A Novel Approach to Rollover Prevention Control of SUVs by Active Camber Control

Behrooz Mashadi a, Saleh Kasiri Bidhendia* and Mohammad Ismaeel Assadib

1Prof, School of Automotive Engineering Iran University of Science and Technology , Tehran, Iran.

2 Saleh Kasiri Bidhendi, School of Automotive Engineering Iran University of Science and Technol- ogy , Tehran, Iran.

3 Mohammad Ismaeel Assadi, School of Automotive Engineering Iran University of Science and Technology , Tehran, Iran. * Corresponding author e-mail: [email protected] Abstract

Roll instability of sport utility vehicles is threatening to the vehicle and traffic safety. A new ap- proach to roll stability control of Sport Utility Vehicles is proposed in this paper. The idea of active camber control to improve roll dynamics is introduced. The study of dynamics of sport utility vehicle is performed using CarSim software package. A rule-based control strategy has been developed which effectively controls camber angle on front axle. Co-simulation is carried out by integrating Matlab/Simulink software with the vehicle simulation environment. It has been shown that active camber can improve roll stability of SUVs and reduce the risk of hazardous traffic accidents.

Keywords: rollover; active camber; SUV

1. Introduction The automotive industry has been experiencing a greedy competence in the variety of products as well as an ever-increasing demand for safety standards. Sport Utility Vehicles have in the recent decade attracted noticeable attention. Among the frequently-occurring accidents, roll-over contrib- utes to a vast majority in SUVs due to their high center of gravity and ground height clearance. Sta- tistics reveal a significant fatality of 59% in roll-over accidents of this category of vehicles[1]. Roll-over accidents generally fall into two categories of tripped and un-tripped. Tripped roll- over occurs either when the vehicle hits an obstacle in sideways direction, or due to the road rough- ness. Un-tripped roll-over, on the other hand happens as a result of excessive lateral acceleration developed by the vehicle in severe manoeuvres on high-friction courses. The static stability factor (SSF) defines a criterion for the maximum lateral acceleration which leads to two wheel lift-off[2]. Nonetheless, when two-wheel lift-off occurs, the lateral acceleration threshold yields a smaller value 1 6th International Conference on Acoustics & Vibration (ISAV2016), K. N. Toosi University of Technology, Tehran, Iran, 7-8 Dec. 2016

than that yielded by SSF due to the displacement of vehicle center of gravity in both lateral and vertical directions. In the recent decade numerous researches have been performed to investigate and improve roll dynamics of SUVs. A bulk of research has been focused on improving roll dynamics of SUVs. The approaches to improve and/or prevent roll-over followed so far fall mainly into three catego- ries: 1) steer control, 2) tire traction and brake control, and 3) active suspension. Imine,et.al. design an active front steer to prevent a heavy vehicle from rollover[3]. The second method to prevent roll- over focuses on the relationship between lateral tire force and longitudinal force. [4]. Another study by Chen, et.al. described a method to prevent rollover via selecting which wheel to brake[5]. Ac- tive geometry systems unlike other methods use a direct method by applying roll-moment to the sprung mass of vehicle. Cimba, et.al[6] studied the effect of anti-roll bar on vehicle dynamics and sprung mass roll angle Suetake ,et.al. have designed a controller based on four-wheel steering sys- tem which tracks an ideal vehicle model [2]. A creative approach proposed by Mashadi,et.al. sug- gested implementing a gyroscopic system in vehicle for prevention of vehicle rollover[7]. Yoshino and Nozaki studied the effect of camber angle variations in negative and positive directions on both tire force generation and yaw rate characteristics. They improve vehicle dynamics in skid mar- gin[8][9]. Park and Sohn studied the effect of front suspension camber control on vehicle dynamics to improve cornering performance [10]. Although differential braking provides a reasonable means of lateral control with minimum requirement of additional hardware installation, it adversely affects longitudinal dynamics of the ve- hicle. In addition, abrupt decrease in longitudinal acceleration may cause the vehicle to oversteer, further worsening the situation. Braking also can lead to increase in tire side slip angle on moderately- severe manoeuvres, further increasing the lateral force developed by the tires and consequently the lateral acceleration of vehicle. Another side effect of roll-over prevention by braking is that when a braking input is applied, the subjective assessment of the driver, that is, his or her correct judgement of the situation will be adversely affected, thus leading him/her to involve the situation and most probably hastening the degradation of stability. The current study is focused on active camber control to prevent un-tripped roll-over in SUVs. As such, the rest of the paper is organized as follows: section two presents vehicle and tire model. A rule- based control strategy is developed in section three. Section four presents the results of the simula- tions and analyses the effectiveness of the proposed method. Conclusion is presented last section.

2. Tire and Vehicle Modelling

2.1 Vehicle Model and steady-state tests CarSim 2016.1 was used to model the vehicle. CarSim is a full-vehicle simulator developed by Mechanical Simulation Corporation. An SUV with the configuration introduced in Table 1. is mod- elled in Carsim to study the effects of front axle camber variations on roll dynamics of the vehicle. In addition, steady-state characteristics of vehicle were studied through slowly increasing steer test as specified by NHTSA. Specifications of slowly increasing steer test have been provided in Table 2. Table 1. Sport Utility Vehicle Parameters Vehicle Model Carsim E-class SUV Sprung Mass 1590 kg Wheel Base 2920 kg Height of CG 720 mm Track 1511 Roll inertia 894.4 kg-m2 Pitch inertia 2687 kg-m2 Yaw inertia 2687 kg-m2 Unsprung mass 270 kg Front Axle Independent SLA Read Axle Solid Axle Tire size 265/70 R17

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Table 2. Specifications of slowly increasing steer test as specified by NHTSA Latac (g) 0.3 Maximum (0.8) Steering Wheel Angle (deg) 42 200

2.2 Tire Characteristics Tire force generation characteristics have significant effects on vehicle behaviour. It is gener- ally acknowledged that the cornering characteristics of tires vary according to camber angle[11] sev- eral efforts have therefore been focused on incorporating camber effects into tire models. Linear and non-linear relationship for camber effects have been developed and addressed in the literature. Most notably, camber alters lateral force irrespective of its direction of change. Variations of tire lateral force against side slip angle for different camber angles has been depicted in Fig. 3. Since tire models have been developed based on different preliminary assumptions and for dif- ferent application scenarios, the effect of camber on tire force generation characteristics differ from one model to another. Thus, depending on the level of accuracy and expected camber contributions to lateral force behaviour, a reliable tire model capable of accommodating large camber variations is necessary for successful study of effectiveness of camber angle variation for roll-prevention. In the current study, Pacjecka 6.2 has been adopted to effectively model tire behaviour and examine camber variations. Pacjecka is a semi-empirical tire model whose reliability and analysis has been presented in detail in [12].The general form of Magic Formula is described in Eq.(1)[13].

푦 = 퐷 sin[퐶 arctan{퐵푥 − 퐸(퐵푥 − arctan 퐵푥)}] (1)

푌(푋) = 푦(푥) + 푆푣 (2) 푥 = 푋 + 푆퐻 (3)

In Eqs. (1) to (3) Y is the output variable 퐹푥, 퐹푦 or possibly 푀푧 and 푋 the input variable 푡푎푛 훼 or 휅, and 퐵 is the stiffness factor, 퐶 the shape factor, 퐷 the peak value, 퐸 the curvature factor, 푆퐻 the horizontal shift, and 푆푉 the vertical shift.

Figure 1. Camber angle in a double wishbone front suspension system

Figure 2. Effect of Camber on Steady State roll angle behavior of SUV

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In order to study the effect of camber on lateral acceleration characteristics of vehicle, a set of slow-steer tests were performed at 80푘푚/ℎ with the steering wheel rate equal to 13.5 푑푒푔푠/푠푒푐 and a final value of 450 degrees for the steering wheel angle. The test has been performed in accordance with NHTSA standards, and has been repeated for different camber angles as depicted in Fig. 2 It can be seen that camber that the smallest values of lateral acceleration are produced when camber angles are equal to (8, 8) or (-8, 8) for left and right wheels respectively. The convergence of both curves suggests that for the range of angles and test conditions introduced, there is a boundary for camber angle beyond which lateral acceleration does not decrease any further. The more or less similar trends of curves at different cambers also imply that in order for optimum efficiency, camber should be altered in proportion to the steering wheel angle inputs of vehicle. the results of the test depicted in Fig. 1 also shows that best lateral force reduction occurs at -8 and +8 camber angles.

Figure 3. Effect of Camber on tire Lateral Force generation It can be seen from Fig. 3 that tire force curves converge at slip angles above 15 푑푒푔푠. This suggests that beyond a specific range, camber variations have no effect on force generation properties irrespective of the direction of camber. This can be attributed to the nonlinear characteristics of tire at large slip angles where tire approaches saturation in lateral direction.

3. Development of Control algorithm for active camber control Lateral acceleration contributes most to un-tripped roll-over incidents. In this regard, the control algorithm developed in this study attempts to decrease lateral acceleration so as to decrease roll mo- ment, thus preventing roll-over. The relationship between lateral force and side slip follows a linear regime as described by Eq. (4).

퐹푦 = 퐶푎푙푝ℎ푎훼 + 퐶훾훾 (4)

Since camber angle becomes ineffective in the areas where tire saturates, a desirable approach to affect tire force generation, most favorably a reduction in lateral force to reduce lateral acceleration is to alter the direction of camber angle over that range. Thus the control scheme developed in this paper is organized to alter the direction of camber angle to prevent roll-over. Also the change in direction of camber angle must be managed fast so as to minimize the time to reach optimum results. In organizing the control scheme, lateral acceleration threshold of 0.4푔, as representative of a moderate latac is considered as the point where the control system signals camber actuation. This ensures that control system functions quick enough to engage when the transition to roll-over occurs fast. In addition, it compensates for the lags in both the mechanism and tire. Furthermore, the studies

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performed by authors suggest that this threshold is effective is subsiding the maximum roll angle. The rule-based control strategy is thus developed according to the following set of considerations:

𝑖푓 푎푦 > 0.4푔 훾 = [−8.8] (5) 𝑖푓 푎푦 < −0.4푔 훾 = [8. −8]

Fig. 4 demonstrates the vehicle system model and the control scheme integrated with it in MatLab/Simulink environment.

Figure 4. Co-simulation of vehicle model in MatLab/Simulink Environment

4. Simulation and Results

4.1 Fishhook test Fishhook test was developed by Toyota and variations of this test were suggested by Nissan and Honda [14]. However, NHTSA has experimented different versions of it and present a fishhook test with roll rate feedback. Fig. 5 describes Fishhook manoeuvre in terms of maximum steering angle and time to counter steer.

Figure 5. variation of steering angle vs time in fishhook test

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(a) (c)

(b) (d) Figure 6. Fishhook Response of SUV for controlled and uncontrolled

Figs. 6.a to 6.d illustrate the effectiveness of the proposed method in preventing roll-over. As depicted in Fig. 6.a, roll angle becomes infinite for the uncontrolled case, suggesting a roll-over. It, however, has been limited to a maximum of −7.3 degrees over the whole duration of the test. Alt- hough threshold value of acceleration to trigger the control system has been set to 0.4 푔, the reversal in the trend of roll angle variation falls behind in time as compared to the corresponding time of lateral acceleration where threshold is set. This supports the preliminary idea of considering a conservative threshold for lateral acceleration to compensate for system lags (Figs. 6. a and b). On the other hand, detailed analysis of the lateral acceleration curve suggests that greatest improvements in lateral ac- celeration also occur at the corresponding time of roll angle curve reversal, extenuating the direct effect of lateral acceleration on roll angle. In addition, the smooth deviation of lateral acceleration curve of controlled case from uncontrolled one emphasizes that camber angle variations have been proportional to latac development. This ensures that the system does not impose adverse effects on the subjective assessment of the driver. Also of significance, yet less frequently addressed in the literature is the decrease in roll rate response of vehicle when camber control is triggered. Roll rate affects both frequency response of vehicle in roll plane and roll-over energy. It also reveals the rate at which roll angle varies, whose effect on vehicle roll stability is more pronounced than roll angle itself. In Fig. 6.c, the roll rate has been effectively controlled both in terms of overshoots and time response. The important fact is that the maximum overshoot in roll rate precedes the overshoots of both latac and roll angle, but corresponds to a significantly higher lateral acceleration as compared to the case of roll angle. This implies that roll angle is more noticeably affected by lateral acceleration than roll angle. In this regard, camber angle has also led the roll rate overshoot to precede in time as compared to uncontrolled case, implying further improvements in roll dynamics behaviour of the vehicle.

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5. Conclusion A roll-over prevention approach based on camber angle control was introduced in this paper. By modelling the tire force generation behaviour, it was first demonstrated that camber angle is suf- ficiently effective for manipulating tire lateral force in a desired range to control roll-over. Effective range of camber angle variations was defined by performing steady state test. Finally a rule-based control strategy was developed to study the effectiveness of the proposed idea. It was shown that camber angle control can efficiently help prevent vehicle roll-over. The effect of roll rate was also considered and discussed in the paper. The research demonstrates that camber angle control is an efficient means of roll-over prevention in SUVs with high CoG and ground clearance height.

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