Multiple Degree of Freedom (MDOF) excitation systems and MDOF vibration control systems continue to improve, and are now standard equipment in many dynamic test laboratories. Determination of an input specification for such MDOF systems is critically dependent on properly acquired field data. Validation of field data will be discussed and demonstrated employing the same transformation tools used in both transformation-based 6-degree-of-freedom (6-DOF) vibration control and generalized MDOF vibration specification development (VSD).

Validation Techniques for 6-DOF Vibration Data Acquisition

An in-flight airframe vibration data sample taken from a propeller driven cargo aircraft is viewed in the wavelet and frequency domains, with an emphasis on propeller blade activity. Close examination in the wavelet domain reveals a mechanism by which this activity is shared between adjacent resolution levels, with subsequent wavelet packet decomposition demonstrating alternatives with fewer basis functions.

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Propeller blade signatures in the wavelet domain

https://iopscience.iop.org/article/10.1088/1361-6501/aaba41/pdf

Validation of a method to measure the vector fidelity of triaxial vector sensors

A simplified modelling and analysis of six degree of freedom random vibration test

Reference criteria for a multiple degree-of-freedom (MDOF) random vibration test is generally provided in terms of an acceleration-based spectral density matrix (SDM). This SDM may be developed in terms of the auto-spectral densities (ASDs) and cross-spectral densities (CSDs) computed from the time histories acquired from an appropriately placed and oriented set of linear accelerometers. Such a direct measurement linear accelerometer based reference criteria will be denoted as SDMmeas. A second technique for defining a reference SDM is in terms of the accelerations associated with the six classical motion degrees-of-freedom as defined at an arbitrary point of origin. Such a reference will be denoted as SDMmotion. The objective at hand is to demonstrate the method of transforming between these two reference criteria spaces.

Spectral Density Matrix Transformations

This paper provides a comprehensive discussion on the benefits and technical challenges of controlling over-determined and over-actuated excitation systems ranging from 1-DOF to 6-DOF. The primary challenges of over-actuated systems result from the physical constraints imposed when the number of exciters exceeds the number of mechanical degree-of-freedom. This issue is less critical for electro-dynamic exciters which tend to be more compliant than servo-hydraulic exciters. To facilitate the technical challenges discussion, generalized methods for determining the drive output commands and the actuator input transform is presented. To further provide insights into the problem, over-actuated 1-DOF and 6-DOF examples are provided. Results are presented to support the discussions.

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Benefits and challenges of over-actuated excitation systems

This study outlines the experimental approach used to determine the design margin of the crystal oscillator which is used as the clock on the Digital Electronics Unit of the TOW 2A and TOW 2B missiles. The test methodology and signal analysis techniques used in the experimentally based investigation are described; the results are then compared to a separate investigation which was primarily based on an analytical and modeling approach.

TOW crystal environmental characterization and experimental design margin determination

Multiple degree of freedom (MDOF) excitation systems and MDOF vibration control systems continue to improve, and are now standard equipment in many dynamic test laboratories. This paper concentrates on the often overlooked process of determination of an input specification for such MDOF systems. A pair of generalized six-degree-of-freedom (6-DOF) vibration specification development (VSD) techniques are proposed, discussed, and illustrated through an example.

Michael T. Hale

Papers

Benefits and challenges of over-actuated excitation systems

Validation Techniques for 6-DOF Vibration Data Acquisition

Spectral Density Matrix Transformations

TOW crystal environmental characterization and experimental design margin determination

A 6-DOF Vibration Specification Development Methodology