F2004F461 AXLE HOUSING AND UNITIZE BEARING PACK SET MODAL CHARACTERISATION 1 Badiola, Virginia*, 2 Pintor, Jesús María, 3 Gainza, Gorka 1 Dana Equipamientos S.A., España, 2 Universidad Pública de Navarra, Dpto. Ingeniería Mecánica, Energética y de Materiales, España, 3 Centro de Innovación Tecnológica de Automoción 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 is attempted to represent dynamic behaviour of the set as a whole. Axle Housing and Wheel End subsets are modal analysed. FEA models are shown and justified, and validity of the models is proved by correlation with experimental results. Different models are studied for modelling the joint between the Axle Housing and the Wheel End and a model is proposed. Finally, the limitations 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 to Ansys. Since in modal analysis the mass of the model plays an important role, it is necessary to work with the whole model. Due to this, several simplifications have been made in the geometrical model in order to minimise the computational cost. Models analysed are the Wheel 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 instrumented hammer. Output is measured in terms of acceleration by piezoelectric accelerometers fixed to the structure with magnetic parts. In the case of the Wheel Hub, the modal analysis has also been 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 minimum interference of the fastening in the lowest vibration mode, rubbers have been placed in the nodes 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 and the Wheel End by modelling rollers as beam elements with E=210Gpa, and considering that there is a torsion coupling between rollers rows with beam elements with E=13.5Gpa. This model is suitable to represent dynamic behaviour of Axle Housing and Wheel End set, has been validated by experimental modal analysis, and correlation error obtained is assumed to be acceptable. Theoretical analyses have been repeated including experimentally adjusted damping 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. The Differential Head transmits the torque from the motor to the wheels by rotating it at 90º. The Axle Housing is the structural part that supports both the Diff. Head and the Wheel End. The Wheel End transmits the torque coming from the Diff. Head to the Wheels. -1/11-
The Wheel End is made of the Wheel Hub, a Bearing Pack, a Self-Locking Nut, a Disc or Rotor and a Disc Brake (Stator). See figure 2. A bolted joint transmits the driving torque through an Axle Shaft to the Wheel Hub. The Hub lies on the Bearing Pack, and it is bolted to the Disc. The Disc Brake is bolted to the Axle Housing. A Self-Locking Nut prevents axial movement 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 Bearing Pack. 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 are developed through Pro Engineer and are exported as IGES files to Ansys. Since in modal analysis the mass of the model plays an important role, it is necessary to work with the whole model. Due to this, several simplifications have been made in the geometrical model in order to 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/m 3 and Young Modulus of 210Gpa. Elements are: SOLID92, BEAM4 infinitely rigid of section 1x1mm 2 (roller simulation in the cup and cone joint of the bearing in the Axle Housing and Bearing set), and COMBIN14 rigid (roller simulation in the cup and cone joint of the bearing in the Axle 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 Axle Housing 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 Hz Figure 4. Wheel Hub FEA results -2/11-
1: 1 st bending XZ: 114,87Hz 2: 1 st bending XY: 185,44Hz 3: 2 nd bending XY: 373,37Hz 4: 2 nd bending XZ: 444,12Hz 5: 1 st Torsión X: 559,21Hz 6: Axial: 615,43Hz Figure 5. Axle Housing and Bearing FEA results Additionally, the following modes have been calculated: the first two modes correspond to the rigid solid modes relating to the Bearing Cups. The next couple of modes correspond to specific modes associated with Brake Flanges. Rigid solid mode. Bearing Packs left/right 787,83 Hz. Bending XY related to brake flanges Figure 6. Solid rigid modes in torsion and local modes 817,29 Hz. Bending XY related to brake flanges 1: 1 st bending XZ: 92,25Hz 2: 1 st bending XY: 144,65Hz 3: 2 nd bending XY: 327,78Hz 4: Axial mode in X, hubs moving in phase: 363,07Hz 5: 2 nd bending XZ: 372,78Hz 6: Axial mode in X, hubs moving in phase: 481,22Hz 7:1 st torsión X: 553,31Hz 8: 3 th 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: 2 nd torsión X: 757,08Hz 14: local bending: 823,89Hz 15: local bending: 830,94Hz Figure 7. Axle Housing and Wheel End FEA results -3/11-
In this case, local modes of the Brake flanges have also been predicted. Furthermore, local modes relating to that of Wheel Hubs as 2 d.o.f system. It must bear in mind that this model corresponds 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 in terms of acceleration by piezoelectric accelerometers fixed to the structure with magnetic parts. In the case of the Wheel Hub, the modal analysis has also been 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 minimum interference of the fastening in the lowest vibration mode, rubbers have been placed in the nodes of the mode and perpendicular to the direction of vibration. It is known that for these types of structures main modes are within a frequency 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 higher rigidity. However experimental modal analysis is done to validate the FEA model. The global FRF obtained and modes adjusted are shown below. All modes are contained in ZY plane, and description is analogous to theoretical modes. Axle Housing and Bearing Mode Damping (%) Frequency (Hz) 1 0,24% 2187,20 2 0,13% 2215,70 3 0,22% 3582,53 4 0,07% 4024,35 5 0,12% 4106,85 6 0,09% 4407,09 Chart 1. Experimental results for Wheel Hub 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 obtained and modes adjusted are shown below (Chart 2). Mode Description Damping (%) Freq (Hz) 1 1 st bending, XZ 0,95% 102,29 2 1 st bending, XY 0,60% 176,15 3 2 nd bending, XY 2,10% 352,51 4 2 nd bending, XZ 3,97% 444,72 5 1 st torsion 1,58% 561,52 6 Axial X 1,47% 596,66 7 2 nd torsion X 1% 745,3 Chart 2. Experimental results for Axle Housing and Bearing set. -4/11-
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). Linearity Mode Description Damping (%) Freq (Hz) 1 1 st bending, XZ 3,93% 79,31 2 1 st bending, XY 2,82% 141,42 3 2 nd bending, XY 3,41% 321,74 4 2 nd bending, XZ 3,84% 381,61 5 Axial X 1,95% 485,65 6 1 st torsión 1,98% 554,24 7 2 nd torsión X 0,95% 749,72 Chart 3. Experimental results for Axle Housing and Wheel End set Experimental analysis is based on the assumption that all components are linear. However, as joints (welded parts, interference adjustment ) exist between components it must be checked that the whole system is linear. The hypothesis of linearity means that transference matrix is symmetrical as consequence of the reciprocity principle. Several test are performed to check linearity, 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) and the housing body (d.o.f. 24). This behaviour suggests that the damping of the system, or at least part of it, is due to a non-lineal phenomena of Coulomb friction that is characterised by non lineal dependence of FRF amplitude with excitation magnitude. -5/11-
In the second test, there is no amplitude difference between signals. Even if this effect can be by the symmetry of the d.o.f. considered, it is concluded that there is higher linearity in this second case. In addition to this, it has been observed (Chart 5) that in some of the FRFs there is a difference in natural frequencies. This phenomena is present in structures that are slightly nonlineal due to a non linear rigidity (cubic, for example) and is characterised by depedence of modes frequency with excitation magnitude. 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 Mode Error (%) TMA EMA (Vibro-meter) EMA (Accelerometers) Vibro-meter Accel. Freq. (Hz) Freq. (Hz) Damping (%) Freq. (Hz) Damping (%) 1 2,83 3,48 2263,3 2201,10 0,15 2187,20 0,24 2 2,65 2,79 2277,6 2218,68 0,05 2215,70 0,13 3 3,65 3,49 3707,6 3577,02 0,19 3582,53 0,22 4 4,33 4,37 4200,4 4026,02 0,04 4024,35 0,07 5 4,22 4,27 4282,1 4108,57 0,03 4106,85 0,12 6 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 Mode Error (%) Theoretical Modal Analysis Experimental Modal Analysis Frequency (Hz) Frequency (Hz) Damping (%) 1 st bending, XZ 12,30 114,87 102,29 0,95 1 st bending, XY 5,27 185,44 176,15 0,69 2 nd bending, XY 5,92 373,37 352,51 2,10 2 nd bending, XZ 0,13 444,12 444,72 3,97 1 st torsion X 0,43 559,12 561,52 1,58 Axial X 3,31 616,43 596,66 1,47 2 nd torsion X 0,81 751,32 745,3 1 Chart 7. Theoretical and experimental result correlation Axle Housing and Wheel End Mode Error (%) Theoretical Modal Analysis Experimental Modal Analysis Frequency (Hz) Frequency (Hz) Damping (%) 1 st bending, XZ 16,32 92,25 79,31 3,93 1 st bending, XY 2,30 144,65 141,42 2,82 2 nd bending, XY 1,90 327,78 321,74 3,41 2 nd bending, XZ 2,31 372,78 381,61 3,84 Axial X - - 495,65 1,95 1 st torsion X 0,17 553,31 554,24 1,98 2 nd torsion X 0,98 757,08 749,72 0,95 Chart 8. Theoretical and experimental result correlation -6/11-
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 first bending mode in XZ is the mode that has worst correlation. This would mean that there is some mass that in the plane XZ that has not properly been modelled. For example, the longitudinal weld that joints both half housing to conform the housing body has not been modelled. In regards to the support of the structures with rubber bands it is concluded that its flexibility 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 first approach. It simulates the rollers of the bearing by spring elements (COMBIN14) joining the bearing cone and cup. This model does not restrict torsion rotation. A sensibility analysis has been carried out (Chart 9) to study the influence of the spring parameter K in the modes predicted. 1,2 1,15 1,1 1,05 1 1º bending, XZ 1º bending XY 2º bending, XY 2º bending XZ 1º torsion X 2º torsion X Null Error It is concluded that the stiffness of the element has no effect in the modes of the model in 10 4-10 8 N/mm variation range. This model predicts bending and axial specific modes related to the wheel hubs that have not been experimentally adjusted, and does not include axial mode for the overall set. 0,95 0,9 0,00E+00 1,00E+06 2,00E+06 3,00E+06 4,00E+06 5,00E+06 Chart 9. Correlation error vs. spring element 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 Young modulus stiffness E in the range 210-210 10 5 GPa does not affect natural frequencies. From this, it is follows that this model represents correctly the bending behaviour of real model and it is defined E=210GPa for beam elements to simulate steel rollers. -7/11-
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 in torsion 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: 1 st bending XZ: 92,08 Hz Modo 2: 1 st bending XY: 144,51 Hz Modo 3: 2 nd bending XY: 329,72 Hz Modo 4: 2 nd bending XY: 375,18 Hz Modo 5: axial X: 507,59 Hz Modo 6: 3 th bending XZ: 664,03 Hz Modo 7: 3 th bending XY: 693,17 Hz Figure 11. Bending modes for Model 3 Modo 8: 4 th bending XY: 767,18 Hz Torsion behaviour: As torsion stiffness E varies, number of torsion modes vary from 2 to 4 (Chart 10): Modes C and D are first and second torsion modes associated to axle housing. Modes A and B are torsion modes associated to wheel hubs. Natural frequencies of modes also vary (Chart 10), and coupling between substructures changes (Figure 12). 1000,000 900,000 800,000 700,000 600,000 500,000 400,000 300,000 200,000 100,000 Mode A Mode B Mode C Mode D 0,000 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 Chart 10. Natural frequencies of torsion modes as function of torsion stiffnes E (Mpa). This implies that the axle housing participates in the torsion modes of the wheel hubs and voiceovers. 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 E increases, the frequency of these modes, like for modes C and D, increase. -8/11-
Modo E=2,10 Gpa Axial rotation free joint E=1.155 Gpa Intermediate situation E=210 10 5 Gpa 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 the experimental modal analysis, torsion modes of the overall model were adjusted at 554,24 Hz the first torsion mode and 749,72Hz the second one. These modes correspond to modes C and D respectively. Modes A and B were not detected in the tests performed. Even if excitation d.o.f. used are not suitable to excite these modes, in 300-450Hz range no torsion modes were detected experimentally in the FRFs measured in the axle housing d.o.f. as it would correspond 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 above mentioned adjusted frequencies of modes C and D, frequencies of modes A and B vary widely. So that, to excite specifically torsion modes related to the hubs and to the axle housing, different tests have been made hitting in the Wheel Hubs and also in the Axle Housing Brake Flanges. It is noticed that: When it is excited in the Wheel Hub, torsion modes A and B related to the Hubs seem to be present in 30Hz and 50Hz in FRFs measured in the Hub. In FRFs measured in the Axle Housing it can also be perceived that vibration modes at these frequencies could be present. Modes C and D related to the axle housing have small amplitude in the axle housing, and can hardly be detected in the hubs (see Chart 11 and 12). -9/11-
Chart 11. Excitation at d.o.f. 1, rotation movement Z. Measures in all points rotation movement Z: red(1), magenta(2), green(3), grey(4), blue(5) and pink(6) Chart 12. Excitation at d.o.f. 1, rotation movement 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 Axle Housing are enhanced in both the Hubs and Axle Housing. However, modes A and B have small amplitude in the FRFs measured in the Hubs and can not be distinguished from the FRFs measured in the Axle Housing (see Chart 13). From Chart 10, considering that natural frequencies for modes A and B are 30 and 50Hz, it can be deduced that E=13,5Gpa in order to get average same error in both A and B modes (see Chart 14). Chart 13. Excitation at d.o.f. 2, rotation movement Z. Measures in all points rotation movement Z: red(1), magenta(2), green(3), grey(4), blue(5) and pink(6) 100 90 80 70 60 Mode B y = 4E-05x 3-0,0169x 2 + 2,3248x + 12,461 R 2 = 1 Mode A y = 4E-05x 3-0,0147x 2 + 2,0063x + 10,783 R 2 = 1 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 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 and the Wheel End by modelling rollers as beam elements with E=210Gpa, and considering that there is a torsion coupling between rollers rows with beam elements with E=13.5Gpa. This -10/11-
model is suitable to represent dynamic behaviour of Axle Housing and Wheel End set at frequencies from 0 to 800Hz. Finite element model has been validated by experimental modal analysis, and correlation error obtained is assumed to be acceptable. Theoretical analyses have been repeated including experimentally adjusted damping values, and no differences have been obtained in frequency values. Supporting of structures with flexible rubbers does not introduce considerable error in experimental modes. It would be interesting to study furthermore possible non-linearity phenomena 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 therefore different Bearing Pack sizes. Other steps could be to include other Wheel End components in the overall assembly. -11/11-