Abstract
This paper presents a validation of the Blocked-Force Transfer Path Analysis (BF-TPA) method that was proposed earlier in 2009 as the Gear Noise Propagation (GNP) method. The method allows to simulate the propagation of noise and vibrations generated by a system component to responses elsewhere in the system. The total systems FRFs are needed in combination with a measurement of the system’s component on a rigid test bench. Although the method is physically correct, a rigid test bench is hard to design up to higher frequencies. Therefore a compensation method for the test bench dynamics was derived. This paper validates the BF-TPA for a vehicle steering gear with and without compensation for its test bench dynamics. In order to be successful, a technique is introduced to obtain the required Rotational DoFs and Moments on both the component test bench measurement and total system FRFs.
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- 1.
Short for Noise, Vibration and Harshness, a common designation for structural/acoustic vibration problems.
- 2.
- 3.
The compensation for test bench dynamics was already proposed in the original publication [3] using an impedance notation.
- 4.
The FRFs in Y A and Y B are measured on the separate components.
- 5.
For more information on the expression of the compatibility condition using signed boolean matrices, the reader is referred to [4].
- 6.
Note that additional excitations on the passive side can formally be included as well by defining f 3 and including it in the force vector in (4.3).
- 7.
It can be verified that (4.6) can also be obtained by development of the LM-FBS notation \({\mathbf{Y}}^{\mathrm{AB}} = \mathbf{Y} -\mathbf{Y}{\mathbf{B}}^{T}{\left (\mathbf{B}\mathbf{Y}{\mathbf{B}}^{T}\right )}^{-1}\mathbf{B}\mathbf{Y}\).
- 8.
The terms motion and loads are used when referred to the 6-DoF set of respectively displacements/rotations and forces/moments.
- 9.
This only applies to FE models containing 6-DoF nodes. A major part of the finite elements consist of 3-DoF nodes.
- 10.
Do note that the displacement vector does not necessarily have to contain virtual point transformed DoFs. As mentioned, the approximation in this section benefits from larger displacement sets and therefore the original sensor displacements are preferred here. However, this also requires the transfer path information (receptance Y) to the original sensor locations. When both the receptance and BF-TPA measurement are performed with the same set of mounted sensors, this gives no problems. In this particular case, the used receptance Y will only be virtual point transformed at the right side associated with the generalised forces/moments.
References
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Acknowledgements
This study was performed in close collaboration with the BMW Group, whom we greatly acknowledge for their support and organisation.
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van den Bosch, D.D., van der Seijs, M.V., de Klerk, D. (2014). Validation of Blocked-Force Transfer Path Analysis with Compensation for Test Bench Dynamics. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04501-6_4
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