## 2 Materials and Methods  
### Structural Configuration of Proposed IAC Actuator  
The structure of the idle air control (IAC) actuator identifies the external physical appearance and internal parts arrangement with their shapes. Figure 1a shows a completely assembled actuator. It has three main parts with different shapes and colours. The bottom part is in rubber colour and the middle part with chromate colour are fixed parts to hold the internal components. The remaining one is a part of the IAC actuator to be fixed into the throttle body. Figure 1b shows the 14 components of a shape memory alloy-based idle air control actuator. Each one has its role in the operation of the actuator. The pintle and rod are the moving components based on the state of the actuator. The stability of the rod holder comes from the vertical support, which assembles it with the outer housing and the fixture plate. The fixture plate supports the actuator onto the throttle body through the bolt holder and bolts with nuts. O ring protects the actuator from leakage of air in the bypass. Electric connectors in the connecting box relate to the electric wires from the engine electronic control module and supply the electric current to the SMA spring. This spring is made from a Nickel-and-Titanium (NiTi) alloy with 52% of Ni and 48% of Ti. The reference  
Figure 1: Structure of proposed idle air control actuator. (**a**) Complete 3D assembled model of the actuator; (**b**) sectioned actuator with all main components (1. Pintle, 2. Rod, 3. Inner housing, 4. Bias spring, 5. O ring, 6. Fixture plate, 7. Bolts-holder, 8. Rod holder, 9. SMA spring, 10. Outer housing, 11. Connecting box, 12. Electric connectors, 13. Vertical support, and 14. Cooling slot). specifications of the SMA spring are from the released datasheet of Nexmetal Corporation, Sheridan, WY, USA, for the NiTi SMA coil spring [35]. The rod holder, bias spring, and rod are made from stainless steel. The fixture plate and vertical support are made of low-carbon steel. Inner and outer housings are made from grey cast iron. Together with the cooling slot, they facilitate a high rate of heat transferred to the ambient from the SMA spring during cooling time. The connecting box is made of ductile cast iron. Using cast iron in these components increases their ability to work outside with different temperatures and vibrations from the engine. Apart from the simple structure of the actuator, it has a low weight of 17.46 g. However, two springs (SMA spring and Bias spring) shown in Figure 2 are the main components to manage this IAC actuator's operation. The bias spring, shown in Figure 2a, is designed to work under compression. Its parameters are indicated by a subscript b (\({}_{b}\)). Figure 2b illustrates an SMA spring. It is designed to work under mechanical extension. Its parameters have a subscript s (\({}_{s}\)) to differentiate them from those of a bias spring. The wire diameter (\(d_{b}\)) was selected from the stainless steel wire available on the market. It is the basic element used to calculate other spring parameters as expressed in Equation (1). It is an equation of modelling modified from a study conducted by [PERSON] et al. [13]. The parameters of the SMA spring were identified based on force (\(F_{b}\)) that should extend to the full displacement of the SMA spring at its martensite phase. \[F_{b}=\frac{8D_{b_{0}}}{\tau_{m}\pi d_{b}^{3}}C_{f} \tag{1}\]  
where \(F_{b}\) is a mechanical driving force to extend the SMA alloy spring, \(C_{f}\) is a shear stress correction factor of the spring and it is calculated based on the spring index (\(i_{s}\)) in Table 1. \(\tau_{m}\) is a maximum shear stress of the spring, which defines the spring's working ability [36]. This stress for coil spring from stainless steel is 515 MPa. The two springs are designed using the same theory of coil spring, but the working conditions and parametric relationship are different.