THE 9thSTUDENT SYMPOSIUM ON MECHANICAL AND MANUFACTURING ENGINEERING

METAL TO COMPOSITE:

REDESIGN OF CENTRIFUGAL PUMP IMPELLER

M. M. N. Frøjk, N. F. H. Bjergmark, R. L. Bjerg, R. Gomila, P. Valero

Department of Materials and Production, Aalborg UniversityFibigerstraede 16, DK-9220 Aalborg East, Denmark

Email: mfrajk17, nbjerg17, rpeder16, rgomil20, pvaler20@student.aau.dk,Web page: http://www.mechman.mp.aau.dk/

Abstract

This article aims to redesign the impeller of the NB 65-200/219 pump from Grundfos, with the objective to reduce theenergy consumption when the impeller is accelerated. This is done by changing the impeller’s material and optimizingits shape, thereby reducing its weight and mass moment of inertia. The original impeller geometry must be alteredwithout affecting the fluid dynamics inside the impeller. In addition, it is bounded to fit inside the original housingas well as the shaft connection and seals.To estimate the stresses and life of the original impeller, a Computational Fluid Dynamic (CFD) analysis is coupledone-way with a Finite Element Analysis (FEA). Regarding the composite alternative, a glass fiber reinforced polyamide(PA66) is selected for redesign which will be manufactured using injection moulding.A simulation of the injection moulding process is done, exporting the results for fiber orientation and length to astructural analysis done with FEM.The same process is used to analyse the optimized impeller, which is obtained using a structural shape optimizationof the 2D cross section. A sequential quadratic programming is used to reduce the impeller’s mass moment of inertia,while constraining the maximum allowed stress and deformation within predetermined limits. The optimized 2Dgeometry is converted to a 3D model and the structural analysis is run. The results show that this design couldreplace the original impeller, while reducing the energy consumption of the pump ensuring the same performance.

Keywords: CFD, Composite, FEA, Impeller, Structural Optimisation, Fiber Orientation, Injection Moulding

Detailed descriptions of content within this article, isfound in the attached appendix report.

1. IntroductionThe focus of this article has been to replace the castiron NB 65-200/219 Grundfos pump impeller, Figure 1,with fiber reinforced polymer. The motivation behindthis replacement is to decrease the pump’s energyconsumption during startup, which is done by reducingthe impeller’s mass moment of inertia. In addition,some beneficial properties can be obtained regardingcavitation and resistance to corrosion by changing toa composite material [1].

The fluid dynamics of the impeller will not be changed,as it is assumed to be at an optimum. The innersurfaces of the impeller will therefore be a constraintin the redesign process. This, along with the rest of theimpeller’s parts can be seen in Figure 2.

Impeller

Front plate

Inlet

Outlet

Shaft

Blade Housing

Volute

Back plate

A A

B B

C C

D D

E E

F F

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

DRAWN

CHK'D

APPV'D

MFG

Q.A

UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:

FINISH: DEBURR AND BREAK SHARP EDGES

NAME SIGNATURE DATE

MATERIAL:

DO NOT SCALE DRAWING REVISION

TITLE:

DWG NO.

SCALE:1:2 SHEET 2 OF 2

A3

WEIGHT:

Crosssection_ballon_notationSOLIDWORKS Educational Product. For Instructional Use Only.

Fig. 1 Centrifugal pump overview.

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A simulation of the impeller’s injection mouldingprocess is done, obtaining the fiber orientation and itslength. These results are taken into account to calculatethe material properties, which are used for the shapeoptimization of the impeller.

AA

Front plate

Back plate

Blade

Front cavity

Back cavityBalancecavity

Volute

Inlet

Balance holes

A A

B B

C C

D D

E E

F F

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

DRAWN

CHK'D

APPV'D

MFG

Q.A

UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:

FINISH: DEBURR AND BREAK SHARP EDGES

NAME SIGNATURE DATE

MATERIAL:

DO NOT SCALE DRAWING REVISION

TITLE:

DWG NO.

SCALE:1:2 SHEET 1 OF 3

A3

WEIGHT:

Crosssection_ballon_notation

Impeller, BZ Mach./unbal

SOLIDWORKS Educational Product. For Instructional Use Only.

Fig. 2 Cross section of the NB 65-200/219 impeller.

Therefore, the following problem formulation arose:

"How can the material of the impeller beswitched to a composite material and theimpeller optimized with respect to mass

moment of inertia, without compromising themechanical properties?"

2. Material and MethodsReducing the impeller’s moment of inertia requiresdifferent analyses, which are outlined in Figure 3. Thepressures acting on the impeller are obtained usingComputational Fluid Dynamics (CFD). The resultingpressures are used to run a structural analysis usingFinite Element Method (FEM), assessing the mechanicalproperties of the original impeller.

To redesign the impeller, the manufacturing method andthe materials are selected. Afterwards, the manufactur-ing process is simulated, to obtain the fiber’s orientationand length. These will then be used to set up the macromechanical properties of the impeller for in the FEmodel.

Based on restrictions from the initial Finite ElementAnalysis (FEA), a structural shape optimization is usedto modify the shape of a 2D cross section of theimpeller. Using the results from the optimization a 3Dmodel is created. The orientation and length of the fibersare obtained for the 3D model, which are used to set upthe final FE model. The results from the last FEA arecompared to those of the original impeller.

CFD analysisof initial design

Structural analysisof original design

using FEM

Optimization on 2D shape

Material propertiesfrom fiberorientation

Process Simulationof fiber direction

from injectionmolding

Selecting fiber andmatrix material

3D shape from the optimization

Process Simulation

Structural analysis using FEM

Fig. 3 Flow chart of different methods and analysesused to reduce the moment of inertia.

2.1 Manufacturing technique and material selectionThe material selected for the further analyses is Zytel®70G30HSLR NC010, from DuPont [2]. The material isa 30wt.% glass fiber reinforced polyamide 66 (PA 66).The manufacturing technique to produce the impellerwill be injection moulding. The fiber length for themanufacturing analyses is assumed to be 3.4mm afterthe screw of the injection unit.

2.2 Injection moulding simulationA simulation of the flow during the injection processis used to predict the fiber orientation in the mouldedimpeller. Furthermore, the average fiber length at theend of the injection moulding is also predicted. Theeffects of the number of gates, gate placement andrunner system will be studied. This will be done toachieve a desired fiber orientation in the impeller.

During injection moulding the fibers tend to align withthe flow direction along the surfaces, and graduallychanging to be transverse to the flow direction in themiddle, as shown in Figure 4. This behavior can be usedto align the fibers with the maximum principal stress,utilizing the strength and stiffness of the fibers.

2

Fig. 4 Visual representation of fiber orientation throughthe thickness.[3]

2.3 Material modelingThe program Digimat is used to obtain a FE modelthat takes the fiber orientation and the fiber lengths intoaccount to calculate the macro mechanical properties.Digimat uses a two-step homogenization process asshown in Figure 5. The real composite representativevolume element (RVE) is replaced with a RVE madeout of pseudo-grains, Figure 5(a). Each of thesepseudo-grains is a two-phase composite that has aphase of inclusions aligned over one small rangeof orientations and a bonding matrix. The next stepconsists of homogenizing each pseudo-grains separately,using the Mori-Tanaka mean-field homogenization,Figure 5(b). The final step uses the Voigt model tocompletely homogenize all the pseudo-grains into oneRVE, Figure 5(c). [4]. Digimat will also be used to setup static- and fatigue failure index with dependence onthe fiber orientation.

(a)

(b)

(c)

Fig. 5 Digimat two-step homogenization.

2.4 Fiber Composite Failure CriterionThe 3D Tsai-Hill transversely isotropic strains basedfailure criteria has been used to assess the strength

of the composite impeller. The criteria presented inEquation 1 is taken from [4]. The maximum strainsat failure, used to define the criteria, were availablein Digimat for the material chosen and are presentedin Table I. The assumption of transverse isotropy isin general not true for the injection moulded impellerhowever at surfaces where the stresses are higher. Thus,where the failure is expected to occur, the fibers areoriented in a preferable direction. In these regions thisassumption is considered valid.

FA(ε) =ε211X2− ε11(ε22 + ε33)

X2+

ε222 + ε233Y 2

+ (1

X2− 2

Y 2)ε22 · ε33 +

(2ε12)2 + (2ε13)

2

S2

+ (1

Y 2− 1

4X2)(2ε23)

2

(1)

Strain at failure

Maximum axial tensile strain X 0.03722Maximum in-plane tensile strain Y 0.04414Maximum transverse shear strain S 0.10556

Tab. I Maximum strains at failure

The fatigue failure criteria used for the fiber compositesis also the Tsai-Hill 3D transversely isotropic. Thesame assumption regarding the fiber orientation is madeas before. This criteria is capable of capturing theeffects of the material’s anisotropy as well as the meanstress influence. In this criteria the material’s strengthparameters for the static failure are substituted by thestress amplitudes at failure (fatigue strengths) for adetermined number of cycles. The S-N curves, both forthe axial tensile loading and transverse tensile loading ofan unidirectional specimen with a fatigue ratio R = 0.1,have been obtained from [5]. In the article, the samematerial as the one selected for the impeller is used.The shear loading S-N curve has been assumed to bethe same as the transverse loading due to limited dataavailable. The constant life diagrams (CLD) presentedin [6] were used. The material in the article does nothave the same fiber weight fraction as selected for theimpeller, therefore, small adjustments are done to theCLD.

2.5 CFDData from the pump operation at its maximum flowrate, Q = 80m3 h−1, is used for the CFD analysis to

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determine the load case for the impeller i.e. the pressuresacting on the impeller. The CFD analysis is a dynamicanalysis that uses implicit time integration for solvingthe Naiver-Stokes equations for a finite volume alongwith continuity equations.

-0.101-0.074-0.047-0.0190.0080.0350.0620.090.1170.144

[MPa]

Fig. 6 CFD pressure results

2.6 FEMThe deformation, stresses and strains in the impellerare determined with a linear static structural analysisusing FEM. This method calculates the displacement ofa model discretized into a mesh of elements by solvingthe linear system of equations shown in Equation 2,where [K] is the global stiffness matrix, D is theglobal displacement vector and R is the global loadvector. After solving this system of equations, strainsand stresses can be calculated.

[K]D = R (2)

The results from the FEA are used as a starting pointfor the redesign.

The maximum deformation value is equal to8.35× 10−3mm. It is located on the front plate,precisely on the cavity closer to the outlet, where thepressure inside the impeller is lower. The maximumvon Mises stress is equal to 60.86MPa and it is locatedon the fillet of the corner, closer to the maximumdeformation where the blade joins the front plate, asshown in Figure 7.

2.7 OptimizationDue to the complexity and computational cost of shapeoptimization, the FEA of the impeller is simplified toa 2D model. This model is a compromise betweenaccuracy and computational efficiency.

0.026.7813.5420.327.0633.8240.5847.3454.160.86

[MPa]

Fig. 7 Von Mises stress on the impeller

The impeller is converted to a 2D axis-symmetric modelwhere this axis symmetry introduces an automaticboundary condition to the 2D model. Thus, the elementscannot displace in the radial direction without strainingin the tangential direction.

The objective of the optimization is to minimize themass moment of inertia of the impeller to be less thanthe original 22.4 · 10−3 kgm2.

To state the general constraints for the optimization, amaximum allowable stress and deformation is evaluated.As the stress concentration in the fillet at the edge ofthe impeller cannot be approximated with the 2D model,some predictions are made. The maximum von Misesstress in the 2D model is associated with the maximumvon Mises stress in the 3D model. This is done vialinear extrapolation. Thus, the relation between the twois approximated to a factor of 10. From this assumptionthe max allowable stress in the 2D model, is found tobe 5.0MPa.

For the deformation, roughly 70% of the total deforma-tion is in the tangential and thus out of plane direction.This allows the 2D model to deform only 30% of thetotal deformation restriction at 0.2mm.

The impeller is given some keypoints, which are definedby a location and a design variable (DV) with one degreeof freedom.

This allows the optimization algorithm to change the DVposition and thus the geometry of the model. The DVmovement is bound by a set of restrictions, chosen to beat the limit of minimum wall thickness in the injectionmoulding process, and so the impeller will still fit withinthe pump housing. The keypoints and the bounds areillustrated in figure Figure 8.

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Fig. 8 Bounds for the design variables used for theshape optimization of the 2D model.

3. Results

3.1 Process SimulationThe injection moulding process is simulated. The runnersystem is designed locating six gates on the front plateat the end of the blades, as seen in Figure 9. This isdone to achieve the melt flow along each one of theblades, orienting the fibers throughout the process.

0.000.380.761.141.521.902.292.673.053.43

[s]

Fig. 9 Runner system setup and melt front advance.

In Figure 10 the first eigenvector of the orientationtensor can be seen at the end of the filling process.The eigenvector shows the orientation with its magni-tude (eigenvalue) describing the degree of orientation.Random orientation would have a value of 0.33 and thecloser it approaches 1, the higher the fiber alignment.Thus, as introduced in Figure 4, a random orientation isexhibited at the center, while closer to the surface thefibers are highly oriented with the flow direction.

0.370.430.50.560.620.680.740.810.870.93

x1

x2

Fig. 10 First eigenvector of the fiber orientation tensorand its magnitude.

In addition, the fiber breakage during the injectionmoulding is calculated. From the original fiber lengthat the sprue of 3.4mm, the resulting average fiberlength, measured by weight, is obtained with a value1.640±0.270mm. The fiber orientation tensor as wellas the average fiber length is exported to set up the staticanalysis.

3.2 Optimization resultsThe final result of the optimization is shown inFigure 11. The algorithm has removed material in mostparts of the impeller. The von Mises stress is also shownin the Figure 11, where it is generally higher in theoptimized impeller.

The results of the optimization is shown in Table II,from which the mass moment of inertia is concluded tohave a reduction of −86.5% after the material changeand optimization. Moreover, the maximum von Mises(vM) stress does not experience a significant change.

Mass Moment of Max. VM Max.Inertia stress Deflection

[kg][10−3 kgm2

][MPa] [mm]

Original 4.51 22.4 60.86 0.008

Optimized 0.62 3.03 63.03 0.271Change −86.3% −86.5% 3.6% 3146%

Tab. II Results

The largest total deformation, with a value of 0.271mmis found on the back plate between two blades, as shownin Figure 12. It is caused by the pressure differencebetween the outside and inside. The fillet where theblade joins the front plate is where the maximum vonMises stress is found with a value of 63.03MPa.

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00.30.60.91.21.41.72.02.32.6

[MPa]

Fig. 11 Comparison of the von Mises stress in across section of the original impeller and the optimizedimpeller.

0.000.030.060.090.120.150.180.2110.240.27

[mm]

Fig. 12 Total deformation of the optimized impeller

In Figure 13, the indicator of alignment between thestress tensor and the fiber orientation tensor is presented.It can be seen that a good alignment has been achievedon the front and back plate, where the highest stressesare located.

Using the SN-curves and constant life diagrams thefatigue failure indexes for the optimized compositeimpeller are calculated. The results for the indexes areshown in Table III, for both the worst case where thelargest stress is transverse to the fiber orientation, andthe best case where they are aligned.

0.150.230.300.380.460.530.610.690.760.84

Fig. 13 Alignment of the stresses and fiber orientation

Cycles Non-aligned stress Aligned stress

109 1.13 0.511010 2.38 0.66

Tab. III Fatigue failure indexes

4. Discussion4.1 OptimizationDuring the initial run, the balancing cavity was theless altered zone as the keypoints here have a smallerinfluence on the moment of inertia. This is due to thefact that it is a cross section of an axis symmetricobject, meaning that the distance from the center makesthe volume of the element greater. Furthermore, thedistance from the center is squared in the calculationof the moment of inertia. Thus the difference betweenthe influence of an element near the center and one atthe edge is proportional to the radius cubed.

The optimization was done for a simplified 2D model ofthe impeller.Out of plane deformations were not takeninto account. This resulted in a total deformation inthe 3D model larger than the constraint. The equivalentconstraint in the 2D model, could be made moreconservative to get a better result. However, it wasassumed the deformation would not affect the fluiddynamics of the impeller significantly.

Better results could be obtained through a full 3Doptimization model. Other simplifications for the struc-tural influence of the blades, the varying anisotropicmechanical properties, and the load case were doneto reduce the computational cost of the optimization.All these compromises are potentially deviating the2D optimum design from the 3D optimum thus a 3Doptimization should be done.

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4.2 Fiber Alignment and FatigueThe worst fatigue failure index for the optimizedimpeller is 2.38 at 1010 cycles. However, this failureindex is only for the case where the alternating stress isacting in the transverse direction of the fiber orientation.Since the fiber orientation in the fillet is in betweenaligned and transverse, it is assessed that the impellerwill not fail due to fatigue before 1010 cycles.

The fatigue failure criteria used in this paper has beenthe 3D Tsai-Hill transversely isotropic failure criteria.Although this assumption is not valid for the wholedomain, it has been the only option available. This is dueto the limited empirical data available.An assumption oforthotropy or full anisotropy would be more accurate ifenough material data was available. Furthermore, withmore material data, it would also be possible to take intoaccount the difference between tension and compressionloading, using a different failure criteria like the Tsai-Wu.

A transient analysis of a full rotation of the impellercould be used to do a more accurate fatigue analysis.This could be used to calculate the correct load ratioat each node thus giving an estimate of fatigue life foreach node of the model. This could also be used toidentify different alternating stresses that have not yetbeen taken into account.

4.3 Cavity pressureThe leak-flow occurring in the front and back cavitiesis not included in the CFD model. This means that theCFD does not calculate the pressure on the outside ofthe impeller. To avoid unrealistic results in the FEA,these pressures are calculated from the velocities insidethe impeller. The velocities have been averaged overthe impeller interface, resulting in a high pressure zoneon the front plate and a low pressure zone inside thechannel closest to the outlet. This pressure differenceprovokes the biggest deformation and highest stressesof the model. Because of this, the critical values usedto assess the integrity of the impeller and dimensionthe redesign, are believed to have a high uncertainty,potentially being higher than the real ones.

4.4 CavitationThe matrix material selection has been partially basedon good properties against wear from cavitation. How-ever, no analysis has been done to try to determinethe wear. The best way to assess this is by doing

experiments from which the results can be used todimension the impeller parts more exposed to cavitation.

4.5 Visco elastic propertiesThe material properties selected were obtained fromliterature for a temperature of 23 °C. However, polymerproperties such as stiffness, strength, and fatigue life arehighly dependent on the temperature. Grundfos statesan operation range from 5 °C to 120 °C thus furtheranalysis with different material properties should bedone.

Moreover, creep might be affect the impeller dueto the applied torque. Although the material’s creepcompliance is high in caparison to common polymers, itwill still result in a 1% strain in the most severe stressconcentration over the course of 1000 h.

5. ConclusionThe impeller of the NB 65-200/219 Grundfos pumpwas redesigned by changing the material from cast ironto glass fiber reinforced polyamide. The shape of theimpeller was changed using an optimization algorithm,reducing its mass moment of inertia. The new impellerdesigned ended up having a mass moment of inertia thatwas 86.5% less than the initial design, while keepingthe estimated fatigue life within the preset limit. Thenew material has some advantageous properties withregard to cavitation and corrosive resistance, whichwould prolong the impeller’s estimated life comparedto cast iron. Further work is necessary before the newimpeller design is ready for production. However, thispaper shows that significant improvements of the massmoment of inertia is obtainable through a redesign ofthe original impeller using composite materials.

AcknowledgementsThe authors of this work gratefully acknowledgeGrundfos for sponsoring the 9th MechMan symposium,as well as Therkel Damm for making a collaborationwith Grundfos possible.

Furthermore, we would like to acknowledge MadsJespersen from FlowHow, for providing a Moldex3Deducational license.

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References[1] “Composite impellers produce significant life-cycle

savings.” https://bit.ly/3sFGWc3, 2011.[2] D. M. D. Center, “Zytel® 70g30hslr nc010.”

https://bit.ly/33yLPt4, 2021. Accessed:2021-05-03.

[3] S. G. Advani and K.-T. Hsaio, Manufacturingtechniques for polymer matrix composites (PMCs).Cambridge: Woodhead Publishing Ltd, 2012.

[4] e Xstream, “Digimat user’s manual,” 2021.[5] Y. Zhou and P. Mallick, “Fatigue performance of

an injection-molded short e-glass fiber-reinforcedpolyamide 6,6. i. effects of orientation, holes, andweld line,” Polymer Composites, vol. 27, 04 2006.

[6] M. J. Kanters, L. F. Douven, and P. Savoyat,“Fatigue life prediction of injection moulded shortglass fiber reinforced plastics,” Procedia StructuralIntegrity, vol. 19, pp. 698–710, 2019. FatigueDesign 2019, International Conference on FatigueDesign, 8th Edition.

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