## 3 Results and Discussion
### Performance Evaluation Outputs  
The results from the performance ability of the designed IAC actuator in the engine's air intake system are presented here. They are compared to previous studies with experiments and practical engines operating in idle mode. This section also verifies the key parameters and inputs from the practical engines, which may reduce the cost of experiments and manufacturing the proposed IAC actuator. The air mass flow rate through the bypass when the IAC actuator opens is shown in Figure 13a. It describes the amount of air that flows into the intake manifold per defined time. The air mass flow rate in a steady state is \(2.76\times 10^{-3}\) kg/s after 6 s of simulation. The air mass flow rate is a triggering characteristic of idle engine operation. The IAC actuator's stroke defines the amount of this air mass flow rate. Figure 13b shows the air pressure through the intake manifold. It is a critical parameter after the air mass flow rate to characterise the intake manifold of an engine operating in idling mode. It is steadily sated after 6 s with an air pressure of \(6.06\times 10^{4}\) Pa. The air mass flow rate variation determines how air pressure changes in the intake manifold. The intake manifold's air pressure is higher with the SMA-based IAC actuator than in the literature study from reference [53], and the air pressure difference in these results is \(1.56\times 10^{4}\) Pa.  
Figure 14a shows the output torque and power of an engine that operates in idling mode. Engine torque is the first output performance characteristic to measure in the simulation. The maximum idling torque is 31.08 Nm. This torque response is steadily stated at 5.3 s with 25 Nm. However, the steady state of output power is 16.5 Kw at the same time as the torque. The maximum simulated idle engine power is 19.78 Kw. The  
Figure 13: Intake manifold characteristics of idling engine. (**a**) Air mass flow rate through the bypass to the intake manifold; (**b**) pressure of air flows in the intake manifold during engine operation in idle mode.  
results demonstrate an improvement in engine idle torque of 1.24% and power of 1.236% compare with the experimental results from the previous works in the literature [48; 51].  
Figure 14b shows the speed of the running engine in idle mode. The output speed curve after 5.3 s of simulation is in a steady state with 650 _RPM_, and the maximum idling speed is 743.8 RPM. All simulated steady-state values are between the maximum and minimum idle performance output characteristics of the practical operated engine. Furthermore, the enhancement of engine idling speed is also shown by comparing with the experimental results from previous research, as cited in references [47; 48; 51; 52; 58]. This means the performance improvement of the engine during idling conditions with the designed IAC actuator is achieved. The engine idling characteristics concerning the IAC actuator's performance are shown in Figure 15. As the actuator's opening stroke increases, the engine's idling torque and speed increase, but in different ways. The maximum idling torque of 31.08 Nm is attained with an opening stroke level of 3.8-4.1 mm and a corresponding idling speed of 540.6 RPM. At an opening stroke level of 5.975 mm, the engine reaches its maximum idling speed of 743.8 RPM, and its corresponding idling torque of 24.7 Nm. With this IAC actuator, the engine cannot stall from the torque disturbance or speed variations. Thus, the operating performance of the proposed SMA actuator contributes to the engine's good idling characteristics.  
Figure 14: Performance characteristics of an engine running in idle mode. (**a**) Idling engine torque and power output; (**b**) output idling engine speed.  
Figure 15: Effect of the SMA-based IAC actuator’s operating performance on the engine’s idling output characteristics.