10 Applying the Transmission Simulator Techniques to the Ampair 600 Wind Turbine Testbed 107 10.2.2.1 Free-Free Modal Transmission Simulator Model The free-free modal TS model is obtained by choosing the modal matrix of the free normal modes ˚ FE as transformation matrixTFE. The motion of the TSFE is described by a linear combination of rigid body modes and elastic free normal modes, i.e. the interface of the TS is free [2]. Projecting the modal matrix of the TS on the equation of motion yields IFERqFE C Ÿ !2 r Ÿ FE qFE D ˚ FE T fFE C ˚ FE T gFE, (10.6) with ˚ FE 2RNu Nk. Nu is the number of physical DoFs and Nk corresponds to the number of kept normal modes of the TS. See [5] for more detail. Inserting Eq. (10.6) into Eq. (10.5) yields IC 0 0 I FE R qC RqFE C" Ÿ!2 r Ÿ C 0 0 Ÿ!2 r Ÿ FE# qC qFE D" ˚ C T fC ˚ FE T fFE#C" ˚ C T gC ˚ FE T gFE# (10.7) with uC uFE D" ˚ C T 0 0 ˚ FE T # qC qFE . (10.8) 10.2.2.2 Craig-Bampton Transmission Simulator Model Using a Craig-Bampton TS model, the motion of the TSFE is described by its fixed-interface normal modes and its constraint modes. For more detail on Craig-Bampton reduction the reader is referred to [5]. Choosing the Craig-Bampton transformation matrixTCB to reduce the FE model of the TS FE yields the equation of motion of the Craig-Bampton TS model, NM FE CBRp FE CB CNK FE CBp FE CB D TFE CB T fFE C TFE CB T gFE, (10.9) withTFE CB 2 RNu .NkCNc/. Nc is the number of constraint DoFs [5]. Inserting Eq. (10.9) into Eq. (10.5) gives "IC 0 0 NM FE CB# RqC RuFE CB C" Ÿ!2 r Ÿ C 0 0 NK FE CB# qC uFE CB D" ˚ C T fC TFE CB T fFE#C" ˚ C T gC TFE CB T gFE# . (10.10) with uC uFE D" ˚ C T 0 0 TFE CB T# qC uFE CB . (10.11) 10.2.3 Coupling Procedures In CMS the substructures are usually coupled at the points where they physically connect, the connection degrees of freedom in the interface [6]. In practice the connection point motion of the combined structure Cnormally is not measured. Instead, the measurements are taken at discrete points distributed on the surface of C. This requires a coupling procedure using the motion at the measured DoF rather than the motion at the connection DoF. Two different approaches are the subject of this section. In the following the subset of physical DoF in the interface of a (sub)structure is denoted with the subscript c. The subset of measurable DoF of the TS is denoted with the subscript m. It is pointed out that if the TS is part of the combined structure C, only the measurable DoF of the physical representation of the TS, TSA, are in this subset (i.e. not those of the structure of
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