Similitudes and sensitivities as contributions to scaling laws in machine acoustics

• Main Author: Adams, Christian
• Format: Others
• Language: en
• Published: 2019
• Online Access: https://tuprints.ulb.tu-darmstadt.de/8726/3/Dissertation_Adams.pdf; https://tuprints.ulb.tu-darmstadt.de/8726/2/D_Digital_appendix.zip; Adams, Christian <http://tuprints.ulb.tu-darmstadt.de/view/person/Adams=3AChristian=3A=3A.html> (2019): Similitudes and sensitivities as contributions to scaling laws in machine acoustics.Darmstadt, Technische Universität, [Ph.D. Thesis]

Noise and vibration engineering faces increasing demands of customers such as noise limits or comfort issues and also requires cost-efficient and adaptable design engineering methods due to shorter product life cycles. Taking advantage of similitudes of designs can address these needs by using scaled prototypes in experimental investigations or by designing size ranges and kits. However, a reliable prognosis of noise and vibration of an original design requires scaling laws that transfer the measurement results from the scaled prototype to the original design or from one design to another one within a size range. Similitude analysis lacks efficient and straightforward methods to derive scaling laws, thus, contradicting the demand for cost-efficient design engineering methods. Furthermore, scaling laws are often limited to complete similitude conditions such as equal damping values of the scaled prototype and of the original design or perfect geometrical similitude of a size range, which are hardly fulfilled in practice. This thesis aims at developing a procedure to straightforwardly derive scaling laws of mechanical structures by combining similitude analysis with sensitivity analysis, which determines the effect of design parameters on the vibration behavior of a mechanical structure. From this, the noise and vibration behavior of mechanical structures can be predicted even if incomplete similitude conditions persist. Similitude analysis and sensitivity analysis methods are first illustrated by potential applications in noise and vibration engineering using a double mass oscillator as a comprehensible example of a mechanical structure. A new scaling method is developed that combines similitude analyses with sensitivity analyses. This allows for deriving scaling laws, which incorporate sensitivities as coefficients. The scaling laws of rectangular plates in complete similitude are directly derived from analytical and finite element calculations for global and local vibration responses such as surface-averaged frequency response functions or vibration velocities at a local receiver point. These scaling laws match those derived from state-of-the-art similitude analysis methods, which verifies the new scaling method. Applying the new scaling method to plate-like structures in complete similitude demonstrates that scaling laws can be straightforwardly derived, whereas state-of-the-art similitude analysis methods would be too time-consuming. The scaling laws derived from the new scaling method accurately predict the vibration responses of scaled structures using the vibration responses of an original structure, which are obtained from numerical calculations or experimental measurements. The new scaling method even replicates the vibration responses of structures in geometrically incomplete similitude sufficiently well by using another scaled structure, which is in complete similitude to the original structure. In order to assess the accuracy of the scaled vibration responses an error measure is developed and validated in a-posteriori analyses. Finally, a size range of gear boxes in geometrically incomplete similitude demonstrates that the natural frequencies of an entire size range can be predicted with a sufficient accuracy by the new scaling method. The new scaling method can be enhanced towards kits since the natural frequencies of the gear boxes with various lumped masses attached can be replicated sufficiently well.