230 N. Okubo et al. Table 21.2 Material properties Density .kg=m3/ Young’s modulus (GPa) Poisson’s ratio (/) Pipe 2,300 57.5 0.330 Drive shaft 7,400 220.0 0.288 Table 21.3 Spring constant and natural frequency Hardness Spring constant (m/N) Natural frequency (Hz) 30 5:0EC05 1,256 40 9:0EC05 1,682 50 1:7EC06 2,300 60 1:8EC06 2,366 70 2:6EC06 2,829 80 2:7EC06 2,881 Mass 0.0075kg Mass 4kg Mass 0.3kg x y z Fig. 21.12 FEM a b Analysis (164Hz) Experiment (166Hz) Fig. 21.13 Comparison of mode shapes 21.3.4 Brush Cutter Modeling The total brush cutter FE modeling is shown in Fig. 21.12 where the handle is expressed by beam element and the engine and the cutting blade by lumped mass 4 and 0.3 kg connected rigidly. Based on this model the target mode is calculated as shown in Fig. 21.13 which shows a good agreement compared with measured natural frequency and mode shape 21.4 Structural Modification In this study two structural modifications on rubber bush: hardness and placement are taken into consideration based on FE model of the brush cutter mentioned above and verified by experiments. 21.4.1 Rubber Bush Hardness Optimization The hardness of six rubber bushes which are evenly spaced is so optimized as to realize the minimum of the largest FRF value for the frequency range of interest in this case between 130 and 190 Hz based on the identified FE model shown in Fig. 21.14, where the reference point is at engine and the response point at handle. The hardness of six rubber bushes, K1–K6 can be modified in the range of #30 to #80 corresponding to identified spring constant as described above. The final result of optimization is shown in Table 21.4 and Fig. 21.15 shows the FRF comparison of before and after the optimization. Although slight the vibration can be reduced in the frequency range.
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