal damping Freq rpm 200 Damping coeff Positive damping = instability rpm This document is the property of SAMTECH S.A. MEF A, Page 12

13 Rotating Parts Asymmetry Origin : - geometrical anisotropy of the shaft: - two poles electric rotor - two bladed propellers - material anisotropy Effects : - as seen in a fixed reference frame: -periodic change of stiffness -periodic change of inertial forces - instability in some ranges of rotational speed - sensitivity to gravity (resonance at half critical speed) This document is the property of SAMTECH S.A. MEF A, Page 13

14 Rotating Parts Temperature effect Cause : -Different operation regimes (aircraft engine, cryogenic turbo pump ) Effects : -Stiffness characteristics function of temperature -> function of the rotational speed -Thermal bow Initial Stress Cause : -Fitting of different elements Effects : -Initial stress distribution -Modification of the stiffness This document is the property of SAMTECH S.A. MEF A, Page 14

15 Rotating Parts Cracked rotors Similar to asymmetric stiffness effects Initial coupling between lateral and torsional vibrations Causes : - Closeness of bending and torsion eigen-frequencies -Gears Effect : - Unstable speed range Multi-rotors systems Different rotational speeds Coupling with intershaft bearing or flexible casing Possible interaction (excitation of one rotor by the other) This document is the property of SAMTECH S.A. MEF A, Page 15

16 Fixed parts Fixed parts effects Introduction of flexibility: - Flexible casing of aircraft engines - Coupling between several rotors - Possible anisotropy Introduction of damping Isolation of the foundation from the rotors - Minimum transmissibility between loading forces (unbalances) and the foundation This document is the property of SAMTECH S.A. MEF A, Page 16

17 Interaction elements Rolling element bearings Classes : - Ball bearing - Tapered roller bearing: axial + radial loading - Cylindrical roller bearing: radial loading Properties: - No damping - No associated destabilizing forces - Clearances -> non linear stiffness - Very small cross coupling This document is the property of SAMTECH S.A. MEF A, Page 17

18 Interaction elements Magnetic bearings Active control of the rotor: separate control of rotor cylindrical and conical whirl Stiffness and damping characteristics function of frequency Loadings limitation Often operation below the first elastic critical speed This document is the property of SAMTECH S.A. MEF A, Page 18

19 Interaction elements Journal bearings Classes : - Plain cylindrical - Partial arc - Elliptical - With lobes - With offset - Tilting-pad Properties: - Non linear dynamic behavior - Stiffness and damping function of the rotational speed - Cross coupling effect - no associated destabilizing forces Effects: - Instability threshold (the tilting-pad bearing is highly stable) - Oil whip: unstable whirling at approximately one half the rotational speed frequency This document is the property of SAMTECH S.A. MEF A, Page 19

20 Interaction elements Journal bearings Example : This document is the property of SAMTECH S.A. MEF A, Page 20

21 Interaction elements Seals Purpose: - Reduction of leakage - Separation Classes : - Floating contact seals - Labyrinth seals - Plain seals : cylindrical, tapered, stepped Properties: - Turbulent flow (large clearances, high axial fluid velocity) - Non linear dynamic behavior - Stiffness and damping function of the rotational speed - Cross coupling effect Effects: - Positive: introduction of damping - Negative: possible instability and non synchronous resonances This document is the property of SAMTECH S.A. MEF A, Page 21

22 Interaction elements Seals Example : Squeeze film dampers This document is the property of SAMTECH S.A. MEF A, Page 22

23 Interaction elements Dry Friction rubs Cause : - Contact between the rotor and the stator - Also occurs in seals and hydrodynamic bearings Effects : - Tangential friction force - Instability Alford s effect: tip clearance excitation Cause: - Variation of blade tip clearance around an axial flow stage - Induced by shaft deflection - Axial machine Effects: - Cross coupled stiffness <-> tangential force - Possible instability This document is the property of SAMTECH S.A. MEF A, Page 23

24 Loadings Unbalances Cause : - Disk or component eccentricity - Oblique-angled component - Eccentric machining - etc. Effects : - Rotating force in a fixed frame - Static force in a rotating frame - Proportional to Ω² and to Ω - Proportional to the eccentricity and to the mass This document is the property of SAMTECH S.A. MEF A, Page 24

25 Loadings Maneuvers loads Cause : - Maneuvers of an aircraft Effects : - Translation loading - Coriolis loading if rotation of the aircraft - Force of static nature - Possible occurrence of contacts Overall Acceleration Cause : - Earthquake origin Effects : - Loading in translation from the foundation - Possible occurrence of contacts This document is the property of SAMTECH S.A. MEF A, Page 25

26 Vibrations Vibrations vocabulary Eigen frequencies - Natural frequencies of the structure - May change with rotational speed - Associated with backward or forward whirl for rotors lateral vibrations Resonance - Excitation of an Eigen frequency (unbalance) - Amplification of vibration amplitude Critical speed - Rotational speed for which a natural frequency coincides with a multiple of the rotational speed - Forward and backward critical speed Subharmonic resonance - Occurs at a frequency equal to 2X, 3X the rotational speed frequency - Non linear behavior Combination resonance - Merging of natural frequencies This document is the property of SAMTECH S.A. MEF A, Page 26

27 Vibrations Bistable vibrations Jump phenomena System with non linearity like clearances : - change of response curves when contact occurs - Several solutions in some frequency ranges Examples : Transient response under unbalance: (very low acceleration rate): Harmonic response under unbalance: (2 clearance cases) Transient response Harmonic response case A case B This document is the property of SAMTECH S.A. MEF A, Page 27