fe analysis in aeroengine discs

*Corresponding author.1On leave from Technische Universitat Munchen.

Finite Elements in Analysis and Design 29 (1998) 173—186

Three-dimensional nonlinear finite element analysisof dovetail joints in aeroengine discs

P. Papanikos, S.A. Meguid*, Z. Stjepanovic1Engineering Mechanics and Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto,

5 King+s College Road, Toronto, Ontario, Canada M5S 3G8

Abstract

Three-dimensional nonlinear finite element analysis is made of the dovetail region in aeroengine compressor discassemblies using contact elements. The study is devoted to examining the effect of the critical geometrical features, such asflank length, flank angle, fillet radii and skew angle upon the resulting stress field. Frictional conditions at the interfacebetween the disc and the blade are also examined. The finite element predictions were validated using three-dimensionalphotoelastic stress freezing results. Comparisons with the two-dimensional finite element analysis made earlier byPapanikos and Meguid (Fatigue Fract. Eng. Mater. Struct. 17 (5) (1994) 539—550) of the same geometry reveal certaininadequacies. Specifically, the earlier analysis underestimates the maximum equivalent stress along the interface by asmuch as 40%. This could have serious implications concerning the safety margins of the disc assembly. ( 1998 ElsevierScience B.V. All rights reserved.

Keywords: Three-dimensional; Finite elements; Aeroengine disc; Contact; Photoelasticity

1. Introduction

Aeroengine compressor disc assemblies are subjected to high thermo-mechanical loads andcontain highly stressed components. Whilst blade loss can be contained within the engine casing onfailure, the catastrophic failure of a compressor disc, on the other hand, could cause the largerfragments of the disc to puncture the engine casing. The consequences of such a failure areparticularly costly resulting in the destruction of the engine and ultimately in the loss of life.

Aeroengine compressor discs (Fig. 1) have basically three critical regions for which lifetimecertification is necessary: the dovetail-rim region, the assembly holes or weld areas and the hub

0168-874X/98/$19.00 ( 1998 Elsevier Science B.V. All rights reservedPII S 0 1 6 8 - 8 7 4 X ( 9 8 ) 0 0 0 0 8 - 0

Fig. 1. Typical aeroengine compressor disc assembly.

region. The loads associated with these regions are the centrifugal forces of the blades, theself-generated loads applied by spacers and assembly bolts, and thermal stresses. These thermo-mechanical stresses are not constant but vary during a flight causing fatigue of the disc. In themajority of cases, cracks are initiated in the dovetail region due to the fretting action at theblade/disc interface.

The stress analysis of the dovetail-rim region of aeroengine discs has received the attention ofseveral investigators. Of particular interest to this study is the work of Kenny et al. [2] and Nurseand Patterson [3]. Their work was concerned with stage two fatigue crack growth paths in fir-treefixtures. Since no allowances were made for contact elements in their model, approximate contactpressures were assumed at the interface between the blade and the disc. The numerical analysis atdovetail joints were also treated by Boddington et al. [4]. In their work, a technique is developed tomodel the relative motion at the interface of the assembly, and thus accounts for contact at theinterface.

Parks and Sanford [5,6] conducted two- and three-dimensional photoelastic analyses of theblade/disc fir-tree region of a turbine disc. Centrifugal, circumferential and antiplane bending loadswere applied at the centroid of the blade for the three-dimensional model, while only centrifugalloads were applied to the two-dimensional model. Their results revealed that the stresses at thecentral region of the three-dimensional disc were approximately twice those found in the two-dimensional study and that the stress concentration in the central region is balanced by a largereduction in the stress at both ends of the fillet. This reduction was associated with the flexibility ofthe dovetail joint at both ends. Durelli et al. [7] conducted a comprehensive study on turbine bladeattachments. They concluded that the most important forms of loading are the radial centrifugalforce due to blade loading and the bending of the blade due to the gas pressure.

The use of a small-scale test specimen which reproduces the stress state and consequently thefailure behavior of the dovetail blade root fixing was introduced by Ruiz and his collaborators in[8,9]. Utilising both photoelastic and biaxial fatigue testing, Ruiz et al. [9] found that the hooploads had a relatively small effect on the peak stresses and the stress distribution in the immediatevicinity of the dovetail. He and Ruiz [10] utilized the small-scale test specimen introduced in [8,9]to predict the location of the severe damage, and of crack initiation at the dovetail blade root fixing.

174 P. Papanikos et al. /Finite Elements in Analysis and Design 29 (1998) 173—186

They proposed the use of a fretting damage parameter (FDP), as a means of predicting the locationof crack initiation. Their results indicate that the maximum value of FDP is reached at thetangential point between the straight flank of the dovetail and the root radius. In [11], Ruiz et al.used high sensitivity Moire interferometry to determine relative normal and tangential displace-ments at the dovetail boundary. They found that in response to the change-over from a stick toa slip, the dovetail joint behaved in an asymmetrical manner under increasing load.

The above review shows that existing research in aeroengine disc stress analysis has beenprimarily concerned with the two-dimensional treatment of the problem. Due to skew angle effectsand thickness variations in a real disc, a triaxial stress state exists, which can be convenientlyevaluated using three-dimensional stress analysis.

In this study, attention is devoted to examining the effect of the critical geometric features andinterface conditions in the dovetail region upon the stress distribution at the blade/disc interface.These features include: inner and outer fillet radii R1 and R2, flank length l, flank angle h, skewangle and the coefficient of friction at the blade/disc interface (see [1] for the definition of thesefeatures). Three aspects of the work were accordingly examined. The first was concerned with thetwo-dimensional finite element analysis of the stress field in an aeroengine disc assembly. Thesecond was concerned with the three-dimensional finite element analysis of the assembly, thusenabling the examination of the effect of the skew angle upon the triaxial state of stress present inthe disc. The third was devoted to the validation of the results using photoelastic stress freezingresults.

This article is divided into four sections. Following this brief introduction, Section 2 describesthe details of the finite element modelling. Section 3 provides a detailed analysis of results andSection 4 concludes the paper.

2. Finite element modelling

The main emphasis of this study is the three-dimensional finite element analysis of the dovetailregion in aeroengine compressor disc assemblies. However, in order to: (i) provide a reference forcomparison with the three dimensional analysis, (ii) provide additional information that theauthors did not account for in their earlier work [1], and (iii) ensure the completeness of thepresent article, additional results concerning the two-dimensional model were included.

Accordingly, two- and three-dimensional nonlinear finite element analyses were conductedin order to assess the effect of the critical geometric features on the stress field of the dovetailregion of an aeroengine compressor disc assembly. The geometries of the disc selected in thisstudy are shown in Fig. 2. Throughout this work, the authors utilised the ANSYS finite elementcode.

The two-dimensional analysis was conducted for the mid-section of the disc, thus pertaining toplane stress conditions. In view of disc symmetry, only one sector of the disc was modelled. In orderto satisfy the compatibility conditions, the blade and the disc should be discretised such that thenodes and elements at the common boundary match in number and in position. Because of thecurved boundary of the model, eight-noded quadrilateral and six-noded triangular plane stresselements were selected. The two-dimensional model is incapable of predicting the stress variationsacross the thickness of a realistic disc. Furthermore, it is incapable of assessing the effect of the skew

P. Papanikos et al. /Finite Elements in Analysis and Design 29 (1998) 173—186 175

Fig. 2. Disc and dovetail geometry examined.

angle on the stress field. Accordingly, the accurate prediction of the stress state in the disc requiresthree-dimensional modelling of the compressor disc assembly.

For the case of a disc with a straight dovetail slot, the same sector of the disc as in thetwo-dimensional analysis was modelled. Due to lack of symmetry, the finite element analysis ofa disc with a skew dovetail slot was conducted using a submodelling technique; detailed in sectionthree.

Both 20-noded hexahedral and ten-noded tetrahedral elements were used in the three-dimen-sional analysis. In order to estimate the optimum number of elements in each model, convergencetests were carried out. Both the accuracy of the solution and computing time were taken intoconsideration. Fig. 3 shows typical three-dimensional meshes used to test convergence.


Fig. 3. Convergence tests for the three dimensional geometry.

To model the blade/disc interface conditions, contact elements were used. The two- andthree-dimensional contact elements used in this study adopt a node-to-segment interface model.The amount of the open gap or the gap penetration of the contact node on the target plane iscalculated along with the point of projection of the contact node. Contact is indicated when thecontact node penetrates the target surface defined by the target nodes. The penetration representedby the magnitude of the gap is a violation of compatibility. In order to satisfy contact compatibility,forces are developed in a direction normal to the target that will tend to reduce the penetration toan acceptable numerical level. In addition to normal forces, friction forces are developed ina direction tangent to the target plane. The Coulomb friction representations require the specifica-tion of the coefficient of sliding friction k.

To satisfy contact compatibility two methods can be employed: the first uses a penalty para-meter, while the second uses a combined penalty-Lagrange multiplier method. The penalty methodenforces compatibility approximately by means of a contact stiffness through the imposition ofa penalty parameter. The combined approach which is used in this study satisfies compatibility toa user-defined precision by the generation of additional contact forces that are referred to asLagrange forces.

A major problem in the implementation of contact elements is the assignment of values to thenormal (K/) and tangential (K4) stiffnesses, which govern the convergence and accuracy of the


Fig. 4. Variation of contact stiffness with relative nodal displacement: (a) normal stiffness K/, and (b) tangential

stiffness K4.

solution. Fig. 4a and b show the variation of K/ and K4 with displacement. The values of K/ andK4 are required to be very large. However, the use of excessively high values of K/ and K4 results inill-conditioned global stiffness matrices, leading to numerical errors and divergence. On the otherhand, the use of smaller values of K/ and K4 results in convergence to the wrong solution allowingfor interpenetration and incorrect estimates of the stick and slip regions [12]. In the current study,the appropriate values of the normal and tangential stiffnesses were selected from convergence testswhere no interpenetration was allowed. It was found, following numerous test runs, that theappropriate values of K/ and K4 for the considered geometries are 1012 and 1010, respectively.

3. Results and discussion

In this study, the dovetail geometries outlined in section two were analysed using the finiteelement method. The material properties used for the modelling of the blade and the disc were thatof titanium alloy Ti-6Al-4V. The mechanical properties of Ti—6Al—4V are: Young’s modulusE"114 GPa, Poisson’s ratio l"0.33, and density o"4429 kg/m3.

Another important parameter which plays a major role at the dovetail region is the coefficient offriction between the blade and the disc. It has been shown in [13] that the coefficient of friction forTi—6Al—4V varies during the fretting fatigue life of the component from 0.1 to 0.4 at roomtemperature. The majority of the work examined in this study was conducted using k"0.25.However, to investigate the effect of different interface friction at the blade/disc contact regionupon the resulting stress field, the coefficient of friction was varied from 0.0 to 1.5 [9].

All the models examined were subjected to centrifugal loading only with an angular velocity of1000 rpm. Due to the presence of nonconservative frictional forces, the loading was appliedincrementally and the load step in each increment was automatically calculated within the finite


element code. The contacting surfaces were modelled using contact elements, as described insection two. No attempt has been made to accurately model the blade except insofar as providingthe necessary centrifugal loading and the associated effect at the interface. In addition, to simplifythe analysis, the effects of thickness and temperature variations of the disc upon the stressdistribution at the dovetail region were not considered.

3.1. Experimental validation with three-dimensional photoelasticity

In order to validate the results from the three-dimensional nonlinear finite element analysis,three-dimensional stress-freezing photoelastic spin tests were conducted on an existing disc. Thephotoelastic disc details were as follows: flank length"6 mm, flank angle"45°, thickness"30 mm. Both straight and skew dovetail slots were examined and compared with the finite elementpredictions. The photoelastic model was made of Araldite CT200 epoxy and it was built to full size.Prior to testing, it was necessary to determine the appropriate spin speed so that adequate numberof fringes are introduced in the disc to enable the accurate measurement of the resulting fringepattern. This was found to be 1000 rpm. Block-type blades were used to exert radial pull on the discperiphery and to simulate the blade centrifugal force.

The three-dimensional photoelastic model was tested to the softening temperature of theAraldite material (135°C), soaked at this temperature for 2 h, and then cooled to room temperatureat a uniform rate of 2.5°C per hour. Fifteen slices, each 2 mm thick, were taken at right angles to theaxis of the dovetail slots by means of a high-speed diamond cutting wheel. A polariscope withcircularly polarised light beam and the normal incident method were used for the measurement ofthe isochromatic fringes.

Fig. 5a shows typical isochromatic fringe patterns for the dovetail region of three slices. Themaximum shear stress distribution at the lower contact line for the case of a straight dovetail slot isshown in Fig. 5b. In view of disc symmetry, the results for only one half of the disc are plotted.Comparison between the finite element predictions and the photoelastic results reveals a maximumdiscrepancy of about 10%.

3.2. Two-dimensional finite element analysis

In order to evaluate the effect of the flank length of the blade and flank outer and inner radii ofthe disc upon the resulting stress field, several geometries were modelled. The effect of friction at theblade/disc interface for sliding and sticking contact upon the resulting stress field was investigatedby varying the values of the coefficient of friction. Values of 0.0, 0.25, 0.5, 1.0 and 1.5 were chosen.Sticking contact between the blade and the disc occurred at the lower contact point for k"1.0 and1.5, while the two bodies were found to be entirely in sliding contact for the smaller values.

The results obtained from the two-dimensional analysis reveal the following:

1. an increase in the outer radius of the disc increases the stresses at the upper contact point,whereas the maximum value changes only by a small amount,

2. a change in the inner radius of the disc does not affect the stress distribution,3. a change in the flank length of the blade relocates the point of maximum stress concentration on

the disc boundary, but leaves the values of the peak stresses virtually unchanged,


Fig. 5. Photoelastic analysis of a compressor disc: (a) typical fringe patterns, and (b) distribution of maximum shearstress along thickness direction at the lower contact line.

4. in the case of sliding contact, an increase in the coefficient of friction decreases the disc boundarypeak stresses, and

5. in the case of sticking contact, the peak stresses increase due to separation at the upper part ofthe interface.

3.3. Three-dimensional finite element analysis

3.3.1. Straight dovetail slotTo create the three-dimensional model for a straight dovetail slot, use was made of the

two-dimensional model. The three-dimensional geometry was then created by extruding thetwo-dimensional sector in the direction normal to its plane. In view of symmetry of geometry andloading, only one half of the disc (t"10 mm) was modelled. The deformation of the aeroenginedisc assembly due to the rotational loading of the blade and the disc is depicted in Fig. 6.

The von Mises stress distribution along the blade/disc interface at two different thicknesslocations is shown in Fig. 7, together with the stress distribution obtained from the two-dimen-sional analysis. The stress distribution for the three-dimensional model reveals that the stress levelin the middle of the disc is much higher than that at the disc surface. As can be seen more clearlyfrom Fig. 8, the magnitude of the peak stress at the lower contact line increases by as much as 40%from the disc surface to the disc central plane. This trend of the stress field is in agreement with thephotoelastic results described in Section 3.1. The two-dimensional analysis underestimates the


Fig. 6. Deformed geometry of an aeroengine compressor disc assembly (undeformed geometry indicated by dashedline).

stress level along the contact region. The maximum value of the von Mises stress obtained from thetwo-dimensional investigation at the lower contact point is 7% smaller in magnitude than themaximum value predicted by the three-dimensional analysis (Fig. 8).

The von Mises stress distribution at the lower contact line for different flank angles is shown inFig. 9. The results for only one half of the disc thickness are plotted. The three-dimensional resultsshow that the stresses at the lower contact region increase for smaller values of the flank angle. Thisobservation is in agreement with the results obtained from the two dimensional analysis.

The three-dimensional model with the straight dovetail slot was also analysed for different valuesof the coefficient of friction. The three-dimensional analysis reveals that the blade and the discexperience sliding contact for all values of the coefficient of friction investigated (0—1.5). As can beseen in Fig. 10, an increase in the coefficient of friction decreases the disc boundary peak stresses.This effect of the coefficient of friction on the stress field at the blade/disc interface was identifiedearlier by the two-dimensional model.


Fig. 7. Von Mises stress along the interface at different thickness locations.

Fig. 8. Von Mises stress across thickness at the lower contact line.

3.3.2. Skew dovetail slotIn the case when a skew angle of 20° was assumed, use was made of submodelling. In this

case, the entire disc assembly was discretised using the coarse mesh shown in Fig. 11a. In the initialruns, the blades and the disc were joined at the interface and no allowances were made for contacteffects. The submodel shown in Fig. 11b was then developed with the appropriate boundaryconditions.


Fig. 9. Effect of flank angle on the von Mises stress across thickness at the lower contact line.

Fig. 10. Effect of the coefficient of friction on the von Mises stress across thickness at the lower contact line.

Due to anti-symmetry, only the stresses at one side of the blade/disc contact region wereexamined. The distribution of von Mises stresses along the blade/disc interface for the front andback surfaces is shown in Fig. 12. The figure indicates a large difference between the correspondingsurfaces in the stress values at the lower contact region. Fig. 13 demonstrates the increase of thevon Mises stress at the lower contact line from the front surface to the back surface of thedisc, where the peak value occurs. It is clear from Fig. 13 that the two-dimensional analysisunderestimates the maximum equivalent stress along the interface by as much as 40%. This couldhave serious implications concerning the safety margins of the disc assembly.


Fig. 11. Discretised geometry of (a) the full model, and (b) the submodel.

Fig. 12. Variation of von Mises stress along the interface of a skew dovetail slot.


Fig. 13. Variation of von Mises stress across thickness at the lower contact line of a skew dovetail slot.

4. Conclusions

Three-dimensional nonlinear finite element analysis is made of the dovetail region in aeroenginecompressor disc assemblies to evaluate the effect of the critical geometric features and frictionalinterface conditions in the dovetail region. Whilst the two-dimensional analysis is a useful startingdesign tool, it cannot be used in the prediction of the stress state in a complex aeroengine discassembly. The results of this work demonstrate the inadequacy of the two-dimensional analysis tomodel the disc. The study also reveals the following:

1. the maximum stress concentration occurs at and just below the lower contact point between theblade and the disc,

2. the flank angle, flank length and coefficient of friction can significantly change the blade/discinterface stress distribution,

3. the three-dimensional results reveal large stress variations through the disc thickness, whichcannot be predicted by a two-dimensional analysis. The two-dimensional results underestimatethe peak stresses, and

4. the skew angle has a significant influence on the stress distribution and the magnitude of thepeak stress at the blade/disc interface.

References

[1] P. Papanikos, S.A. Meguid, Theoretical and experimental studies of fretting-initiated fatigue failure of aeroenginecompressor discs, Fatigue Fract. Eng. Mater. Struct. 17 (5) (1994) 539—550.

[2] B. Kenny, E. Patterson, M. Said, K. Aradhya, Contact stress distributions in a turbine disc dovetail type joint— A comparison of photoelastic and finite element results, Strain 27 (1991) 21—24.


[3] A.D. Nurse, E. Patterson, Experimental determination of stress intensity factors for cracks in turbine discs, FatigueFract. Eng. Mater. Struct. 16 (1993) 315—325.

[4] P.H.B. Boddington, K. Chen, C. Ruiz, The numerical analysis of dovetail joints, Comput. Struct. 20 (1985) 731—735.[5] V.J. Parks, R.J. Sanford, Experimental stress analysis of the TF-30 turbine engine third-stage fan-blade/disc

dovetail region, NRL Report, NRL 8149, August 1977.[6] V.J. Parks, R.J. Sanford, Three-dimensional photoelastic stress analysis of the dovetail region of the tf-30 turbine

engine third-stage fan, NRL Report, NRL 8276, December 1978.[7] A.J. Durelli, J.W. Dally, W.F. Riley, Stress and strength studies on turbine blade attachment, SESA Proc. XVI (1)

(1957) 171—186.[8] P.H.B. Boddington, C. Ruiz, A biaxial fatigue test for dovetail joints, Proc. ASME, Int. Conf. on Advances in Life

Prediction Methods, Albany, April 1983, pp. 277—283.[9] C. Ruiz, P.H.B. Boddington, K.C. Chen, An investigation of fatigue and fretting in a dovetail joint, Exp. Mech. 24

(3) (1984) 208—217.[10] M.J. He, C. Ruiz, Fatigue life of dovetail joints: verification of a simple biaxial model, Exp. Mech. 29 (2) (1989)

126—131.[11] C. Ruiz, D. Post, R. Czarnek, Moire interferometric study of dovetail joints, ASME J. Appl. Mech. 52 (1985)

109—114.[12] R.D. Cook, Finite Element Modeling for Stress Analysis, Wiley, New York, 1995.[13] M.M. Hamdy, R.B. Waterhouse, The fretting wear of Ti-6Al-4V and aged Inconel 718 at elevated temperatures,

Wear 71 (1981) 237—248.


fe analysis in aeroengine discs

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