Coupled Rotor Housing Dynamics Component Mode Synthesis · • Natural frequencies compared between...

© 2011 ANSYS, Inc. September 8, 20111

Coupled Rotor‐Housing Dynamics Using Component Mode Synthesis

Presented by Stephen JamesEngineer, Rotating Machinery Dynamics GroupSouthwest Research InstituteSan Antonio, Texas


Objective• Use the Component Mode Synthesis (CMS) reduction technique available inANSYS® to aid in the analysis of rotordynamic systems

• Most rotordynamic analysis codes use 2D models to analyze the rotor and casing– Rotors can be analyzed using beam elements– Casing structures can be simplified into beam or shell models

• What happens when the casing cannot be simplified?

• Casing structures require 3D solid elements• Overall model results in large number of elements and associated nodes

Introduction

X

Y

Z

Image Courtesy:Turbo Exchange & Performance TEP Turbocharger (http:// www.tepturbos.com)


In this example:• 6 degrees of freedom per node (lateral & rotational)• 4‐node model has 24 DOFs 24 equations to solve

Actual models have large number of nodes• Rotor models in the range of 101 – 102• Casing models in the range of 104 – 106

Mathematically complex and computationally time‐consuming due to largedimensionality

Model Reduction – Why is it necessary?

1Rz1

x1

Rx1

Ry1

y1

φz12 3

4Rz2

x2

Rx2

Ry2

y2

φz2

Rz3

x3

Rx3

Ry3

y3

φz3

Rz4

x4

Rx4

Ry4

y4

φz4


Guyan Reduction Technique• Rewrite equations of motion with a reduced number of degrees of freedom• Build a detailed model and then use only dynamic portion

• Reduces dimensionality by directly eliminating physical coordinates• Defines a set of interior coordinates in terms of boundary (exterior) coordinates

Reduction Techniques – 1

12 3

4

f1(t) f2(t)

M x C x K x F

ExteriorCoordinates

InteriorCoordinates

“Exterior”“Master”“Retained”

“Interior”“Slave”

“Discarded”


Guyan Reduction Technique• Rearranging equations

• Retain master DOFs and eliminate slave DOFs

Reduction Techniques – 1 (continued)

12 3

4

f1(t) f2(t)Exterior

Coordinates

InteriorCoordinates

11 12 13 141 1 1 1

21 22 23 242 2 2

31 32 33 343 3 3

41 42 43 444 4 4 4

0 0 00 0 0 00 0 0 00 0 0

k k k km x x fk k k km x xk k k km x xk k k km x x f

11 12 13 14 1 1

21 22 23 24 2

31 32 33 34 3

41 42 43 44 4 4

00

k k k k x fk k k k xk k k k xk k k k x f

11 14 12 13 1 1

41 44 42 43 4 4

21 24 22 23 2

31 34 32 33 3

00

k k k k x fk k k k x fk k k k xk k k k x

mm ms m m

sm ss s s

k k x Fk k x F

0

mm m ms s m

sm m ss s

k x k x F

k x k x

1

s ss sm mx k k x

mm m

s

Ixx B x

Bx

For details on Guyan Reduction see ANSYS Help§17.6 Substructuring Analysis (17.6.3 Statics)


Guyan Reduction Technique• Based on the assumption that the dynamic content of the system can be definedby the retained coordinates

• The reduced stiffness matrix is exact, whereas the reduced mass and dampingmatrices are approximate.

• Need to have a good understanding of the system before selecting thosecoordinates to be retained. Reduced mass matrix (and hence the accuracy of thesolution) depends on the number and location of masters.



Component Mode Synthesis (CMS)• More accurate than a Guyan reduction• Coordinates are separated into boundary and interior coordinates• Advantage of CMS is that interior coordinates get absorbed into modalcoordinates therefore retaining all dynamic content of the system

• Define static constraint modes– producing a unit displacement of each boundary coordinate in turn, with allother boundary coordinates fixed and all interior coordinates unconstrainedand unloaded

• Define constraint normal modes– set boundary coordinates to zero– solve free vibration problem forthe interior coordinates

Reduction Techniques – 2

12 3

4

1 i bx B x

2 0i i ij ijm k a


Component Mode Synthesis (CMS)• Coordinate transformation used to express the interior coordinates as thesuperposition of two types of displacement modes:– Constraint modes: displacement produced by displacing boundary coordinates– Constrained normal modes – displacement relative to the fixed componentboundaries

• Truncating the number of constrained normal modes determines the number ofdegrees of freedom to be retained for the entire system

• CMS allows significant reduction in model size while retaining essential dynamiccharacteristics


i b jx b x a q

0 b

j

Ix

xq

B a


Casing built with solid element models – SOLID185, SOLID186, SOLID187

Superelement – MATRIX50

Structural supports built with spring‐damper elements – COMBIN14

Rotor built with beam elements – BEAM4 (legacy), BEAM188

Interconnecting bearings and seals – COMBI214

Analysis Components

c1c2 c3

c4

r1 r2 r3 r4 r5 r6 r7

cs1 cs2ks1 ks2kb1 kb2

kb3 kb4


Casing Model• Axisymmetric and Non‐Axisymmetric models built

Analysis Methodology


Casing Model (continued)• Models imported into ANSYS Classic



Casing Model (continued)• Creating bearing center node



Rotor Model• Rotor model built and validated withXLTRC2 ™ beam‐element based 2Drotordynamic modeling tool. (XLTRC2 ™ is developed by Texas A&M University)

• VB‐script developed to read XLTRC2model and convert it into ANSYS APDL script


Sub GenerateFilesBeam188()Dim fsoAPDLDim objFileAPDL As ObjectstrLineToWrite = strSeperator & vbCrLf & "! BEAM188 APDL DEFINITION FILE" & _"ET, 1188, BEAM188" & vbCrLf & _

"KEYOPT, 1188, 1, 0" & vbCrLf & _"N, " & N1 & ", " & ((ShftStart + x) * XModifier) + XOffset& ", " & ((ShftStart + y) * YModifier) + YOffset & ", " _

objFileAPDL.WriteLine (strLineToWrite)

…

FINISH ! ** HEADER INFORMATION **/CLEAR,START/input,start110,ans,'C:\Program Files\AnsysInc\v130\ANSYS\apdl\',,,,,,,,,,,,,,,,1 /TITLE, COUPLED AXISYMM ROTOR‐CASING MODAL ANALYSIS

! ** RESUME ROTOR MODEL **RESUME,rotor,DB

! Define rotor component CM, ROTOR, ELEM

/FILNAME,symm_rc_modal,1


Combined rotor‐casing model with bearings and seals



• Natural frequencies compared between coupled rotor‐axisymmetric casing model,coupled rotor‐non‐axisymmetric casing model, and rotor‐only model

Results – Natural Frequency Comparison

Mode Coupled rotor–axisymmetric casing model

Coupled rotor–non‐axisymmetric casing model Rotor‐only model

1 1804.3 1785.7 2430.52 2139.1 2100.8 2508.33 3429.7 3368.1 3774.1

Damped Eigenvalue 3-D Mode Shape Plot

Rotor Model with seal - Mode Shape 1

f=2430.5 cpmd=1.6469 logd

Running Speed =3600 rpm

forwardbackward



f=2508.3 cpmd=3.2852 logd


forwardbackward



f=3774.1 cpmd=1.2889 logd


forwardbackward


• Unbalance response show different trends between the various cases

Results ‐ Unbalance Response Comparison

Rotor relative to Casing Horizontal Unbalance Response at midspan

0.00

0.04

0.08

0.12

0.16

0 2000 4000 6000 8000Rotor Speed, rpm

Res

po

nse

, m

m p

k-p

k

Symmmodel

Non-Symmmodel

3600rpm

Rotor relative to Casing Vertical Unbalance Response at midspan

0.00

0.04

0.08

0.12

0.16

0 2000 4000 6000 8000Rotor Speed, rpm

Res

po

nse

, m

m p

k-p

k

Symmmodel

Non-Symmmodel

3600rpm

Horizontal Unbalance Response at Rotor midspan

0.00

0.04

0.08

0.12

0.16

0 2000 4000 6000 8000Rotor Speed, rpm

Res

po

nse

, m

m p

k-p

k

Symmmodel

Non-SymmmodelXLTRC2rotor-onlymodel3600 rpm

Vertical Unbalance Response at Rotor midspan

0.00

0.04

0.08

0.12

0.16

0 2000 4000 6000 8000Rotor Speed, rpm

Res

po

nse

, m

m p

k-p

k

Symmmodel

Non-SymmmodelXLTRC2rotor-onlymodel3600 rpm


Component Mode Synthesis used as a reduction method• Model size is much smaller (290 MB db 4.5 MB db)• Computation time is significantly reduced (by at least 10 times)

APDL script‐generator developed• User need not know how to write APDL script• Can be used to convert a rotor model into equivalent APDL script• Bearing and seal models are also automatically built from tabular inputs• Multiple cases can be analyzed more quickly

Results point to the obvious• A valid model is one that is as close as possible to the actual machine/structure• The impact of the non‐axisymmetric casing is evident• Using axisymmetric models may be sufficient for some cases but not all

What ANSYS® technology does this bring to the table?• Using Component Mode Synthesis to analyze complex coupled rotor‐non‐axisymmetric rotordynamic systems

Summary and Conclusions


QUESTIONS?

Stephen JamesEngineer, Rotating Machinery Dynamics GroupSouthwest Research InstituteSan Antonio, Texas

Coupled Rotor Housing Dynamics Component Mode Synthesis · • Natural frequencies compared between...

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