Investigating CURVIC coupling behavior by utilizing the ... · Investigating CURVIC coupling...

Investigating CURVIC coupling behavior

by utilizing the two- and three-dimensional

boundary and finite element methods

S.R. Pisani*, J.J. Rencis*

"General Electric Company, 1000 Western

Avenue, Lynn MA 01910, USA

^Mechanical Engineering Department, Worcester

Polytechnic Insitute, 100 Institute Road,

Worcester MA 01609, USA

ABSTRACT

This work investigates the behavior of CURVIC® [1] couplings throughtwo- and three-dimensional boundary and finite element models. TheCURVICs are used to couple multiple rotors in an aircraft engine compressor,and are subjected to rotational loading. The models generated include ageometrically complex three-dimensional linear elastic body with curvedsurfaces, and are analyzed with the BEASY® [2] boundary element andANSYS® [3] finite element software packages. The following comparisons aremade between BEASY and ANSYS: Three-dimensional modellingcapabilities, the effort required to generate the models, the accuracy of resultsand the ability to adequately post-process the results into meaningful data.

1. INTRODUCTION

Proper analyses of complex aircraft components requires a completeunderstanding of the behavior of the component under sometimes severeoperational loads. Present day commercial structural analysis packages allowthe engineer to evaluate such complex components in two and three dimensionsunder many loading conditions to ensure adequate performance and endurance.

A widely used structural analysis package is the ANSYS 4.4A finite elementmethod (FEM) program. The package is extremely powerful for analyzingaxisymmetric rotating structures such as those commonly found in aircraftengine compressors. However, non—axisymmetric features of a rotatingcomponent require a more complex three—dimensional analysis. While ANSYSis quite capable of performing a complex three-dimensional structural analysis,

Transactions on Modelling and Simulation vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X

598 Boundary Elements

the boundary element method (BEM) may prove to be better suited due to its lackof an internal mesh.

The BEM in the form of BEASY 4.0 was recently evaluated as a quickeralternative to the FEM through a three-dimensional linear elastic stress analysisof CURVTC couplings. CURVICs are sometimes used in aircraft engine designwhere multiple rotor stacks are required. First introduced in 1942 by GleasonWorks [4], a CURVIC is a precision ground face spline. The CURVIC allowstorque transmission between individual rotors, and the self centering feature ofthe CURVIC face centralizes each rotor in the stack.

Stress analyses of CURVICs at GE have incorporated both simpletwo—dimensional and more complex three-dimensional finite element analyses.Photoelastic and strain gage test results are used to substantiate the analyses, andextensive testing of individual components and rotor assemblies validate theCURVIC life predictions. The more complex three-dimensional analyses andcomponent testing are typically done after the design has been established.Accurate and timely complex analyses are needed early in the desing process.This investigation will compare the CURVIC three-dimensional stress resultsand relative ease of using both BEASY and ANSYS as a preliminary design tool.

2. BACKGROUND

2.1 CURVIC ApplicationsCURVICs are sometimes used in aircraft engine design to join rotating

components so that they operate as a single unit. A typical CURVIC applicationis the aircraft engine compressor shown in Figure 1. This particular engineutilizes a five stage axial and one stage centrifugal compressor. The compressorsjob is to take ambient air from outside the engine and compress it. Thecompression is accomplished by a series of rotating blades and disks which forcethe air through smaller and smaller areas. Once at a higher pressure (andtemperature) the air will be mixed with fuel and combusted. The energy releasedduring combustion is then converted to power the aircraft.

Compressor

Figure 1: Aircraft engine with compressor area highlighted.


Boundary Elements 599

The rotating components that make up the compressor are shown in Figure2. The blisks labelled in the figure are solid metal disks and blades machinedfrom a single forging. The fact that the blades and disk are one continuous pieceleads to the term 'blisk'. Each blisk in the assembly is stacked together andjoined by the CURVICs cut into the forward and aft faces of the blisks. Thisanalysis focuses on the stage 2 blisk aft CURVIC, which is a life limiting locationin the blisk.

Figure 2: Compressor assembly.



2.2 Axisvmmetric AnalysisThe stage 2 blisk analysis consists of an axisymmetric model of the

component subjected to rotational body forces. Non-axisymmetric features ofthe component, such as the blades and CURVICs, are modelled as plane stressregions. For this study only rotational loading is included.

Figure 3 shows the FEM mesh for this model. The axisymmetric portionslie below the dotted line (974 quadratic elements, ANSYS element type Stif 82,and 3117 nodes), and the plane stress (549 elements, Stif 82, and 1804 nodes)blade lies above the dotted line. The CURVICs at the front and back of the modelare also modelled with plane stress elements. Each plane stress element isassigned a thickness to represent to actual thickness of the component. Thismodel will be subjected to rotational loading and will be used to evaluate thenominal hoop stress in the aft CURVIC. The stress is referred to as nominalbecause the geometric stress concentrations in the CURVIC root (see Figure 4)are not accounted for in the axisymmetric model. Future work will model thestage 2 blisk with BEASY.

Blade

AftCURVIC(Figure 4a)

r\Analysis

Disk Region

ForwardCURVIC

Figure 3: ANSYS mesh of stage 2 blisk.

2,3 Need for Three-Dimensional ModellingComplex three-dimensional modelling is required to predict the peak stress

in the aft CURVIC due to the stress concentration. The peak stress is then used



to determine an appropriate stress concentration factor (kt) which will be appliedto the axisymmetric nominal stress results. Once the kt is determined theaxisymmetric model may be subjected to various rotational speeds and may beincluded in a more complex model with other interacting components. The ktis then applied to the nominal stress to determine the peak stress in the CURVICat the new operating conditions. Using the kt eliminates the need to run a costlythree-dimensional analysis for every potential loading condition.

3. PROBLEM DEFINITION

An accurate CURVIC stress deteminatino early in the desing process isrequired. Three-dimensional models were created in BEASY and ANSYS, andare described in the following sub-sections. Although the stage 2 aft CURVICis modelled, similar techniques may be applied to other curvic locations.

3.1 Geometry and Material Properties.A kt is only needed for the aft CURVIC, so only the portion of the blisk

containing the CURVIC is modelled in three dimensions. This sub-modellingapproach was employed to keep the model sizes manageable.

Figure 4a includes the geometry for the arm leading to the CURVIC, andFigure 4b illustrates the profile of the CURVIC teeth. There are 24 teeth equallyspaced about the circumference of the blisk, which yields a symmetric sectionfor every 1.5". The analysis region and material properties for the model arestated in Figure 4b. As indicated, the material is a semi-austenitic stainless steelwhich is linear, homogeneous and isotropic.

3.2 Geometry ModellingThe stage 2 aft geometry was created in the I-DEAS® [5] program before

being meshed in either BEASY or ANSYS. IDEAS was chosen because it hasthe capability to use boolean logic to generate boundaries from intersectingobjects - a very useful capability when generating the CURVIC. Thethree-dimensional geometries were then written from IDEAS in IGES formatto be read into the appropriate analysis package for discretization.

3.3 BEASY Model GenerationCreating the boundary element mesh required that the surface boundary read

in from the IGES file be broken into surface areas called 'patches'. The patchesmay only be three or four sided, and are defined by existing geometry lines orpoints. The patches are then discretized and grouped into three-dimensionalzones. A zone is a fully enclosed portion of the volume. Breaking a model intomultiple zones may increase accuracy for volumes with large surface to volumeratios (aspect ratio) and can also decrease the amount of CPU time required tosolve the model. This CURVIC model has a good aspect ratio and thereforecontains only one zone.



.176—̂ 1

.010; 11" .170

Pitch Plane

Figure 4a: Geometry of arm leading to aft CURVIC.

..034

3-DAnalysisRegion

Material Properties

Stainless Steel

E = 29.429x10̂p =.73049x10"

|i=. 290559

All lengths in inches

CURVIC Tooth

.121

Pitch Plane

Figure 4b: Geometry of CURVIC teeth profile from a radial view.

This comparison between BEM and FEM results utilized common elementtypes, and the surface discretization was approximately the same for bothmodels. In BEASY only quadrilateral or triangular elements are available.ANS YS allows linear brick elements, but warns that linear tetrahedral elementsare not recommended. Quadrilateral elements with linear shape functions weretherefore selected. Since only quadrilateral elements were desired, the patches



were all forced to be four sided. Generating only four sided patches proved tobe somewhat difficult on the curved surfaces.

3.4 BEASY DiscretizationFigure 5 shows the final BEASY mesh. The mesh was generated using the

auto mesh generator in BEASY after specifying a maximum element size of .3inches and forcing all patches to be quadrilaterals. A total of 903 elements(BEASY type Q2) and 3816 mesh points were generated. Each element has aquadratic geometry and linear displacement and traction surface functions (theelements are not isoparametric). The elements vary between continuous anddiscontinuous based on a BEASY meshing algorithm. The algorithm allowsdiscontinuous elements along patch boundaries and at any location where theloading is discontinuous. All other surface areas are meshed with continuouselements.

Figure 5: BEASY model discretization.

3.5 ANSYS Model GenerationCreating the ANSYS finite element mesh required that the object be broken

up into six-sided volumes. Six—sided volumes are required to allow the objectto be entirely meshed with brick elements. Bricks were desired to maintain asmuch consistency with the BEASY model as possible, although the BEASYelements have a quadratic geometry versus a linear geometry for the ANSYSbricks. Creating the six—sided volumes was somewhat labor intensive, but nomore difficult than forcing the patches in the BEASY model to be four sided.In general meshing a surface is easier than meshing a volume, but creating foursided patches added difficulty to meshing the surface.



3.6 ANSYS DiscretizationOnce the CURVIC was broken into volumes the ANSYS automesher was

capable of filling the volumes with eight-noded isoparametric linear brickelements (ANSYS Stif 45). Figure 6 shows the final ANSYS mesh. There area total of 3276 elements and 4130 nodes contained in the model.

6 = 7.5°SymmetryPlane

ZeroY-displacement

8 = 0* SymmetryPlane

Figure 6: ANSYS model discretization and loading.

3.7 Loading and Boundary ConditionsThe BEASY and ANSYS models were both subjected to the same boundaryconditions and loading. First, the models were rotated about the Y-axis with aspeed of 44720 rpm (4683.07 rad/sec). The aft side of the models was restrainedto zero Y-deflection to eliminate rigid body motion. Planes of symmetry (zeronormal displacement) were defined at 8 = 0° (X-Y Plane) and 8 = 7.5°. Theloading and boundary conditions are indicated in Figure 6 for the ANSYS modeland are identical to the BEASY model. Similar boundary conditions wereapplied to the two-dimensional model.

3.8 Computer PlatformsBoth the BEASY and ANSYS models were pre- and post-processed on a

Hewlett Packard Apollo Series 700 workstation and solved on the GE SEARCRAY Y-MP8/5128 Supercomputer.



4. ANALYSIS RESULTS

The next few sub-sections summarize the BEASY and ANSYS results. Ingeneral there was excellent agreement between the BEASY and ANSYSsolution. However, the BEASY post-processor does not have the capability ofdisplaying stress components in the 0 (hoop) direction, i.e., BEASY cannotdisplay results in a cylindrical coordinate system. Since the CURVIC is acylindrical object, the o@ is the hoop stress in the cylinder. The Z-direction stressis the closest available in BEASY. Comparisons are therefore made between theZ-stress in BEASY and ANSYS, and the amount of deviation from the hoopstress is checked through the ANSYS solution.

4.1 Stresses - BEASY and ANSYSAn averaged stress contour plot of the BEASY Z-stress is shown in Figure

7. All stresses have been normalized by the nominal stress obtained from theANSYS two-dimensional axisymmetric model of Figure 3. As would beexpected, the geometry of the CURVIC root causes the highest concentratedstress and therefore the highest kt. Note that the peak kt is 1.87 and is locatedas shown in Figure 7. The unaveraged contours were also checked and do notshow much discontinuity between elements which indicates an adequate meshdensity.

The ANSYS Z-stress is shown in Figure 8. Again, the peak stress is locatedin the CURVIC root where the kt is 1.89. The maximum ANSYS stress is alsowithin 1 % the BEASY result. As mentioned, however, the hoop stress is of moreconcern than the Z-stress. Fortunately, the CURVIC was modelled with the rooton the 0 = 0° plane, which makes the Z-stress at the peak location the same asthe hoop stress. Also, for such a small segment of the overall blisk the changein stress between the Z and 0 directions is negligible. Figure 9 shows that theANSYS hoop stress is nearly identical to the Z-stress. However, when usingBEASY to analyze geometries with more of a 0 dependence care must be takento model the area of interest as close to the 0 = 0° plane as possible.

4.2 Computation TimesWhile the stress results compared well between BEASY and ANSYS, the

amount of computation time did not. The BEASY solution required almost 40times as much CPU time as the ANSYS solution, as shown in Table 1. The totalelapsed time, which includes the time required to transfer the necessary files toand from the CRAY as well as the CPU time, was 26 times longer for BEASY.The much larger BEASY solution time shows the need for a more conscientiousdiscretization, forcing the areas away from the peak stress to be less denselymeshed. Additional time savings may be obtained by breaking the model intomultiple zones, although there may be a trade off in accuracy. Also, recall thatthe BEASY element geometry uses a quadratic shape function whereas theANSYS elements are linear. The quadratic shape function will add to therequired solution CPU time.



All Stresses Normalizedto Two—DimensionalNominal Stress

Maxkt

Figure 7: BEASY Z-direction stress results.

All Stresses Normalizedto Two-DimensionalNominal Stress

= -.027= 36= .74= 1.08= 1.51= 1.89

Maxkt

Y

Figure 8: ANSYS Z-direction stress results.


Boundary Elements

All Stresses Normalizedto Two-DimensionalNominal Stress

607

= -.029= .36= .74= 1.12= 1.51= 1.89

Maxkt

Figure 9: ANSYS 6-direction stress results.

BEASY

ANSYS

Elapsed Time

105 16 Seconds

837 Seconds

System CPU Time

398 Seconds

21 Seconds

Table 1: Comparison between BEASY and ANSYS solution times.

5. CONCLUSIONS

Overall, the solution quality between the BEASY and ANSYS packages wascomparable, but the BEASY solution CPU time was significantly different.Based on the CPU times it seems that BEASY should be used only forcomplicated geometries where many small fillet radii and intersecting shapesmake FEM meshing much more complex. The assumption that the meshdiscretization should be the same between the BEASY and ANSYS modelsunfairly eliminated the unique meshing capabilities, such as discontinuouselements for better mesh grading and a lack of an internal mesh, of the BEM.Future models will investigate whether or not BEASY can reduce the totalnumber of elements needed to a point where the CPU times would be morecomparable without sacrificing solution quality. The mathematics behind the



BEM should allow for a coarser mesh than the FEM while maintaining qualityresults.

The pre-processing capabilities of both packages were also comparablewhen requiring quadratically shaped elements (or bricks in the FEM). However,changing to a tetrahedral element in ANSYS would have allowed automeshingthe CURVIC without the need to break the object into six-sided volumes. TheCURVIC would have therefore been much easier to mesh. Changing totriangular elements in BEASY would not have helped because the surface wouldstill have to be broken up into three or four sided patches. Creating the patcheswas the most labor intensive part of developing the BEASY model. BEASY 4.1,which is just becoming available at GE, will alleviate the patch problem byallowing multiple sided patches (more than four) which can be read in from anIGES file. Eliminating the need to manually create patches should make creatingthe BEASY mesh comparable to automeshing with ANSYS tetrahedrons.

In terms of post—processing, the BEASY package shows some limitationsdue to its rigid adherence to a global Cartesian coordinate system. A cylindricalcoordinate system is really necessary to accurately predict hoop stresses incylindrical components.

REFERENCES

1. CURVIC is a trademark of The Gleason Works, 1000 UniversityAvenue, Rochester, NY, 14603, USA.

2. BEASY is a registered trademark of Computational MechanicsBEASY Ltd, Ashurst Lodge, Ashurst, Southampton S04 2AA, Eng-land.

3. ANSYS is a registered trademard of Swanson Analyis Systems, Inc.,P.O. Box 65, Houston, PA 15342, USA.

4. Gleason Works, 1000 University Ave, Rochester, NY, 14603, USA.

5. I—DEAS is a registered trademard of Structural Dynamics ResearchCorporation, Cincinnati, OH, USA.


Investigating CURVIC coupling behavior by utilizing the ... · Investigating CURVIC coupling...

Documents

Transcript of Investigating CURVIC coupling behavior by utilizing the ... · Investigating CURVIC coupling...