162 S.K. Cheah 17.2 Theoretical Background The majority of the large mass method application has been on base excitation for shaker table or seismic analysis [2, 3]. The theory is applicable to multi-point excitation that are independent of each other. The finite element model equation of motion [4] could be symbolically represented with the following equation: ŒM f RygCŒC f PygCŒK fygDfFg (17.1) where M, C & K are respectively the mass, damping and stiffness matrix; y vector represents the response of the system and F vector is the external force on the system. The enforced motion is applied by attaching a large mass to the node where enforced motion is desired. The force is computed by Newton’s second law: fFgDLMfRubg (17.2) where LM is the large mass and ub is the enforced motion at the corresponding FEA node. The scalar value of the large mass should be sufficiently big such that the damping and spring forces adjacent to the node are negligible, i.e. cij/LMDkij/LMD0. It was found through numerical experiments [5] that large mass ratio of 10 3 to 1010 provides accuracy that matches theoretical results. The large mass method [6] is introduced into Eq. (17.1) by replacing the ith equation with the following: LMi Ryi CXj¤i mij Ryj CXj cij Pyj CXj kijyj DLMi Rubi (17.3) 17.3 Experiment Setup A prototype diesel generator set shown in Fig. 17.1 was tested for both linear vibration and strain simultaneously. Ten triax consisting of PCB 353B33 accelerometers were used on the chassis. An example accelerometer triax configuration is shown in Fig. 17.2. Vibration data acquisition was taken using LMS SCADAS III & Test.Lab 11B at 2,048 samples/s. Strain measurements were acquired with CEA-06-062UW-350 single element gage. An example strain gage is shown in Fig. 17.3. 5 V DC excitation were applied on all strain gages from the SOMAT e-DAQ acquisition system. Furthermore, dynamic axial loading of a bolt was measured with HBM KML style load washer as shown in Fig. 17.4. While multiple different runs were performed, only the full load steady state 50 Hz power generation at 1,500 RPM operation was considered for this analysis. Fig. 17.1 Prototype generator set
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