328 F. Altunel and M. Aykan 104340 104340 104316 104316 24 24 24 24 Mmm Kmm kms Kss Ksm Mms Msm Mss Fig. 31.5 System mass and stiffness matrix reduction [6] Then, reduction is performed at these modal coordinates. In this way, the reduced dynamic equation of motion is obtained as follows: Mbb Mbq Mqb Mqq „ ƒ‚ … Freduced Rum Rq C Kbb 0 0Kqq „ ƒ‚ … Kreduced um q D Fm 0 „ƒ‚… Freduced (31.4) where subscript “q” represents the modal coordinates, “b” stands for reduced boundary representation. If damping is added to the equation and reduction is performed by using Craig-Bampton method, reduced dynamic equation of motion is written as follows: Mbb Mbq Mqb I Rum Rq C 0 0 0 2 ! Pum Pq C Kbb 0 0 !2 um q D Fm 0 (31.5) where and ! stand for damping ratio and eigenfrequency, respectively. For example, if 104,340 DOF system is reduced into 24 DOF, then system matrices become as given in Fig. 31.5. Using the reduction process, dynamic characteristics of elastic parts can be included in the multibody analysis of the entire system with ease. Pan et al. [7] carried out dynamic simulations of a power generator using this method, and compared with the test results. While the frequencies found are not exactly the same with the test results, values are considered acceptable by authors. Thus, he reported that the method is effective and accurate for practical cases. This method is being used as a standard method for many companies in recent years. Inside many actuated systems, there are components like gearbox, motor, bearing, etc. that are not suitable to model as flexible elements by classical FEM tools in terms of time required and complexity level. On the other hand, their flexibilities must be added to the system analysis since they have an important contribution to the flexibility of the entire system. In this study, the most suitable approach is considered as including these flexibilities as spring and damper elements to the system. 31.3 Turret Case Study 31.3.1 Prototype Modal and Torque Frequency Sweep Tests For this study, a prototype of the turret was manufactured. On this prototype, two different tests are performed with the aim of validating the VL simulation model. Firstly, accelerometers are placed at designated locations on the prototype and then impact testing is performed by a modal hammer. This process is performed for elevation chassis, azimuth chassis and the gun. Secondly, turret system is given motion in azimuth direction by applying torque on the azimuth motor, keeping the accelerometers at the same location as the modal test. Torque sweep is applied for the 1–100 Hz bandwidth and acceleration response is acquired.
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