European Test Blanket Modules (TBMs) are attached to radiation shields through mechanical joints. The structural integrity of the joints must be ensured under non-periodic dynamic loading caused by accidental electro- magnetic events. This requires the transient dynamic analysis of the TBM- Joint-Shield under multiple loading scenarios. As temperatures and dynamic characteristics of the TBM-Joint-Shield system are updated under the course of the ITER project, the design process of the joints can become very time- consuming. This work presents a methodology based on a response spectrum to simplify the design process of the joint under electromagnetic loads. The mechanical system TBM-Joint-Shield was modeled as a single degree of free- dom lumped spring-mass-dashpot system. The dynamic ampli cation was determined for a wide range of frequencies using the Finite Element Method. Eventually, a design envelope for each loading category was obtained, which can be readily used for determining the dynamic ampli cation factor of any potential new design of the TBM + Joint + Shield system. Results showed that HCLL undergoes higher loads than HCPB, resulting in a dynamic am- pli cation factor which varies from 1.25 to 2.0 for a damping of 4%. Keywords: Test Blanket Module, Electromagnetic Loads, Finite Element Analysis, Email address: fjcalvo@idom.com (Francisco J. Calvo) Preprint submitted to Fusion Design and Engineering September 22, 2017 Figure 1: Detail of the TBM-Joint-Shield system. HCLL TBMSHIELD radialtoroidal poloidalJOINTSCLAMPED TO THE PORT PLUG FRAMEFIRST WALL Response Spectrum 1. Introduction European Test Blanket Modules (TBMs) are being developed with the aim of testing two tritium breeder blanket concepts in ITER: the helium- cooled lithium-lead (HCLL), which uses the liquid Pb-16Li as both breeder and neutron multiplier, and the helium-cooled pebble-bed (HCPB) with lithium orthosilicate ceramic pebbles as breeder and beryllium pebbles as neutron multiplier [1]. TBMs will be located inside the equatorial port 16 for testing purposes. The front part is a plasma facing surface ( rst wall) and consequently, will be exposed to extreme conditions of temperature and radiation. A neutronic shield, mainly composed of stainless steel and water, is placed behind each TBM to provide protection against fusion plasma neutron ux and gamma radiation. The rear side of the shield is clamped to the port plug frame, whereas the opposite side is attached to the TBM through a metallic joint. The TBM-Joint-Shield system behaves then like a cantilever beam clamped at the rear side of the shield (Fig. 1). The Joint is particularly critical from the structural standpoint, as it must be capable of withstanding three main loads: (i) the weight of the TBM, (ii) thermal stresses due to the temperature di erence that arises between the two plates connected during plasma operation and outgassing; and (iii) the accidental electromagnetic (EM) loads. 2 The traditional approach to analyze the joint is to generate a detailed 3D Finite Element (FE) and perform a transient dynamic analysis of the TBM- Joint-Shield system. However, the design of the TBMs is still in progress, which makes such procedure una ordable because every design modi cation of the TBM would entail the generation of a new 3D FE model and recalcu- lation of the joint for every EM load. A response spectrum based methodology is proposed here to simplify the analysis of the TBM-Joint-Shield system under transient dynamic non- periodic loading caused by EM loads. The methodology is valid for any mechanical system analogous to a single degree of freedom lumped spring- mass-dashpot system undergoing that speci c dynamic loading, regardless of the values of mass and sti ness of the system. 2. Methodology The TBM-Joint-Shield has been modeled as a single degree of freedom lumped spring-mass-dashpot model, where the TBM and the Joint contribute to the rotational inertia and the rotational sti ness, respectively. The shield is not modeled explicitly, as it is considered perfectly rigid and clamped. The TBM-Joint-Shield may be subjected to the 15 time-dependent EM loads collected in Table (8 for HCLL and 7 for HCPB), where the category refers to the likelihood of occurrence de ned by IO. Loads can be resolved into toroidal, vertical and radial components. As shown in Figure 2, toroidal and vertical forces are negligible, whereas the radial force works in tension, which may have a favorable e ect; likewise, as indicated in Figure 3, toroidal and vertical moments are much smaller than the radial moment. Hence, the radial moment (i.e. twisting moment) has been the only load component considered in the analysis. As EM loads are non-periodic and suddenly applied (time duration of ap- proximately 50 ms), the equation of motion of the TBM-Joint-Shield system has been solved numerically using the Finite Element Method. The main output of simulations is the reaction to the input load. The Dynamic Ampli cation Factor (DAF) is an indicator of how much the dynamic response of the system is ampli ed. It was determined as the ratio of the maximum reaction Mdynamic and the maximum input moment Mstatic in the radial direction, equation (1). DAF =Mdynamic Mstatic(1) 3 Figure 2: Resultant forces acting on the HCLL due to a magnetic disruption event of category II. Note that radial force Fx separates the TBM from the Shield. -300-250-200-150-100-50 0 50 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4(x 103) MD_DW_ exp16ms_ catII_ with_ HCPBForce (N) Time (s)HCLL TBM - TOTAL F ORCES FX RADIA FY TOROI FZ VERTI Figure 3: Radial, Toroidal and Vertical moments acting at the center of gravity of HCLL during MD DW exp16ms CatII with HCPB 316LN loading. -50 0 50 100 150 200 250 300 350 400 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4(x 103) MD_DW_ exp16ms_ catII_ with_ HCPBMoment (N⋅ m) Time (s)HCLL TBM - TOTAL M OMENTS MX RADIA MY TOROI MZ VERTI 4 For no ampli cation, the value of DAF is 1. This procedure was repeated for a wide range of frequencies spanning from 0 to 500 Hz of each EM load and considering two values of damping separately: 4% and no damping. A total of 15,000 simulations were conducted. The process was parametrized using python scripts. After that, the DAF were grouped by EM load categories I&II, III and IV. Note that categories I&II were included in the same group because they are assigned the same structural service level (Level A). An envelope curve of the maximum DAF values for each category was generated afterwards. Each envelope represents the TBM response spectrum for accidental EM loads. The spectrum is used for structural analysis under transient EM loads in the same way as response spectra are used for seismic analysis. This curve will be called Dynamic Ampli cation Factor Envelope (DAFE). Given the natural frequency of our system, the design moment Mdesign can be readily determined by using the DAFE of that speci c EM load, equation (2). Mcategory design =Mstaticmax(DAF ) (2) In summary, the procedure of determination of the design moment is the following: Calculate the reactions of the simpli ed TBM-Joint-Shield model to each EM loading scenario. Calculate DAF for each frequency, EM load and damping value of in- terest. Group DAF by categories and plot the envelope curve. Given the natural frequency of the system, make use of the envelope curve to calculate the design moment. Validate the structural integrity of the system by using the design mo- ment. 5 Figure 4: Schematic of the lumped mass-spring-dashpot system clamped at one side and subjected to a time-dependent load on the other side. /BW/CP/D7/CW/D4 /D3/D8 /CT/D0/CT/D1/CT/D2 /D8/CC/CW/CX/D2 /D4/D0/CP/D8/CT/D7 /CP/D8/D8/CP /CW/D1/CT/D2 /D8 /CC/BU/C5/CB/CW/CX/CT/D0/CS /CC/BU/C5 /CZ /B4/D8/D3/D6/D7/CX/D3/D2/CP/D0 /D7/D8/CX/AR/D2/CT/D7/D7/B5/CB/D4/D6/CX/D2/CV /CT/D0/CT/D1/CT/D2 /D8 /C1 /B4/D6/D3/D8/CP/D8/CX/D3/D2/CP/D0 /CX/D2/CT/D6/D8/CX/CP/B5/C5/CP/D7/D7 /CT/D0/CT/D1/CT/D2 /D8 /BV/D0/CP/D1/D4 /B4/CS/CP/D1/D4/CX/D2/CV/B5/BY/B4/D8/B5 /CC/C1/C5/BX /B4/D7/B5/CU/D6/D3/D1 /BX/C5 /D0/D3/CP/CS/D7 /CC /DB/CX/D7/D8/CX/D2/CV /D1/D3/D1/CT/D2 /D8 /C5/CG/CN/CA/BT/BW/C1/BT/C5/C7/C5/BX/C6/CC /B4/C6 · /D1/B5 3. Description of the Finite Element Model 3.1. Modeling approach A Finite Element (FE) model of the TBM-Joint-Shield system was cre- ated in the nite element software Abaqus Standard 6.13. The FE model aims at calculating the reaction forces of the TBM-Joint-Shield system due to the dynamic application of EM loads. The FE model includes three Abaqus elements: mass, spring2 and dash- pot2, which represent the rotational inertia of the TBM, the torsional sti ness of the joint and the damping of the system, respectively. The dashpot and the spring are clamped on one side and attached to the mass on the other side. This system has only 1 dof, and is subject to the time-dependent radial moment of the EM loads included in Table 1. The model is illustrated in Figure 4. To get equally spaced values of the natural frequency fn, mass was kept constant, whereas the sti ness was varied according to equation (3): fn=1 2r K I(3) whereKis the torsional sti ness of the joint and Ithe rotational inertia of the TBM around the radial axis [2]. 6 Table 1: Load cases analyzed separately for HCLL and HCPB Category EM load I md dwexp22ms II vde dwlin36ms mddwexp16ms mddwexp16ms with hcpb 316ln1 III vde upexp16ms vdedown exp16ms vdedown lin36ms IV md upslow fast 1This load case is only applied to HCLL Likewise, the damping ratio was kept constant for each natural fre- quencyfn. The damping parameter cwas modi ed for each input le ac- cording to equation (4). c= 4If (4) 3.2. Solver and time integration A direct-integration transient dynamic analysis was conducted for each EM load. The solver uses the implicit Hilber-Hughes-Taylor time operator, which has the advantage of being unconditionally stable for linear systems while keeping at a minimum the amount of numerical damping [3]. The time integration dtwas determined from a sensitive numerical anal- ysis in which the reaction force history was plotted for decreasing values of dtuntil the outcome does not change. The time integration selected was dt= 0:0001s(Figure 5). 3.3. Torsional natural frequencies of HCLL and HCPB The natural frequencies of the HCLL and the HCPB are required to ob- tain the dynamic ampli cation factor and, subsequently, the design moment. They were previously determined in a detailed 3D FE model. As indicated in Figure 6, results showed that the rst torsional natural frequencies corre- sponding to HCLL and HCPB are 64 Hz and 96 Hz, respectively. 7 Figure 5: In uence of the time increment on the reactions of the TBM-Joint-Shield system against the EM load MD DW exp16ms catII 0100200300400 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38MD_DW_exp_16ms_c at II 64 Hz Undamped(x103)T wisting Moment (N⋅ m) Time (s)Inﬂuence of time inc rement -dt- during d ynamic Finite Eleme nt Analysis dt=1x10-1 s dt=1x10-2 s dt=1x10-3 s dt=1x10-4 s dt=1x10-5 s (a) HCPB (96 Hz) (b) HCLL (64 Hz) Figure 6: First torsional modes of TBMs viewed from plasma. 8 Figure 7: In uence of damping on the dynamic response at a frequency of 96 Hz. Only the relevant time interval is displayed. 0100200300400 0.26 0.28 0.3 0.32 0.34 0.36 0.38(x103)T wisting Moment (N⋅ m) Time (s)Inﬂuence of damping on the dynamic resp onse - MD_DW_exp_ 16ms_cat II (96 Hz) EM load Reaction (undamped ) Reaction (damping 4 %) 4. Results and discussion 4.1. Dynamic response of the system As shown in Figure 7, the TBM-Joint-Shield system ampli es the input EM load. As expected, damping attenuates progressively the oscillations. The maximum value of each EM load and the corresponding reactions are depicted in Figure 8. Values were obtained with a damping of 4% and for frequencies of 64 Hz and 96 Hz, which correspond to the rst torsional natural frequencies of the HCLL and HCPB, respectively. Interestingly, ra- dial moments are much higher in HCLL than in HCPB due to the presence of the PbLi in the HCLL. The highest EM load acting on the HCLL cor- responds to the EM load MD DW exp16ms CatII with HCPB 316LN (Fig- ure 8), whereas in the case of HCPB the highest input corresponds to the MDDW exp16ms CatII. It is worth noting that, as the dynamic ampli - cation depends on the frequency content of the input load and the dynamic characteristics of the TBM-Joint-Shield system, the highest input load acting on the HCLL does not lead to the highest reaction. 9 Figure 8: Input radial moment and corresponding ampli ed dynamic reaction. HCLL is subjected to higher moments than HCPB. 050100150200250300350400450500Maximum twisting moment (N ∙m)Static Moment (HCPB) Dynamic Moment (HCPB) Static Moment (HCLL) Dynamic Moment (HCLL)(×103) 4.2. Dynamic Ampli cation Factor Envelope The DAFE of the EM loads corresponding to the HCPB and category III is shown in Figure 9. The curve is plotted by joining the maximum values of the DAF generated for each EM load of this category. By using an envelope curve, this design approach becomes more conservative, because the design moment is always equal or higher than the resultant reaction. For example, although the DAF obtained for the EM load MD DW exp16ms CatII at 96 Hz was lower than that of the VDE DW lin36ms CatII(1.25vs1.80), the design moment was calculated from equation 3 with the highest value (1.80). The DAFE corresponding to HCLL and HCPB are depicted in Figures 10 and 11, respectively. The maximum ampli cation occurs in both cases for the Category III, with a value approximately equal to 1.8 for the HCPB case. The DAF corresponding to categories I&II of EM loads acting on HCLL and HCPB are compared in Figure 12, revealing that the response of the HCPB is more ampli ed than that of the HCLL. Moreover, as expected, it is shown that ampli cation is higher when the system is undamped. 10 Figure 9: Generation of Dynamic Ampli cation Factor Envelope curve from DAF curves of category III (HCPB). 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0 50 100 150 200 250 300 350 400 450 500HCPB (96 Hz)HCPB (96 Hz)Dynamic Ampliﬁcati on Factor Frequency (Hz)Category III - dampin g 4% VDE_UP_exp16ms_C atIII_HCPB VDE_DW_exp16ms_C atIII_HCPB VDE_DW_lin36ms_Ca tIII_HCPB ENVELOPE Figure 10: Dynamic Ampli cation Factor envelopes of HCLL for all categories. 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0 50 100 150 200 250 300 350 400 450 500HCLL (64 Hz)HCLL (64 Hz)Dynamic Ampliﬁcati on Factor Frequency (Hz)Dynamic Ampliﬁcati on Factor Envelopes of HCLL (damping 4 %) Categories I and II Category III Category IV 11 Figure 11: Dynamic Ampli cation Factor envelope of HCPB for all categories. 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0 50 100 150 200 250 300 350 400 450 500HCPB (96 Hz)HCPB (96 Hz)Dynamic Ampliﬁcati on Factor Frequency (Hz)Dynamic Ampliﬁcati on Factor Envelopes of HCPB (damping 4 %) Categories I and II Category III Category IV Figure 12: Dynamic Ampli cation Factor envelope of HCLL and HCPB for category I&II. Damped and undamped values are compared. 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0 50 100 150 200 250 300 350 400 450 500HCLL (64 Hz)HCLL (64 Hz) HCPB (96 Hz)HCPB (96 Hz)Dynamic Ampliﬁcati on Factor Frequency (Hz)Envelope categories I & II - Inﬂuence of d amping HCLL damped 4% HCLL undamped HCPB damped 4% HCPB undamped 12 5. Conclusions A response spectrum based methodology has been presented to simplify the dynamic analysis of the TBM-Joint-Shield system under EM loads. Re- sults show that values of the dynamic ampli cation factor range from 1.25 to 2.0. It can be concluded that HCLL is more critical than HCPB from the Joint prospective. In particular, the design driver of the Joints is the EM load MD DW 16ms CatII with HCPB 316LN.