AN INTEGRATED ROLLOVER MITIGATION STRATEGY FOR MILITARY TRUCKS

Transcription

1 010 NDIA GROUND VEHICLE SYSTEMS ENGINEERING AND TECHNOLOGY SYMPOSIUM MODELING & SIMULATION, TESTING AND VALIDATION (MSTV) MINI-SYMPOSIUM AUGUST DEARBORN, MICHIGAN AN INTEGRATED ROLLOVER MITIGATION STRATEGY FOR MILITARY TRUCKS Brad Hopkins Saied Taheri, PhD Mehdi Ahmadian, PhD Department o Mechanical Engineering Virginia Tech Blacksburg, VA Alexander Reid, PhD U.S. Army RDECOM- TARDEC Warren, MI ABSTRACT Military vehicles in the ield are oten required to perorm severe emergency maneuvers to avoid obstacles and/or escape enemy ire. This paper proposes a combined direct yaw control (DYC) and emergency roll control (ERC) system to mitigate rollover in the studied military vehicle. The DYC uses a dierential braking strategy to stabilize the vehicle yaw moment and is intended to reduce the risk o untripped rollovers and also help prevent the vehicle rom skidding out, thus allowing the driver to maintain control o the vehicle. The ERC uses actuators located near the vehicle suspension to apply an upward orce to the vehicle body to counter the roll angle. An o-road tire model was used with the overall vehicle model in commercially available vehicle simulation sotware to simulate emergency maneuvers on various driving suraces. Simulation results show that the proposed control strategy helps prevent both tripped and untripped rollovers on various driving suraces. INTRODUCTION Severe driving maneuvers perormed by a military vehicle on unexpected terrain can cause the vehicle to be prone to rollover. Several stability control algorithms exist that provide yaw and roll stability control, which have the potential o improving the o-road stability o a military vehicle. [1] proposes a yaw-roll stability control scheme that uses lateral acceleration measurements as eedback to generate a control signal applied by a dierential braking strategy. [] and [3] present yaw stability control schemes that utilize active ront steering and direct yaw-moment control to stabilize the vehicle yaw moment. [4] discusses the use o electronic brake system (EBS) or vehicle rollover prevention. [5] proposes a Roll Stability Control (RSC) system that can be easily integrated into an existing electronic stability control (ESC) system which can improve vehicle roll stability. [6,7] present a yaw stability control algorithm based on Lyapunov direct method that uses a dierential braking strategy to apply a corrective yaw moment to the vehicle. [8] presents a lateral acceleration based roll coeicient that warns o an impending rollover. In developing a rollover prevention control algorithm and testing it in a virtual environment, it is important to include a tire model. [9] discusses the Magic Formula (MF) tire model, which is a semi-empirical tire model that can provide the orces and moments acting on the tire or various vertical loads, slip angles, camber angles, orward speeds, and driving suraces. [10] presents the determination o scaling actors or the MF or various driving suraces, including dry asphalt, wet asphalt, ice, and snow. This paper presents an integrated roll stability control strategy or enhanced military vehicle stability and rollover avoidance. The strategy consists o two parts, the irst being a direct yaw-moment controller (DYC) [6,7] that uses a dierential braking strategy to stabilize the vehicle yaw moment. This helps the driver to maintain control over the vehicle to steer clear o potential obstacles or uneven terrain, as well as reduces the vehicle lateral acceleration and lateral velocity, decreasing the risk o untripped and tripped

2 Proceedings o the 010 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) rollovers, respectively. The second part o the control strategy is an additional layer o protection called emergency roll control (ERC), which was added to improve the roll stability o the vehicle. ERC utilizes a roll coeicient [8] related to vehicle static stability actor (SSF) to detect an impending rollover and applies an upward orce to the vehicle body through actuators located near the vehicle suspension as necessary. The proposed control strategy is evaluated on a military vehicle driven on various driving suraces in a virtual environment. Dry asphalt, dirt, and gravel driving suraces are simulated by utilizing a developed o-road tire model or the studied military vehicle. This paper is organized as ollows. First, the o-road tire model is presented. Next, the development o the rollover mitigation control strategy is presented. Finally, the control strategy is tested by simulating potential tripped and untripped rollovers on dry asphalt, dirt, and gravel driving suraces. OFF-ROAD TIRE MODEL A tire model was developed to simulate vehicle response on dry asphalt, dirt, and gravel driving suraces. The tire o the studied military vehicle was irst tested on a rolling road in an indoor tire test acility to develop a dry asphalt tire model. The tire was driven on a stainless steel lywheel that closely resembles a dry asphalt driving surace and was subjected to 0 degrees slip angle sine wave sweeps and 16 degrees camber angle sine wave sweeps at each combination o seven dierent vertical loads (700, 7650, 9000, 10800, 1600, 14400, lbs.) and our dierent orward speeds (5, 0, 40, 65 mph). All three orces and all three moments were measured in response to the various conditions previously described. The collected data was then curve itted to the Magic Formula [9] to obtain a tire model. Equations (1-8) show the ormulas or the lateral orce MF tire model: ( α+ SH) SV ( B( α+ S ) arctan( B( α+ S ))) B F y = Dsin C arctan + E H H D (1) C = a 0 () ( )( a F + a F a ) = (3) 1 z z 1 15γ ( a6 Fz + a7) ( 1 ( a16γ + a17) sign( S H )) (4) E = α + = a sin( arctan( F / a ))( a γ ) (5) K 3 z = K ( CD) (6) B / SH a8fz + a9 + a10γ = (7) = a F + a + ( a F a ) F γ (8) S V 11 z 1 13 z + 14 where F y is the tire lateral orce, F z is the tire vertical load, α is the tire slip angle, γ is the tire camber angle, B, C, D, E, S H, S V are Magic Formula parameters, and a 0, a 1,, a 17 are Pacejka coeicients or lateral orce. For each orward speed the Pacejka coeicients were solved or by using a curve itting routine. Table 1 shows the Pacejka coeicients that give the lateral orce tire model or the military tire on dry asphalt. They can be used with equations (1-8) to predict the lateral orce that will occur or a given vertical load, slip angle, and camber angle. Table 1. Lateral orce Pacejka coeicients or the military tire on dry asphalt Speed (mph) a a a a a a a a a a a a a a a a a a O-road tire testing was then perormed on a passenger tire to develop scaling actors that could be applied to the dry asphalt tire model to make it applicable or o-road terrain. It was ound in [10] that the majority o the scaling in lateral orce between two driving suraces can be quantiied in the peak value (D, equation (3)) scaling actor and the cornering stiness (K, equation (5)) scaling actor. It was also ound that the lateral orce scaling actors are primarily independent o vehicle type, vehicle orward speed, or tire type. As a result, the current research attempts to determine universal peak lateral orce and cornering stiness scaling actors that can be applied to any tire to transorm a dry asphalt lateral orce tire model into a dirt or gravel lateral orce tire model. Equation (3) then becomes: z An Integrated Rollover Mitigation Strategy or Military Trucks, Hopkins, et al. Page o 6

3 Proceedings o the 010 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) K where λ and D ( a1fz + afz)( 1 a15γ ) D= λd (9) = λ a sin( arctan( F / a ))( a5γ ) (10) K 3 z 4 1 λk are the peak value and cornering stiness scaling actors, respectively. To determine the scaling actors, a passenger tire was tested on dry asphalt, dirt, and gravel driving suraces using a portable tire test rig. Slip angle sweeps were perormed at six dierent vertical loads on all three driving suraces and the lateral orce response was measured. Peak value and cornering stiness were extracted rom each vertical load test and these values were used with equations (9-10) to determine the scaling actors or each driving surace. The results are shown in Table. Table. Peak value and cornering stiness scaling actors or dirt and gravel Driving Surace λ D λ K Dry Asphalt 1 1 Dirt Gravel The scaling actors rom Table can be used with the Pacejka coeicients rom Table 1 and equations (1-8) (with equation (9) substituted or equation (3) and equation (10) substituted or equation (5)) to determine the lateral orce tire model or the military vehicle tire on dry asphalt, dirt, and gravel driving suraces. STABILITY CONTROL STRATEGIES The roll stability control strategy or the military vehicle consists o a combined direct yaw-moment control (DYC) and emergency roll control (ERC) system. The DYC uses lateral acceleration and yaw rate measurements to calculate the corrective yaw moment required to get the vehicle yaw rate to match the desired (stable) yaw rate. The corrective yaw moment is applied through a dierential braking strategy. The goal o the DYC is to stabilize the yaw behavior o the vehicle so that the driver can maintain control, which is necessary or obstacle avoidance and escape maneuvers. The DYC also helps to reduce high vehicle lateral accelerations which is beneicial or preventing untripped rollovers, and also helps to reduce high vehicle lateral velocities, which can help to prevent potential tripped rollovers. The ERC is added as an extra layer o roll protection or the military vehicle. The ERC operates on lateral acceleration measurements and i a potential rollover is detected, applies an upward orce to the vehicle body via actuators located near the suspension. The combined DYC and ERC system is intended to assist the driver in maintaining control o the vehicle and helping to prevent rollovers during severe maneuvers. Direct Yaw Control The DYC algorithm was derived using a two degree o reedom bicycle model with lateral velocity and yaw rate motions considered. The equations o motion or the vehicle are: where v m 0 Cα δ x =, A=, r 0 I z W = acα δ Cα r Cα = u B acα bcα r u A& x+ Bx+ W = 0, (11) bcα r acα + mu u, a Cα b Cα r u v is the vehicle lateral velocity, r is the vehicle yaw rate, m is the vehicle mass, I z is the yaw moment o inertia, C α is the ront axle cornering stiness, C α r is the rear axle cornering stiness, a is the distance rom the vehicle center o gravity to the ront axle, b is the distance rom the vehicle center o gravity to the rear axle, u is the vehicle orward speed, and δ is the ront wheel steer angle. The control algorithm is then derived by irst adding a control law, U = [0 M s ] T, to the right hand side o equation (11) to get, A x& + Bx+ W = U, (1) where M s is the corrective yaw moment required to stabilize the vehicle. The control law, U, and an adaptation law are derived by using Lyapunov Direct Method as ound in [6,7]. The ollowing candidate Lyapunov unction is considered: Where x = x x [ T x Ax T p p] T + Γ + x Bx dt V ( x, t) = 1 (13) d is the state error vector, x is the state vector, x d is the desired state vector, p [ Cˆ Cˆ ] T = α α r is the An Integrated Rollover Mitigation Strategy or Military Trucks, Hopkins, et al. Page 3 o 6

4 Proceedings o the 010 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) adaptive parameter vector, and Γ is the adaptation gain matrix. In order to ensure system asymptotic stability, it is necessary to choose the control law and adaptation law such that V ( x, t) is positive deinite and V & ( x, t) is negative deinite. These criteria are ulilled when the control law is chosen to be: U = Ax ˆ& d + Bx ˆ d + Wˆ Λ x (14) where Λ is the control gain matrix, A = A ˆ A, B = B ˆ B, W = W ˆ W, and ^ denotes an estimated value, and the adaptation law is chosen to be: p & 1 T = Γ H x (15) Λ must be a positive diagonal matrix and Γ must be a positive deinite matrix in order to ensure asymptotic stability o the system. We can then deine H p= Ax& d + Bxd + W (16) where H is the adaptation matrix. I we insert equation (16) into the derivative o equation (13) we can solve or H, which is: vd ard + δ u H = avd a rd + aδ u vd + brd u bvd + b rd u (17) where v d is the desired lateral velocity and r d is the desired yaw rate, deined by: rd = uδ ( a+ b)( 1+ K u ) where K us is the understeer gradient. Emergency Roll Control us (18) The emergency roll control operates on a rollover coeicient that is presented in [8], which can be approximated by: h a R CG y tw g (19) where R is the rollover coeicient, h CG is the height o the center o gravity o the vehicle, t w is the vehicle track width, g is acceleration due to gravity, and a y is the lateral acceleration o the vehicle. When R = 1, it is expected that the vehicle will begin to rollover. A rollover coeicient reerence value, Rˆ, is chosen such that the ERC preventative strategy deploys when R Rˆ. So i R Rˆ and the vehicle is rolling to the let, the ERC will apply a 6000 N upward orce to the vehicle body via an actuator located near the suspension on the ront let and rear let o the vehicle; and i R Rˆ and the vehicle is rolling to the right, the ERC will apply a 6000 N upward orce to the vehicle body via an actuator located near the suspension on the ront right and rear right o the vehicle. VECHICLE ROLLOVER SIMULATIONS Potential tripped and untripped rollovers were simulated in a virtual environment by using commercially available vehicle simulation sotware. The sotware contains nonlinear multiple degrees-o-reedom models or various vehicle components, including steering, tires, suspension, and aerodynamics. Dry asphalt, dirt, and gravel driving suraces were simulated using the o-road tire model. In both the untripped and tripped rollover simulations the vehicle was given a NHTSA standard 140 degree ishhook steer input. During the untripped simulations the military vehicle was driven at a constant orward speed o 90 km/h and during the tripped simulations the vehicle was driven at a constant orward speed o 75 km/h. To simulate the vehicle striking an obstacle or the potential tripped rollover, a x0 multiplier was applied to the lateral riction during the constant steer angle portion o the ishhook maneuver. For both the tripped and the untripped rollover simulations, the vehicle was driven on dry asphalt, dirt, and gravel or the cases where it was uncontrolled (not equipped with DYC or ERC), equipped with just DYC, and equipped with both DYC and ERC. Table 3 shows the results rom the untripped rollover simulations. The table displays the maximum yaw rate (deg/s) and the maximum vehicle roll angle (deg) or the ishhook maneuver or each driving surace and controller condition. The results show that the addition o DYC can decrease both the maximum yaw rate and roll angle. The results show that the urther addition o the ERC to the DYC slightly improves the vehicle yaw stability, and signiicantly improves the vehicle roll stability. In such a case where there is a potential untripped rollover, like the dry asphalt case, the combined DYC + ERC system can prevent vehicle rollover. The riction coeicient o the An Integrated Rollover Mitigation Strategy or Military Trucks, Hopkins, et al. Page 4 o 6

5 Proceedings o the 010 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) dirt and gravel driving suraces is too low or the vehicle to rollover without hitting something. Table 3. Results rom untripped rollover simulations on dry asphalt, dirt, and gravel Max yaw rate (deg/s) / Controller max roll angle (deg) Uncontrolled DYC DYC + ERC Surace Dry Asphalt Dirt Gravel / 0.3 / / / / / / / / 3.01 Table 4 shows the results rom the tripped rollover simulations. As was illustrated in the untripped rollover simulations, the DYC + ERC system both reduces the vehicle yaw rate and roll angle during severe maneuvers. The aect o the proposed control system on the military vehicle when it strikes an object while moving laterally can be seen in table 4. The DYC signiicantly improves the yaw response o the vehicle so that when the vehicle strikes the lateral obstacle, the vehicle is already moving at a slow enough lateral velocity such that the obstacle will not cause a tripped rollover. The addition o the ERC does not signiicantly improve the vehicle yaw stability; however, it does continue to provide additional roll protection which is beneicial both beore and ater the vehicle strikes the obstacle. Table 3 and 4 illustrate the capabilities o the DYC and ERC control systems. The DYC helps the vehicle maintain yaw stability, decreasing dangerous levels o lateral velocity and lateral acceleration, thus decreasing the likelihood o potential tripped and untripped rollovers. The ERC provides an extra layer o roll protection that is not otherwise available rom the DYC system. A good example is the case o the untripped rollover simulation on dry asphalt where the DYC system is applying ull braking in order to decrease vehicle yaw rate due to the severe maneuver. The vehicle equipped with only DYC despite the act that a maximum control signal is already being applied. The urther addition o ERC in this situation provides an extra layer o roll protection that prevents the vehicle rom rolling over. Table 4. Results rom tripped rollover simulations on dry asphalt, dirt, and gravel Max yaw rate (deg/s) / Controller max roll angle (deg) Uncontrolled DYC DYC + ERC Surace Dry Asphalt Dirt Gravel CONCLUSIONS 7.0 / / / / / / / / / 4.87 A combined direct yaw-moment control and emergency roll control algorithm was proposed to improve the yaw and roll stability o a military vehicle. The algorithm was tested on o- and on-road driving suraces by utilizing a developed on- and o-road tire model or the military vehicle tire. Results o potential untripped and tripped rollover simulations show that the proposed control algorithm improves the vehicle yaw and roll response on a variety o driving suraces, and has the potential to prevent both tripped and untripped rollovers. REFERENCES [1] Chen, B-C., Peng, H., Dierential-braking-based rollover prevention or sport utility vehicles with human-inthe-loop evaluations. Vehicle System Dynamics, Vol. 36 (4-5), p , 001. [] Guvenc, B.A., Acarman, T., Guvenc, L., Coordination o steering and individual wheel braking actuated vehicle yaw stability control. IEE Con., 003. [3] Karbalaei, R., Ghaari, A., Kazemi, R., Tabatabaei, S.H., A new intelligent strategy to integrated control o AFS/DYC based on uzzy logic. International Journal o Mathematical, Physical and Engineering Sciences 1; 1, p.47-5, 007. [4] Palkovics, L., Semsey, A., Gerum, E., Roll-over prevention system or commercial vehicles additional sensorless unction o the electronic brake system. Vehicle System Dynamics, Vol. 3, p.85 97, [5] Lu, J., Messih, D., Salib, A., Roll rate based stability control the Roll Stability Control TM system. [6] Tamaddoni, S.H., Taheri, S., Yaw stability control o tractor semi-trailers, SAE Technical Paper , 008. [7] Tamaddoni, S.H., Taheri, S., A new control algorithm or vehicle stability control, ASME Proc. O 10 th Intl. Con. An Integrated Rollover Mitigation Strategy or Military Trucks, Hopkins, et al. Page 5 o 6

6 Proceedings o the 010 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) on Advanced Vehicle and Tire Technologies (AVTT), NY, USA, 008. [8] Odenthal, D., Bunte, T., Ackerman, J., Nonlinear steering and braking control or vehicle rollover avoidance, in European Control Conerence, [9] Pacejka, H.B., Tire and Vehicle Dynamics. Second ed. 006: SAE International. [10] Braghin, F., Cheli, F., Sabbioni, E. (006). Environmental eects on Pacejka s scaling actors. Vehicle System Dynamics 44(7): ACKNOWLEDGEMENTS This project was supported in part by a grant rom the Tank and Automotive Command (TACOM) o the U.S. Army, with Dr. Alexander Reid as Program Manager. The views expressed in this paper are those o the authors, and not the U.S. Government, the U.S. Army, or TACOM. The authors would also like to thank the Department o Animal and Poultry Sciences at Virginia Tech and Danville Regional Airport in Danville, VA or providing acilities or tire testing. An Integrated Rollover Mitigation Strategy or Military Trucks, Hopkins, et al. Page 6 o 6