# Idle Vibration Reduction of a Diesel Sport Utility Vehicle
## 5 Design Optimization for the Idle Vibration Reduction

Table 4: Present values, the lower and upper limits, and optimized values of the design variables. bushing stiffness of the radiator (refer to Figure 19c), and the lower hose stiffness of the intercooler (Figure 19h). However, the idle vibrations are relatively less affected by the rubber bushing stiffness of the intercooler (refer to Figure 19d), the upper hose stiffness of the radiator (Figure 19e), the lower hose stiffness of the radiator (Figure 19f), and the upper hose stiffness of the intercooler (Figure 19g). The sensitivities of the design variables were analyzed to determine the variables that considerably influence the idle vibration. To perform the sensitivity analysis, an established experimental design was adopted, which can extract the maximum information for a minimal number of experiments. For the experimental design, the idle vibration level was selected as the objective function along with the aforementioned eight design variables, and the variables were set in three levels: the lower limit, present value, and upper limit. Figure 19: Idle vibration levels for the variations of the eight design variables: (**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 incorporation of levels is advantageous because a greater number of levels will yield more accurate results; however, this method significantly increases the experimental time and cost involved. Accordingly, three levels were implemented in this analysis. After the evaluation of the idle vibration levels for each of 117 experiments using the \(L_{117}\big{(}3^{8}\big{)}\) orthogonal array table, the effect of each design variable on the idle vibration was analyzed through analysis of variance (ANOVA) [27]. ANOVA is a widely used statistical formula for comparing variances across the means (or average) of different variables. The sensitivity analysis results of the design variables with respect to the idle vibration within the specified design ranges are illustrated in Figure 20. The following design variables that affect idle vibration are listed in decreasing order of sensitivity: the rubber bushing stiffness of the radiator, the radiator mass, the lower hose stiffness of the intercooler, the intercooler mass, the lower hose stiffness of the radiator, the rubber bushing stiffness of the intercooler, the upper hose stiffness of the intercooler, and the upper hose stiffness of the radiator. In particular, the sensitivity analysis results depicted in Figure 20 are consistent with those of the parametric study presented in Figure 19.  
To minimize the idle vibration level, the optimal design was implemented within the range constraints of the design variables. The design was optimized using the progressive quadratic response surface modeling (PQRSM) method, which is included in the commercial design optimization software package PIAnO [28]. To perform the design optimization using the eight design variables listed in Table 4, the idle vibration level was selected as the objective function, and these design variables were varied from their lower to upper limits, as depicted in Table 4. The convergence results of design optimization are shown in Figure 21, in which the lower and upper dashed lines represent the minimum and maximum values of each design parameter range, respectively. This figure presents the numbers of iterations where the design parameters converge to their optimum values in the process of design optimization. All design parameters converged within 15 iterations. The idle vibration level obtained through the design optimization was 9 dB lower than the level yielded by the present design. This reduction of 9 dB in vibration level corresponds to a reduction of 60.7 mm/s\({}^{2}\) on a linear scale.