## 2 Materials and Methods
### Structural Configuration of Proposed IAC Actuator
#### 2.2.2 Working Principle of SMA-Based Actuator  
The operating principle of the proposed IAC actuator is to close and open the idle air path (pypass) in the throttle body. The SMA spring manages the operation mechanism through its phases such as the martensite and austenite phases. The martensite phase plays a role in the closing state and the austenite phase acts in the opening state of the actuator. In the closing state, the bias spring extends the SMA spring mechanically with its force (\(F_{b}\)), as shown in Figure 3a. The force (\(F_{b}\)) expressed in Equation (1) is transformed according to the operating principle of the SMA-based IAC actuator and expressed by Equation (2). This is a pseudo-elastic phenomenon of SMA spring. Then, the rod assembled with the SMA spring moves into the rod holder and causes the pintle to displace. Within this state, environmental air passes through the throttle valve from entering the engine \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & \multicolumn{2}{c}{**Value**} \\ \cline{2-3}  & **Bias Spring (\(\epsilon_{b}\))** & **SMA Spring (\(\epsilon_{s}\))** \\ \hline Wire diameter (\(d\)) & 2 mm & 1.7 mm \\ Free length of coil (\(L_{f}\)) & 23 mm & 15.5 mm \\ Coil diameter (\(D_{0}\)) & 16 mm & 10.2 mm \\ Spring index (\(l_{s}\)) & 8 & 6 \\ Generated force (\(F\)) & 2.25 N & 2.416 N \\ Number of active coils (\(N_{c}\)) & 7 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the spring. \begin{table}
\begin{tabular}{c c} \hline \hline
**Property** & **Value** \\ \hline Maximum allowable stress (\(\sigma_{0}\)) & 690 Nmm\({}^{-2}\) \\ Minimum allowable stress (\(\sigma_{1}\)) & 70 Nmm\({}^{-2}\) \\ Operating number of cycles (\(N_{cy}\)) & 10\({}^{5}\) \\ Operating temperature & 0–60 \({}^{\circ}\)C \\ Ambient temperature (\(T_{e}\)) & 25 \({}^{\circ}\)C \\ Density (\(\rho_{s}\)) & 6.45 gmm\({}^{-6}\) \\ Poison’s ratio (\(r_{s}\)) & 0.33 \\ Electric resistivity\_Martensite (\(\rho_{eM}\)) & \(8.7\times 10^{-4}\)\(\Omega\)mm \\ Electric resistivity\_Austenite (\(\rho_{eA}\)) & \(7.2\times 10^{-4}\)\(\Omega\)mm \\ Specific heat (\(c_{p}\)) & 0.2 Cal(g\({}^{0}\)C)\({}^{-1}\) \\ Martensite young’s modulus (\(E_{M}\)) & 33,500 Nmm\({}^{-2}\) \\ Austenite young’s modulus (\(E_{A}\)) & 62,500 Nmm\({}^{-2}\) \\ Coefficient of thermal expansion (\(C_{th}\)) & \(11\times 10^{-6}\)\(\mathrm{K}^{-1}\) \\ Maximum pulling force (\(F_{smax}\)) & 4 N \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of SMA spring. intake manifold. The stress of the SMA spring induced by mechanical force (\(F_{b}\)) should be less than the maximum allowable working stress (\(\sigma_{0}\)) in Table 2. However, the contrary operation is the opening state of the actuator, as shown in Figure 3b. In the opening state of the IAC actuator, the SMA spring should return to its original position, but generate force (\(F_{s}\)) to compress the bias spring. The generated force \(F_{s}\) is expressed by Equation (2). It depends on the fraction volume (\(\theta\)) and the SMA spring displacement (\(S\)). This force should be able to suppress the mechanical driving force from the bias spring (\(Fb\)). The process is a pseudoplastic phenomenon of the SMA spring. With a compressed bias spring, the pintle with the rod follows the motion of the SMA spring and moves in the opposite direction to open the air flows into the bypass of the throttle body. The thermal mechanical behaviour of the SMA alloy spring is the key parameter to activate the opening state, which will be defined in the phase transformations and control techniques in the next sections. \[F_{b}=F_{\text{p}}+F_{t}+K_{s}x \tag{2}\] \[F_{s}=\frac{\pi d_{s}^{2}}{6D_{s}^{2}}\left\{\left(\frac{d_{s}}{ \pi D_{s}^{2}N_{sc}}G_{s}\right)x_{s}+(\eta_{1}+\eta_{2}G_{s})(\theta_{M}- \theta_{A})\right\}=F_{\text{p}}+F_{t}+K_{b}x\]  
where, \(\eta_{1,2}\), are the parameters associated with the stress-strain curve. \(\theta_{M,A}\), stands for the martensite fraction volume and Austenite fraction volume.