Experimental-Analytical Dynamic Substructuring

Substructuring is the process of decomposing a structure into parts, modelling these parts separately and assembling them again. In analytical dynamic substructuring the component mode synthesis (CMS) methods such as the Craig-Bampton method have been successfully used since the 1960s, usually employed to couple analytical models, but also as reduction methods. In this content, analytical models denote models from first principles, e.g. FE models, and experimental models denote models derived from measured data, e.g. from vibration tests where models are identified by system identification. With the recently renewed interest in experimental-analytical dynamic substructuring, methods requiring less information become competitive. Frequency-based substructuring (FBS) methods have usually been used to overcome the CMS shortcomings; these suffer from numerical ill-conditioning due to noisy data and introduce difficulties in the system identification of the coupled systems, however. A state-space based synthesis method developed by Sjövall and Abrahamsson has been proposed to circumvent difficulties which exist with both CMS and FBS methods. For researchers to have a common testbed and be able to share data, the Society for Experimental Mechanics (SEM) Substructuring Focus Group have initiated a research project in experimental dynamic substructuring using the Ampair 600 wind turbine as a testbed. Previously, the blade-to-blade spread of said testbed has been quantified and a Finite Element (FE) model of the blades has been calibrated. The next step in the research project is to couple the wind turbine parts by dynamic substructuring. The blades are coupled to analytical models of their mounting brackets using both experimental and analytical models of the blades. The coupled systems are validated by vibration measurements of the blade and bracket systems. Further, three blades are coupled to the wind turbine hub, where both experimental and analytical models of the blades are used with FE models of the hub and brackets. These couplings are also validated with respect to measurements of the assembled structure. The state-space based substructuring method is focused on in this work where a quantitative and qualitative comparison with the widely used CMS and FBS methods is performed. It has been found that the state-space method is numerically unstable for higher order models, and an evaluation of these problems is performed. The state-space synthesis (SSS) method has been theoretically compared to the CMS method and the synthesis procedure translated to the general framework. From this study it can be concluded that further work with the state-space method is necessary, especially with the numerical problems encountered, but also with the relatively high demand on pre-processing of data in order to couple systems in a valid manner. For experimental-analytical coupling where experimental models satisfy Newton’s second law the state-space method has been shown to produce the same results as the FBS method. Thus, the method is very promising due to its simplicity. It has also been found that the dynamics of the coupling is of very high importance as only the low frequency modes correlated well. The spread between the blades is considerable and it is found that the blade bracket coupling correlates better for experimental models of the blades relative validation data. Inconclusive results for the hub assembly are obtained.