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F2004F461

AXLE HOUSING AND UNITIZE BEARING PACK SET MODALCHARACTERISATION1Badiola, Virginia*, 2Pintor, Jesús María, 3Gainza, Gorka1Dana Equipamientos S.A., España, 2Universidad Pública de Navarra, Dpto. IngenieríaMecánica, Energética y de Materiales, España, 3Centro de Innovación Tecnológica deAutomoción de Navarra (CITEAN), España

KEYWORDS - Unitize Bearing, Torsion Coupling, Modal Analysis, Finite Element Model,Correlation

ABSTRACT - In this paper, finite element modelling of Axle Housing and Wheel End set isattempted to represent dynamic behaviour of the set as a whole. Axle Housing and Wheel Endsubsets are modal analysed. FEA models are shown and justified, and validity of the modelsis proved by correlation with experimental results. Different models are studied for modellingthe joint between the Axle Housing and the Wheel End and a model is proposed. Finally, thelimitations of the approached model are pointed out.

Theoretical Modal Analysis: Ansys has been used as the solver to run FEA modal analysis.Geometrical models are developed through Pro Engineer and are exported as IGES files toAnsys. Since in modal analysis the mass of the model plays an important role, it is necessaryto work with the whole model. Due to this, several simplifications have been made in thegeometrical model in order to minimise the computational cost. Models analysed are theWheel Hub, the Axle Housing and Bearing Pack set, and the Axle Housing and Wheel End(Wheel Hub and Bearing Pack).

Experimental Modal Analysis: The systems are excited by impact with an instrumentedhammer. Output is measured in terms of acceleration by piezoelectric accelerometers fixed tothe structure with magnetic parts. In the case of the Wheel Hub, the modal analysis has alsobeen performed with a laser vibro-meter, which measures the response in terms of velocity.All components were held up by elastic rubber bands. In order to assure minimuminterference of the fastening in the lowest vibration mode, rubbers have been placed in thenodes of the mode and perpendicular to the direction of vibration.

A finite element model has been proposed to simulate the joint between the Axle Housing andthe Wheel End by modelling rollers as beam elements with E=210Gpa, and considering thatthere is a torsion coupling between rollers rows with beam elements with E=13.5Gpa. Thismodel is suitable to represent dynamic behaviour of Axle Housing and Wheel End set, hasbeen validated by experimental modal analysis, and correlation error obtained is assumed tobe acceptable. Theoretical analyses have been repeated including experimentally adjusteddamping values, and no differences have been obtained in frequency values.

MAIN SECTION - AXLE HOUSING AND WHEEL END DEFINITION

Drive Axles (Figure 1) consists of Differential Head, Axle Housing and Wheel End. TheDifferential Head transmits the torque from the motor to the wheels by rotating it at 90º. TheAxle Housing is the structural part that supports both the Diff. Head and the Wheel End. TheWheel End transmits the torque coming from the Diff. Head to the Wheels.

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The Wheel End is made of the Wheel Hub, a Bearing Pack, a Self-Locking Nut, a Disc orRotor and a Disc Brake (Stator). See figure 2. A bolted joint transmits the driving torquethrough an Axle Shaft to the Wheel Hub. The Hub lies on the Bearing Pack, and it is bolted tothe Disc. The Disc Brake is bolted to the Axle Housing. A Self-Locking Nut prevents axialmovement of the Bearing Pack and provides the preload to the bearing rollers. In this paper,as a first step it is considered that the Wheel End is made of the Wheel Hub and the BearingPack.

Figure 1. (1) Differential Head (2) Axle Housing (3)Wheel End

Figure 2. Wheel End Cross Section

THEORETICAL MODAL ANALYSIS (TMA)

Ansys has been used as the solver to run FEA modal analysis. Geometrical models aredeveloped through Pro Engineer and are exported as IGES files to Ansys. Since in modalanalysis the mass of the model plays an important role, it is necessary to work with the wholemodel. Due to this, several simplifications have been made in the geometrical model in orderto minimise the computational cost, as for example eliminate fillet radius, draft angles, etc.

It is assumed that:

Boundary conditions correspond to components that are free. Components have no damping All components are made of steel, with density of 7.850kg/m3 and

Young Modulus of 210Gpa. Elements are: SOLID92, BEAM4 infinitely rigid of section

1x1mm2 (roller simulation in the cup and cone joint of the bearingin the Axle Housing and Bearing set), and COMBIN14 rigid(roller simulation in the cup and cone joint of the bearing in theAxle Housing and Wheel End set, first approach)

No torsion restriction is included in the models Figure 3. Bearing

Models analysed are the Wheel Hub, the Axle Housing and Bearing Pack set, and the AxleHousing and Wheel End (Wheel Hub and Bearing Pack)

1: 2.263,3 Hz 2: 2.277,6 Hz 3: 3.707,6 Hz 4: 4.200,4 Hz 5: 4.282,1 Hz 6: 4.548,2 HzFigure 4. Wheel Hub FEA results

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1: 1st bending XZ: 114,87Hz 2: 1st bending XY: 185,44Hz 3: 2nd bending XY: 373,37Hz

4: 2nd bending XZ: 444,12Hz 5: 1st Torsión X: 559,21Hz 6: Axial: 615,43HzFigure 5. Axle Housing and Bearing FEA results

Additionally, the following modes have been calculated: the first two modes correspond to therigid solid modes relating to the Bearing Cups. The next couple of modes correspond tospecific modes associated with Brake Flanges.

Rigid solid mode. BearingPacks left/right

787,83 Hz. Bending XYrelated to brake flanges

817,29 Hz. Bending XYrelated to brake flanges

Figure 6. Solid rigid modes in torsion and local modes

1: 1st bending XZ: 92,25Hz 2: 1st bending XY: 144,65Hz 3: 2nd bending XY: 327,78Hz

4: Axial mode in X, hubsmoving in phase: 363,07Hz 5: 2nd bending XZ: 372,78Hz

6: Axial mode in X, hubsmoving in phase: 481,22Hz

7:1st torsión X: 553,31Hz 8: 3th bending XZ: 574,47Hz 9: 3 th bending XY: 619,10Hz

10: bending XY: 666,53Hz 11: bending XZ: 680,51 Hz 12: local bending: 721,02Hz

13: 2nd torsión X: 757,08Hz 14: local bending: 823,89Hz 15: local bending: 830,94HzFigure 7. Axle Housing and Wheel End FEA results

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In this case, local modes of the Brake flanges have also been predicted. Furthermore, localmodes relating to that of Wheel Hubs as 2 d.o.f system. It must bear in mind that this modelcorresponds to a first approach to help later experimental analysis to be focused.

EXPERIMENTAL MODAL ANALYSIS (EMA)

The systems are excited by impact with an instrumented hammer. Output is measured interms of acceleration by piezoelectric accelerometers fixed to the structure with magneticparts. In the case of the Wheel Hub, the modal analysis has also been performed with a laservibro-meter, which measures the response in terms of velocity. All components were held upby elastic rubber bands. In order to assure minimum interference of the fastening in the lowestvibration mode, rubbers have been placed in the nodes of the mode and perpendicular to thedirection of vibration. It is known that for these types of structures main modes are within afrequency range from 0 to 800Hz. Then, the frequency range of interest is set to 0-800Hz.

Wheel Hub

In the case of the Wheel Hub, the main modes are out of range of interest due to its higherrigidity. However experimental modal analysis is done to validate the FEA model. The globalFRF obtained and modes adjusted are shown below. All modes are contained in ZY plane,and description is analogous to theoretical modes.

Mode Damping (%) Frequency (Hz)1 0,24% 2187,202 0,13% 2215,703 0,22% 3582,534 0,07% 4024,355 0,12% 4106,85

6 0,09% 4407,09Chart 1. Experimental results for Wheel Hub

Axle Housing and Bearing

In the modal analysis of the Axle Housing and Bearing set, the excitation points are d.o.f. 51(direction –R), d.o.f. 15 (direction +Y) and d.o.f. 16 (direction +Z). The global FRF obtainedand modes adjusted are shown below (Chart 2).

Mode Description Damping (%) Freq (Hz)

1 1st bending, XZ 0,95% 102,29

2 1st bending, XY 0,60% 176,15

3 2nd bending, XY 2,10% 352,51

4 2nd bending, XZ 3,97% 444,72

5 1st torsion 1,58% 561,52

6 Axial X 1,47% 596,66

7 2nd torsion X 1% 745,3

Chart 2. Experimental results for Axle Housing and Bearing set.

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Axle Housing and Wheel End

In the modal analysis of the Axle Housing and Wheel End set, the excitation points are d.o.f.51 (direction –R) and d.o.f. 15 (direction +Y).

Mode Description Damping (%) Freq (Hz)

1 1st bending, XZ 3,93% 79,31

2 1st bending, XY 2,82% 141,42

3 2nd bending, XY 3,41% 321,74

4 2nd bending, XZ 3,84% 381,61

5 Axial X 1,95% 485,65

6 1st torsión 1,98% 554,24

7 2nd torsión X 0,95% 749,72

Chart 3. Experimental results for Axle Housing and Wheel End set

Linearity

Experimental analysis is based on the assumption that all components are linear. However, asjoints (welded parts, interference adjustment…) exist between components it must be checkedthat the whole system is linear. The hypothesis of linearity means that transference matrix issymmetrical as consequence of the reciprocity principle. Several test are performed to checklinearity, and in the charts below a brief summary of conclusion obtained is shown:

Chart 4. Linearity in the Axle Housing and Wheel End set

It is observed (Chart 4) that in the first test there is a loss of amplitude between both FRF.This could be due to friction welding between a sub-component called spindle (d.o.f. 16) andthe housing body (d.o.f. 24). This behaviour suggests that the damping of the system, or atleast part of it, is due to a non-lineal phenomena of Coulomb friction that is characterised bynon lineal dependence of FRF amplitude with excitation magnitude.

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In the second test, there is no amplitudedifference between signals. Even if this effectcan be by the symmetry of the d.o.f.considered, it is concluded that there is higherlinearity in this second case. In addition tothis, it has been observed (Chart 5) that insome of the FRFs there is a difference innatural frequencies. This phenomena ispresent in structures that are slightly nonlinealdue to a non linear rigidity (cubic, forexample) and is characterised by depedenceof modes frequency with excitationmagnitude.

Chart 5. Red: point mobility at d.o.f. 52.Green/Magenta: excitation at d.o.f. 52 -R,

measure at d.o.f. 52 –Y/73 –R

THEORETICAL AND EXPERIMENTAL RESULTS CORRELATION

Wheel Hub

Error (%) TMA EMA (Vibro-meter) EMA (Accelerometers)Mode Vibro-meter Accel. Freq. (Hz) Freq. (Hz) Damping (%) Freq. (Hz) Damping (%)1 2,83 3,48 2263,3 2201,10 0,15 2187,20 0,242 2,65 2,79 2277,6 2218,68 0,05 2215,70 0,133 3,65 3,49 3707,6 3577,02 0,19 3582,53 0,224 4,33 4,37 4200,4 4026,02 0,04 4024,35 0,075 4,22 4,27 4282,1 4108,57 0,03 4106,85 0,126 3,11 3,20 4548,2 4411,06 0,07 4407,09 0,09

Chart 6. Theoretical and experimental result correlation

Axle Housing and Bearing

Theoretical Modal Analysis Experimental Modal AnalysisMode Error (%) Frequency (Hz) Frequency (Hz) Damping (%)1st bending, XZ 12,30 114,87 102,29 0,951st bending, XY 5,27 185,44 176,15 0,692nd bending, XY 5,92 373,37 352,51 2,102nd bending, XZ 0,13 444,12 444,72 3,97

1st torsion X 0,43 559,12 561,52 1,58Axial X 3,31 616,43 596,66 1,47

2nd torsion X 0,81 751,32 745,3 1Chart 7. Theoretical and experimental result correlation

Axle Housing and Wheel End

Theoretical Modal Analysis Experimental Modal AnalysisMode Error (%) Frequency (Hz) Frequency (Hz) Damping (%)1st bending, XZ 16,32 92,25 79,31 3,931st bending, XY 2,30 144,65 141,42 2,822nd bending, XY 1,90 327,78 321,74 3,412nd bending, XZ 2,31 372,78 381,61 3,84

Axial X - - 495,65 1,951st torsion X 0,17 553,31 554,24 1,982nd torsion X 0,98 757,08 749,72 0,95

Chart 8. Theoretical and experimental result correlation

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It is concluded that correlation for the assembly models is worse than that for the Wheel Hub.At low frequencies, the influence of the mass is very important. For assembly models, the firstbending mode in XZ is the mode that has worst correlation. This would mean that there issome mass that in the plane XZ that has not properly been modelled. For example, thelongitudinal weld that joints both half housing to conform the housing body has not beenmodelled. In regards to the support of the structures with rubber bands it is concluded that itsflexibility in Y direction is appropriate since modes at XY plane are correctly adjusted.

MODAL CHARACTERIZATION OF AXLE HOUSING AND WHEEL END SET

Model 1

This model (Figure 8) corresponds to the firstapproach. It simulates the rollers of the bearingby spring elements (COMBIN14) joining thebearing cone and cup. This model does notrestrict torsion rotation. A sensibility analysishas been carried out (Chart 9) to study theinfluence of the spring parameter K in the modespredicted.

It is concluded that the stiffness of the elementhas no effect in the modes of the model in 104-108N/mm variation range. This model predictsbending and axial specific modes related to thewheel hubs that have not been experimentallyadjusted, and does not include axial mode for theoverall set.

0,9

0,95

1

1,05

1,1

1,15

1,2

0,00E+00 1,00E+06 2,00E+06 3,00E+06 4,00E+06 5,00E+06

1º bending, XZ1º bending XY2º bending, XY2º bending XZ1º torsion X2º torsion XNull Error

Chart 9. Correlation error vs. springelement K parameter (N/mm)

Figure 3. Bearing Figure 8. Model 1 Figure 9. Model 2 Figure 10. Model 3

Model 2

In order to overcome the limitations of the previous model, a second model is considered(Figure 9). In this case, the rollers of the bearing are simulated by beam elements (BEAM4).This model does not restrict torsion rotation.

Modes calculated do not include specific bending and axial modes related to the wheel hubs,and moreover include complete axial mode. It is demonstrated that the influence of the Youngmodulus stiffness E in the range 210-210·105 GPa does not affect natural frequencies. Fromthis, it is follows that this model represents correctly the bending behaviour of real model andit is defined E=210GPa for beam elements to simulate steel rollers.

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Model 3

This model (Figure 10) is based on previous Model 2, but includes beam elements (Green)joining different rows of rollers (Magenta) to represent torsion restriction. The stiffness intorsion is adjusted by the Young modulus of the elements. For bending beam elements,E=210Gpa is adopted as concluded in Model 2.

Bending behaviour:

Finite Elements Model Modo 1: 1st bending XZ:92,08 Hz

Modo 2: 1st bending XY:144,51 Hz

Modo 3: 2nd bending XY:329,72 Hz

Modo 4: 2nd bending XY:375,18 Hz

Modo 5: axial X: 507,59 Hz

Modo 6: 3th bending XZ:664,03 Hz

Modo 7: 3 th bending XY:693,17 Hz

Modo 8: 4 th bending XY:767,18 Hz

Figure 11. Bending modes for Model 3

Torsion behaviour:

As torsion stiffness E varies, number oftorsion modes vary from 2 to 4 (Chart10):

Modes C and D are first and secondtorsion modes associated to axlehousing.

Modes A and B are torsion modesassociated to wheel hubs.

Natural frequencies of modes also vary(Chart 10), and coupling betweensubstructures changes (Figure 12).

0,000

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

1000,000

1,0E-08 1,0E-05 1,0E-02 1,0E+01 1,0E+04 1,0E+07 1,0E+10 1,0E+13 1,0E+16 1,0E+19

Mode AMode BMode CMode D

Chart 10. Natural frequencies of torsion modes asfunction of torsion stiffnes E (Mpa).

This implies that the axle housing participates in the torsion modes of the wheel hubs andvoiceovers. Three regions can be defined in the chart 10: torsion free zone, intermediate zone,and torsion rigid zone. For low values of E, modes A and B are solid rigid modes, but as Eincreases, the frequency of these modes, like for modes C and D, increase.

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ModoE=2,10 Gpa

Axial rotation free joint

E=1.155 Gpa

Intermediate situation

E=210·105Gpa

Axial rotation rigid joint

A

14,932 Hz 239,192 Hz 302,608 Hz

B

17,269 Hz 304,217 Hz 454,415 Hz

C

555,401 Hz 635,042 Hz 773,268 Hz

D

756,728 Hz 804,154 Hz 923,97 Hz

Figure 12. Torsion modes for Model 3 as function of torsion stiffness E

In order to define completely this model, it is necessary to adjust the torsion stiffness E. In theexperimental modal analysis, torsion modes of the overall model were adjusted at 554,24 Hzthe first torsion mode and 749,72Hz the second one. These modes correspond to modes C andD respectively. Modes A and B were not detected in the tests performed. Even if excitationd.o.f. used are not suitable to excite these modes, in 300-450Hz range no torsion modes weredetected experimentally in the FRFs measured in the axle housing d.o.f. as it wouldcorrespond for modes A and B if the torsion joint was rigid and there was complete coupling.Therefore, values of E within torsion rigid region are rejected.

However, to define the value of E, it is necessary to adjust modes A and B since for the abovementioned adjusted frequencies of modes C and D, frequencies of modes A and B varywidely. So that, to excite specifically torsion modes related to the hubs and to the axlehousing, different tests have been made hitting in the Wheel Hubs and also in the AxleHousing Brake Flanges. It is noticed that:

When it is excited in the Wheel Hub, torsion modes A and B related to the Hubs seem tobe present in 30Hz and 50Hz in FRFs measured in the Hub. In FRFs measured in the AxleHousing it can also be perceived that vibration modes at these frequencies could bepresent. Modes C and D related to the axle housing have small amplitude in the axlehousing, and can hardly be detected in the hubs (see Chart 11 and 12).

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Chart 11. Excitation at d.o.f. 1, rotationmovement Z. Measures in all points rotationmovement Z: red(1), magenta(2), green(3),

grey(4), blue(5) and pink(6)

Chart 12. Excitation at d.o.f. 1, rotationmovement Z. Measures in points 1 (red) and 2(blue) rotation movement Z. Test at 0-400Hz

When it is excited in the Axle Housing,torsion modes C and D related to the AxleHousing are enhanced in both the Hubsand Axle Housing. However, modes Aand B have small amplitude in the FRFsmeasured in the Hubs and can not bedistinguished from the FRFs measured inthe Axle Housing (see Chart 13).

From Chart 10, considering that naturalfrequencies for modes A and B are 30 and50Hz, it can be deduced that E=13,5Gpain order to get average same error in bothA and B modes (see Chart 14).

Chart 13. Excitation at d.o.f. 2, rotationmovement Z. Measures in all points rotationmovement Z: red(1), magenta(2), green(3),

grey(4), blue(5) and pink(6)

y = 4E-05x3 - 0,0169x2 + 2,3248x + 12,461R2 = 1

y = 4E-05x3 - 0,0147x2 + 2,0063x + 10,783R2 = 1

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Mode A

Mode B

Chart 14. Frequencies of modes A (red) and B (black) vs E (GPa).

CONCLUSIONS

A finite element model has been proposed to simulate the joint between the Axle Housing andthe Wheel End by modelling rollers as beam elements with E=210Gpa, and considering thatthere is a torsion coupling between rollers rows with beam elements with E=13.5Gpa. This

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model is suitable to represent dynamic behaviour of Axle Housing and Wheel End set atfrequencies from 0 to 800Hz.

Finite element model has been validated by experimental modal analysis, and correlationerror obtained is assumed to be acceptable. Theoretical analyses have been repeated includingexperimentally adjusted damping values, and no differences have been obtained in frequencyvalues.

Supporting of structures with flexible rubbers does not introduce considerable error inexperimental modes. It would be interesting to study furthermore possible non-linearityphenomena in order to conclude the accuracy of hammer impact excitation technique.For a reliable model it would be convenient to validate it for different Axle sizes and thereforedifferent Bearing Pack sizes. Other steps could be to include other Wheel End components inthe overall assembly.