198 B. Winter et al. 0 Contact x2-x1-u(w) K3 No Contact Fig. 16.3 Bi-linear spring stiffness, K3, as a function of distance between M1 and M2 in Fig. 16.9. Therefore, by the spring stiffness going to zero in the out of contact condition, the force being applied to the system will not be transferred to the bottom mass, inducing nonlinear behavior. Nonlinearity in the model can be seen in Fig. 16.3, where the red areas display the harmonic response frequencies. Resonant frequencies are also seen around 150 Hz and 220 Hz, corresponding to the first mode of the plate alone and the first mode of the plate and drill in contact, respectively. 16.3 Experimental Study of Model Parameters The experimental approach discussed in this paper is used to obtain necessary parameters for the developed model. First, each component was studied separately through modal testing to gain an understanding of their dynamic characteristics. Parameter estimation was used to interpret the data and determine the spring and damping parameters needed for the model. During the drilling process, bit-bounce causes the drill bit and plate to come out of contact at some points in time, resulting in nonlinear behavior. To understand the changes introduced by the change in contact condition, the components were also tested while in contact to determine the dynamics of the entire system. By progressing in this manner, the interacting dynamics between different components when in contact and out of contact can be observed. 16.3.1 Experimental Study of Independent Model Parameters For this study, a Jet JDP-15MF drill press was the drilling tool analyzed. Modal analysis of the drill press was completed to determine the dynamics that the tool will contribute to the vibrations of the material being drilled. Impact testing using a PCB Piezotronics impact hammer was conducted with 27 PCB Piezotronic accelerometers attached to nine locations of the drill press for tri-axial data acquisition, using a National Instruments LabVIEW system. The experimental test setup is shown in Fig. 16.4. Results of the modal analysis showed the plate of the drill press to support the drilling material had the most motion. For this reason, the decision was made to use a separate table to support the drilling material to isolate the dynamics of the drilling components of the system and remove the dynamics of the supporting plate, which is a better representation of real-world drilling scenarios. For initial model development, aluminum plates (30.0 30.0 0.6 cm) were used as the drilling material. Plates were clamped at the corners to the supporting table. Nine accelerometers were placed on the plate, evenly spaced on a 7.5 7.5cm grid to measure acceleration in the vertical direction. The plate was impacted with an impact hammer at the node in the center of the plate. The experimental setup is shown in Fig. 16.5. 16.3.2 Parameter Estimation Modal parameter estimation is the process of determining frequency, damping ratios, and mode shapes from experimental data. Input force data measured by the impact hammer and acceleration data measured by accelerometers were used to create the frequency response function (FRF) for the two components individually. This FRF was then used with parameter estimation techniques to determine the modal parameters, such as frequency and damping ratio, for each component. This
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