MATLAB Simulation and Analysis of Effect of Stiffness to Damping Ratio and Variable Road Elevations on Vehicular Driving Comfort and Safety

1.1. Background

There is considerable work on autonomous vehicles covering their suspension control in relation to cruise control at adaptive speeds and the selection of automation level-related dynamics of driving (comfort, handling) in conjunction with collision avoidance and safety strategy. Cruise control used by autonomous vehicles, particularly adaptive cruise control, is related to the longitudinal motion of the vehicle and affects suspension dynamics and gets affected by road profile and trajectories for a particular speed, which affects the comfort and handling of the vehicle [12]. Much work needs to be done relating driving comfort, vehicle handling and suspension control under an integrated strategy, which enables an autonomous vehicle to select the best mode of driving as a function of road profile, taking vehicle speed into account, to ensure stability and safety [13, 14].

Mobility benefits greatly from autonomous driving since highly automated vehicles will help drivers relieve some of the difficult responsibilities while providing safer and more dependable driving away from distraction and poor reaction times that some drivers experience under specific circumstances. The Advanced Driving Assistance System (ADAS) is advantageous for automated driving [15].

Most drivers are not trained professional vehicle pilots, making it very difficult to accomplish comfort and handling goals and safe driving. Even the most talented drivers struggle to do some tasks without the aid of sophisticated mechatronic systems. The mechatronic systems provide comprehensive information (fused) from the installed advanced sensors regarding the vehicle's status, road, and environment. This information is gathered and processed at very high speed, enabling very quick reaction times with the ability to be applied to specific vehicle components. Safety can be increased significantly with intra- and inter-vehicle networking, which, when paired with sensors and intelligent systems, will prevent many issues and accidents brought on by people. Thus, intelligently correlating road profiles with speed and the vehicle suspension system in autonomous vehicles can contribute effectively to safety enhancement and reduction of accidents [16, 17].

Vehicular stability can be optimized and automated through a systematic control approach by moving away from the separate design of the vehicle controlling circuits and systems and adopting an integrated vehicle control approach, which includes the driver, vehicle and road using networked devices within the vehicle-computing infrastructure. This integrated approach can function by designing and implementing supervised controllable systems related to vehicle dynamics. A three-layer architecture comprises sensing, instruction, and application layer, as presented in Fig. (1) [18, 19], to enable such critical dynamic control.

The instruction layer holds high-level programs for longitudinal and lateral vehicular control, including speed, acceleration, road profile, and direction. After considering such parameters, the computed optimum data will be communicated through the intra-vehicle network to the vehicle powertrain. Feedback regarding the action taken is returned for further optimization.

The instruction layer provides necessary commands to the application layer regarding actions required to achieve optimal stability and comfort. The application layer actively and dynamically exchanges data and affects the powertrain operations related to vehicle movements and trajectories. This can all be carried out automatically and intelligently in the autonomous vehicle environment, ensuring the safety and reliability of the travelled journey and balancing between handling, stability and comfort [20].

Due to the recent development in the automotive industry and vehicular control and computing power, using optimization, simulation, and intelligent algorithms, focus on the vehicle suspension design for both comfort and handling become possible using techniques ranging from numerical analysis to simulation of vehicular operations [21-23]. Active and semi-active suspension systems for automotive applications are designed and tested using mechatronics systems. Sensors and actuators are used within the vehicle control environment to enable higher safety and optimum comfort levels [24-27].

This paper aims to establish a selection strategy for driving mechanisms in autonomous vehicles as a function of both road profile and tire and suspension springs interaction in order to achieve either optimum handling and/or optimum comfort and will establish criteria for a selection that presents good comfort and good handling, which deals with both longitudinal and vertical dynamics.

3. RESULTS AND DISCUSSION

Tables 2-4 display MATLAB simulation results for Tire and Suspension Spring length variations as a function of different road profiles that cover different elevations, bumps, and general roughness. The displayed values are noted at a vehicular velocity of 60 km/h. The suspension stiffness to damping ratios is selected to examine and determine both comfort and road handling conditions for smooth and rough roads to enable optimization of design parameters for vehicles' active suspension.

Table 5 illustrates further investigation carried out through simulation to establish a point beyond which further changes in the spring ratios (SLVR) will have no effect on the vehicle's overall performance for a specific fixed mechanical at the specified fixed road roughness.

The following are the three cases considered in this work:

A: k:c=1

Figs. (2-4) show the following:

At a smooth road profile with normal elevation and no hard bumps or road holes (E=1), both tire spring and suspension spring vary in parallel but in opposite manner, as shown in Fig. (1). The k:c=1 ratio indicates an un-optimized vehicle condition, where suspension stiffness equals damping.

As the road profile is changed to E=3, which includes more road pattern variation, both springs responses, even though they stay as required in terms of polarity, points of crossover and intersection points are observed as presented in Fig. (3). {(0.44, 0.36), (0.47, 0.36)}. The closeness of the springs' responses and the intersection between the curves, in addition to the increase in spring length variation amplitude, indicate the need to optimize the k:c ratio.

The effect of introducing changes in the road profile to simulate stronger road elevation changes (E=5) is presented in Fig. (4). More intersections and higher levels of spring variation are realized due to the need for both springs to exert higher responses to the road profile due to the non-optimized k:c ratio and the higher road profile. {(0.28, 0.34), (0.355, 0.37), (0.43, 0.35), (0.48, 0.36)}. Also, an increase in each spring variation amplitude is realized. Thus k:c=1 is not the optimum setting for (E=5).

The effect of road profile coupled with the suspension stiffness to damping ratio is further shown in Figs. (5-7), where the Sprung Mass Acceleration (SMA) amplitude increases in response to road profile factor (E) increases but no change in response characteristics. The displayed pattern in the plots reflects the effect of damping on the overall response of the vehicle suspension system as a function of road profile.

B:k:c=20

Fig.s (8-13) show the following:

At a smooth road profile with normal elevation and (E=1), tire spring and suspension spring vary in parallel but opposite manner (closer to each other than the case where k:c=1), as shown in Fig. (8). The k:c=20 ratio indicates an optimized vehicle condition, where suspension stiffness is much higher than damping, which reflects a setting for smooth roads and comfortable driving, providing that the road stays at the road profile (E=1).

Fig. (9) shows tire and suspension spring responses to road profile (E=3). The curves present a clear intersection between the responses with a higher length variation due to road state. The k:c=20 ratio is designed more for comfort than another driving strategy. This is also illustrated in the number of intersections compared to the case where k:c =1, from two intersection to eight intersections, {(0.33,0.35), (0.35, 0.36), (0.35, 0.43), (0.47, 0.35), (0.64, 0.36), (0.67, 0.36), (0.75, 0.36), (0.77, 0.36)}. The increase in the number of intersections indicates that the vehicle is not tuned correctly for road profile (E=3) as the ratio k:c=20 should be optimized.

Fig. (10) clearly proves that k:c=20 with E=5, is not a proper optimization for the vehicle, whereby higher levels of spring length variation observed with fourteen intersection points, {(0.04, 0.35), (0.05, 0.35), (0.14, 0.37), (0.16, 0.37), (0.31, 0.33), (0.36, 0.35), (0.43, 0.35), (0.48, 0.35), (0.54, 0.37), (0.56, 0.38), (0.63, 0.38), (0.68, 0.35), (0.74, 0.35), (0.79, 0.35). Thus at this high road profile, k:c:20 will not be effective for such a road profile.

The previous argument is further supported by Figs. (11-13), whereby Sprung Mass Acceleration increases as road profile increases, but with lower values and smoother curves than k:c=1 due to damping. The difference in ratio and the effect of damping as the ratio is moved to k:c=20.

C:k:c = 0.27

Figs (14-19) show the following:

At a smooth road profile with normal elevation (E=1), tire spring and suspension spring vary in parallel but opposite manner (closer to each other than the case where k:c=20), as shown in Fig. (14). The k:c=0.27 ratio indicates an optimized vehicle condition, where suspension stiffness is lower than damping, which reflects a setting for reliable and safe road handling.

Fig. (15) shows tire and suspension spring responses to a road profile (E=3). The curves present a clear indication of the effect of optimizing a vehicle suspension system for rough road conditions as both curves for tire spring and suspension spring stay parallel but much closer compared to the case where (E=1), due to new road condition with length variation close to the smooth road case (R=1). Thus, no intersection at (E=3).

Fig. (16) shows intersection, which are expected at this level of road profile, and when counted found to be six points of intersection, {(0.29, 0.33), (0.36, 0.39), (0.47, 0.37), (0.48, 0.38), (0.78, 0.38), (0.80, 0.38). The number of intersections is less than in the previous cases of k:c=1 and k:c=20. This means that a vehicle suspension ratio optimized using the ratio k:c=0.27 will have better road handling over five profile levels (E from 1 to 5), considering other mechanical coefficients in the design process.

These findings for k:c=0.27 is further supported by the sprung mass acceleration responses for the three considered road profiles, as shown in Figs. (17-19). The plots show the massive difference in acceleration to overcome road profile values and enable safer and more reliable driving through a significant increase in acceleration from E=1 through to E=5.

Further investigation for better optimization with road profile (E=5) is shown in Table 4 and Figs. (20-22), where different k:c values are simulated per the same spring mass, tire stiffness, and speed. The result indicates that the optimized k:c:=0.27 is optimum for handling, slightly improving if the k:c ratio is lowered.

Figs. (20-22) show the obtained four intersection points for:

1. k:c=0.25: {(0.25, 0.325), (0.36, 0.39), (0.79, 0.38), (0.81, 0.385)}

2. k:c=0.2: {(0.29, 0.32), (0.36, 0.395), (0.7, 0.365), (0.8, 0.39)}.

3. k:c=0.17: {(0.3, 0.31), (0.36, 0.4), (0.7, 0.36), (0.71, 0.37}.

It is evident that there is very little change in the spring curves intersection as the k:c values are reduced below 0.27. However, general mechatronic design changes with such simulation could lead to fewer intersection points, reducing the current value from six to four points. (Figs. 23-25) show increased sprung mass acceleration with a reduction in k:c.

Figs. (26-28) show the equation (3) application to the spring response for both the tire and the suspension systems. It is evident from the plots that the lowest variation ratio (SLVR) is at k;c=0.27 as it is designed for handling different road profiles.

Figs. (29-31) further support this work's findings as it shows the effect of road profile on suspension and tire system performance under different stiffness and damping conditions.

The findings are supported by the presented results in Table 5, where it is evident that for better handling on different road profiles, the Average SLVR ratio describing tire spring and suspension spring variations as a function of road profile and both stiffness and damping per fixed speed, the sprung and un-sprung mass and tire stiffness values should be:

(1) Lower than 1 in value.

(2) Smoothly change in value from low to the high road but not exceeding 1.

Together with sprung mass acceleration and number of intersections, shown in Tables 6 and 8, a three-parameter indicator can be used to enable optimization and driving strategy selection in the design and operation of autonomous vehicles, such that for better handling, the vehicle k:c should be optimized to have a low number of intersections, systematic and proportional increase in MAS, and SLVR less than 1.