better computation of fiber-reinforced engine …...localization homogenization multi-scale modeling...

118

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SIMULATION Structural Parts

The lower material stiffness and greater damping of plastics compared with

metallic materials allow an improvement in the component’s acoustic behavior. Lower component vibrations reduce both the emission of direct airborne sound and the transmission of structure-borne noise within the vehicle structure. In combination with the engine mount, the engine bracket represents a crucial component in the transmission path be-tween engine and vehicle body (Fig. 1). In-formation on the vibration behavior of the engine bracket is therefore important for the component development pro-cess.

However, the specific material beha-vior of thermoplastic polymers in gen-eral, and of short fiber-reinforced types in particular, complicates the computation. Key parameters here are the anisotropy of the material behavior resulting from the fiber orientation and the damping of the material. Using fairly simple ap-proaches, however, a prediction of the vibration behavior can be obtained that can be used as the basis for an acoustic optimization. The method is based on a simulation carried out using the finite element method (FEM). The approach in-troduced here allows complex compo-nent and full-vehicle evaluations and ex-perimental component optimizations to be reduced. The model used is an injec-tion molded engine bracket made of PA66-GF50.

Computational Prediction of the Influence of Fiber Orientation

As the properties of components made from short fiber-reinforced polymers have a certain dependence on the fiber orientation, a holistic consideration using “integrative simulation” is necessary for a precise computational assessment. The injection molding process gives the fibers a characteristic orientation profile due to the flowing of the melt. The fiber orien-tation varies here both at different points in the component and over the wall thickness. The local fiber orientation can be computed by means of an injection molding simulation; in our case, the soft-ware Cadmould (producer: simcon kunst -stofftechnische Software GmbH, Wür-selen, Germany) was used. The orien-tation tensor indicates on the one hand

the principal local orientation directions of the fibers, and on the other hand the degree of orientation.

Multi-scale material models were used here to take account of the in-fluence of the fiber orientation on the mechanical properties of the component [1]. These models allow the behavior of the composite to be computed on the basis of the material properties of its con-stituent parts, i. e. matrix polymer and re-inforcing fibers. The constituents with their specific individual properties and their spatial configuration determine the material behavior of the composite at component level (Fig. 2).

As a micro-scale model is not poss-ible for macroscopic parts, “homogeniz-ation methods” are used. The homogen-ization method computes the anisotro -pic properties of the composite on the

Better Computation of Fiber-Reinforced Engine Components

Precise Prediction of the Vibration Behavior of Structural Parts through FEM Simulation

Fiber-reinforced plastics are playing an ever more important role in the development of low-noise engines.

Taking the example of an automobile engine bracket, a method is presented here with which the vibration

behavior of short fiber-reinforced structural parts can be more precisely predicted. The method developed is

further characterized by its comparatively simple application and scalability. It therefore allows even large

models to be efficiently computed.

[VEHICLE ENGINEERING] [MEDICAL TECHNOLOGY] [PACKAGING] [ELECTRICAL & ELECTRONICS] [CONSTRUCTION] [CONSUMER GOODS] [LEISURE & SPORTS] [OPTIC]

Fig. 1. Sound paths

from the power unit

to the driver’s ear

(source: Daimler)

Engine bracket (PA66-GF50)

p~

p~

Fy

Fz F~Fx

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Structural Parts SIMULATION 119

Kunststoffe international 10/2019 www.kunststoffe-international.com

occur are very small and a linearized view of the material behavior is therefore per-missible. The fiber orientation distribution functions (ODF) are reconstructed from the orientation tensor using a maximum entropy method [3].

The homogenization is performed in two steps. In the first step, volume averag-ing of the mechanical properties is per-formed on the basis of the Mori-Tanaka model [4]. This gives the homogenized transversal isotropic properties of a repre-sentative volume element consisting of fiber and surrounding matrix. The influence of the local fiber orientation distribution is incorporated in the second step by means of orientation averaging using the recon-structed ODF. The influence of a single fiber class on the stiffness of the composite is then considered using corresponding weighting factors.

basis of the mechanical properties of its constituents and their spatial configur-ation without the need for micro-scale modeling of each constituent. This method provides the equivalent hom-ogenized properties (e. g. stiffness) as the real inhomogeneous composite. The homogenized material parameters can then be used to carry out a FEM analysis of the part. As the FE mesh topology gen-erally differs between injection molding simulation and structure simulation, map-ping is also necessary (Fig. 3).

The homogenized material properties are computed using the software Con-verse [2] from Part Engineering and the fiber orientation is transferred from the in-jection molding simulation to the struc-tural simulation. An anisotropic linear-elastic material model was used here. In vi-bration analysis, the deformations that

Fig. 2. Multi-scale material model: fundamentals for the computation of the composite

material behavior on the basis of the reinforcing fibers and the matrix polymer

(source: Part Engineering, based on [1])

Localization

Homogenization

Multi-scale modeling

Mesoscale MicroscaleMacroscale

Fig. 3. The integrative computation approach necessitated mapping between the computation

models (source: Part Engineering)

Pre-processing

Material modeling &data transfer

Mapping of fiber orientation

Anisotropic material properties

Natural frequencies,modes shapes,

frequency response function

Injectionmolding

simulation

FEMsimulation

Post-processorConverse

Post-processing

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»


120 SIMULATION Structural Parts


static tensile test of all the test speci-mens reflected the behavior determined experimentally with adequate precision. An example of the whole procedure is shown in Figure 4.

The quantitatively correct prediction of the frequency response function of a component in FEM is possible if a par-ameter to describe the material damping is known in addition to the static model parameters for describing the composite stiffness. The anisotropic linear-elastic material model used shows no implicit damping, as the real visco-elastic be -havior of the plastic cannot be consider-ed by the model. For this reason, an easi ly defined frequency-dependent modal

damp ing factor as a percentage of the critical damping was used. In order to characterize these, flexural vibration tests were performed in accordance with DIN EN ISO 6721–3. The test configuration is shown schematically in Figure 5.

The test specimen was securely clamped at one end while the other end was excited using an electro-mag-netic shaker. This is firmly attached to the test specimen in order to ensure the best possible loss-free excitation. The vi-bration response was recorded using a scanning laser vibrometer by measur-ing the vibration acceleration of the whole specimen surface. Examples of the vibration forms of a firmly clamped

Experimental Parameter Identification

Calibration of the material model, i. e. quantitative determination of the model parameters, was performed using an ex-perimentally-based re-engineering ap-proach. For this, specimen taken at 0°, 90° and 30° to the flow direction were taken from injection-molded test plaques and tested in short-term tensile tests until fracture. The local fiber orien-tation distributions in the test specimens were determined using an injection molding simulation of the test plaque. The parameters of the multi-scale ma-terial model were modified iteratively until the FEM computation of the quasi-

Fig. 4. Parameter identification for the anisotropic material model: the fiber orientation distributions determined experimentally in test specimens

serve for calibration of the material model (source: Part Engineering)

Strain [%]

FEM tensile test specimen

Anisotropic material parameters(exemplary orthotropic material model):

Injection molding simulation of test

EMatrixL/D…

ODF

• Tensile moduli E11, E22, E33• Shear moduli G12, G13, G23• Poisson ratios ν12, ν13, ν23

Multi-scale modelIterative0°-flow

30°-flow

90°-flow

Stre

ss [M

Pa]

MeasurementFEM

90 °

30 °

0 °

Static tensile test specimen

Meltcross flow

in flow

0°

90°

Fig. 5. Schematic test configuration and transmission behavior in the flexural vibration test (source: Daimler)

Frequency

1.0

0.5

00

Ampl

itude

1000 2000 3000 4000 5000

Material: PA66-GF50

Excitation Specimen

Fixation

3D laservibrometer

Hz 6000

90 °

45 °

0 °3

1

2

0° 45° 90°

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© Kunststoffe




bar are also shown up to the third order in Figure 5. Using this method, frequen-cy-dependent characteristics can be identified, allowing for the fiber orien-tation, up to frequencies of several 1000 Hz [5].

By analogy with the method used to determine the static composite stiffness-es, a re-engineering approach was also followed to identify the material damp-ing. For this, the flexural vibration test de-scribed above was simulated dynamically in the frequency range using the stati-cally calibrated material model (Fig. 4) in FEM. As an additional parameter, the fre-quency-dependent modal damping was varied until the measured and computed response behavior corresponded suffi-ciently closely (Fig. 6). »

Fig. 6. Flexural vibration test: result of the material model calibration (source: Daimler)

Frequency

1.0

0.5

00

Ampl

itude

1000 2000 3000

90°-flow

4000 5000 Hz 6000

90 °

45 °

0 °

FEMMeasurement

Frequency

1.0

0.5

00

Ampl

itude

1000 2000 3000

0°-flow

4000 5000 Hz 6000

90 °

45 °

0 °

FEMMeasurement

Frequency

1.0

0.5

00

Ampl

itude

1000 2000 3000

45°-flow

4000 5000 Hz 6000

90 °

45 °

0 °

FEMMeasurement

Fig. 7. FEM model and test configuration: engine bracket on crankcase (source: Daimler)

3D laservibrometer

Elastic soft support

Crankcase

Engine bracket

Excitation

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122 SIMULATION Structural Parts


Validation on the Part

The computation approach was vali-dated using an automobile engine bracket made of PA66-GF50. The engine bracket was mounted on an aluminum crankcase and the whole assembly sus-pended from a soft support. The test con-figuration is shown schematically on the

FEM model in Figure 7. Here again, the vi-bration response was recorded using a 3D scanning laser vibrometer. The accel-eration over the whole component sur-face was measured. This revealed the natural frequencies, natural modes and the response behavior.

The test was simulated using FEM by analogy with the specimen simulations.

A good correlation is to be seen be-tween the measured and computed natural frequencies for all three direc-tions: the relative deviations lie below 5 % over the whole frequency range. Fur-thermore, the mean levels of the peaks of the response function have a sufficient correlation. The best correlation is to be seen in the 45° direction.

Fig. 8. Integrative computation approach: overview of the method for the engine bracket (source: Part Engineering)

Fiber orientation

Injection moldingsimulation

Injection moldingsimulation

(orientation)

FEM model

Multi-scalehomogenization

Multi-scale model

Mapping

Pre-processing

Compute anisotropicmaterial parameters

45 material cards

Material properties

(anisotropiccomposite)

FEMsolver-builtin

anisotropicmaterial model

Ready-to-useFE-input deck

1×

Fig. 9. Computed and measured natural frequencies of the engine bracket (source: Daimler)

Mode

140

%

100

80

60

40

20

01 2 3 4 5

[Test = 100 %]

“Verticalbending“

“Horizontalbending“

“Torsion“ “Rolling“

Mode 3 is a natural modeof the crankcase and isnot shown here

Eige

nfre

quen

cy

FEM (anisotropic)

FEM (isotropic 100 %)

1 2 4 5

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test are observed for the isotropic simu-lation. The isotropic analysis computes the natural frequencies significantly too high, a fact that is attributable to the assumed homogeneous stiffness in flow direction of the specimen in the whole part. The visual evaluation of animations of the natural modes in the comparison between measurement and simulation shows a very good correlation.

Figure 10 shows the response functions of the anisotropic and isotropic simu-lations by comparison with the measure-ment for a selected evaluation point on the engine bracket in the three spatial di-rections. Even if deviations in the height of the peaks in the anisotropic simulation are still clearly recognizable, it can also be seen that the anisotropic simulation leads to a significantly better prediction of the response behavior. That applies to both the position of the peaks and their height.

Conclusion and Outlook

The studies conducted show a good suit-ability of the integrative computation ap-proach presented for predicting the vi-bration behavior of short fiber-reinforced plastic parts. They also show that for an acceptable prediction quality of the com-putation, it is indispensable to consider the molding process for parts of short fiber-reinforced plastics. The method fre-quently used of isotropic analysis with a possibly globally “smeared” stiffness in the part using reduction factors leads to large uncertainties and could at most be used as part of a preliminary assessment. The additional work necessary for the inte-grative computation approach is reason-able by comparison with the gain in precision and the resulting higher assess-ment security.

Overall it can be seen that the com-paratively simple description of the ma-terial behavior using an anisotropic linear-elastic orientation-dependent material model and a global frequency-dependent damping factor results in an acceptable prediction of the vibration behavior in re-lation to the measurement. The method presented can serve as a solid basis for a subsequent acoustic simulation.

The pre-homogenized material cards used here allow the use of solver-built-in standard material models so that the ap-proach is also suitable for large models. The method is numerically stable and fast. The integration of the approach into the easy-to-use commercial software, Converse, allows its practice-oriented ap-plication. W

The basis for the computation here again was the fiber orientation distribution de-termined with the injection molding simulation (Fig. 8). The anisotropic material model calibrated using the specimens was used. The required incorporation of the ODF was done by defining 45 differ-ent material model parameter sets for specific local ODFs in the part. With this approach, the multi-scale material mo-deling for computation of the material parameters of the anisotropic material model was performed once during the pre-processing.

A solver-built-in material model was used for the FEM simulation that was fed with the anisotropic material model par-ameters (material card) computed in this way. The computing-intensive multi-scale homogenization during runtime of the analysis is therefore no longer necess-ary. The whole process is implemented in automated form in the Converse soft-ware (producer: Part Engineering GmbH, Bergisch Gladbach, Germany). The pro-cedure has already been successfully vali-dated also for other applications [6–8].

The computation results are shown below. The natural frequencies and modes in the frequency range of the first five relevant modes are considered, whereby the third mode is a purely natu-ral mode of the crankcase and is therefore not discussed in greater detail here. In Figure 9, the results of an isotropic FEM analysis also performed without making allowance for the fiber orientation are compared in standardized form: 100 % correlate with the measurement.

The relative deviations between com-puted and measured natural frequencies for the anisotropic simulation lie between 2 and 5 %, whereas deviations of between approx. 20 and 34 % compared with the

Frequency [Hz]

Anisotropic simulation Isotropic simulation

FRF

[m/s

2 /N]

x directiony directionz direction

x directiony directionz direction

P1z

yx

Frequency [Hz]

FRF

[m/s

2 /N] P1

z

yx

Fig. 10. Transmission

function: anisotropic

(left) vs. isotropic

simulation of the

engine bracket,

dotted line:

measurement, solid

line: FEM (source:

Daimler)

The AuthorsDr.-Ing. Kristin Raschke is Project Man-

ager at NVH Powertrain: CAE + CAT Kunst -

stoffkomponenten, Daimler AG, Stuttgart,

Germany.

Dr.-Ing. Wolfgang Korte is Managing

Director of Part Engineering GmbH,

Bergisch Gladbach, Germany;

[email protected]

ServiceReferences & Digital VersionB You can find the list of references

and a PDF file of the article at www.kunststoffe-international.com/2019–10

German VersionB Read the German version of the

article in our magazine Kunststoffe or at www.kunststoffe.de

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better computation of fiber-reinforced engine …...localization homogenization multi-scale modeling...

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