20 Finite Element Model Updating of an Assembled Aero-Engine Casing 203 ⎧ ⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ σxx σyy σzz σxy σyz σxz ⎫ ⎪⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎪⎭ = ⎡ ⎢⎢ ⎢⎢ ⎢⎢ ⎢⎣ c11 c22 c33 c44 c55 c66 ⎤ ⎥⎥ ⎥⎥ ⎥⎥ ⎥⎦ ⎧ ⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ εxx εyy εzz εxy εyz εxz ⎫ ⎪⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎪⎭ (20.10) The off diagonal elements are 0 and there are only 6 parameters which represent the normal and shear stiffnesses to be identified. 20.3 Case Study: Model Updating of a Jointed Aero-Engine Casing In order to demonstrate the effectiveness of the two-step strategy for updating complex structures, a joint assembly of two aero engine casings is used. First, models of two single casings are updated individually with modal test data to reduce the possible modeling errors of each casing. Then, the assembled model of both casings with bolts is updated with emphasis on updating the joint parameters (Fig. 20.2). 20.3.1 Aero-Engine Casings and Modal Test The investigated physical casings are shown in Fig. 20.4. Both individual casings are made of two separate parts (the upper and the lower bodies) that are connected together with spot welds. Also, there are 36 identical bolt holes distributed at the flange of the casings, which are used to assemble the casings, and 4 mounting bases placed at the upper part to fix attachments. The FE model for each individual casing is developed using the ANSYS software tool. Modeling the spot weld, shown in Fig. 20.3, is the most difficult task since there are many local effects such as geometrical irregularities, residual stresses and defects due to the welding process, which are not taken into account in the FE modeling. Furthermore, the casing contains many spot welds and modeling each of them in detail would require a major computational effort. Thus, the welded regions are simplified to rigid connections. In order to save computational effort, the holes and the mounting bases are also removed from the FE model. The FE model of the rear casing is show in Fig. 20.4, and is formed using ten-noded solid elements. The model has 32,827 elements and 66,247 nodes. The Young’s modulus of the casing is 180 GPa and the mass density is 7,920kg/m3. Free-free boundary conditions were employed for the measurements by supporting the casings with elastic bands. A roving hammer test was chosen for the force excitation. Figure 20.5 shows that the optimum suspension locations of the rear casing are within the blue regions, where is not easy to suspend the structure. Hence the casing was suspended by the small flange. Figure 20.6 shows the optimum transducer locations for the rear casing. Clearly the best transducer locations are in the middle region of the casing. In order to have sufficient spatial resolution to correlate with the finite element model, a test model with 128 DOFs was established for the single casing, shown in Fig. 20.7. Two reference accelerometers were placed at orthogonal directions. The frequency range of interest is 0–1,000 Hz and the number of spectral lines was set to 3,200, which provided sufficient resolution. Fig. 20.2 The aero-engine casings. (a) Front casing and (b) rear casing
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