Coupled Rotor Housing Dynamics Using Component Mode Synthesis

Transcription

1 Coupled Rotor Housing Dynamics Using Component Mode Synthesis 1 Presented by Stephen James Engineer, Rotating Machinery Dynamics Group Southwest Research Institute San Antonio, Texas

2 Introduction Objective Use the Component Mode Synthesis (CMS) reduction technique available in ANSYS 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? Y Z X Image Courtesy: Turbo Exchange & Performance TEP Turbocharger ( Casing structures require 3D solid elements Overall model results in large number of elements and associated nodes 2

3 Model Reduction Why is it necessary? R y1 R y2 R y3 R y4 R x1 R x2 R x3 R x4 x1 y1 x2 y2 x3 y3 x4 y4 1 R z1 φ z2 R z2 φ z1 2 3 φ z3 R z3 4 φ z4 R z4 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 Casing models in the range of Mathematically complex and computationally time consuming due to large dimensionality 3

4 Reduction Techniques 1 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 f 1 (t) Exterior Coordinates f 2 (t) Exterior Master Retained Interior Coordinates 4 Interior Slave Discarded M x Cx Kx F 4

5 Reduction Techniques 1 (continued) Guyan Reduction Technique Rearranging equations f 1 (t) Exterior Coordinates f 2 (t) m x k k k k x f m2 0 0 x 2 k21 k22 k23 k 24 x m3 0 x3 k31 k32 k33 k 34 x m4 x4 k41 k42 k43 k44 x4 f Interior Coordinates 4 k11 k12 k13 k14 x1 f1 k k k k x k31 k32 k33 k 34 x3 0 k41 k42 k43 k44 x4 f4 k11 k14 k12 k13 x1 f1 k k k k x f k21 k24 k22 k 23 x2 0 k31 k34 k32 k33 x3 0 Retain master DOFs and eliminate slave DOFs kmm kms xm Fm k k x F sm ss s s kmm xm kms xs Fm k x k x 0 sm m ss s x k 1 k x s ss sm m x I m x s x m B xm B For details on Guyan Reduction see ANSYS Help 17.6 Substructuring Analysis ( Statics) 5

6 Reduction Techniques 1 (continued) Guyan Reduction Technique Based on the assumption that the dynamic content of the system can be defined by the retained coordinates The reduced stiffness matrix is exact, whereas the reduced mass and damping matrices are approximate. Need to have a good understanding of the system before selecting those coordinates to be retained. Reduced mass matrix (and hence the accuracy of the solution) depends on the number and location of masters. 6

7 Reduction Techniques 2 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 modal coordinates therefore retaining all dynamic content of the system Define static constraint modes producing a unit displacement of each boundary coordinate in turn, with all other boundary coordinates fixed and all interior coordinates unconstrained and unloaded x Bx i Define constraint normal modes set boundary coordinates to zero solve free vibration problem for the interior coordinates 2 i mi k ij aij0 b

8 Reduction Techniques 2 (continued) Component Mode Synthesis (CMS) Coordinate transformation used to express the interior coordinates as the superposition of two types of displacement modes: Constraint modes: displacement produced by displacing boundary coordinates Constrained normal modes displacement relative to the fixed component boundaries xi bxb aqj x I Truncating the number of constrained normal modes determines the number of degrees of freedom to be retained for the entire system CMS allows significant reduction in model size while retaining essential dynamic characteristics 0 xb q j B a 8

9 Analysis Components 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 r1 r2 r3 r4 r5 r6 r7 k b1 c s1 k s1 c s2 k s2 k b2 c1 c2 c3 c4 k b3 k b4 9

10 Analysis Methodology Casing Model Axisymmetric and Non Axisymmetric models built 10

11 Analysis Methodology Casing Model (continued) Models imported into ANSYS Classic 11

12 Analysis Methodology Casing Model (continued) Creating bearing center node 12

13 Analysis Methodology Casing Model (continued) Creating bearing center node 13

14 Analysis Methodology Casing Model (continued) Creating bearing center node 14

15 Analysis Methodology Rotor Model Rotor model built and validated with XLTRC 2 beam element based 2D rotordynamic modeling tool. (XLTRC 2 is developed by Texas A&M University) 15 VB script developed to read XLTRC2 model and convert it into ANSYS APDL script Sub GenerateFilesBeam188() Dim fsoapdl Dim objfileapdl As Object strlinetowrite = 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\Ansys Inc\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

16 Analysis Methodology Combined rotor casing model with bearings and seals 16

17 Results Natural Frequency Comparison Natural frequencies compared between coupled rotor axisymmetric casing model, coupled rotor non axisymmetric casing model, and rotor only model Mode Coupled rotor axisymmetric casing model Coupled rotor non axisymmetric casing model Rotor only model Damped Eigenvalue 3-D Mode Shape Plot Rotor Model with seal - Mode Shape 1 forward backward f= cpm d= logd Running Speed =3600 rpm Damped Eigenvalue 3-D Mode Shape Plot Rotor Model with seal - Mode Shape 2 forward backward f= cpm d= logd Running Speed =3600 rpm Damped Eigenvalue 3-D Mode Shape Plot Rotor Model with seal - Mode Shape 3 forward backward f= cpm d= logd Running Speed =3600 rpm 17

18 Results Unbalance Response Comparison Unbalance response show different trends between the various cases Horizontal Unbalance Response at Rotor midspan Vertical Unbalance Response at Rotor midspan Response, mm pk-pk Symm model Non- Symm model XLTRC2 rotor-only model 3600 rpm Response, mm pk-pk Symm model Non- Symm model XLTRC2 rotor-only model 3600 rpm Rotor Speed, rpm Rotor Speed, rpm Rotor relative to Casing Horizontal Unbalance Response at midspan Symm model Response, mm pkpk Non- Symm model 3600 rpm Rotor relative to Casing Vertical Unbalance Response at midspan Symm model Response, mm pkpk Non- Symm model 3600 rpm Rotor Speed, rpm Rotor Speed, rpm 18

19 Summary and Conclusions 19 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 nonaxisymmetric rotordynamic systems

20 QUESTIONS? 20 Stephen James Engineer, Rotating Machinery Dynamics Group Southwest Research Institute San Antonio, Texas