146 J. Furlich et al. 5 6 7 8 9 10 11 12 Frequency, f (Hz) Imag FRF, Gxf (g/N) 5 6 7 8 9 10 11 12 Frequency, f (Hz) Real FRF, Gxf (g/N) T1:+Z/P4:+Z T1:+Z/P5:+Z T1:+Z/P6:+Z T2:+Z/P4:+Z T2:+Z/P5:+Z T2:+Z/P6:+Z Fig. 13.6 Powerplant roll mode at 9.5 Hz and 2.96% damping with uni-axial input and tri-axial response locations Table 13.2 that a coupled stiffness of roughly 100 kN m/rad is required to achieve a natural frequency of ∼1550 Hz, closer to realistic physical conditions. The resulting differential roll mode was found using a polyreference MPE algorithm with truncated results shown in Fig. 13.5. The results show the roll mode to occur at 132 Hz with 0.72% damping. The frequency of this mode is as expected but has a lower damping estimate than anticipated. The truncated FRF data shown in Fig. 13.5 shows the two sides of the shaft D5 and D7 out of phase with the other measurements at D6 and D8 as expected for a roll mode. It is possible that the mode found is in fact a torsion mode. Additional testing would be ideal to further confirm this frequency to be the roll mode and not a torsional mode of the differential, however current spatial resolution of the data has a strong indication that this frequency is in fact the differential roll mode. Like the differential modal analysis, a truncated set of FRF’s is shown in Fig. 13.6 for results of modal testing on the powerplant (combined engine and transmission). The results of polyreference MPE indicate the powerplant roll mode to be at 9.5 Hz with 2.96% damping. These values are close to what was anticipated for the powerplant roll mode and animation of the mode shapes show good indication of a roll mode as well. Additional modes such as bounce (near ∼5.5 Hz) are observed in the data set and found through MPE but are not deemed necessary for the lumped parameter vehicle model in the CAE simulation. The stationary step relaxation testing results are shown in Fig. 13.7 for both time data of the cold and hot tire tests as well as frequency content of the data. The response to a step relaxation is like that of a pluck test where it is seen that the fore-aft response of the vehicle in the X direction decays logarithmically as expected for a viscously damped system. The step-relaxation force was not captured during data acquisition, thus only output acceleration was recorded. The output data is processed with Eq. (13.1) and yields a damping value of 2.73% and 3.71% for the hot and cold tire tests respectively. This indicates that when the tire’s get warmer they become less effective at damping out fore-aft vibrations and have lower amounts of shear allowing for viscous damping. The frequency of oscillation can be found in the linear spectrum of the data, like that of an ODS. The fore-aft mode of the vehicle was found to be 1 Hz and 1.13 Hz for the cold and hot tire test’s respectively. This indicates that as the tire heat’s up either the effective stiffness increases, or the effective inertia decreases. For an elastomer, this is counter intuitive for the stiffness to increase with increasing temperature. Thus, it is understood that as the longitudinal tire stiffness decreases, the tire contact patch increases reducing the amount of coupled inertia. Also, with an increased tire contact patch there is a higher capacity for tractive force in the tire to increase the effective fore-aft stiffness.
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