2 Experimental Dynamic Substructuring of the Ampair Wind Turbine Test Bed 23 20 40 60 80 100 120 140 40 45 50 55 60 65 70 75 80 o o o o ooooo o o oo o oo oooooo s vs s s vsv ov s v sv osf v v fsv v vv s vs s s vss oss s v vs fvf v v osss v sv s v s s vvoos s v sv fvd v fsv v vs s v s s sv vs s vss vf v osss s s s s ov s s ss vv s vss svo v sss v ss s vs s s sv sv s vss vof s osss v v f s vs s s vss vv s v ss ovsf v vsss v sv s vs ss o vsv vov v v ss vfsf v fsss s sv s v ss v vss vss s v svo svsf v vsss s vv s s s s v vss vvs s v ssv vss v ssss s ss s ov s s o s s vsv s ssv vsf s vssos s s v s s s s vs so vvv o s o ssv svsd v sssos s s f s ov s s so sv vv v v ssv vvsf s vssv s s s s vv os s o vsvv vv vov o ssv vds v vsss v s v s vv vs s v ovsvo vvs vov v sv vsf s vssso s s v s vv vs s v vs s o vov sv v ssv svds v o vsssv s sv s vv vs s v vss v vvs vso v ssv vf s ssssv s s s s vv vs s v vss o vvs vsv vo ss ss s vsssv s s v o s vv o vs s v vss v vvo vsv v v svs svf s vsssf s s s v s vv v vs s v svss o vvs vs s f ossv svds s vsssv s s s o sovv o ovs s svss v vs vsv v sv ssof s o ssssv s sv v svvs v vvs s sss v vs ssv vo ss sof s v ssss s s s o svvv o ovs s o o vss o os vsv vv ssv ssof s v vssso s ss o svvsv vvss o vv sosv v vv vsv f osv ss s v vsssv s ss o ssvs s vvss v vv vsso vos sss vsv sso s v sssos s ss s svvs s svs os s v v osss s vs ssv oo vsvs ssf s v sssof s s v o svvv v vs sv v v v vosso vov ssv o f vss ssof o o s v vssf s s s s ssvv s vvs sv v v v svssv ov ssv vov vss sso o v s v sssos s s s o svvv s vvs sv v v s ovsss vs ssv v fv vss ssv vs s v vssvs s s s o svvs v vvs sv v v ovossv ovo ssv v fv ssvs vvs vv v v sssfs s s v o svvs v vvs sv v s vvsss vs ssv vvs vsvs vsf v v s v sssvs s s v v ssvs s vs so o v s vvsss ssv vsv vfs vss ssf vv s v ssss s s v o svvs v ss sv v v v vosss vsv ssv vvs ss ssv sv s v ssss s sv o ssvs s vvs sv v v s svsss sv vss vsv vss ss sv s v ssss s ss o svvs s vvs sv v s v svsss vov ssv vsv vss ss ov s s v vssvs s s s o svss v ssf so v v v svsss vso vsv vsv vs ssv fs v s s vssvs s s f o ssss s sds s v s s svsss ovs vsv vvs vss ssf vv s s v vssvs s s s o svvs s ssf sv f v s vsoss ovsoo ssv vsv ss ss vvs s v fsss s ss s svvs s svs sv s v s sssv vov v vsv vvs vss oss vv v s v ssss s s v o svvs v svss f s s ssoss vvsv ssv vvs ss sssvs s v ssss sss Frequency [Hz] Frequency [Hz] Model Order 4 5 6 7 8 9 10 a b |H50x,22x| 20 40 60 80 100 120 140 -2 0 2 phase(H50x,22x) Experimental Fitting Log Σ |FRF| 10−2 100 102 Fig. 2.7 Modal identification of the two bladed turbine subsystem. (a) Stabilization plot of the Poly-LSCF. (b) Identification results 10−1 10 −2 100 100 102 101 102 |H2z,2x| |H50x,22x| 20 40 60 80 100 120 140 −2 0 2 −2 0 2 Frequency [Hz] a b Frequency [Hz] phase(H2z,2x) Experimental Fitting Synthesis 20 40 60 80 100 120 140 phase(H50x,22x) Experimental Fitting Synthesis Fig. 2.8 Comparison between experimental, fitted and synthesized FRFs. (a) Mass loaded blade subsystem. (b) Two bladed turbine subsystem and an average value c can be used to find the r-th modal participation vector as: fLgr Dcf gr (2.17) Finally, the full matrix of FRFs (inertances) defined also on unmeasured DoFs can be expressed as: ŒH.i!/ D !2 n Xr D1 f gr fLg T r i! r C f g? r fLg T? r i! ? r ! (2.18) In this case, due to the complexity, to the high nonlinearity of the dynamic behavior of the system and to the lack of coherence between different measurement, it can be more convenient to select a single proportionality constant rather than to average the different proportionality constants on all the reference DoFs. For the mass loaded blade subsystem, the proportionality constant used to compute the participation vectors is the one corresponding to the reference DoF on Node 2 in x local direction. For the two bladed turbine the selected DoF used to compute the proportionality constant is the one corresponding to node 22 on the x local direction. The response synthesized according to Eq. (2.18) are reported in Fig. 2.8. Below 15 Hz, the absence of low frequency residuals, that are taken into account in the curve fitting but cannot be considered in the synthesized FRFs, produces a relevant error. Synthesized FRFs are quite reliable for frequency higher than 15 Hz.
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