## 3 Results and Discussion
### Analytical Results
However, the fraction volume curve confirms the ability of this SMA spring to perform well at such applied temperature without fail. Figure 10b shows the hysteresis curves of stress and strain for both extension and SMA regaining its initial position. The maximum mechanical stress with the SMA spring under extension is 452 Mpa. It is below the maximum allowable working stress (\(\sigma_{0}\)) of 690 Mpa. The corresponding extension strain to complete the cycle is 0.0219. The regaining process of the SMA spring pulls the bias spring, which causes it to have a maximum stress of 347 Mpa with a strain of 0.016 from the thermal effect. The strength operation of the SMA spring in this actuator is advantageous to the design to prevent overstressing and overstraining of the actuator to increase its life span. The operating with repeatability of the actuator is shown in Figure 10c,d. The actuator performs 100 operating cycles in 5 s with a time interval of 0.0001. They are very congested but indicate that the stress and strain curves of the 1 st cycle are the same as the ones recorded in the 100 th cycle. The recorded strain from multiple cycles is below the transformation strain in the material properties. The output stress at the 100 th cycle is also less than the maximum allowable stress of the SMA spring. They designate the high repeatability and long-life operation of the SMA-based actuator [50]. Figure 10: Effect of shape memory alloy in actuation mechanism of the proposed actuator. (**a**) Fraction volume of SMA spring concerning temperature taken during phase transformation; (**b**) hysteresis curve of stress–strain from the mechanical extension of SMA spring and stress–strain curve during spring regains its initial position; (**c**) stress of SMA within multiple numbers of operating cycles; (**d**) operating strain of SMA spring from a multiple number of cycles; (**e**) the change in vertical path to the extension and regaining position of the SMA spring for closing and opening states of the actuator; (**f**) closing and opening strokes of the proposed IAC actuator. Figure 10e shows the change in vertical pitches of the coils of the SMA spring. The vertical pitch of each coil changes to extend during the closing state of the actuator. It starts from the initial pitch and extends until the final displacement of the SMA spring. The displacement from a coil covers the initial vertical pitch and its change. The extension starts from the initial pitch of 2.23 mm and ends at 3.5 mm. Regaining axial pitch starts and the SME boosts to activate the SMA spring to the opening state of the actuator. The pitch is changed in the opposite direction from the extension but does not reach the starting point of the extension stage, because of the residual resistance from the bias spring. The final extension pitch becomes the starting point of the regaining pitch, and the final regaining pitch is 2.3 mm. The change in vertical pitch for extension is 1.27 mm, while the vertical pitch for regaining is 1.2 mm. Figure 10f shows the IAC actuator's closing and opening strokes. The maximum stroke of both states is 6.5 mm, but achieved at different times. The closing stroke curve is not smooth and takes a full simulation time of 5 s to complete. The opening curve from zero to the maximum stroke is smooth and was achieved in 3 s of simulation. The maximum closing stroke is the sum of the total changes of axial pitches and the initial pitch, and the maximum opening stroke is the total change in the axial pitches for regaining. The maximum stroke was settled based on the existing operating space of the pintle from previous research on idle engine speed [51; 52; 53]. The quick opening of the actuator is required to facilitate the idle speed activation in a short time.