0 5 10 15 20 2 4 6 8 10 12 14 16 18 EMA FEA 0 20 40 60 80 100 0 5 10 15 20 2 4 6 8 10 12 14 16 18 EMA FEA 0 20 40 60 80 100 Figure 11 – MAC index between mode-shapes of different angle configuration: curve crossing involving the 6th and 7th modes (left), curve veering involving the 5th and 6th modes (right). TEST RIG DESIGN AND EXPERIMENTAL RESULTS Some practical approximations and physical dimensions are neglected or not simulated in the FE model, therefore to design and build the test rig some engineering choices are adopted to reproduce the numerical behaviour in physical reality. The most important characteristic is to have a tunable parameter in the structure to vary and tune the angle of the middle beam. A manual rotary table is chosen in the first lumped mass. It guarantees the rotation of the middle beam and controls the orthogonality of the third beam by means of a clamp with a device integrated in the second lumped mass. One main peculiarity of the test bench is the flexibility, in fact the structure allows different lumped masses and beam element dimensions in a simple way. Figure 12 shows 3D drawings and photographs of the lumped masses in which is possible to see the rotary table and other parts of the group. An exploded view of the group shows rotational pins, jaws and twice parts necessary to obtain the tunable angular parameter. Beam elements used to join the lumped masses and to obtain correct stiffness properties are chosen in order to reproduce the dynamic properties predicted in Figure 10. These elements are interchanging with others that have rectangular section but with different dimensions and length. This is a further flexibility characteristic of the test bench. To obtain the reciprocal position (parallel or orthogonal) between the first and the third beam of the test bench during variation of the angular parameter , an alignment profile is developed (transparent light blue profile of Figure 12). This profile must be used only during the tuning of test bench, to guarantee alignment, but it must be removed during the experimental test. To constrain the test bench, a bracket that joins the main structure with a seismic mass is designed. This bracket has its first bending mode over 250 Hz, in order to not interact in the frequency range of experimental testes. After the assembly of the test bench, a preliminary experimental campaign has been conduct to validate theoretical results. Three three-axial accelerometers are set on every lumped mass (Figure 13), and subsequently rowing hammer technique is implemented for data acquisition. A mean of 10 impact tests are used for the measurement of FRF for each testing configuration. In particular 19 different configurations are taken into account, from = 0° to = 90° with a step of 5°. An updating procedure is now necessary to validate the numerical result of Figure 10. By means of experimental data two main results are obtained for the FE model: the calibration of equivalent length of beam elements, considering lumped masses and the updated stiffness parameter for the analytical FE data with respect to the experimental modes. To calibrate beam elements in the model, torsional modes are used because they are not influenced by length of actual masses, but only by section and length of beams. To be more confident with respect to the numerical model, the following step is to use a commercial FE model integrated in a CAD software, like SolidWorks-Cosmos, to predict more accurately the dynamic behaviour with respect to the angle parameter . Modes = 69° Modes = 45° Modes = 68° Modes = 44° 334
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