# Steering Pull Model and Its Sensitivity Analysis
## 6 Sensitivity Analysis and Discussion  
In this study, a sensitivity analysis on various design parameters is performed based on the steering pull model. The sensitivity values of each factor were obtained by Equation (23). \[\textit{Sensitivity}=\frac{\left(\frac{d_{M}}{d_{R}}\right)}{\left(\frac{P_{M}}{ P_{R}}\right)} \tag{23}\]  
where \(d_{M}\) = steering pull distance with modified parameter, \(d_{R}\) = steering pull distance with reference parameter, \(P_{M}\) = modified parameter, \(P_{R}\) = reference parameter. To observe individual parameter sensitivity on steering pull, a single parameter is changed, and its sensitivity is obtained while the other parameters are fixed to be their reference parameters. For the design parameters, caster angle, kingpin angle, camber angle, rack friction force, and ARS stiffness are considered. The variation of each factor is described in Table 3.  
First of all, it is certainly expected that the steering pull distance will increases with the increase of bank angle. The sensitivity analysis results showed that the steering pull distance proportionally increases as the bank angle increases from 0.5 to 2.5 degrees, as shown in Figure 13a. Figure 12: Verification results. \begin{table}
\begin{tabular}{l c} \hline \hline Bank angle (deg) & 0.5 \(\sim\) 2.5 \\ Caster angle (deg) & 2 \(\sim\) 7 \\ Kingpin angle (deg) & 5.5 \(\sim\) 20.5 \\ Camber angle (deg) & \(-\)3.5 \(\sim\) 1.5 \\ Rack friction force (N) & 60 \(\sim\) 260 \\ Anti-rattle spring stiffness (N/mm) & 0 \(\sim\) 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variation of steering pull parameters. The reference value of caster angle is 4.5 degrees. The caster angle is changed from 2 to 7 degrees with 0.5 degrees increments. As shown in Figure 13b, the caster angle hardly has any influence on the steering pull. Figure 13c shows the sensitivity of the kingpin angle. The kingpin angle is changed from 5.5 to 20.5 degrees and its reference value is 12.7 degrees. As shown in Figure 13c, the steering pull distance rapidly decreases as the kingpin angle increases. The sensitivity of the kingpin is not completely linear, but its mean value is \(-0.01\). Figure 13: Sensitivity analysis (**a**) bank angle (**b**) caster angle (**c**) kingpin angle (**d**) camber angle (**e**) rack friction force (**f**) ARS stiffness. The camber angle, on the other hand, also has a substantial influence on the steering pull as shown in Figure 13d. Its reference value is \(-2.0\) degrees and it is changed from \(-3.5\) to \(1.5\) degrees with \(0.5\) degrees increments. As the tendency of kingpin angle, the steering pull distance rapidly decreases as the camber angle increases. The sensitivity of the camber angle is \(-0.071\), which means that it also has a substantial influence on the steering pull, but it is slightly less than the kingpin angle. From the sensitivity results of the camber angle, a positive camber angle is thought to be desirable for steering pull. However, considering that modern passenger vehicles generally adopt a negative camber angle for the improvement of cornering performance [24], the camber angle setting needs to be compromised. Among five design parameters except the bank angle, the rack friction force has the most influence on the steering pull as shown in Figure 13e. Its reference value is \(160\) N and it is changed from \(60\) to \(260\) N with \(20\) increments. The sensitivity of the rack friction force is \(-0.271\). It has the highest sensitivity on steering pull among the design parameters and can be easily adjusted by tightening the yokenut. However, considering that a high friction force can lead to a sticky and bad steering feel, this also needs to be compromised [22]. The ARS stiffness also has a considerable influence on the steering pull. The sensitivity result is shown in Figure 13f. The reference value is \(30\) N/mm and it is changed from \(0\) to \(30\) N/mm with \(3\) N/mm increments.