Article by: Juan Jesús García, Ph.D., Product Manager, Braking Systems in Applus IDIADA
Part One of Article | Part Two of Article
In the two first parts of the article, the fundamental theory of the so-called Judder Transfer Path Analysis (JPA), and its application to the actual brake judder problem, were introduced. Finally, a case was presented – main results and conclusion will be presented herein.
We note that the results of the JPA method can be used to identify the reasons why some suspension and chassis elements might tend to amplify vibration in the vehicle body. We note that the JPA tool allows the assessment of the dominant structural points through which the vibration energy is injected or transmitted in the vehicle body.
Table 1 shows an example of how the condition number affects that relative position of the transfer paths in order of contribution after calculating the inverse matrix of the JPA. The table shows that as we modify the dimension of the JPA model in terms of the number of relevant axes for the forces and the operational accelerations, the condition number of matrix [H] changes considerably. In the case shown in Table 1, we note that the simplification of the model for the JPA based on neglecting the y and z direction of the accelerations at the targets points deteriorates de condition number and therefore, the precision of the JPA results
We observe that the condition number decreases as we increase the number of axes that we take into account for the applied forces and the operational acceleration responses in the seat rail.
Figures 9 to 11 show the JPA contribution for the vehicle under study for the target point at the seat-rail in the x-direction. We observe that the contribution through path at point 26 (see Figure 7) takes more relevance as the condition number of the FRF matrix has a lower condition number. This change of the relative contribution of the path through point 26 is shown with a blue arrow in Figures 9 to 11. The condition numbers are listed in Table 1. This reinforces the assumption that path 26 has a noticeable contribution to control judder sensitivity.
Figures 12 to 14 show the JPA contribution for the target point at the steering wheel in the x-direction. We observe the same behaviour for the partial contribution going through point 26 versus the condition number of matrix [H] (see blue arrows in Figures 12 to 14).
The results depicted in Figures 9 to 14 suggest that point 26 in the model of Figure 7 should be modified to reduce its contribution. A modification on this part of the chassis of the test vehicle was implemented, as it is shown in Figure 15, in which a supporting sub-structure of the chassis was reinforced to reduce the vibration at point 26. The modified structure (prototype) is shown on the left picture of Figure 15.
Figures 16 and 17 show the effect that the sub-chassis modification shown in Figure 15 produces on the operational judder response at the seat rail and the steering wheel of the test vehicle. We note an important reduction in the overall acceleration at the control points between 5 and 10 dB in both control points, which improves judder performance considerably.
The vibration level during judder braking has been monitored in a judder sensitive vehicle order to identify critical components that boost vibration transmission into the vehicle structure, pedal and steering wheel. Judder operational vibrations of steering wheel and the seat rail have been investigated, showing a good correlation with subjective driver ratings. The JPA tool has been applied allowing an assessment of the points at which the vibration energy is injected or transmitted in the vehicle body from the brake. In this work, the JPA results are successfully used for troubleshooting definition and the reduction of vehicle judder response.
An objective detection of vibration transmission paths and an alternative way of confirmation, based on the effect of the condition number of the FRFs matrix on the relative path contributions has been used allowing a more robust chassis design and development in terms of brake judder optimization.
Finally, the vehicle sub-chassis has been modified so that an important contributing vibration path was modified. The re-assessment of the judder performance for the modified vehicle shows an important reduction of vehicle sensitivity to judder.
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