Effects of Disk Geometry on Strength of a Centrifugal Compressor Impeller for a High Pressure Ratio Turbocharger

7282019 Effects of Disk Geometry on Strength of a Centrifugal Compressor Impeller for a High Pressure Ratio Turbocharger

httpslidepdfcomreaderfulleffects-of-disk-geometry-on-strength-of-a-centrifugal-compressor-impeller-for 18

1 Copyright copy 2012 by ASME

Proceedings of ASME 2012 Gas Turbine India Conference

December 1 2012 Mumbai Maharashtra India

GTIndia2012-9690

EFFECTS OF DISK GEOMETRY ON STRENGTH OF A CENTRIFUGALCOMPRESSOR IMPELLER FOR A HIGH PRESSURE RATIO TURBOCHARGER

ZHENG Xinqian JIN Lei ZHANG Yangjun

State Key Laboratory of Automotive Safety and Energy

Tsinghua University Beijing China 100084

zhengxqtsinghuaeducn

QIAN Huihua

SinoTurbo Co Ltd

Beijing China 100084

LIU Fenghu

FuYuan Turbochargers Co Ltd

Weifang Shandong China 261205

ABSTRACTHigh pressure ratio turbocharger technology is widely used

to lower fuel consumption reduce emissions and improvepower density of internal combustion engines The centrifugalcompressor is the key component of turbochargers Thereliability of compressor impeller becomes critical withincreasing pressure ratio For extending its maximum rotationalspeed limits it is important to improve the impellerrsquos disk

geometry to decease stress In order to investigate the effects of disk geometric parameters on the strength of a centrifugalcompressor impeller a 3-D finite element analysis (FEA) withvarious disk geometric parameters was performed in this paperSubsequently the impellerrsquos disk geometry was improved todecrease the maximum stress The results show that themaximum von Mises equivalent stress in the core of the disk of the improved impeller could be decreased by 19 Further themaximum stress of another improved impeller without shaftbore decreases by 50 That means the improved impeller canbear higher pressure ratios or use cheaper material with lowerultimate tensile strength

1 INTRODUCTION The worldrsquos increasing energy consumption accompanied

by various environmental problems has become a focus of public attention As the main power devices of mosttransportation vehicles and engineering machinery inindustrialized societies internal combustion engines areresponsible for roughly 25 of the global energy consumptionand

2CO emissions While maintaining engine performance

high pressure ratio turbocharger technology can reduce engine

displacement by improving engine power density Therebyengine fuel economy is enhanced and

2CO emissions are

reduced [12] Additionally in order to reduce the

xNO emissions and meet increasingly stringent emission

regulation requirements exhaust gas recirculation (EGR) areused much more widely and the high pressure ratio turbochargetechnology is required too [3-5]

The centrifugal load of high pressure ratio centrifuga

compressor disks is increasing significantly as a consequence othe increased impeller tip speed and pressure ratio Adequatereliability and durability will have to be ensured throughgeometry design Hence the study of centrifugal compressostructure reliability is attracting considerable attention

In order to keep the balance between performance andreliability within the continuously shortening duration of theproduct development phase numerical analyses should becarried out during designing a centrifugal compressor impelle[67] Finite element analysis (FEA) is the main method forstudying the stresses in a centrifugal impeller numerically [8]In recent years several authors [910] have reportedoptimization methods to obtain best performance or lowes

stress Bonaiuti [9] developed a strategy for the parametricanalysis and optimization of transonic centrifugal impellersusing a technique of experiment design coupled with a threedimensional fluid-dynamic solver Valakos [10] used adifferential evolution algorithm to optimize the back-facegeometry of a centrifugal impeller with respect to thecalculated maximum stress and extend its speed limits In thesestudies optimization results are presented directly withoushowing the effect of each geometry parameters on the stress I




is thus difficult for designers to obtain the optimized designs fortheir individual application-specific parametric requirements If general relationships between geometric parameters of animpeller and its strength can be established it will be helpful toimprove the geometry to decrease the strength

In this paper a detailed investigation of the effects of five

impeller disk geometric parameters on maximum stress andstiffness was performed by using 3-D FEA Subsequentlygeometric parameters of an original impeller were improved onthe basis of this analysis to decrease the maximum stress

2 NUMERICAL METHODS

21 Structural Analysis Theory The FEA is an efficient numerical technique to research the

detailed response of structure to all types of loads includingstress strain deformation and so on The equilibrium equationsfor linear structural static analysis are

0=+

part

part+

part

part+

part

part

bx

xzxyx Fzyx

τ τ σ (1)

0=+part

part+

part

part+

part

part

by

yzyyxF

zyx

τ σ τ (2)

0=+part

part+

part

part+

part

part

bzzzyzx Fzyx

σ τ τ (3)

where bxF byF and bzF are the body forces per unit volume

acting along the directions x y and z respectively σ

and τ are the normal and shear stress components Subscriptsare used to describe their directions

In the case of linear elastic isotropic 3D solid the stress-strain relations are given as

( )[ ]zyxxE

σ σ micro σ ε +minus=1

G

xy

xy

τ γ = (4)

( )[ ]xzyyE


G

yz

yz

τ γ = (5)

( )[ ]yxzzE


Gzx

zx

τ γ = (6)

where E is Youngrsquos modulus G is shear modulus and micro

is Poissonrsquos ratio of the material ε and γ are normal strain

and shear strain components respectively Subscripts are usedto describe their directions

The strains induced in the body can be expressed in terms

of the deformations as shown below

x

ux

part

part=ε

x

v

y

uxy

part

part+

part

part=γ (7)

y

vy

part

part=ε

y

w

z

vyz

part

part+

part

part=γ (8)

z

wz

part

part=ε

z

u

x

wzx

part

part+

part

part=γ (9)

where u v and w are the deformations along thedirectionsx y and z respectively

The primary aim of static stress analysis is to obtain thedistribution of stresses and deformations under the stated loadsand boundary conditions The effects and sensitivities of theprincipal geometric parameters on the strength of the impelle

were investigated by means of a linear elastic FEA whichprovides a good understanding into the internal responses of thestructure

22 FEA Model and Boundary ConditionIn this paper the effects of the geometric parameters of

impeller disk were investigated by means of a linear elasticFEA excluding the effect of non-linear material properties Thestudied impeller has 7 main blades and 7 splitter blades Insteadof dealing with the whole structure 17 of the cyclic symmetricstructure was analyzed to reduce the numerical solution time The mechanical model of the impeller is shown in Fig 1 Thecorresponding finite element mesh shown in Fig 2 was buil

using 3D 20-nodes solid elements in global cylindricacoordinate system and consists of 36736 elements For bettecomparability uniform FEA mesh size was used for all theimpellers with varies geometric parameters throughout theanalysis

It is suggested that the influence of aerodynamic forces inegligible comparing to the centrifugal loads The followingboundary conditions and loads were applied for the structuraanalysis 1) Centrifugal loads at design rotational speed withpressure ratio of 421 2) The nodes attached to both the fronand reverse ends of the impeller (as shown in Fig 2) are fixedand the deformations along circumferential and axial directionsare set to zero 3) The constraint equations that tie together the

low and high edges of the model (cyclic symmetric faces) aregenerated automatically with a cyclic symmetry analysis

Fig 1 Mechanical model of the impeller




Fig 2 FEA model of the impeller

The centrifugal compressor impeller is made fromaluminum alloy LD7 The Youngrsquos modulus is 744 GPa The

Poissonrsquos ratio is 03 and density is 27603mkg ultimate

tensile strength is 412MPa

3 RESULTS AND ANALYSIS The stress of centrifugal compressor impellers caused by

centrifugal force is relative to the rotating speed disk geometryand blade geometry The rotating speed and blade geometry aredecisive for the aerodynamic performance and not considered inthis paper The parameters of disk geometry considered in this

paper are tip thickness1h (

01Rh ) rear-disk thickness

2h (02 Rh ) rear-disk height

3h (03 Rh ) fillet radius

1r (01 Rr ) and bore radius

2r (02 Rr )

0R is the radius of the

impeller The definition of the parameters is shown in Fig 3

Fig 3 Definition of the geometric parameters of impellerdisk

Firstly Structural analysis was made on the originalimpeller which has being used in market for many years Thenthe effect of the five disk geometric parameters on the stresswas analyzed Each one of these geometric parameters ismodified keeping other parameters unchanged Based on the

simulation results the impeller structure was improved todecrease the stress

31 Structural Analysis of Original Impeller The geometric parameters of the original impeller disk are

listed in Tab 1 Figure 4 shows the von Mises stress distribution

of the original impeller Tab 1 Geometric parameters of the original impeller disk

Parameters Value

1h 0040 2h 0080 3h 0107 1r 0160 2r 0120

Fig 4 Stress distribution of the original impeller

Figure 4 shows that the maximum stress under centrifugaload occurs at the core of the disk and the second-maximumstress occurs at the fillet region (marked by A and B in Fig 4) The maximum stress at the core of the disk (region A) is foundto be 360 MPa and the maximum stress at the fillet (region B) isfound to be 292 MPa The impeller has a safety factor of 114(the ratio of the ultimate tensile strength of material 412 Mpa tothe maximum stress 360 MPa) which is very small focommercial application This highlights the requirement oimprovement of disk structure

32 Effects of Geometric Parameters of

Impeller Disk

321 Effects of Tip Thickness Stresses and deformations of

11 impellers with different 1h were calculated and compared

with the original impeller Figure 5 shows the effects of 1h on

the relative maximum von Mises stress in regions A and B The




relative maximum stress is the ratio of the maximum stress tothe original impellerrsquos maximum stress in region A (360 MPa)

Figure 6 shows the effects of 1h on the maximum relative

deformations along the radial circumferential and axialdirections of the impeller The relative maximum deformation isthe ratio of the maximum deformation to the radius

0R of the

original impeller The results for the original impeller aremarked by hollow squares in Figs 5 and 6

05

06

07

08

09

10

11

12

0 001 002 003 004 005 006 007

tip thickness

r e l a t i v e m a x i m u m s

t r e s s

region A

region B

Fig 5 Effects of 1h on the relative maximum stresses of

impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 001 002 003 004 005 006 007

tip thickness

r e l a t i v e m a x i m u m

d e f o r m a t i o n

radial

circumferential

axial

Fig 6 Effects of 1h on relative deformation of impeller

Across the 11 simulated cases the tip thickness 1h ranges

from 0001 to 0067 Due to the effect of the centrifugal loadcaused by the additional mass it is obvious that the maximumstress values in region A and region B severely increase with

increasing 1h Variations of the maximum stresses at these two

regions are quite similar over the entire range of 1h The vonMises equivalent stress in region A is between 078 and 112

times that of the original impeller Variations of 1h also lead to

large changes in deformations along the radial circumferentialand axial directions It can be seen that the maximumcircumferential deformation decreases but the axial deformation

increases with increasing 1h The effect of 1h on radial

deformation is comparably small

Reducing the impeller tip thickness 1h has two

advantages Firstly it is easier to meet the safety requirementsdue to a lower level of von Mises stress In addition it canprevent blades to scrape the shroud casing which is caused by

deformations of the impeller Reducing 1h is a feasible and

effective approach to improve strength of impellers Howeverthe impeller should keep a certain tip thickness to meet therequirements of the dynamic balance to remove material Basedon comprehensive considerations of the strength dynamic

balance feasibility and deformations the tip thickness 1h o

the improved impeller is set to 0013 which is marked byhollow triangles in Figs 5 and 6

322 Effects of Rear-Disk Thickness Stresses and

deformations of 13 impellers with various 2h were calculated

and compared with the original impeller Figure 7 shows the

effects of 2h on the relative maximum von Mises stresses in

regions A and B Figure 8 shows the effects of 2h on the

relative maximum deformations along radial circumferentiaand axial directions The results for the original impeller aremarked by hollow squares in Figs 7 and 8

07

08

09

10

11

12

13

14

15

0 004 008 012 016

rear-disk thickness


t r e s s

region A

region B

Fig 7 Effects of 2h on relative maximum stresses of

impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 004 008 012 016

rear-disk thickness r

e l a t i v e m a x i m u m d

e f o r m a t i o n

radial

circumferential

axial

Fig 8 Effects of 2h on relative deformations of impeller




The parameter range for the rear-disk thickness 2h is 0 -

0160 Due to the centrifugal load being shared by the rear-diskthe maximum stress in region A decreases severely with

increasing 2h when 08002 leh However 2h has little

influence on maximum stress when 08002 geh The von Mises

equivalent stress in region A is between 144 to 094 times thatof the original impeller In region B 2h has a negligible

influence on the maximum stress over the entire range of 2h

Variations of 2h also lead to some changes in deformations

along the radial circumferential and axial directions I t can beseen that the maximum circumferential deformation increases

while the axial deformation decreases with increasing 2h The

effect of 2h on radial deformation is relatively not significant

Mass and inertia increase with increasing 2h while the

maximum stress decreases Based on comprehensive

considerations of strength and mass the rear-disk thickness 2h

is set to 0080 for the improved impeller which is same as thatof the original impeller

323 Effects of Rear-Disk Height Stresses and

deformations for 16 impeller designs with varying 3h were

calculated and compared with the original impeller Figure 9

shows the effects of 3h on the relative maximum von Mises

stress in regions A and B Figure 10 shows the effects of 3h on

the relative maximum deformations along the radial

circumferential and axial directions The results for the originalimpeller are marked by hollow squares in Figs 9 and 10

05

06

07

08

09

10

11

12

0 01 02 03 04

rear-disk height


t r e s s region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04

rear-disk height

r e l a t i v e m a x

i m u m d

e f o r m a t i o n

radial

circumferential

axial


Across the 16 cases the rear-disk height 3h ranges from

0027 to 033 It can be observed that the maximum stress in

region B decreases with increasing 3h I t should be noted tha

the maximum stress in region A decreases with increasing 3hwhen 3h is small increases slightly when 16003 geh and

then increases strongly when 26703 geh due to the additiona

centrifugal load caused by additional material The von Misesequivalent stress in region A is between 098 and 112 times thaof the original impeller However the minimum stress wa

obtained when 16003 =h Variations in 3h also lead to some

changes in deformations along the radial circumferential andaxial directions It can be seen that the maximumcircumferential deformation increases while the axia

deformation decreases with increasing 3h The effect of 3h on

radial deformation is comparably small

Considering the effect of increasing 3h on the maximum

stress in region A the rear-disk height 3h of the improved

impeller is selected to be 0160 which is marked by hollowtriangles in Figs 9 and 10

324 Effects of Fillet Radius Stresses and deformations fo

9 values of 1r were calculated and compared with the origina

impeller Figure 11 shows the effects of 1r on the relative

maximum von Mises stresses in regions A and B Figure 12

shows the effects of 1r on the relative maximum deformationsalong the radial circumferential and axial directions Theresults for the original impeller are marked by hollow squares inFigs 11 and 12




05

06

07

08

09

10

11

12

0 01 02 03 04 05 06

fillet radius

r e l a t i v e

m a x i m u m s

t r e s s

region Aregion B

Fig 11 Effects of 1r on relative maximum stresses of

impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04 05 06

fillet radius

r e l a t i v e m a x i m u m d e

f o r m a t i o n

radial

circumferential

axial

Fig 12 Effects of 1r on relative deformations of impeller

The fillet radius 1r ranges from 007 to 053 Due to the

effect of a larger fillet radius the maximum stress in region B

decreases significantly with increasing 1r On the other hand

variations in the maximum stress in region A are quite slight

over the entire range of 01 Rr The minimum stress can be

obtained when 26701 =r Variations in 1r also lead to little

changes in deformations along the radial circumferential andaxial directions It can be seen that the maximum

circumferential deformation increases with increasing 1r while

the axial deformation decreases The effect of 1r on radial

deformation is relatively insignificantGenerally speaking the maximum stress in region A is

higher than that in region B so the increase of 1r isinsignificant for the overall strength of impellers The filletradius of the improved impeller is selected to be 26701 =r

which is marked by hollow triangles in Figs 11 and 12

325 Effects of Bore Radius The stresses and deformations

of 12 impellers with varying 2r were calculated and compared

with the original impeller Figure 13 shows the effects of 2r on

the relative maximum von Mises stresses in regions A and B

Figure 14 shows the effects of 2r on the relative maximum

deformations along the radial circumferential and axiadirections The results for the original impeller are marked byhollow squares in Figs 13 and 14

05

06

07

08

09

10

11

0 005 01 015

bore radius


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 005 01 015

bore radius

r e l a t i v e m a x i m u m d

e f o r m a t i o n

radial

circumferential

axial


The bore radius 2r is varied from 0 to 0150 It can be

noted that 2r decreases with decreasing 2r However the

maximum stress in region A decreases significantly with

decreasing 2r when 04002 ler The von Mises equivalen

stress in region A is 053 to 103 times that of the originaimpeller That is the von Mises equivalent stress in region A is

found to be 053 times the original impeller when 02 =r (with

no bore) The maximum stress in region A is smaller than that in

region B for 03002 ler It should also be noted that 2r ha

little influence upon the maximum stress in region B over the

entire range of 2r Variations of 2r also lead to some changes in

deformations along the radial circumferential and axiadirections It can be seen that the axial deformation decrease

obviously with increasing 2r The effect of 2r on radial and

circumferential deformation is not significant




Although the maximum stress in region A decreases with

decreasing 2r a small 2r means a slim shaft Furthermore it is

difficult to redesign a new shaft system to adapt to the changes

of the bore radius The bore radius 2r of the improved

impeller is selected to be 0120 which is same as the originalimpeller that has been used for many years

33 Structural Analysis of Improved ImpellersAfter finishing the above analysis of effects of geometric

parameters of impeller disk the improved impeller (impeller I)is designed using the improved parameters to reduce the stress The geometric parameters of the impeller I are summarized in Tab 2

As discussed earlier due to the fact that the maximumstress in region A is reduced by the factor 053 compared to theoriginal impeller a solid impeller is a further promising methodto reduce stress Therefore a second improved impeller(impeller II) is designed on the basis of impeller I Impeller II

features the same geometric parameters as impeller I except for2r The geometric parameters of the impeller II are listed in

Tab 2 Figures15 and 16 show the stress distributions of theimproved impellers under the same centrifugal load and thesame boundary conditions with the original impeller

Tab 2 Geometric parameters of the improved impellers

Fig 15 Stress distribution of improved impeller I

Fig 16 Stress distribution of improved impeller II

Figure 15 shows that the stress distribution in the improvedimpeller I is similar to that of the original impeller with thesame stress concentration regions but the maximum stress leve

is reduced significantly The calculations show encouragingresults the maximum von Mises equivalent stress in region A i293MPa a decrease of 19 compared to the original impeller The von Mises equivalent stress in region B is 215MPa adecrease of 26

Figure 16 shows that the maximum von Mises equivalenstress in region A in the improved impeller II is 180MPa adecrease of 50 compared to the original impeller The vonMises equivalent stress in region B in the improved impeller Iis higher than that in region A with a value of 231MPa Thisrepresents a decrease by 21 compared to the original impeller That is the solid impeller greatly reduces the maximum stressHowever a new shaft system needs to be developed to match

the solid impellerWhen the stress level of the impeller is in the elastic region

speed scaling of elastic results is straight forward Therelationship is that the stress increases with the square of thespeed Thus the results of the improved designs can be used toextend the maximum speed and then obtain a higher pressureratio for a specific impeller On the other hand it can be used todecrease the cost of an impeller by replacing titanium withaluminum Titanium has a higher ultimate tensile strength but itis much more expensive than aluminum This matters fodesigners because the cost of the turbocharger is a key factor forcommercial market

4 CONCLUSIONS AND REMARKSIn this paper finite element analysis has been used to

model the effects of disk geometric parameters on the strengthand deformation of a high pressure ratio centrifugacompressorrsquos impeller For the high pressure ratio centrifugacompressors high stress will restrict its design and application The geometric parameters of the impeller disk are important foits stress and deformation As the results of the investigation thefollowing findings could be established

parameters impeller I impeller II

1h 0013 0013 2h 0080 0080 3h 0160 0160 1r 0267 0267 2r 0120 0




The Tip thickness1h the rear-disk thickness

2h and the

bore radius 2r are important parameters for both stress and

deformation of the impeller Relatively the rear-disk height3h

and fillet radius 1r are not important After finishing the above

analysis of effects of geometric parameters of impeller disk the

improved impeller is designed using the improved parameters toreduce the stress

The stress distribution in the improved impellers and thatof the original impeller are similar with the same stressconcentration regions but the maximum stress for the improvedimpellers could be reduced significantly Comparing to theoriginal impeller the maximum von Mises equivalent stress of the improved impeller I in region A could be decreased by 19and the maximum von Mises equivalent stress of the improvedimpeller II in region A could be decreased by 50 Theimproved impeller can bear higher pressure ratios or usecheaper material with lower ultimate tensile strength

ACKNOWLEDGMENTS This research was supported by the National Natural

Science Foundation of China (Grant No 51176087)

REFERENCES

[1] Zheng X Q Huenteler J Yang M Y et al Influence of thevolute on the flow in a centrifugal compressor of a high-pressure ratio turbocharger Proc IMechE Part A Journalof Power and Energy 2011 224 pp 1157-1169

[2] Ricardo M B Apostolos P Yang M Y Overview of boosting options for future downsized engine Sci China Tech Sci 2011 54 (2) pp 318-331

[3] Clenci A C Descombes G Podevin P et al Some aspectsconcerning the combination of downsizing withturbocharging variable compression ratio and variableintake valve lift Proc IMechE Part D Journal ofAutomobile Engineering 2007221 (10) pp 1287-1294

[4] Maiboom A Tauzia X Heacuteteta J F Experimental study o

various effects of exhaust gas recirculation (EGR) oncombustion and emissions of an automotive direcinjection diesel engine Energy 2008 33(1) pp 22-34

[5] Zheng X Q Zhang Y J Yang M Y et al Stabilityimprovement of high-pressure-ratio turbochargecentrifugal compressor by asymmetric flow controlmdashmdashpart II non-axisymmetric self recirculation casingtreatment ASME Paper No GT2010-22582 2010

[6] Raya G S Sinhaa B K Computation of centrifugastresses in a radial-flow impeller Comput Struct 199140 pp 731-740

[7] Subramani D A Ramamurti V Sridhara K Numericaanalysis and experimental verification of the radial growth

of a turbocharger centrifugal compressor impeller JStrain Anal Eng Des 1997 32 pp 119-128[8] Bhope D V Padole M P Experimental and theoretica

analysis of stresses noise and flow in centrifugal fanimpeller Mech Mach Theory 2004 39 pp 1257-1271

[9] Bonaiuti D Arnone A Ermini M Baldassarre L LAnalysis and optimization of transonic centrifugacompressor impellers using the design of experimentstechnique J Turbomach 2006 128 pp 786-797

[10] Valakos I M Ntipteni M S Nikolos I K Structuraoptimization of a centrifugal impeller using differentiaevolution in CATIA environment Operational Research2007 7 pp 185-211




is thus difficult for designers to obtain the optimized designs fortheir individual application-specific parametric requirements If general relationships between geometric parameters of animpeller and its strength can be established it will be helpful toimprove the geometry to decrease the strength

In this paper a detailed investigation of the effects of five

impeller disk geometric parameters on maximum stress andstiffness was performed by using 3-D FEA Subsequentlygeometric parameters of an original impeller were improved onthe basis of this analysis to decrease the maximum stress

2 NUMERICAL METHODS

21 Structural Analysis Theory The FEA is an efficient numerical technique to research the

detailed response of structure to all types of loads includingstress strain deformation and so on The equilibrium equationsfor linear structural static analysis are

0=+

part

part+

part

part+

part

part

bx

xzxyx Fzyx

τ τ σ (1)

0=+part

part+

part

part+

part

part

by

yzyyxF

zyx

τ σ τ (2)

0=+part

part+

part

part+

part

part

bzzzyzx Fzyx

σ τ τ (3)

where bxF byF and bzF are the body forces per unit volume

acting along the directions x y and z respectively σ

and τ are the normal and shear stress components Subscriptsare used to describe their directions

In the case of linear elastic isotropic 3D solid the stress-strain relations are given as

( )[ ]zyxxE


G

xy

xy

τ γ = (4)

( )[ ]xzyyE


G

yz

yz

τ γ = (5)

( )[ ]yxzzE


Gzx

zx

τ γ = (6)

where E is Youngrsquos modulus G is shear modulus and micro

is Poissonrsquos ratio of the material ε and γ are normal strain

and shear strain components respectively Subscripts are usedto describe their directions

The strains induced in the body can be expressed in terms

of the deformations as shown below

x

ux

part

part=ε

x

v

y

uxy

part

part+

part

part=γ (7)

y

vy

part

part=ε

y

w

z

vyz

part

part+

part

part=γ (8)

z

wz

part

part=ε

z

u

x

wzx

part

part+

part

part=γ (9)

where u v and w are the deformations along thedirectionsx y and z respectively

The primary aim of static stress analysis is to obtain thedistribution of stresses and deformations under the stated loadsand boundary conditions The effects and sensitivities of theprincipal geometric parameters on the strength of the impelle

were investigated by means of a linear elastic FEA whichprovides a good understanding into the internal responses of thestructure

22 FEA Model and Boundary ConditionIn this paper the effects of the geometric parameters of

impeller disk were investigated by means of a linear elasticFEA excluding the effect of non-linear material properties Thestudied impeller has 7 main blades and 7 splitter blades Insteadof dealing with the whole structure 17 of the cyclic symmetricstructure was analyzed to reduce the numerical solution time The mechanical model of the impeller is shown in Fig 1 Thecorresponding finite element mesh shown in Fig 2 was buil

using 3D 20-nodes solid elements in global cylindricacoordinate system and consists of 36736 elements For bettecomparability uniform FEA mesh size was used for all theimpellers with varies geometric parameters throughout theanalysis

It is suggested that the influence of aerodynamic forces inegligible comparing to the centrifugal loads The followingboundary conditions and loads were applied for the structuraanalysis 1) Centrifugal loads at design rotational speed withpressure ratio of 421 2) The nodes attached to both the fronand reverse ends of the impeller (as shown in Fig 2) are fixedand the deformations along circumferential and axial directionsare set to zero 3) The constraint equations that tie together the

low and high edges of the model (cyclic symmetric faces) aregenerated automatically with a cyclic symmetry analysis

Fig 1 Mechanical model of the impeller















2r (02 Rr )









Parameters Value

1h 0040 2h 0080 3h 0107 1r 0160 2r 0120




Impeller Disk











0R of the


05

06

07

08

09

10

11

12

0 001 002 003 004 005 006 007

tip thickness


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 001 002 003 004 005 006 007

tip thickness



radial

circumferential

axial






















07

08

09

10

11

12

13

14

15

0 004 008 012 016

rear-disk thickness


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 004 008 012 016



e f o r m a t i o n

radial

circumferential

axial


























05

06

07

08

09

10

11

12

0 01 02 03 04

rear-disk height


t r e s s region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04

rear-disk height


i m u m d

e f o r m a t i o n

radial

circumferential

axial























05

06

07

08

09

10

11

12

0 01 02 03 04 05 06

fillet radius

r e l a t i v e

m a x i m u m s

t r e s s

region Aregion B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04 05 06

fillet radius


f o r m a t i o n

radial

circumferential

axial




















05

06

07

08

09

10

11

0 005 01 015

bore radius


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 005 01 015

bore radius


e f o r m a t i o n

radial

circumferential

axial







































1h 0013 0013 2h 0080 0080 3h 0160 0160 1r 0267 0267 2r 0120 0





2h and the









REFERENCES



























2r (02 Rr )









Parameters Value

1h 0040 2h 0080 3h 0107 1r 0160 2r 0120




Impeller Disk











0R of the


05

06

07

08

09

10

11

12

0 001 002 003 004 005 006 007

tip thickness


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 001 002 003 004 005 006 007

tip thickness



radial

circumferential

axial






















07

08

09

10

11

12

13

14

15

0 004 008 012 016

rear-disk thickness


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 004 008 012 016



e f o r m a t i o n

radial

circumferential

axial


























05

06

07

08

09

10

11

12

0 01 02 03 04

rear-disk height


t r e s s region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04

rear-disk height


i m u m d

e f o r m a t i o n

radial

circumferential

axial























05

06

07

08

09

10

11

12

0 01 02 03 04 05 06

fillet radius

r e l a t i v e

m a x i m u m s

t r e s s

region Aregion B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04 05 06

fillet radius


f o r m a t i o n

radial

circumferential

axial




















05

06

07

08

09

10

11

0 005 01 015

bore radius


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 005 01 015

bore radius


e f o r m a t i o n

radial

circumferential

axial







































1h 0013 0013 2h 0080 0080 3h 0160 0160 1r 0267 0267 2r 0120 0





2h and the









REFERENCES



















0R of the


05

06

07

08

09

10

11

12

0 001 002 003 004 005 006 007

tip thickness


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 001 002 003 004 005 006 007

tip thickness



radial

circumferential

axial






















07

08

09

10

11

12

13

14

15

0 004 008 012 016

rear-disk thickness


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 004 008 012 016



e f o r m a t i o n

radial

circumferential

axial


























05

06

07

08

09

10

11

12

0 01 02 03 04

rear-disk height


t r e s s region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04

rear-disk height


i m u m d

e f o r m a t i o n

radial

circumferential

axial























05

06

07

08

09

10

11

12

0 01 02 03 04 05 06

fillet radius

r e l a t i v e

m a x i m u m s

t r e s s

region Aregion B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04 05 06

fillet radius


f o r m a t i o n

radial

circumferential

axial




















05

06

07

08

09

10

11

0 005 01 015

bore radius


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 005 01 015

bore radius


e f o r m a t i o n

radial

circumferential

axial







































1h 0013 0013 2h 0080 0080 3h 0160 0160 1r 0267 0267 2r 0120 0





2h and the









REFERENCES





































05

06

07

08

09

10

11

12

0 01 02 03 04

rear-disk height


t r e s s region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04

rear-disk height


i m u m d

e f o r m a t i o n

radial

circumferential

axial























05

06

07

08

09

10

11

12

0 01 02 03 04 05 06

fillet radius

r e l a t i v e

m a x i m u m s

t r e s s

region Aregion B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04 05 06

fillet radius


f o r m a t i o n

radial

circumferential

axial




















05

06

07

08

09

10

11

0 005 01 015

bore radius


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 005 01 015

bore radius


e f o r m a t i o n

radial

circumferential

axial







































1h 0013 0013 2h 0080 0080 3h 0160 0160 1r 0267 0267 2r 0120 0





2h and the









REFERENCES
















05

06

07

08

09

10

11

12

0 01 02 03 04 05 06

fillet radius

r e l a t i v e

m a x i m u m s

t r e s s

region Aregion B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 01 02 03 04 05 06

fillet radius


f o r m a t i o n

radial

circumferential

axial




















05

06

07

08

09

10

11

0 005 01 015

bore radius


t r e s s

region A

region B


impeller

10E-03

15E-03

20E-03

25E-03

30E-03

0 005 01 015

bore radius


e f o r m a t i o n

radial

circumferential

axial







































1h 0013 0013 2h 0080 0080 3h 0160 0160 1r 0267 0267 2r 0120 0





2h and the









REFERENCES





































1h 0013 0013 2h 0080 0080 3h 0160 0160 1r 0267 0267 2r 0120 0





2h and the









REFERENCES

















2h and the









REFERENCES













Documents

Effects of Disk Geometry on Strength of a Centrifugal Compressor Impeller for a High Pressure Ratio Turbocharger