# Idle Vibration Reduction of a Diesel Sport Utility Vehicle
## 5 Design Optimization for the Idle Vibration Reduction
In fact, the idle vibration of the optimized design is reduced by 64.5% on a linear scale than that of the present design. The design variable values obtained from the design optimization are summarized in Table 4. In this table, the optimized values of the rubber bushing stiffness of the radiator and the intercooler mass represent the upper limits of the design ranges, whereas the optimized values of the lower hose stiffness of the radiator, the upper hose stiffness of the intercooler, and the lower hose stiffness of the intercooler comprise the lower limits. Conversely, the optimized  
Figure 20: Results of the sensitivity analysis for the variations of each design variable. values of the radiator mass, the upper hose stiffness of the radiator, and the rubber bushing stiffness of the intercooler do not exhibit any significant differences compared with the present design values. A comparative study of the computed natural frequencies for the present and optimized designs reveals the modes that are affected by the optimization. Table 5 compares the natural frequencies computed via simulation for the present and optimal designs are compared in Table 5. In this table, the natural frequencies of the modes related to the powertrain and body floor do not change significantly. However, the natural frequencies of the bounce and roll modes of the radiator for the current design, which are 19.4 and 30.3 Hz, increased to 26.7 and 34.1 Hz in the optimal design. The increments in the natural frequencies for these modes are relatively large, 7.3 and 3.8 Hz. The natural frequency of the intercooler bounce mode in the current design, which is 31.0 Hz, is slightly reduced to 28.9 Hz in the optimal design. In other words, the natural frequencies of the modes for the radiator and intercooler are more affected by the design optimization than the modes for  
Figure 21: Convergence plots of the eight design variables in the design optimization: (**a**) radiator mass; (**b**) intercooler mass; (**c**) rubber bushing stiffness of the radiator; (**d**) rubber bushing stiffness of the intercooler; (**e**) upper hose stiffness of the radiator; (**f**) lower hose stiffness of the radiator; (**g**) upper hose stiffness of the intercooler; and (**h**) lower hose stiffness of the intercooler. the powertrain and body floor. This is because only design variables related to the radiator and intercooler were considered in the design optimization. The frequency response function of the dynamic model with the optimized design variables was compared with that of the model with the present design variables. Through this comparison, we investigated the reason of the dynamic model with the optimized variables exhibiting a lower idle vibration level than the model with the present variables. The frequency response functions for the dynamic models with the present and optimized design variables are compared in Figure 22, wherein the blue and red lines represent the frequency response functions for the present and optimal designs, respectively. As displayed in this figure, the frequency response function curves adjacent to the peaks of 1.2, 1.7, 6.7, and 15.3 Hz do not undergo significant changes, which are the natural frequencies of the bounce and pitch modes of the body floor and powertrain. However, a large variation can be observed in the curves corresponding to the idling frequency of 27.7 Hz. Owing to the design optimization, the frequency response function exhibits an anti-resonance point at idling frequency, significantly lowering the vibration level at the driver's seat. Therefore, the optimal design reduces the natural frequencies for the bounce modes of the radiator and intercooler (26.7 and 28.9 Hz, respectively) to a value proximate to the idling frequency (27.7 Hz), which causes the radiator and intercooler to act as vibration absorbers.