## 3 Results and Discussion
### Analytical Results  
Analytical simulation results were obtained based on the equations in the analytical method. Figure 9a shows the extension displacement of the shape memory alloy spring from the input mechanical driving force (\(F_{b}\)). The extension displacement of the SMA spring can be the same as the closing stroke moved by the pintle of the IAC actuator during the closing state. The SMA spring keeps stretching as the input force increases. With the maximum force of 2.39 N, the displacement reached 6.26 mm. However, a coil spring (bias spring) pulled another coil spring (SMA spring), and the displacement curve became rough because the coils were not stretching equally. The heating and cooling cycles of the SMA spring are shown in Figure 9b. Before 1 s, the heating cycle curve rises from the ambient temperature (25 \({}^{\circ}\)C) to the final austenite temperature (50.5 \({}^{\circ}\)C), but the final one was achieved at 3.8 s. The main input here was the controlled current (I) from the current converter. The heating cycle remained active when the actuator opened until the SMA spring's current supply stopped. The choice of a maximum heating temperature of 50.5 \({}^{\circ}\)C prevents an actuator from overheating and high electricity consumption. It reduces the time needed to cool it down for another operational state. However, the cooling cycle curve starts to fall after 1.2 s of off-current supply. It takes 4.75 s to complete cooling the SMA spring from the maximum heating temperature to the ambient temperature of 25 \({}^{\circ}\)C. It implies that the time required to cool the SMA spring is more than its heating time. Figure 9c shows the generated force of the SMA spring used to compress the bias spring and regain its position. The generated force is zero when the temperature of the heating cycle is between 25 \({}^{\circ}\)C and 30 \({}^{\circ}\)C. The increasing temperature provides the rise of the generated force. With maximum heating temperature, the spring generates its maximum force of 2.46 N. However, the variation in output force generated by the SMA spring depends on the supplied current, as shown in Figure 9d. This force increases proportionally with the electric current supplied to the SMA spring increases. The current of 2 A provides the highest generated force of 2.46 N. The rising curve of force is active every time the current is on and starts descending directly after the supply current is off for all force curves. Figure 9e shows the displacement of the SMA spring under the electrical supply. The extended coils of the SMA spring return to their original positions  
Figure 9: Shape memory effect outputs in the operating mechanism of the proposed IAC actuator. (**a**) Mechanical force versus the extension displacement of proposed actuator caused by bias spring; (**b**) heating and cooling cycles with used time to the final stage; (**c**) generated force of SMA spring to pull the bias spring with heating temperature; (**d**) output generated force of SMA spring produced by different supplied electric current; (**e**) displacement of SMA spring to regain its normal position. when it heats up, causing the spring to regain its original length. In 3.8 s, the maximum settling displacement of 6.5 mm is reached. This displacement of the SMA spring from the input current can be the same as the opening stroke moved by the actuator's pintle. The fraction volume curve that defines the transformation of the SMA spring is shown in Figure 10a. According to this curve, the SMA spring's operability ranges from 0.01 to 0.14 for the austenite fraction volume and 1 to 0.5 for the martensite fraction volume. However, no fraction volume curve passes the settled maximum fraction volume of martensite and austenite. With more repeating cycles, the required temperature for phase transformation is lower. The applied maximum temperature is 54 \({}^{\circ}\)C instead of the 50.5 \({}^{\circ}\)C to test the performance ability of the SMA spring in the actuator.