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Article Developing a Strategy to Improve Handling Behaviors of a Medium-Size Electric Bus Using Active Anti-Roll Bar

Hsiu-Ying Hwang 1 , Tian-Syung Lan 2,* and Jia-Shiun Chen 1

1 Department of Vehicle Engineering, National Taipei University of Technology, Taipei 10608, Taiwan; [email protected] (H.-Y.H.); [email protected] (J.-S.C.) 2 College of Mechatronic Engineering, Guangdong University of Petrochemical Technology, Maoming 525000, China * Correspondence: [email protected]

 Received: 15 June 2020; Accepted: 6 August 2020; Published: 10 August 2020 

Abstract: Electric vehicles are a major trend in research and development in the automobile industry. A vehicle’s handling ability is changed when the structure of the power system is altered, which is more obvious in medium-sized buses with higher load and a longer body whose body stiffness is relatively less stiff. In this context, flexible multi-body dynamic modeling, instead of rigid body modeling, is used to reflect the stiffness effects of the vehicle body and systems. A control strategy is developed with an active variable stiffness anti-roll bar to improve vehicle handling characteristics by using the flexible body dynamic simulation with consideration of the step and single sinusoidal input tests. Through simulation, it was learned that the proposed control strategy could reduce the time of stabilization by 54.08% and suppress undesired handling behaviors in the step steering input test. Moreover, at high speed, the original unsteady condition became stabilized with little sacrifice in yaw velocity. In the single sinusoidal steering input test, the time of stabilization could be reduced by 8.43% and with 14.6% less yaw angle changes in the improved design. The overall handling was improved.

Keywords: multi-body dynamic simulation; flexible body; anti-roll bar

1. Introduction Internal combustion engine vehicles have been developed for many years, and most of the techniques used in passenger nowadays are based on internal combustion engine vehicles. However, factors such as the oil crisis and the rise of environmental conservation awareness have led the vehicle industry towards energy-saving and carbon-reducing development. In addition to improving the efficiency of the internal combustion engine and to developing hybrid electric vehicles, the advantages of electric vehicles, like zero-emission and zero pollution, have become the focus of research and development of various vehicle manufacturers. Most electric vehicles only replace the power systems with electric motors, but the differences in the engine power curve, the increase of overall battery load, and the shifts of the center of gravity configuration, etc. can change the vehicle steering characteristics and may directly affect the vehicles’ handling behaviors. This research focused on the control strategy development of a set of active anti-roll bars to improve vehicle handling characteristics by using the flexible body dynamic simulation. With the help of simulation, the development time and number of iterations could be significantly reduced. Ambrósio et al. [1] proposed a flexible multi-body dynamic simulation method for vehicle research, and used ANSYS to build a flexible vehicle body for simulation. The final result was greatly different

Symmetry 2020, 12, 1334; doi:10.3390/sym12081334 www.mdpi.com/journal/symmetry Symmetry 2020, 12, 1334 2 of 33 from the rigid body model. In their study, the road bump scenario showed that the flexible model had much higher accelerations and a more uneven response than the rigid model. Moreover, in the directional response of handling, quantified by the time required for lateral acceleration, the rigid body model had a higher tendency to oversteer. The flexible model had a slightly slower response than that of the rigid model which could quickly develop the maximum lateral acceleration for the turning situation. The differences between flexible and rigid models in terms of lateral position and acceleration could be up to 20%. Oversteer in general was not desired since the vehicle became difficult to drive at higher speeds. Suh et al. [2] performed a dynamic stress analysis on a vehicle frame, which imported a flexible body model into a multi-body mechanical model for stress analysis, and the analysis results showed that the accuracy of flexible body model was improved by 14.42% compared to rigid bodies Ma et al. [3] used HyperWorks to build a flexible body model of the shell, which integrated into the ADAMS multi-body dynamics software for comfort simulation analysis, and its result was afterward compared with the result from actual experiment. In terms of lateral acceleration, the results of flexible body model are much closer to the measured results than those of the rigid body model. Gonçalves et al. [4] optimized the comfort and handling of a flexible multi-body dynamic model of a car body, using the stiffness and damping coefficient of the suspension system as variable parameters, and optimizing the comfort by the driving performance index. Mirone [5] established a flexible body model of a go-kart frame. After verification, a multi-body dynamic simulation with fixed circle test was performed, and the rigidity of the frame was changed numerically. The results confirmed the argument that frame rigidity affected vehicle handling performance. Shiiba et al. [6] performed a constant-speed pulse steering test on a baseline model and on the same baseline model but with added structural members to increase the rigidity of the frame. These two frames had yaw rate and steady state gain differences numerically and experimentally. Guo et al. [7] used a numerical calculation to simulate a quarter model, and controlled hysteresis damping with an adaptive neural control system to improve vehicle comfort. Azadi et al. [8] established a rigid-flexible multi-body dynamic model and designed a body dynamic control system. Their results concluded that the flexible body model was more realistic than rigid bodies, and was more suitable for dynamic control. Zhang et al. [9] used the AGC-ViewerG stereo observation system to test the closed-loop handling characteristics of the vehicle. They put forward that the vehicle visualized experimental system could observe the , and measuring the values of the experiments, which could save the cost and improve the quality of the experiments. Angel et al. [10] designed a control system and a control logic through the optimization method to control the air spring and magnetorheological damper parameters in order to improve vehicle handling and comfort. Darling et al. [11] established a prototype active anti-roll bar control system to control its damping solenoid valve with a simple control system. A Ford Fiesta Mark II was used as the platform for the active roll control study. With limited changes to the existing system and the active components had to be accommodated within a very limited envelope. Its actuator connected the anti-roll bar to the suspension tie rods. As a result, in the circular steering test, the prototype vehicle demonstrated excellent steady state and dynamic roll cancellation within the lateral acceleration range of 0.5 g. The comparison between the active and passive roll response is quite dramatic with being reduced by over 80%. Cronje et al. [12] designed an active anti-roll bar to improve the handling performance of off-road vehicles, and used the commercial software, ADAMS, to establish a multi-body dynamic simulation, and verified the initial model through actual experiments. After improvement, the roll angle was much lower than the original model. Vu et al. [13] used numerical calculations to simulate a heavy vehicle with an active anti-roll bar, and used a secondary linear regulator to find the best control strategy based on lateral load transfer to improve rollover of heavy vehicles. Danesin et al. [14] designed an active rolling control system to increase vehicle handling and comfort. The roll stiffness of the front and the rear was changed based on vehicle lateral acceleration, and the simulation results were verified by actual vehicle experiment. Struss and Urbach [15] designed a set of variable stiffness anti-roll bars. They used a device which was a fluid filled with an electrorheological fluid that could be Symmetry 2020, 12, 1334 3 of 33

Symmetry 2020, 12, x FOR PEER REVIEW 3 of 34 actuated for varying the torsional stiffness of the portion of the anti-roll bar. At least one sensor senses a vehicleUrbach characteristic [15] designed and a set generates of variable a signalstiffness indicative anti-roll bar of thes. They sensed used vehicle a device characteristic. which was a fluid coupIn theling earlier filled research, with an electrorheological not many focused fluid on that developing could be control actuated strategy for varying to improve the torsional handling utilizingstiffness flexible of the multi-body portion of the models anti-roll with bar. active At least variable one sensor stiffness senses/damping a vehicle anti-roll characteristic bar, especially and notgenerates much for a medium-sizesignal indicative electric of the busessensed norvehicle for electriccharacteristic. buses. In a highly dense population area, medium-sizeIn the buses earlier are research, one common not many mass focused transportation on developing system. control A medium-size strategy to improve electric bushandling is used as utilizing flexible multi-body models with active variable stiffness/damping anti-roll bar, especially the target vehicle. The longer vehicle body become less stiff, and the rigid body model relatively would not much for medium-size electric buses nor for electric buses. In a highly dense population area, not be a perfect fit for this less stiff type of vehicle. Since it is an , the power system medium-size buses are one common mass transportation system. A medium-size electric bus is andused the load as the distribution target vehicle. are not The the longer same vehicle as the body regular become gasoline less engine stiff, and vehicles. the rigid It is body diff erent model from commonlyrelatively seen would cases. not Basedbe a perfect on earlier fit for study,this less there stiff type can beof vehicle. more than Since 20% it is di anff erenceselectric vehicle, between the rigid bodypower and flexiblesystem and body the in load lateral distribution position are and not lateral the same acceleration as the regular [1], andgasoline flexible engine body vehicles. model It was moreis realistic different than from rigid commonly body one seen [8 ]. cases. Therefore, Based in on this earlier research, study, a the multi-bodyre can be dynamic more than simulation 20% of thedifferences coupling between flexible rigid body body for and a medium-size flexible body in electric lateral busposition was and carried lateral out acceleration and a set [1], of and control strategyflexible for body the active model anti-roll was more bar system realistic was than proposed, rigid body under one the[8]. premise Therefore, that in the this movement research, a such as themulti pitch-body of dynamicY-axis, the simulation vertical of displacement the coupling of flexibleZ-axis, body and for the a medium vibration-size of suspensionelectric bus was system causedcarried by roadout and surface a set wereof control not astrategyffected. for The the objective active anti is- toroll study bar system the handling was proposed, performance under the of this medium-sizepremise that electric the movement bus and such to improve as the pitch the of vehicle Y-axis, stability the vertical by reducingdisplacement the of severe Z-axis, oversteering and the vibration of suspension system caused by road surface were not affected. The objective is to study and unstable condition. The proposed control strategy was based on the steering characteristics to the handling performance of this medium-size electric bus and to improve the vehicle stability by provide a quick response in order to adjust the stiffness and damping of the anti-roll bar. The system reducing the severe oversteering and unstable condition. The proposed control strategy was based wason designed the steering to alter characteristics the roll stiff ness to provide and the a quickdamping response coeffi incient order of the to adjustsuspension the stiffness system and during differentdamping steering of the maneuvers. anti-roll bar. The system was designed to alter the roll stiffness and the damping coefficient of the suspension system during different steering maneuvers. 2. Research Background 2.This Research study Background used the finite element vehicle body built by Lin [16] and the flexible multi-body dynamicThis chassis study model used the built finite by element Yang [vehicle17], and body incorporated built by Lin both[16] and models the flexible into the multi commercial-body software,dynamic HyperWorks. chassis model All built the by rest Yang model [17], and build, incorporated and settings both models of material into the properties commercial for all componentssoftware, and HyperWorks. boundary All conditions the rest model were done build, in and HyperWorks settings of /Optistruct, material properties and then forutilized all the Craig-Bamptoncomponents and substructureboundary conditions modal methodwere done [18 in,19 HyperWorks/Optistruct,] to create the flexible bodiesand then which utilized were the then fed intoCraig HyperWorks-Bampton substructure/MotionView modal to setmethod up all [18,19 the joints] to create and the connections flexible bodies for all which of the were parts, then as fed well as the tireinto modelHyperWorks/MotionView and the pseudo-road to set for up the all flexible the joints multi-body and connections dynamic for analyses.all of the parts, The analyses as well as were the model and the pseudo-road for the flexible multi-body dynamic analyses. The analyses performed using HyperWorks/MotionSolve. were performed using HyperWorks/MotionSolve. 2.1. Specifications of the Simulation Model 2.1. Specifications of the Simulation Model A medium-sized electric bus was used for simulation research, as shown in Figure1. The vehicle A medium-sized electric bus was used for simulation research, as shown in Figure 1. The specificationsvehicle specifications were summarized were summarized in Table1 in, according Table 1, according to the manufacturer’s to the manufacturer’s catalog catalog [20]. [20].

Figure 1. A medium-sized eclectic bus. Symmetry 2020, 12, 1334 4 of 33

Table 1. Vehicle specifications [20].

Parameters RAC-300 Dimensions L*W*H 7000 2135 2603 (mm mm mm) × × Base (mm) 3800 Curb Weight (N) 58,958 Vehicle Load (N) 16,579 GVWR (N) 75,537 Front Axle Load (N) 30,794 Rear Axle Load (N) 44,773 Passengers (seat/stand) 19 + 1/10 Top Speed (km/h) >100 Max. Climbing Angle (%) >30% (full load) Charging Time (h) 6–7 h (30 Kw) Battery Type Yttrium Lithium Battery Battery Capacity (kWh) 107 Motor Type AC Induction Air-cooled Motor Power (kW) Rated 75/Peak 150 Motor Torque (Nm) Rated 284.5/Max 706 Front/Rear Axle 2500/5000 Braking Systems Air + WABCO ABS Assisted Braking Regenerative Braking Gearbox 6-Speed MT Vehicle Operating System BMS/VCU

2.2. Flexible Body Model The vehicle was mainly constructed from the vehicle body, powertrain/power, and chassis system. The vehicle body included body frame, floor panels, body panels, seats, interior/exterior trim items and front/rear bumpers. All vehicle body components used fixed joints to connect to the body frame. Therefore, the whole vehicle body was treated as one flexible body which was then decked onto the chassis main frame, shown in Figure2. The rest chassis components and powertrain /power systems were mounted to the chassis frame. In this study, flexible bodies were used in the multi-body dynamic analysis. In order to account for the flexibility of bodies, the Craig–Bampton substructure modal method was used. This method reduced the degrees of freedom of the finite element model to the interface degrees of freedom and a set of normal modes, and significantly reduced the analysis time. The interface points were the connecting, constrained or force applied points. The chassis main frame had twelve interface points which the body or chassis components mounted on. This study used the medium-size electric bus with a non-integrated type of chassis, which was body on frame type of vehicle structure. The forces and interaction were through the interface points. The whole vehicle body was treated as one flexible body, and only global body normal modes were chosen for the flexible multibody dynamic analyses. The local modes of body components were not included. The flexible body model contained all the components of the body and the frame, and the global modes, such as torsion and bending modes. In the modal analysis, no damping or constrains were applied. The chassis main frame, body frame, and body panels are presented in Figures2–4, respectively. Symmetry 2020, 12, x FOR PEER REVIEW 5 of 34

Symmetry 2020, 12, x FOR PEER REVIEW 5 of 34

SymmetrySymmetry 20202020, ,1122, ,x 1334 FOR PEER REVIEW 55 of of 34 33

Figure 2. Vehicle chassis main frame.

Figure 2. Vehicle chassis main frame. Figure 2. Vehicle chassis main frame. Figure 2. Vehicle chassis main frame.

Figure 3. Vehicle body frame. Figure 3. Vehicle body frame.

Figure 3. Vehicle body frame. Figure 3. Vehicle body frame.

Figure 4. Vehicle body panels. Figure 4. Vehicle body panels. 2.3. The Multi-Body Dynamic Model of the Chassis 2.3. TheThe Multi construction-Body Dynamic of theModel chassis of the C includeshassis the system, the steering system, Figure 4. Vehicle body panels. the suspensionThe construction system, of and the the chassis . includes The vehicle the model transmission used in thissystem, research the steering was a non-integrated system, the suspensiontype chassis, system, and its and components the tires. The were vehicle installed model on the used chassis in this rails. research was a non-integrated type 2.3. The Multi-Body Dynamic Model ofFigure the Chassis 4. Vehicle body panels. chassis,2.3.1. Transmission and its components System were installed on the chassis rails. 2.3. TheThe M constructionulti-Body Dynamic of the M odel chassis of the includes Chassis the transmission system, the steering system, the 2.3.1.suspension BasedTransmission onsystem, the research Sandystem the purpose,tires. The the vehicle test was model focused used onin thethis vehicleresearch response was a non in di-integratedfferent steering type The construction of the chassis includes the transmission system, the steering system, the chassis,maneuvers, and its and components the vehicle were motion ins intalled the lateral on the direction chassis rails. was measured. To prevent the interference suspensionBased system, on the researchand the tires. purpose, The vehicle the test model was used focused in this on research the vehicle was responsea non-integrated in different type from longitudinal motion, the longitudinal motion of vehicle was carried out at a fixed speed. chassis,steering andmane itsuvers components, and the were vehicle installed motion on inthe the chassis lateral rails. direction was measured. To prevent the 2.3.1.The drivelineTransmission system System provided a steady torque to maintain the vehicle speed, and the variation of interference from longitudinal motion, the longitudinal motion of vehicle was carried out at a fixed powertrain output was not included the modeling. Without considering the vibration changes in power speed.2.3.1. BasedTransmission The on driveline the S researchystem system purpose, provided the a steady test was torque focused to maintain on the vehicle the ve hicle response speed, in different and the steeringtransmission, maneuvers the construction, and the vehicle could motion be simplified. in the lateral The universal direction jointwas wasmeasured. a standard To prevent connection the variationBased of onpowertrain the research output purpose, was not the included test was the focused modeling. on Without the vehicle considering response the in vibration different interferenceapplied in the from long longitudinal driving shafts motion, of buses the andlongitudinal trucks. As motion the same of vehicle joint applied was carried in the out target at a electric fixed steeringchanges mane in poweruvers transmission,, and the vehicle the motion construction in the couldlateral be direction simplified. was Themeasured. universal To prevent joint was the a speed.bus, the The universal driveline joint system was retained provided to connect a steady the transmission torque to maintain and the di thefferential vehicle so that speed, the vibration and the interference from longitudinal motion, the longitudinal motion of vehicle was carried out at a fixed variationof the suspension of powertrain system output could was be truly not included simulated the during modeling. the test. Without In the considering test, the drive the shaft vibration drove speed. The driveline system provided a steady torque to maintain the vehicle speed, and the changesthe rear in power directly transmission, with a speed the command. construction The could simulation be simplified. results of The the handling universal characteristic joint was a variation of powertrain output was not included the modeling. Without considering the vibration changes in power transmission, the construction could be simplified. The was a

Symmetry 2020, 12, x FOR PEER REVIEW 6 of 34 Symmetry 2020, 12, x FOR PEER REVIEW 6 of 34 standard connection applied in the long driving shafts of buses and trucks. As the same joint appliedstandard in the target connection electric applied bus, the in universal the long joint driv ingwas shaftsretained of to buses connect and the trucks. transmission As the same and joint the differentialapplied in so the that target the vibrationelectric bus, of the suspensionuniversal joint system was couldretained be trulyto connect simulated the transmission during the and test. Inthe the differential test, the sodrive that theshaft vibration drove theof the rear suspension wheels directly system could with abe speed truly simulated command. during The the Symmetrysimulationtest.2020 In,results12 , the 1334 of test, the the handling drive characteristicshaft drove thewere rear obtained wheels without directly considering with a speed the influence command.6 of 33of The the transmissionsimulation results system. of the The handling transmission characteristic system conwerestruction obtained is without shown considering in Figure 5 the, and influence the of connectionsthe transmission of the transmission system. components The transmission are shown system in Table cons truction2. is shown in Figure 5, and the were obtainedconnections without of the considering transmission the components influence of theare transmissionshown in Table system. 2. The transmission system construction is shown in Figure5, and the connections of the transmission components are shown in Table2.

Figure 5. Transmission system construction. FigureFigure 5. Transmission 5. Transmission system system construction. construction. Table 2. Connections table of the transmission system components. Table 2.TableConnections 2. Connection tables of table the transmissionof the transmission system system components. components. Component 1 Component 2 Connect Method Component 1 Component 2 Connect Method TransmissionComponent Front 1 driveshaftComponent Y 2- Z UniversalConnect joint Method TransmissionFront driveshaftTransmission FrontRear driveshaftFront driveshaft Y-Z UniversalY-Z Y-Z Universal Universal joint joint joint Front driveshaftFront driveshaft Rear driveshaftRear driveshaft Y-Z Y-Z Universal Universal joint joint Rear driveshaftRear driveshaft DiDifferentialfferential Y-Z Universal Y-Z Universal joint joint Rear driveshaft Differential Y-Z Universal joint 2.3.2. Steering System 2.3.2. Steering2.3.2. Steering System System The steering system used in the simulation test was the pitman arm steering system, which The steering system used in the simulation test was the pitman arm steering system, which had a had a fourThe-bar steering double systemswing mechanism used in the, wa simulations often used test was in steering the pitman system arm with steering integral system front, which four-bar double swing mechanism, was often used in steering system with integral front suspension, suspension,had a and four -conformbar doubleed to swing Ackermann mechanism steering, wa geometrys often used. The in steering steering force system in the with simulation integral front and conformed to Ackermann steering geometry. The steering force in the simulation test was test wassuspension, entered by and the conform rotationaled jointto Ackermann between the steering gearbox, geometry fixed to. theThe c hassissteering rail, force and in the the pitman simulation entered by the rotational joint between the gearbox, fixed to the chassis rail, and the pitman arm. arm. Thetest constructionwas entered byof thethe steeringrotational system joint betweenand connect the iongearbox, methods fixed of to the the components chassis rail, are and shown the pitman The construction of the steering system and connection methods of the components are shown in in Figurearm. 6 Theand constructionTable 3, respectively. of the steering system and connection methods of the components are shown Figurein6 and Figure Table 6 and3, respectively. Table 3, respectively.

Figure 6. Steering system construction. Figure 6. Steering system construction. Figure 6. Steering system construction.

Symmetry 2020, 12, x FOR PEER REVIEW 7 of 34 Symmetry 2020, 12, 1334 7 of 33 Table 3. Connections table of the steering system components.

ComponentTable 1 3. ConnectionsComponent table of the2 steering systemConnect components. Method Steering gearbox output Pitman arm Y rotational joint Component 1 Component 2 Connect Method Pitman arm Drag link Y-Z Universal joint Steering gearbox output Pitman arm Y rotational joint Drag link Left steering arm Y-Z Universal joint LeftPitman steering arm arm Left Drag Tie link rod Z rotational Y-Z Universal joint joint DragLeft link tie rod Left steeringwheel hub arm Z rotational Y-Zjoint Universal (left-front joint Kingpin) LeftRight steering steering arm arm Right Left Tie tie rodrod Z rotational Z rotational joint joint LeftRight tie rod tie rod Right Left wheelwheel hub hub Z rotational Z rotational joint joint (right (left-front-front Kingpin) Kingpin) Right steering arm Right tie rod Z rotational joint 2.3.3. Suspension System Right tie rod Right wheel hub Z rotational joint (right-front Kingpin) The used in this simulation test was built up by beam element, which was able to 2.3.3.endure Suspension the force System and deform. Each steel plate was divided into eight equal pieces. Each beam element was connected to each other by a fixed joint, and its center point was connected to the axle in a fixedThe leaf way. spring The front used end in this was simulation connected testto the was spring built hanger up by,beam which element, was connected which wasto the able beam. to endureThe rear the end force was and first deform. connected Each to steel the plate spring was shackle divided, and into then eight connected equal pieces. to the Each chassis beam rail element with wasthe spring connected hanger. to each The other suspension by a fixed system joint, included and its center the displacement point was connected in longitudinal to the axledirection. in a fixed The way.side friction The front between end was the connected upper and to lower the spring steel hanger,plates was which not was included connected in the to simulation. the beam. TheThe rearleaf endspring was was first made connected of AISI5160 to the spring manganese shackle, steel; and its then mec connectedhanical properties to the chassis were rail shown with in the Table spring 4. hanger.After simulation The suspension measurement, system included the equivalent the displacement vertical stiffness in longitudinal of the front direction. and rear The leaf side spring friction was between490.15 N/mm the upper and and146.96 lower N/mm steel, respectively. plates was not The included upper ends in the of simulation. the four shock The leafabsorbers spring were was madeconnected of AISI5160 to the manganesechassis beam steel; by itsrotational mechanical joint propertiess, and the were lower shown end inwas Table connected4. After to simulation the front measurement,and rear theby rotational equivalent joints. vertical All stiofff theness shock of the absorbers front and were rear vertically leaf spring installed was 490.15 between N/mm the andchassis 146.96 railN and/mm, the respectively. axle. The upper The upperand lower ends components of the four shockof the absorbersshock absorbe werers connected were connected to the chassisto each beam other by by rotational cylindrical joints, joint ands, the as lower shown end in was Figure connected 7 and to Table the front 5. According and rear axles to theby rotationalmass-spring joints.-damper All ofsystem, the shock the damping absorbers ratio were vertically was set to installed 0.7, and between the damper the chassis values railof front and theand axle. rear Thesuspension upper and were lower 315 componentsNs/mm and of525 the Ns shock/mm, absorbersrespectively. were The connected parameters to eachare shown other by in cylindricalTable 6. joints, as shown in Figure7 and Table5. According to the mass-spring-damper system, the damping ratio ζ was set to 0.7, and the damper values of front and rear suspension were 315 Ns/mm and 525 Ns/mm, respectively. TheTable parameters 4. Mechanical are properties shown in of Table AISI51606. .

MaterialsTable P 4.ropertiesMechanical propertiesAISI5160 of AISI5160.Manganese Steel Elastic coefficient E (MPa) 205,000 MaterialsPoisson Properties’s ratio AISI51600.29 Manganese Steel Elastic coeYieldfficient strength E (MPa) (MPa) 275 205,000 Poisson’s ratio 0.29 Yield strength (MPa) 275

Figure 7. Suspension system construction. Figure 7. Suspension system construction.

Symmetry 2020, 12, 1334 8 of 33

Table 5. Connections table of the suspension system components.

Component 1 Component 2 Connect Method Chassis rail Front leaf spring hanger Fixed joint Front leaf spring hanger Leaf spring 1 Y rotational joint Leaf spring n (n = 1–31) Leaf spring n + 1 Fixed joint Leaf spring 29 Wheel hub Fixed joint Leaf spring 32 Leaf spring shackle Y rotational joint Leaf spring shackle Rear leaf spring hanger Y rotational joint Rear leaf spring hanger Chassis rail Fixed joint Chassis rail Shock absorbers damping cylinder Y rotational joint Shock absorbers damping cylinder Shock absorbers piston rod Z cylindrical joint (damper) Shock absorbers piston rod Wheel hub Y rotational joint

Table 6. Parameters of the suspension system components.

Equivalent vertical stiffness of the front leaf spring 490.15 N/mm Equivalent vertical stiffness of the rear leaf spring 146.96 N/mm Damping coefficient of the front shock absorbers 315 Ns/mm Damping coefficient of the rear shock absorbers 525 Ns/mm

2.4. Model of the Tires and Road Surface HyperWorks/MotionView built-in LIALA/HTIRE tire model was used and calculated with the COSIN road modeling to simulate the behavior of tire during driving such as longitudinal slip, lateral slip, and tire deformation delay, which might seriously affect the handling characteristic of the vehicle. The effective diameter of the tire was calculated to be 627 mm, the cornering stiffness of the front wheel was 57,502.1 N/rad, and the cornering stiffness of the rear wheel was 84,293.6 N/rad.

2.5. Model of the Anti-Roll Bar The anti-roll bar was modeled with right/left connecting rods, right/left arms, right/left half anti-roll bars and . The torsion spring was used to simulate the controllable variable stiffness of anti-roll bar, located at the center of the anti-roll bar. One end of the connecting rod was connected to the wheel hub assembly using universal joint, and the other end was ball-joined with the arm of the anti-roll bar. The arm then was connected to the half anti-roll bar using fixed joint. The right half anti-roll bar and left anti-roll bar were joined using revolute joint with torsional spring damper. Each half anti-roll bar was hold in place to the chassis rail using revolute joints which allowed the anti-roll bars to rotate with respect to the vehicle chassis and to transform vertical displacement into angular displacement. Two sets of anti-roll bars were used, one at the front of the vehicle and the other at the rear, as shown in Figures8 and9. Table7 shows the part connection of the anti-roll bar. Based on the vehicle configuration, the anti-roll bar was mounted 468.5 mm forward of the wheel hub, and its diameter was 18 mm, made of manganese steel, as shown in Table4. The angle of twist, , could be calculated as shown in Equation (1). From Equation (1), the torsional stiffness could be ∅ derived as shown in Equation (2), where T was the torque, G was the shear modulus, L was the length of the bar, and J was the cross section’s polar moment of inertia, shown in Equation (3). The torsional stiffness of the anti-roll bar of the vehicle was calculated to be 1.5 107 mm/rad. × TL ∅ = (1) GJ

T GJ = (2) ∅ L πd4 J = (3) 32 Symmetry 20202020,, 1122,, xx FORFOR PEERPEER REVIEWREVIEW 99 of 3434

(3)(3) = Symmetry 2020, 12, 1334 32 9 of 33

FigureFigure 8.8. Front anti-rollanti--rollroll barbar construction.conconsstructiontruction..

FigureFigure 9.9. Rear anti-rollanti--rollroll barbar construction.conconsstructiontruction.. Table 7. Connections of the anti-roll bar components (front axle as the example). Table 7. Connectionss of the anti--rollroll barbar componentscomponents (front(front axleaxle asas thethe example)example).. Component 1 Component 2 Connect Method Component 1 Component 2 Connect Method Left connecting rod Left wheel hub assembly Y-Z universal joint Leftft connectingconnecting rodrod Left wheel hub assembly Y--Z universal joint Left arm Left connecting rod Ball joint Left halfLeft anti-roll arm barLeft connecting Left arm rod Ball Fixed joint joint LeftLeft halfhalf anti-roll anti--rollroll bar barbar LeftLeft chassis arm rail Fixed Y revolute joint joint Y revolute joint LeftLeft halfhalf anti-roll anti--rollroll bar barbar RightLeft halfchassis anti-roll rail bar Y revolute joint (withY Torsionrevoluterevolute spring-damper) jointjoint RightLeftft half anti-rollanti--rollroll bar barbar Right Right half chassisanti--rollroll rail barbar Y revolute joint (with Torsion spring-damper) Right half anti-roll bar Right arm(with Torsion Fixed spring joint-damper) Right Right half anti arm--rollroll barbar Right Right connectingchassis rail rod Y revoluterevolute Ball joint jointjoint RightRight connectinghalf anti--rollroll rod bar Right wheelRight hubarm assembly Y-ZFixed universal joint joint Right arm Right connecting rod Ball joint 2.6. SimulationRight Testingconnecting Method rod Right wheel hub assembly Y--Z universal joint Two kinds of handling characteristic tests were simulated in this research; one was the step 2.6. Simulation Testingesting Methodethod steering input test by reference to ISO7401 [21], the other was the input open-loop test of single sinusoidalTwo kinds steering of handling by reference characteristic to ISO/TR8725 tests [ were22]. Data simulated for the in vehicle’s this research;research; handling one characteristics was the step weresteeringsteering obtained input input totest test numerically by by reference reference compare to to ISO7401 ISO7401 and analyze[21][21],, the thethe other other characteristics was was the the input input such open open as lateral--looploop test test acceleration, of singlesingle yawsinusoidalsinusoidal velocity, steeringsteering roll angle, by reference and steering to ISO/TR8725 characteristic. [22][22].. DataData forfor thethe vehicle’’ss handlinghandling characteristiccharacteristicss were obtained to numericallyly comparecompare aand analyze thethe characteristicscharacteristics suchsuch asas llateral acceleration,, 2.6.1.yaw velocity Step Steering,, rroll angle Input,, andand Test ssteeringteering characteristiccharacteristic.. According to the test specification of ISO7401, the testing vehicle must reach the specified speed before inputting the turn signal. The step steering input test is carried out at different speeds, each with Symmetry 2020, 12, x FOR PEER REVIEW 10 of 34 Symmetry 2020, 12, x FOR PEER REVIEW 10 of 34 2.6.1. Step Steering Input Test 2.6.1. StepAccording Steering to Input the test Test specification of ISO7401, the testing vehicle must reach the specified speedAccording before inputting to the test the turn specification signal. T he of step ISO7401, steering the input testing test vehicle is carried must out reach at different the specified speeds , speedeach withbefore incremental inputting theinterval turn signal.of 20 km/h. The stepAt the steering same time,input the test yaw is carried velocity out must at different be in a balanced speeds, eachSymmetrystate with within2020 incremental, 12 +/,− 13340.5 deg/s. interval When of the20 km/h. turn signalAt the is same inputted time,, thethe yawtime velocity taken to must increase be in from a balanced 10%10 of 33of statethe maximumwithin +/− value0.5 deg/s. to 90 When% must the be turn less signalthan 0.15 is inputted s, and the, the angle time of taken the acceleration to increase pfromedal 10%is fixed of theduring maximum the test, value as shown to 90% in must Figure be 10.less This than type 0.15 of s, testand is the to anglesimulate of the the acceleration condition whereby pedal is a fixed fixed incremental interval of 20 km/h. At the same time, the yaw velocity must be in a balanced state within duringsteering the angle test, as is shown suddenly in F igure turned, 10. This and type to evaluateof test is to the simulate dynamic the stabilitycondition and whereby steady a fixed state +/ 0.5 deg/s. When the turn signal is inputted, the time taken to increase from 10% of the maximum steeringperformance− angle of isthe suddenly vehicle. It turned,is expected and that to after evaluate the turn the signal dynamic input, stability the vehicle and path steady should state be value to 90% must be less than 0.15 s, and the angle of the acceleration pedal is fixed during the test, performancea circle with of a the fixed vehicle. radius, It is and expected the yaw that velocity after the should turn signal be a input, fixed valuethe vehicle while path vehicle should is atbe a as shown in Figure 10. This type of test is to simulate the condition whereby a fixed steering angle is aconstant circle with speed. a fixed radius, and the yaw velocity should be a fixed value while vehicle is at a suddenly turned, and to evaluate the dynamic stability and steady state performance of the vehicle. constantThe speed. total simulation time of this test was 50 s. Because the structure and load of the real vehicle It is expected that after the turn signal input, the vehicle path should be a circle with a fixed radius, wereThe not total symmetrical, simulation time the of suspension this test was system 50 s. Because had unsymmetrical the structure and deformation load of the and real inducedvehicle and the yaw velocity should be a fixed value while vehicle is at a constant speed. wereunsymmetrical not symmetrical, lateral forces the on suspension tires. The systemvehicle had had a unsymmetricalconstant lateral deformationforce when the and steering induced was The total simulation time of this test was 50 s. Because the structure and load of the real unsymmetricalat neutral. A 0.15 lateral degree forces of onsteering tires. Theangle vehicle was entered had a constant between lateral the 5th force and when 6th second the steering in order was to vehicle were not symmetrical, the suspension system had unsymmetrical deformation and induced atadjust neutral. for Athe 0.15 small degree yaw ofangle steering and toangle keep was the entered vehicle betweenstraight continuouslythe 5th and 6th up secondto the 15th in order second. to unsymmetrical lateral forces on tires. The vehicle had a constant lateral force when the steering was at adjustAt the for 15th the small second, yaw a angle 28-degree and to steering keep the angle vehicle was straight entered continuously with transition up to timethe 15th 0.15 second. s, and neutral. A 0.15 degree of steering angle was entered between the 5th and 6th second in order to adjust Atmaintained the 15th this second, steering a 28 angle-degree until steering the end angle of the was test, entered as shown with in transition Figure 10. time The 0.15 vehicle s, and was for the small yaw angle and to keep the vehicle straight continuously up to the 15th second. At the maintainedtested at speeds this steering of 40, 60, angle and until80 km/h, the endas shown of the in test, Figur as eshown 11. In this in Figure research, 10. the The vehicle vehicle was was a 15th second, a 28-degree steering angle was entered with transition time 0.15 s, and maintained this testedmedium at -speedssize electric of 40, vehicle60, and with80 km/h, rear -aswheel shown drive. in Figur The e speed11. In signalthis research, was inputted the vehicle to the was rear a steering angle until the end of the test, as shown in Figure 10. The vehicle was tested at speeds of 40, mediumwheels -withsize angular electric speeds vehicle of with 35.436, rear 53.153,-wheel and drive. 70.871 The rad/s speed respectively. signal was The inputted vehicle towas the not rear yet 60, and 80 km/h, as shown in Figure 11. In this research, the vehicle was a medium-size electric vehicle wheelsstabilized with until angular the 5thspeeds second. of 35.436, Therefore, 53.153, the and speed 70.871 signal rad/s wasrespectively. input at The the 5thvehicle second, was not and yet the with rear-wheel drive. The speed signal was inputted to the rear wheels with angular speeds of 35.436, stabilizedvehicle was until accelerated the 5th second. until the Therefore, 9th second the tospeed reach signal the target was input speed, at and the 5th then second, maintained and the the 53.153, and 70.871 rad/s respectively. The vehicle was not yet stabilized until the 5th second. Therefore, vehiclesame speed was accelerateduntil the end until of the the test. 9th second to reach the target speed, and then maintained the the speed signal was input at the 5th second, and the vehicle was accelerated until the 9th second to same speed until the end of the test. reach the target speed, and then maintained the same speed until the end of the test.

Figure 10. Steering input signal in the step steering test. Figure 10. Steering input signal in the step steering test. Figure 10. Steering input signal in the step steering test.

FigureFigure 11.11. VehicleVehicle speedsspeedsin inthe thestep stepsteering steering test. test. Figure 11. Vehicle speeds in the step steering test. 2.6.2. Single Sinusoidal Steering Input Test The speed input specification is the same as the former test as in the test of ISO/TR8725 [23]. The specified vehicle speed must be reached before inputting the turn signal, and the yaw velocity must be balanced. The main difference between the step and single sinusoidal steering input tests is the turn signal. The turn signal is entered with a complete sinusoidal signal at a frequency of 0.5 Hz, Symmetry 2020, 12, x FOR PEER REVIEW 11 of 34

2.6.2. Single Sinusoidal Steering Input Test Symmetry 2020, 12, x FOR PEER REVIEW 11 of 34 The speed input specification is the same as the former test as in the test of ISO/TR8725 [23]. 2.6.2.The specifiedSingle Sinusoidal vehicle speed Steering must Input be reachedTest before inputting the turn signal, and the yaw velocity must be balanced. The main difference between the step and single sinusoidal steering input tests is the turnThe signal.speed inputThe turn specification signal is entered is the same with asa complete the former sinusoidal test as in signal the test at a of frequency ISO/TR8725 of 0.5 [23]. Hz, Theallowing specified a +/ −vehicle5% error speed at the must first be pe reachedak of the before turn signal. inputting The the acceleration turn signal, pedal and is the fixed yaw during velocity the must be balanced. The main difference between the step and single sinusoidal steering input tests is Symmetrytest. This2020 type, 12, 1334of test is used to simulate the condition of vehicle lane changing with a sinusoidal11 of 33 thesteering turn signal. signal The suddenly turn signal applied, is entered and to with evaluate a complete the dynamic sinusoidal peak signal values at a of frequency the vehicle of 0.5 during Hz, allowingturning anda +/− 5% the error time at of the stabilization first peak of and the all turn other signal. steady The- stateacceleration performances pedal is after fixed the during steering the test.allowingreturns This back atype+/ to 5%of neutral. test error is atusedAs the a resultto first simulate peak of the of thetest, the condition turn the vehicle signal. of Thepathvehicle acceleration should lane bechanging a pedalsingle iswith lane fixed achange sinusoidal during path. the − steeringtest.After This the signal steering type suddenly of testangle is returns used applied, to to simulate andthe neutral to evaluate the conditionposition, the dynamicthe of yaw vehicle rate peak lane will values changing return of to the withzero, vehicle aand sinusoidal the during yaw turningsteeringangle will and signal remain the suddenly time unchanged. of stabilizationapplied, and and to evaluate all other the steady dynamic-state peak performances values of the after vehicle the steering during returnsturningThe back and total theto simulationneutral. time of stabilizationAs time a result of this of and thetest all test, was other the 30 steady-state vehicles. Since paththe performancesstructure should be and a single after load the oflane steeringthis change real returnsvehicle path. Afterbackwere tothe not neutral. steering symmetrical, As angle a result returns the of the suspension to test,the neutral the vehicle system position, path had shouldthe unsymmetrical yaw be rate a single will return lanedeformation change to zero, path. andand Afterthe induced yaw the anglesteeringunsymmetrical will angle remain returns lateral unchanged. to forces the neutral on tires. position, A 0.15 the-degree yaw ratesteerin willg returnangle was to zero, inputted and the at yawthe angle5th to will6th remainsecondThe unchanged.to total keep simulation the vehicle time straight of this continuously test was 30 ups. Since to the the 15th structure second. and After load the of vehicle this real was vehicle stable, wereat the The not 15th total symmetrical, second, simulation a single time the suspensionofsinewave this test was steering system 30 s. Since angle had the unsymmetrical input structure with and a frequency loaddeformation of this of real 0.5 and vehicle Hz induced and were an unsymmetricalnotamplitude symmetrical, of 19.5 lateral the degr suspension forcesees was on entered. systemtires. A had At0.15 the unsymmetrical-degree 17th second,steerin deformationg the angle end was of andthe inputted steering induced at input unsymmetricalthe 5th cycle, to 6th the secondlateralsteering forcesto was keep onreturned the tires. vehicle A to 0.15-degree 0.15straight degrees continuously steering to keep angle the up wasvehicleto the inputted 15th straight second. at theand 5thAfter maintained to the 6th vehicle second that was toangle keep stable, until the atvehiclethe the end 15th straight of the second, test. continuously The a single steering upsinewave to gear the 15thanglesteering second. displacement angle After input the is vehiclewith shown a in was frequency Figure stable, 12 of at. The the 0.5 15th Hz vehicle and second, was an amplitudeatested single at sinewave speeds of 19.5 of degr steering 40, 60,ees andwas angle 80 entered. inputkm/h, with asAt shown the a frequency 17th in Figuresecond, of 13. 0.5 the Hz end and of anthe amplitude steering input of 19.5 cycle, degrees the steeringwas entered. was returned At the 17th to second,0.15 degrees the end to ofkeep the the steering vehicle input straight cycle, and the steeringmaintained was that returned angle to until 0.15 thedegrees end of to keepthe test. the vehicleThe steering straight gear and angle maintained displacement that angle is shown until thein endFigure of the12. test.The The vehicle steering was testedgear angle at speeds displacement of 40, 60, is and shown 80 km/h, in Figure as shown 12. The in vehicle Figure was13. tested at speeds of 40, 60, and 80 km/h, as shown in Figure 13.

Figure 12. Steering gear input signal for the single sinusoidal steering test.

FigureFigure 12. 12. SteeringSteering gear gear input input signal signal for for the the single single sinusoidal sinusoidal steering steering test. test.

FigureFigure 13.13. Vehicle speedsspeeds inin thethe singlesingle sinusoidalsinusoidal steeringsteering test.test.

3. Active Anti-Roll Bar (AARB) Control Strategy The object of thisFigure research 13. isVehicle to improve speeds vehiclein the single handling sinusoidal characteristics steering test by. developing a control strategy to an active anti-roll bar (AARB), in flexible-body dynamic analysis simulating vehicle hardware tests. Vehicle handling characteristics refer to vehicles’ responses to steering commands and to their environmental inputs that affect vehicles’ direction of motion. Undesired or unexpected handling behavior can cause traffic accidents. Two basic issues in vehicle handling: one is the control of the vehicle direction of motion; the other is the ability to stabilize its direction of motion. Especially, Symmetry 2020, 12, x FOR PEER REVIEW 12 of 34

3. Active Anti-Roll Bar (AARB) Control Strategy The object of this research is to improve vehicle handling characteristics by developing a control strategy to an active anti-roll bar (AARB), in flexible-body dynamic analysis simulating vehicle hardware tests. Vehicle handling characteristics refer to vehicles’ responses to steering commands and to their environmental inputs that affect vehicles’ direction of motion. Undesired or

Symmetryunexpected2020, 12handling, 1334 behavior can cause traffic accidents. Two basic issues in vehicle handling:12 of one 33 is the control of the vehicle direction of motion; the other is the ability to stabilize its direction of motion. Especially, instability in rolling has seriously effects on the handling characteristic of the instabilitywhole vehicle. in rolling Therefore, has seriously a set of eff ectscontrol on thestrateg handlingy for characteristicactive anti-roll of thebar wholesystem vehicle. was designed Therefore, to aadjust set of controlthe roll strategy stiffness for and active the anti-rolldamping bar coefficient system was of designed the whole to suspension adjust the roll system, stiffness without and the or dampingwith little coe effectfficient on of the the whole vehicle suspension pitch, in system,Y-axis, thewithout vertical or with displacement, little effect on in theZ-axis, vehicle or pitch, other inmovementY-axis, the o verticalf suspension displacement, system. inIn Z th-axis,is paper, or other the movement step steering of suspension input test andsystem. single In this sinusoidal paper, thesteering step steering input test input were test used and for single vehicle sinusoidal’s handling steering characteristic input test study were. used for vehicle’s handling characteristicThe objective study. is to improve vehicle handling performance by adjusting the stiffness and dampinTheg objective of the anti is to-roll improve bars to vehicle reduce handling the roll angle performance of the vehicle, by adjusting to have the better stiffness control and dampingof vehicle ofdirection the anti-roll and barsto have to reduce shorter the responding roll angle oftime. the The vehicle, data to of have lateral better acceleration, control of yaw vehicle velocity, direction roll andangle, to havesteering shorter characteristic, responding and time. the The time data of of stabiliza lateral acceleration,tion are all observed. yaw velocity, The rollcontrol angle, strategy steering is characteristic,based on the steer and thecharacteristics. time of stabilization The design are intend all observed. is to bring The large control understeer strategy or is large based oversteer on the steerto be characteristics. closer to the acceptable The design range intend since is to they bring are large generally understeer better or in large control oversteer within to that be closer range. toEs thepecial acceptablely for some range dangerous since they oversteering are generally conditions, better in the control proposed within design that could range. help Especially to improve for somethe condition. dangerous When oversteering oversteer conditions, occurred, the the proposed strategy design is to could increase help the to improve front rolling the condition. stiffness, Whenreducing oversteer load occurred, shifting to the the strategy front is outer to increase wheel,the increasing front rolling the sti frontffness, inner reducing tire traction. load shifting That toincreases the front the outer front wheel, , increasing reducing the the front slip inner angle tire differences traction. Thatbetween increases the front the and front rear slip wheels, angle, reducingreducing the vehicle slip angle roll angle, differences and increase between the the vehicle front andstability. rear wheels, When the reducing vehicle vehicle is understeer roll angle, too andmuch, increase the strategy the vehicle is to stability. increase When the rear the vehiclerolling stiffness, is understeer reducing too much, load theshifting strategy to the is to rear increase outer thewheel, rear increasing rolling stiff theness, rear reducing inner tire load traction, shifting increasing to the rear the outer rear wheel, slip increasingangle. The thecontrol rear innerprocess tire is traction,shown in increasing Figure 14, the where rear “ slip ” angle.is the subtracting The control value process of the is shown front slip in Figureangle and 14, whererear slip “a angle.” is the In subtractingthe first state, value when of the < front−1 slip, it angleis large and oversteering. rear slip angle. The Infront the firstanti- state,roll bar when will a be< activated,1◦, it is large and − oversteering.the rear anti-roll The bar front will anti-roll be deactivated. bar will be In activated, the second and state, the rear > 1 anti-roll, it is large bar will understeering. be deactivated. The Infront the secondanti-roll state, bar will a > 1be◦, itdeactivated is large understeering. and the rear The anti front-roll anti-rollbar will barbe activated. will be deactivated In the third and state, the rearwhen anti-roll −1 ≤ bar ≤ will1 , be the activated. steering In characteristic the third state, is when considered1◦ acceptable,a 1◦, the steering and the characteristic front and rear is − ≤ ≤ consideredanti-roll bar acceptable, systems ar ande both the deactivated. front and rear anti-roll bar systems are both deactivated.

Figure 14. The control process of the active anti-roll bar (AARB).

While the vehicle turning, the larger steering angle it was, the larger the lateral force of the tire was subjected to, and the larger rolling angle which was caused by the centrifugal force. When under the same steering angle, a higher vehicle speed would cause a larger instant overshoot and larger stable value in tire lateral force, similarly that caused a larger rolling angle due to the centrifugal force. Symmetry 2020, 12, 1334 13 of 33

Therefore, in this study both steering angle and vehicle speed were considered to set the torsional stiffness of the active anti-roll bars, as shown in Equations (4) and (5). K f and Kr were the torsional stiffness of the front and rear anti-roll bars, respectively, where δ was the steering angle, V was the vehicle speed, and G f and Gr were magnified factors. The values of G f and Gr were critical. If they were too high, the torsional stiffness values of the anti-roll bars would become too high and that would cause the tire to lift when the vehicle rolled. If they were set too low, the torsional stiffness values of the anti-roll bars would become too low and the anti-roll bars would lose their purpose for 5 2 5 2 improving vehicle handling. In this study, G = 1.2 10 Ns/rad , Gr = 1.2 10 Ns/rad , values f × × which are chosen based on the baseline values of K f and Kr. The damping value was set as 0.7 which was commonly used for the system. K = G δ V (4) f f ·| |· Kr = Gr δ V (5) ·| |· 4. Results

4.1. Analysis of the Step Steering Input Test In the step steering input test, the first 10 s were used to keep the vehicle straight with constant velocity, which was not part of the steering behavior study. The steering angle was turned at the 15th second, therefore the results were recorded starting at the 10th second. This studied vehicle was a medium-size electric bus. Since this chassis system response was within 10 Hz, a low pass filter 10 Hz was used to filter out noise. The time of stabilization was to measure the time entering to and maintaining within the 2% variation range relative to the final converged steady state average value. The total simulation time was 50 s. To easily distinguish between without AARB and with AARB, the locally zoomed-out plot was shown as well. Figures 15–18 are the results of the 40 km/h step steering input test. Figure 15a is the lateral acceleration in the 40 km/h step steering input test. The left one shows the whole simulation time frame. To be easily seen the differences between with AARB and without AARB, the locally zoomed-out plot is shown at the right. Figure 15b shows the lateral acceleration difference between with and without AARB, where the maximum difference is within 0.3 m/s2. The steering was turned at the 15th second. The maximum difference happened after the steering was turned, and in the transition to the stable state. At the end, the two had about 0.01 m/s2 difference in the final lateral acceleration. The time taken to reach steady state was around the 21.23 s for the case without AARB, which took about 6.23 s after the steering turned. For the case with AARB, the time to reach the steady state was around the 21.83 s, which took about 6.83 s after the steering turned. Figure16a is the yaw velocity in the 40 km /h step steering input test. The left one shows the whole simulation time frame. The right one has the local area zoomed out. Figure 16b shows the yaw velocity differences between with and without AARB, where the maximum difference is within 0.0025 rad/s. Over the 50 s, the difference between the cases with and without AARB kept around 0.002 rad/s in yaw velocity. The both yaw velocity values remained in balanced state. The time taken to reach steady state was around the 15.87 s for the case without AARB, which took about 0.87 s after the steering turned. For the case with AARB, the time taken to reach steady state was around the 15.85 s, which took about 0.85 s after the steering turned. Figure 17a is the roll angle in the 40 km/h step steering input test. The left one shows the whole simulation time frame. The right one has the local area zoomed out. Figure 17b shows the roll angle differences between with and without AARB, where the maximum difference is within 0.035 degrees. Over the 50 s, the final difference between the cases with and without AARB kept around 0.006 degree in roll angle. The time taken to reach steady state was around the 21.22 s for the case without AARB, which took about 6.22 s after the steering turned. For the case with AARB, the time taken to reach steady state was around the 21.84 s, which took about 6.84 s after the steering turned. Symmetry 2020, 12, 1334 14 of 33

Figure 18a is the steering characteristic in the 40 km/h step steering input test. The left one shows the data of the whole simulation time. The right one has the local area zoomed out. Figure 18b shows the differences between with and without AARB, where the maximum difference is within 0.22 degrees. Over the 50 s, the final value difference between the cases with and without AARB was around 0.12 − degrees. The time taken to reach the steady state was around the 20.39 s for the case without AARB, which took about 5.39 s after the steering turned. For the case with AARB, the time taken to reach steady state was around the 21.13 s, which took about 6.13 s after the steering turned. The comparisons of the data in the 40 km/h step steering input test were summarized in Table8.

TheSymmetry differences 2020, 12, between x FOR PEER the REVIEW cases with AARB and without AARB were 0.28% changes in14 lateralof 34 acceleration, 0.6% in yaw velocity, 0.94% in roll angle, and 3.91% in steering characteristic. When the − − vehicledifferences velocity between was 40 with km/h, and the withoutdifferences AARB, between where the the cases maximum with AARB difference and without is within AARB 0.035 were notdegree significant.s. Over From the 50 the s, simulationthe final difference results, thebetween rear anti-roll the cases bar with stiff andness without was increased. AARB kept The around roll angle increased0.006 degree by 0.94% in roll caused angle. the The front time slip taken angle to reach decreased, steady but state the was rear around slip angle the 21.22 did not s for significantly the case increase,without and AARB, the yawwhich velocity took about was 6.22 reduced s after by the 0.6%. steeri Theng turned. difference For betweenthe case with the frontAARB, and the rear time slip anglestaken was to reach decreased. steady Thestate steering was around characteristic the 21.84 s of, which understeering took about was 6.84 reduced s after the by steering 3.91%. turned. TableFigure9 lists 18a the is stabilization the steering time characteristic required from in the steering 40 km/h turned step to steering vehicle input stabilized. test. The To distinguish left one theshows time ditheff erences,data of the data whole were simulation presented time. with twoThe right digits one after has decimal the local point. area Thezoomed stabilization out. Figure time 18b shows the differences between with and without AARB, where the maximum difference is differences between the cases with AARB and without AARB for lateral acceleration, yaw velocity, within 0.22 degrees. Over the 50 s, the final value difference between the cases with and without roll angle, steering characteristic, and the total time of stabilization were 9.63%, 2.30%, 9.97%, 13.73%, AARB was around −0.12 degrees. The time taken to reach the steady state was− around the 20.39− s and 9.79%, respectively. The total stabilization time was used to select the longest time within each for the case without AARB, which took about 5.39 s after the steering turned. For the case with case. The stabilization time for steering characteristic had bigger differences between the cases with AARB, the time taken to reach steady state was around the 21.13 s, which took about 6.13 s after the AARBsteering and turned. without AARB, which was around 13.73%. The one for yaw velocity was the relatively smallest one.

(a)

(b)

FigureFigure 15. 15.(a )(a Lateral) Lateral acceleration acceleration in thein the 40 km 40 / km/hh step step steering steering input input test. test. (b) The(b) The diff erences differences of lateral of accelerationlateral acceleration between between two simulations two simulations (with AARB (with AARB and Without and Without AARB). AARB).

SymmetrySymmetry2020 2020, ,12 12,, 1334 x FOR PEER REVIEW 1515 of of 33 34 Symmetry 2020, 12, x FOR PEER REVIEW 15 of 34

(a) (a)

(b) (b) Figure 16. (a) Yaw velocity in the 40 km/h step steering input test. (b) The differences of yaw FigureFigure 16. 16. a(a) Yaw velocity in the 40 km/h step steering input b test. (b) The differences of yaw velocity between( ) Yaw the velocity two simulations in the 40 km (with/h step and steering without input AARB). test. ( ) The differences of yaw velocity betweenvelocity thebetween two simulations the two simulations (with and (with without and AARB). without AARB).

(a) (a) Figure 17. Cont.

Symmetry 2020, 12, x FOR PEER REVIEW 16 of 34 Symmetry 2020, 12, 1334 16 of 33 Symmetry 2020, 12, x FOR PEER REVIEW 16 of 34

(b) (b) Figure 17. (a) Roll angle in the 40 km/h step steering input test. (b) The differences of roll angle Figurebetween 17. the((aa)) Rolltwo Roll anglesimulations angle in in the the 40(with km40 km/h/hand step without step steering steering AARB). input input test. ( test.b) The (b di) Thefferences differences of roll angle of roll between angle betweenthe two simulationsthe two simulations (with and (with without and AARB).without AARB).

(a) (a)

(b) (b) FigureFigure 18. 18.( a(a)) Steering Steering characteristic characteristic in in the the 40 40 km km/h/h step step steering steering input input test. test.( b(b)) The The di differencesfferences of of FigureSteeringSteering 18. characteristic characteristic(a) Steering between characteristicbetween the the two twoin simulationsthe simulations 40 km/h (with (withstep andsteering and without without input AARB). AARB). test. (b ) The differences of Steering characteristic between the two simulations (with and without AARB).

Symmetry 2020, 12, 1334 17 of 33

Table 8. Comparisons of the data in the 40 km/h step steering input test.

Lateral Acceleration Yaw Velocity Roll Angle Steering Characteristic Items (m/s2) (rad/s) (deg) (deg) Without AARB (A) 3.58 0.335 0.637 +3.07 − − With AARB (B) 3.59 0.333 0.643 +2.95 − − Difference +0.28 0.60 +0.94 3.91 (B A)/A 100 (%) − − − ×

Table 9. Stabilization time comparison for 40 km/h step steering input test.

Lateral Acceleration Yaw Velocity Roll Angle Steering Total Stabilization Time Stabilization Time Stabilization Stabilization Characteristic Stabilization (s) Time (s) Time (s) Stabilization Time (s) Time (s) Without AARB (A) 6.23 0.87 6.22 5.39 6.23 With AARB (B) 6.83 0.85 6.84 6.13 6.84 Difference 9.63 2.30 9.97 13.73 9.79 (B A)/A 100 (%) − − ×

Figures 19–22 are the results of the 60 km/h step steering input test. Figure 19 is the lateral acceleration in the 60 km/h step steering input test. The left one shows the whole simulation time frame. To be easily seen the differences between with AARB and without AARB, the locally zoomed-out plot is shown at the right. The maximum difference is within 0.4 m/s2. At the end, the two had about 0.14 m/s2 difference in the final lateral acceleration. The time taken to reach steady state was around the 48.50 s for the case without AARB, which took about 33.50 s after the steering turned. For the case with AARB, the time taken to reach steady state was around the 29.30 s, which took about 14.30 s after the steering turned. Figure 20 is the yaw velocity in the 60 km/h step steering input test. The left one shows the whole simulation time frame. The right one has the local area zoomed out. The maximum difference in yaw velocity between with and without AARB is within 0.025 rad/s. Over the 50 s, the difference between the cases with and without AARB kept around 0.009 rad/s in yaw velocity. The time taken to reach steady state was around the 23.64 s for the case without AARB, which took about 8.64 s after the steering turned. For the case with AARB, the time taken to reach steady state was around the 20.51 s, which took about 5.51 s after the steering turned. Figure 21 is the roll angle in the 60 km/h step steering input test. The left one shows the whole simulation time frame. The right one has the local area zoomed out. The maximum roll angle difference between with and without AARB is within 0.18 degree. Over the 50 s, the final difference between the cases with and without AARB kept around -0.098 degree in roll angle. The time taken to reach steady state was around the 48.67 s for the case without AARB, which took about 33.67 s after the steering turned. For the case with AARB, the time taken to reach steady state was around the 30.46 s, which took about 15.46 s after the steering turned. Figure 22 is the steering characteristic in the 60 km/h step steering input test. The left one shows the data of the whole simulation time. The right one has the local area zoomed out. The maximum difference between with and without AARB is within 0.9 degree. Over the 50 s, the final value difference between the cases with and without AARB was around 0.45 degree. The time taken to reach steady − state was around the 47.37 s for the case without AARB, which took about 32.37 s after the steering turned. For the case with AARB, the time taken to reach steady state was around the 28.97 s, which took about 13.97 s after the steering turned. From each figure, it can be seen that the stabilized time of the vehicle was significantly shortened with the AARB. Symmetry 2020, 12, x FOR PEER REVIEW 19 of 34 Symmetry 2020, 12, x FOR PEER REVIEW 19 of 34 Symmetryaround 20the20, 28.9712, x FOR s, whichPEER REVIEW took about 13.97 s after the steering turned. From each figure, it 19can of be34 Symmetryaroundseen that 20the20 the , 28.9712 stabilized, x FOR s, whichPEER time REVIEW took of theabout vehicle 13.97 was s after significantly the steering shortened turned. with From the each AARB. figure, it can19 of be34 seenaround that the the 28.97 stabilized s, which time took of the about vehicle 13.97 was s aftersignificantly the steering shortened turned. with From the eachAARB. figure, it can be aroundseen that the the 28.97 stabilized s, which time took of theabout vehicle 13.97 was s after significantly the steering shortened turned. with From the each AARB. figure, it can be Symmetry 2020, 12, 1334 18 of 33 seen that the stabilized time of the vehicle was significantly shortened with the AARB.

Figure 19. Lateral acceleration in the 60 km/h step steering input test. Figure 19. Lateral acceleration in the 60 km/h step steering input test. Figure 19. Lateral acceleration in the 60 km/h step steering input test. FigureFigure 19.19. LateralLateral acceleration inin thethe 6060 kmkm/h/h stepstep steeringsteering inputinput test.test.

Figure 20. Yaw velocity in the 60 km/h step steering input test. Figure 20. Yaw velocity in the 60 km/h step steering input test. Figure 20. Yaw velocity in the 60 km/h step steering input test. Figure 20. Yaw velocity in the 60 km/h step steering input test. Figure 20. Yaw velocity in the 60 km/h step steering input test.

Figure 21. Roll angle in the 60 km/h step steering input test. FigureFigure 21.21. RollRoll angleangle inin thethe 6060 kmkm/h/h stepstepsteering steeringinput inputtest. test. Figure 21. Roll angle in the 60 km/h step steering input test. Figure 21. Roll angle in the 60 km/h step steering input test.

Figure 22. Steering characteristic in the 60 km/h step steering input test.

The comparisons of the data in the 60 km/h step steering input test were summarized in Table 10. The differences between the cases with AARB and without AARB were 3.49% changes in − Symmetry 2020, 12, 1334 19 of 33 lateral acceleration, 3.63% in yaw velocity, 13.74% in roll angle, 22.5% in steering characteristic. − − − These differences between the cases with AARB and without AARB become much more significant than the cases shown in 40 km/h. From the simulation results, the front anti-roll bar stiffness was increased. The roll angle was effectively reduced by 13.74%. The steering characteristic of oversteering was suppressed by 22.5%, and therefore the lateral acceleration of the vehicle was reduced by 3.49%, and the yaw velocity was reduced by 3.63%. Table 11 listed the stabilization time required from steering turned to vehicle stabilized. The stabilization time differences between the cases with AARB and without AARB for lateral acceleration, yaw velocity, roll angle, steering characteristic, and the total stabilization time were 57.31%, 36.23%, 54.08%, 56.84%, and 54.08%, respectively. The stabilization time for vehicle − − − − − lateral acceleration had bigger difference between the cases with AARB and without AARB, which was around 57.31%. The one for yaw velocity was the relatively smallest one.

Table 10. Comparisons of the data in the 60 km/h step steering input test.

Lateral Acceleration Yaw Velocity Roll Angle Steering Characteristic Items (m/s2) (rad/s) (deg) (deg) Without AARB (A) 4.01 0.248 0.713 2.00 − − − With AARB (B) 3.87 0.239 0.615 1.55 − − − Difference 3.49 3.63 13.74 22.5 (B A)/A 100 (%) − − − − − ×

Table 11. Stabilization time comparison for 60 km/h step steering input test.

Lateral Acceleration Yaw Velocity Roll Angle Steering Total Stabilization Time Stabilization Time Stabilization Stabilization Characteristic Stabilization (s) Time (s) Time (s) Stabilization Time (s) Time (s) Without AARB (A) 33.50 8.64 33.67 32.37 33.67 With AARB (B) 14.30 5.51 15.46 13.97 15.46 Difference 57.31 36.23 54.08 56.84 54.08 (B A)/A 100 (%) − − − − − − ×

Figures 23–27 are the results of the 80 km/h step steering input test. Figure 23 is the lateral acceleration in the 80 km/h step steering input test. The left one shows the whole simulation time frame. To be easily seen the differences between with AARB and without AARB, the locally zoomed-out plot is shown at the right. The case without AARB was not stable with oscillation magnitude of +/ 4 m/s2 − with respect to mean value 3.76 m/s2. At the end, the case with AARB had lateral acceleration around − 3.91 m/s2. The time to reach steady state was around the 36.77 s for the case with AARB, which took − about 21.77 s after the steering turned. Figure 24 is the yaw velocity in the 80 km/h step steering input test. The left one shows the whole simulation time frame. The right one has the local area zoomed out. The case without AARB was not stable with oscillation between 0.1 and 0.3 rad/s with respect to mean value 0.183 rad/s. At the − − − end, the case with AARB had a yaw velocity around 0.181 rad/s. The time taken to reach steady state − was around the 28.33 s for the case with AARB, which took about 13.33 s after the steering turned. Figure 25 is the roll angle in the 80 km/h step steering input test. The left one shows the whole simulation time frame. The right one has the local area zoomed out. The case without AARB was not stable with oscillation between 0.5 and 2 degrees with respect to mean value 0.707 degrees. At the − end, the case with AARB had roll angle around 0.555 degree. The time taken to reach steady state was around the 36.91 s for the case with AARB, which took about 21.91 s after the steering turned. Figure 26 is the steering characteristic in the 80 km/h step steering input test. The left one shows the data of the whole simulation time. The right one has the local area zoomed out. The case without AARB was not stable with oscillation between 1.3 and 2.5 degrees with respect to mean value − − Symmetry 2020, 12, x FOR PEER REVIEW 21 of 34 Symmetry 2020, 12, x FOR PEER REVIEW 21 of 34 notSymmetry stable 20 with20, 12 oscillation, x FOR PEER between REVIEW −0.5 and 2 degrees with respect to mean value 0.707 degrees.21 ofAt 34 thenot end,stable the with case oscillation with AARB between had roll−0.5 angle and 2 around degrees 0.555 with degree.respect toThe mean time va takenlue 0.707 to reach degrees. steady At statethenot end, stablewas the around with case oscillation withthe 36.91 AARB betweens forhad the roll − case0.5 angle and with 2around degreesAARB, 0.555 whichwith degree. respect took Theabout to mean time 21.91 vataken lues after 0.707to reachthe degrees. steering steady At turned.statethe end,was the around case thewith 36.91 AARB s for had the roll case angle with around AARB, 0.555 which degree. took about The time 21.91 taken s after to thereach steering steady turned.stateFigure was around 26 is the the steering 36.91 s charactefor the caseristic with in the AARB, 80 km/h which step took steering about input21.91 s test. after The the leftsteering one showsturned.Figure the data 26 isof the whole steering simulation characteristic time. inThe the right 80 km/hone has step the steering local area input zoomed test. out. The The left case one SymmetrywithoutshowsFigure the2020 AARB data, 12 26,1334 was of is the the not whole steering stable simulation with characte oscillation time.ristic The inbetween the right 80 one− km/h1.3 has and step the −2.5 local steering degrees area input zoomedwith test.respect out. The Theto left20 mean case of one 33 valuewithoutshows −1717 theAARB datadegrees. was of the not At whole thestable end, simulation with the oscillationcase time.with AARBThebetween right had − one1.3 steering andhas the− 2.5characteristic local degrees area withzoomed angle respect around out. to The mean−1.81 case without AARB was not stable with oscillation between −1.3 and −2.5 degrees with respect to mean degree.value1717 − degrees. 1717The timedegrees. At taken the At end, to the reach the end, case steady the with case state AARB with was AARB had around steering had the steering characteristic 25.94 characteristics for the angle case around withangle AARB, around1.81 degree.which −1.81 −value −1717 degrees. At the end, the case with AARB had steering characteristic angle− around −1.81 Thetookdegree. time about The taken 10.94 time to s reachtaken after steadytheto reach steering state steady wasturned. state around was the around 25.94 sthe for 25.94 the case s for with the AARB, case with which AARB, took which about degree. The time taken to reach steady state was around the 25.94 s for the case with AARB, which 10.94took Fromabout s after each10.94 the steering figs afterure, the it turned. can steering be observed turned. that the case without AARB continued oscillating. The took about 10.94 s after the steering turned. instabilityFromFrom of each the fig figure,vehicleure, it was it can can caused be be observed observed by the thatrolling that the dynamic. the case case without withoutHowever, AARB AARB for continued the continued case with oscillating. AARB oscillating. wasThe From each figure, it can be observed that the case without AARB continued oscillating. The Thestabilizeinstability instabilityd afterof the the of vehicle theturn vehicle signal was caused was was input caused by theted .rollingby It can the bedynamic. rolling found dynamic. that However, the roll However,for angle the wascase for stable with the AARBand case under with was instability of the vehicle was caused by the rolling dynamic. However, for the case with AARB was AARBcontrol,stabilize was sod after the stabilized lateral the turn afteracceleration, signal the turnwas the signalinput yawted was velocity,. It inputted. can be and found Itthe can steeringthat be foundthe rollcharacteristic that angle the was roll were stable angle all wasand stable stableunder. stabilized after the turn signal was inputted. It can be found that the roll angle was stable and under andcontrol, under so control,the lateral so acceleration, the lateral acceleration, the yaw velocity, the yaw and velocity, the steering and thecharacteristic steering characteristic were all stable were. control, so the lateral acceleration, the yaw velocity, and the steering characteristic were all stable. all stable.

Figure 23. Lateral acceleration in the 80 km/h step steering input test. Figure 23. Lateral acceleration in the 80 km/h step steering input test. FigureFigure 23. 23.Lateral Lateral acceleration acceleration in in the the 80 80 km km/h/h step step steering steering input input test. test.

Figure 24. Yaw velocity in the 80 km/h step steering input test. Figure 24. YYawaw velocityvelocity in the 80 kmkm/h/h stepstep steeringsteering inputinput test.test. Figure 24. Yaw velocity in the 80 km/h step steering input test.

Figure 25. RRolloll angle in the 80 km/h km/h step steering input test. Figure 25. Roll angle in the 80 km/h step steering input test. Figure 25. Roll angle in the 80 km/h step steering input test.

Symmetry 2020, 12, 1334 21 of 33 Symmetry 2020, 12, x FOR PEER REVIEW 22 of 34

FigureFigure 26. 26.Steering Steering characteristic characteristic in in the the 80 80 km km/h/h step step steering steering input input test. test.

The comparisons of the data in the 80 km/h step steering input test were summarized in Table 12. The comparisons of the data in the 80 km/h step steering input test were summarized in Table Since the case without AARB continued oscillating, the average mean was calculated and used as a 12. Since the case without AARB continued oscillating, the average mean was calculated and used reference. The behaviors were quite different between the cases with AARB and without AARB and as a reference. The behaviors were quite different between the cases with AARB and without AARB become much more significant than the cases shown in 40 km/h and in 60 km/h. With the active anti-roll and become much more significant than the cases shown in 40 km/h and in 60 km/h. With the active bar, the front anti-roll bar stiffness was increased to effectively reduce the roll angle. The steering anti-roll bar, the front anti-roll bar stiffness was increased to effectively reduce the roll angle. The characteristic of oversteering was suppressed and effectively preventing the possible danger of inner steering characteristic of oversteering was suppressed and effectively preventing the possible wheel from lifting off the ground. danger of inner wheel from lifting off the ground. Table 13 listed the time of stabilization for 80 km/h step steering input test. Since the vehicle Table 13 listed the time of stabilization for 80 km/h step steering input test. Since the vehicle was not stabilized for the case without AARB, only the time of stabilization for the case with AARB was not stabilized for the case without AARB, only the time of stabilization for the case with AARB was recorded. The time of stabilization for lateral acceleration, yaw velocity, roll angle, steering was recorded. The time of stabilization for lateral acceleration, yaw velocity, roll angle, steering characteristic, and total were 21.77, 13.33, 21.91, 10.91, and 21.91 respectively. characteristic, and total were 21.77, 13.33, 21.91, 10.91, and 21.91 respectively.

Table 12. Comparisons of the data in the 80 km/h step steering input test. Table 12. Comparisons of the data in the 80 km/h step steering input test. Lateral Acceleration Yaw Velocity Roll Angle Steering Characteristic Items Lateral Steering (m/s2) Yaw(rad /Velocitys) (deg)Roll Angle (deg) Items Acceleration Characteristi (rad/s) (deg) Without AARB (m/s2) c (deg) Oscillation mean 3.76 * 0.183 * 0.707 * 1.71 * Without AARB − − − (A) −3.76 * −0.183 * 0.707 * −1.71 * Oscillation mean (A) With AARB (B) 3.91 0.181 0.555 1.81 With AARB (B) − −3.91 − −0.181 0.555 −−1.81 Difference Difference 3.99 1.09 21.50 5.85 (B A)/A 100 (%) 3.99 − −1.09 − −21.50 5.85 − (B×−A)/A×100 (%) Note: * indicates that the system is not stable, and the values are the system mean for reference. Note: * indicates that the system is not stable, and the values are the system mean for reference. Table 13. Stabilization time comparison for 80 km/h step steering input test. Table 13. Stabilization time comparison for 80 km/h step steering input test. Lateral Acceleration Yaw Velocity Roll Angle Steering Total Stabilization Time StabilizationLateral Time Stabilization Stabilization CharacteristicSteering Stabilization Yaw Velocity Roll Angle Total Stabilization Acceleration(s) Time (s) Time (s) StabilizationCharacteristic Time (s) Time (s) Stabilization Stabilization Stabilization WithoutTime AARB Stabilization NA NA NAStabilization NA NA Time (s) Time (s) Time (s) With AARBTime 21.77(s) 13.33 21.91Time 10.94 (s) 21.91 Without NA NA NA NA NA FigureAARB 27 shows the tire force and the body force distribution at the 17th second for the cases with andWith without AARB AARB. In21.77 the case with AARB,13.33more vehicle21.91 body parts were10.94 subjected to deformation,21.91 while it was not seen much in the case without AARB. The adjustment in the anti-roll bar stiffness and the deformationFigure 27 shows in body the helped tire force in balancing and the body the sti forceffness distribution between the at chassisthe 17th system second and for the the body, cases andwith reducing and without the roll AARB. angle, stabilizing In the case the with vehicle, AARB, and preventing more vehicle vehicle body from parts large were oversteering subjected or to innerdeformation, wheel lifting while condition. it was not seen much in the case without AARB. The adjustment in the anti-roll bar stiffness and the deformation in body helped in balancing the stiffness between the chassis system and the body, and reducing the roll angle, stabilizing the vehicle, and preventing vehicle from large oversteering or inner wheel lifting condition.

Symmetry 2020, 12, 1334 22 of 33 Symmetry 2020, 12, x FOR PEER REVIEW 23 of 34

FigureFigure 27.27. TireTire forceforce andand bodybody forceforce distributiondistribution inin thethe 8080 kmkm/h/h stepstep steering steering input input test test ( t(t= = 1717s). s).

Table 1414 summarizedsummarized thethe steeringsteering characteristiccharacteristic for the step steering input tests under didifferentfferent speeds.speeds. The The case case of 40 kmkm/h/h was was understeering. understeering. The The baseline case, without AARB, had the finalfinal steeringsteering characteristiccharacteristic angleangle ++3.07.3.07. The The one one with AARB had the steeringsteering characteristiccharacteristic angle ++2.95.2.95. TheThe understeering condition condition was was reduced reduced 0.12 0.12 degree, degree, but but the the time time of ofstabilization stabilization was was increased increased by by0.61 0.61 s. Thes. The case case of of 6060 km/h km/ h was was oversteering. oversteering. The The baseline baseline case, case, without without AARB, AARB, had had the final final steeringsteering characteristic characteristic angle angle −2.0. The The one one with AARB had the steering characteristic angle −1.55. − − TheThe oversteeringoversteering conditioncondition waswas reduced reduced 0.45 0.45 degree degree which which was was about about 22.5% 22.5% changes, changes, and and the the time time of stabilizationof stabilization was was reduced reduced by 18.21by 18.21 s which s which was was about about 54.08% 54.08% improvement. improvement. The The case case of 80 of km 80/h km/h was oversteering.was oversteering. The baselineThe baseline case, case, without without AARB, AARB, was notwas stabilized. not stabilized. The vehicle The vehicle traveled traveled at 80 kmat 80/h withkm/h a with sudden a sudden steering steering turn, its turn, steering its characteristicsteering characteristic continued continued changing, changing and was, notand stabilized. was not Thatstabilized. was an That unwanted was an andunwanted dangerous and condition. dangerous While condition. the proposed While the control proposed strategy control with strategy AARB, thewith vehicle AARB, could the bevehicle stabilized could in be 21.91 stabilized s with thein 21.91 steering s with characteristic the steering angle characteristic1.81. The oversteeringangle −1.81. − conditionThe oversteering was well condition under control. was well under control.

Table 14.14. Comparisons of step steering input test under didifferentfferent speeds.speeds.

VV = =4040 km/h km /h VV= = 60 kmkm/h/h VV= =80 80 kmkm/h/h SteeringSteering SteeringSteering SteeringSteering ItemsItems StabilizationStabilization StabilizationStabilization StabilizationStabilization CharacteriCharacteristic Characteristic CharacteristicCharacteristic TimeTime (s) (s) TimeTime (s) (s) TimeTime (s) (s) stic (deg)(deg) (deg)(deg) (deg)(deg) Without AARB Without AARB (A) +3.07+ 3.076.23 6.23 −2.0 33.6733.67 −1.711.71 * * NANA (A) − − With AARB (B) +2.95 6.84 1.55 15.46 1.81 21.91 With AARB (B) +2.95 6.84 −−1.55 15.46 −−1.81 21.91 DifferenceDifference −3.91 3.919.79 9.79 −22.522.5 −54.0854.08 5.855.85 NANA (B(B−A)/AA)/×A100100 (%) (%) − − − − × Note:Note: * indicates * indicates that that the the system system is isnot not stabilized, stabilized, andand the the values values are are the the mean mean used used for reference. for reference.

Figure 2828 showsshows thethe pathspaths of of the the cases cases with with AARB AARB for forthe thestep stepsteering steering input inputtest. They test. are They all circular. are all circular.The path The was path recorded was recorded in Table in Table 15. Comparing15. Comparing the the difference difference between between before before and and after after the the improvement,improvement, the diameter diameter was was increased increased by by 1. 1.57%57% in in the the 40 40 km/h km/ htest, test, increas increaseded by by 4.01 4.01%% in inthe the 60 60km/h km /testh test but but decr decreasedeased by by 2.65 2.65%% in in n nthe the 80 80 km/h km/h test. test. For For 80 80 km/h km/h case, case, since since the the original baseline waswas notnot stable,stable, thethe averageaverage yawyaw velocityvelocity wouldwould notnot bebe suitablesuitable forfor comparison.comparison. ForFor 40 and 60 kmkm/h/h cases, it could be seen that the smaller yaw v velocity,elocity, the larger the path diameter, in a general sense. However, it was not quite completely inversely inversely proportional. proportional. Coupling Coupling effects effects altered altered the the number number a alittle. little. The The yaw yaw motions motions created created the the lateral lateral accelerations accelerations which which led led roll motions. The roll motions motions aaffectedffected thethe yawyaw responseresponse byby changingchanging thethe tiretire corningcorning forcesforces duedue toto thethe laterallateral loadload shiftingshifting [ 23[23]]..

Symmetry 2020, 12, 1334 23 of 33 Symmetry 2020, 12, x FOR PEER REVIEW 24 of 34

FigureFigure 28. 28. PathsPaths of of each each speed speed in in the the step step steering steering input input test test generated generated after after improving improving..

Table 15. Comparisons of the path diameters before and after the step steering input test. Table 15. Comparisons of the path diameters before and after the step steering input test. V = 40 km/h Path V = 60 km/h Path V = 80 km/h Path Path Diameter V = 40 km/h Path V = 60 km/h Path V = 80 km/h Path Path Diameter Diameter (m) Diameter (m) Diameter (m) Diameter (m) Diameter (m) Diameter (m) WithoutWithout AARB AARB (A) (A)63.7 63.7130.3 130.3 245.6245.6 With AARBWith AARB (B) (B)64.7 64.7135.6 135.6 239.1239.1 DifferenceDifference +1.57% +4.07% 2.65% (B A)/A 100 (%) +1.57% +4.07% −−2.65% (B−A)/A−×100 ×(%)

4.2.4.2. Analysis Analysis of of the the S Singleingle S Sinusoidalinusoidal S Steeringteering I Inputnput T Testest InIn the the single single sinusoidal steeringsteering inputinput test, test, the the first first 10 10 s weres were used used to keepto keep the the vehicle vehicle straight straight and andup toup the to requiredthe required speed, speed, which which was was not partnot part of the of steeringthe steering behavior behavior study. study. The The steering steering angle angle was waturneds turned between between the 15ththe 15th second second and 17thand 17th second, second, therefore therefore the results the results were were recorded recorded starting starting at the at10th the second. 10th second. Since Since this chassis this chassis system system response response is within is within 10 Hz, 10 a lowHz, passa low filter pass 10 filter Hz was10 Hz used was to usedfilter toout filter noise. out For noise. those For final those average final steady average state steady values stat aree close values to zero, are close the time to zero, of stabilization the time of is stabilizationto measure theis to time measure entering the to time and entering maintaining to and within maintaining the 2% of within the peak the values;2% of the and peak for those values; the andfinal for average those steady the final state average values are steady not zero, state the values time ofare stabilization not zero, the is to time measure of stabilization the time entering is to measureto and maintaining the time en withintering the to and 2% variation maintaining range within relative the to 2% the variation final converged range relative average to steady the final state convergedvalues. The average total time steady of the state simulation values. test The was total 30 time s. Since of the the simulationsteering input test was was completed 30 s. Since by the the steering17th second, input most was ofcompleted the data remainedby the 17th the second, same after most 24th of the second. data Theremained following the figuressame after depicted 24th second.data from The the following 10th to 24thfigures second. depicted data from the 10th to 24th second. FiguresFigures 29 29––3232 are are the the results results of the of 40 the km 40/h single km/h sinusoidal single sinusoidal steering input steering for lateral input acceleration, for lateral acceleration,yaw velocity, yaw roll velocity, angle, and roll steering angle, and characteristic, steering characteristic, respectively. respectively. The maximum The lateral maximum acceleration lateral accelerationdifference between difference with between and without with and AARB without is within AARB 0.15 is mwithin/s2., as 0.15 shown m/s2 in., as Figure shown 29 .in In Figure Figure 29. 30 , Inthe Figure two curves 30, the are two almost curves identical. are almost The identical. maximum The di maximumfference in difference yaw velocity in yaw is within velocity 0.0025 is within rad/s. 0.0025Figure rad/s. 31 shows Figure the 31 roll shows angle the data roll in angle the 40 data km/ hin single the 40 sinusoidal km/h single steering sinusoidal input steering test. The input maximum test. Theroll maximum angle diff erenceroll angle between difference with between and without with AARBand without is within AARB 0.06 is degree.within 0.06 There degree. were There small wereoscillations small around oscillations the peaks. around Figure the 32 peaks. depicts Figure the steering 32 depicts characteristic. the steering The maximum characteristic. difference The maximumbetween with difference and without between AARB with is and within without 0.05 degree. AARB Thereis within are 0.05 not manydegree. di ffThereerences are between not many the differencesone with AARB between and the without one with AARB, AARB except and around without the AARB, peak areaexcept with around little discrepancy.the peak area with little discrepancy.

Symmetry 2020, 12, x FOR PEER REVIEW 25 of 34

Symmetry 2020, 12, x FOR PEER REVIEW 25 of 34

SymmetrySymmetry2020 20,2012, ,1 13342, x FOR PEER REVIEW 2425 of of 33 34

Figure 29. Lateral acceleration in the 40 km/h single sinusoidal steering input test.

Figure 29. Lateral acceleration in the 40 km/h single sinusoidal steering input test.

Figure 29. Lateral acceleration in the 40 km/h single sinusoidal steering input test. Figure 29. Lateral acceleration in the 40 km/h single sinusoidal steering input test.

Figure 30. Yaw velocity in the 40 km/h single sinusoidal steering input test.

Figure 30. Yaw velocity in the 40 km/h single sinusoidal steering input test. Figure 30. Yaw velocity in the 40 km/h single sinusoidal steering input test.

Figure 30. Yaw velocity in the 40 km/h single sinusoidal steering input test.

Figure 31. Roll angle in the 40 km/h single sinusoidal steering input test. Figure 31. Roll angle in the 40 km/h single sinusoidal steering input test.

Figure 31. Roll angle in the 40 km/h single sinusoidal steering input test.

Figure 31. Roll angle in the 40 km/h single sinusoidal steering input test.

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Figure 32. Steering characteristic in the 40 km/h single sinusoidal steering input test. Figure 32. Steering characteristic in the 40 km/h single sinusoidal steering input test. Table 16 summarized the time of stabilization in the 40 km/h single sinusoidal steering input test, which wasTable the 16 time summarized after steering the turntime completedof stabilization to the in time the vehicle40 km/h stabilized. single sinusoidal The stabilization steering time input ditest,fferences which between was the the cases time with after AARB steering and turn without completed AARB for to lateral the time acceleration, vehicle stabilized. yaw velocity, The rollstabilization angle, steering time characteristic, differences and betw theeen total the stabilization cases with time AARB were alland 0%, without since these AARB two fordata lateral sets wereacceleration, almost the yaw same. velocity, roll angle, steering characteristic, and the total stabilization time were all 0%, since these two data sets were almost the same. Table 16. Stabilization time comparison for 40 km/h single sinusoidal steering input test.

Table 16. StabilizationLateral Acceleration time comparisonYaw Velocity for 40 km/hRoll Angle single sinusoidalSteering steering input test.Total Stabilization Time Stabilization Time Stabilization Stabilization Characteristic Stabilization Lateral Steering (s) YawTime Velocity (s) RollTime (s)Angle Stabilization Time (s) TimeTotal (s) Stabilization Acceleration Characteristic Without AARB (A) 0.71Stabilization 0.74 Stabilization 0.97 0.34Stabilization 0.97 Time Stabilization Stabilization With AARB (B) 0.71Time 0.74 (s) Time 0.97 (s) 0.34Time 0.97 (s) Difference Time (s) Time (s) 0.00% 0.00% 0.00% 0.00% 0.00% Without(B A)/A 100 AARB (%) − × 0.71 0.74 0.97 0.34 0.97 (A) WithFigures AARB 33– (B)36 are the results0.71 of the 60 km0.74/h single sinusoidal0.97 steering input0.34 for lateral acceleration,0.97 yaw velocity,Difference roll angle, and steering characteristic, respectively. The maximum lateral acceleration 0.00% 0.00% 0.00% 0.00% 0.00% diff(Berence−A)/A between×100 (%) with and without AARB is within 0.35 m/s2., as shown in Figure 33. In Figure 34, the two curves are almost identical. The maximum difference in yaw velocity is within 0.007 rad/s. Figure Figures35 shows 33 the–36 roll are angle the data results in the of 60 the km 60/h single km/h sinusoidal single sinusoidal steering input steering test. input The maximum for lateral rollacceleration, angle difference yaw velocity, between roll with angle, and and without steering AARB characteristic, is within respectively. 0.08 degree. The There maximum were small lateral oscillationsacceleration around difference the peaks. between Figure with 36 and depicts without the steeringAARB is characteristic. within 0.35 m/s The2., maximumas shown in di Figurefference 33. betweenIn Figure with 34, and the withouttwo curves AARB are isalmost within identical. 0.13 degrees. The maximum It was understeer, difference then in yaw oversteer, velocity and is within then understeer,0.007 rad/s. and Figure oversteer 35 shows again. the The roll peaks angle in data the secondin the 60 cycle km/h were single bigger sinusoidal than the steering ones in input the first test. cycle.The maximum Even so, there roll angle were notdifference many dibetweenfferences with between and without the one AARB with AARB is within and 0.08 without degree. AARB, There exceptwere around small the oscillations peak area around with little the discrepancy peaks. Figure in the 36 lateral depicts acceleration the steering and roll characteristic. angle. The maximum difference between with and without AARB is within 0.13 degrees. It was understeer, then oversteer, and then understeer, and oversteer again. The peaks in the second cycle were bigger than the ones in the first cycle. Even so, there were not many differences between the one with AARB and without AARB, except around the peak area with little discrepancy in the lateral acceleration and roll angle.

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Figure 33. Lateral acceleration in the 60 km/h single sinusoidal steering input test. Figure 33. Lateral acceleration in the 60 km/h single sinusoidal steering input test. Figure 33. Lateral acceleration in the 60 km/h single sinusoidal steering input test. Figure 33. Lateral acceleration in the 60 km/h single sinusoidal steering input test.

Figure 34. Yaw velocity in the 60 km/h single sinusoidal steering input test. Figure 34. Yaw velocity in the 60 km/h single sinusoidal steering input test. Figure 34. Yaw velocity in the 60 km/h single sinusoidal steering input test.

Figure 34. Yaw velocity in the 60 km/h single sinusoidal steering input test.

Figure 35. Roll angle in the 60 km/h single sinusoidal steering input test. Figure 35. Roll angle in the 60 km/h single sinusoidal steering input test. Figure 35. Roll angle in the 60 km/h single sinusoidal steering input test.

Figure 35. Roll angle in the 60 km/h single sinusoidal steering input test.

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Figure 36. Steering characteristic in the 60 km/h single sinusoidal steering input test. Figure 36. Steering characteristic in the 60 km/h single sinusoidal steering input test. Table 17 summarizes the time of stabilization in the 60 km/h single sinusoidal steering input test, which wasTable the 17 time summarize after steerings the time turn completedof stabilization to the in time the vehicle60 km/h stabilized. single sinusoidal The stabilization steering time input ditest,fferences which between was the the cases time with after AARB steering and turn without completed AARB for to lateral the time acceleration, vehicle stabilized. yaw velocity, The rollstabilization angle, steering time characteristic, differences andbetween the total the stabilization cases with time AARB were and8.08%, without 0%, AARB2.75%, for1.56%, lateral − − − andacceleration,2.75%, respectively. yaw velocity, The roll total angle, stabilization steering characteristic, time was to choose and the the total longest stabilization time within time each were − case.−8.08%, The lateral0%, −2.75%, acceleration −1.56%, had and bigger −2.75%, diff respectively.erence between The the total cases stabilization with AARB time and was without to choose AARB, the whichlongest was time around within8.08%. each case. The yawThe velocitylateral acceleration difference was had the bigger relatively difference smallest between one, whichthe cases is 0. with AARB and without− AARB, which was around −8.08%. The yaw velocity difference was the relativelyTable smallest 17. Stabilization one, which time is 0. comparison for 60 km/h single sinusoidal steering input test.

Lateral Acceleration Yaw Velocity Roll Angle Steering Total Table 17. Stabilization time comparison for 60 km/h single sinusoidal steering input test. Stabilization Time Stabilization Time Stabilization Stabilization Characteristic Stabilization (s) Time (s) Time (s) Stabilization Time (s) Time (s) Lateral Steering Yaw Velocity Roll Angle Total WithoutStabilization AARB (A) Acceleration 0.99 0.85 1.09Characteristic 0.64 1.09 Stabilization Stabilization Stabilization WithTime AARB (B)Stabilization 0.91 0.85 1.06Stabilization 0.63 1.06 Difference Time (s) Time (s) Time (s) Time8.08% (s) 0.00% 2.75% 1.56%Time (s) 2.75% (B A)/A 100 (%) − − − − Without− × AARB 0.99 0.85 1.09 0.64 1.09 (A) WithFigures AARB 37 –(B)40 are the results0.91 of the 80 km0.85/h single sinusoidal1.06 steering input0.63 for lateral acceleration,1.06 yaw velocity,Difference roll angle, and steering characteristic, respectively. Figure 37 shows the data of lateral −8.08% 0.00% −2.75% −1.56% −2.75% acceleration.(B−A)/A×100 There (%) is obvious oscillation during the steering returning period. The case with AARB was stabilized faster than the case without AARB. The maximum lateral acceleration difference between with and without AARB was 3.5 m/s2. In Figure 38, it compared the yaw velocity data. The two Figures 37–40 are the − results of the 80 km/h single sinusoidal steering input for lateral curvesacceleration, were almost yaw velocity, identical roll during angle, the and first steering half cycle. characteristic, The discrepancy respectively. could beFigure seen 37 in shows the 2nd the halfdata cycle. of lateral The maximum acceleration. diff erenceThere is in obvious yaw velocity oscillation is within during 0.05 the rad stee/s. Itring can returning be clearly period. seen that The thecase stabilization with AARB time was of the stabilized yaw velocity faster was than shorter, the and case the without yaw velocity AARB. was The smaller maximum at the lateral first peakacceleration but larger difference at the second between peak forwith the and case without with AARB. AARB Figure was − 393.5 shows m/s2. theIn Figure roll angle 38, datait compared in the 80the km / yawh single velocity sinusoidal data. steering The two input curves test. were The patterns almost areidentical verysimilar during to the the lateralfirst half acceleration cycle. The butdiscrepancy opposite in could signs. be There seen is in obvious the 2nd oscillation half cycle. during The maximum the steering difference returning in period. yaw velocity The maximum is within roll0.05 angle rad/s. diff Iterence can be between clearly withseen andthat without the stabilization AARB is abouttime of 0.8 the degree. yaw velocity The roll anglewas shorter, was reduced, and the andyaw its veloci stabilizationty was smaller time was at reducedthe first sincepeak but the vibrationlarger at the was second suppressed. peak for Figure the case 40 depicts with AARB. the steeringFigure characteristic.39 shows the roll The angle maximum data in ditheff erence80 km/h between single sinusoidal with and withoutsteering input AARB test. is within The patterns 0.45 degree.are very It wassimilar understeer, to the lateral then oversteer,acceleration and but then opposite understeer, in signs and. There oversteer is obvious again. Theoscillation peaksin during the secondthe steering cycle were returning bigger period. and sharper The maximum than the ones roll angle in the difference first cycle. between with and without AARB is about 0.8 degree. The roll angle was reduced, and its stabilization time was reduced since the vibration was suppressed. Figure 40 depicts the steering characteristic. The maximum difference

Symmetry 2020, 12, x FOR PEER REVIEW 29 of 34 Symmetry 2020, 12, x FOR PEER REVIEW 29 of 34 Symmetry 2020, 12, x FOR PEER REVIEW 29 of 34 between with and without AARB is within 0.45 degree. It was understeer, then oversteer, and then between with and without AARB is within 0.45 degree. It was understeer, then oversteer, and then betweenundersteer, with and and oversteer without AARBagain. Theis within peaks 0.45 in thedegree. second It was cycle understeer, were bigger then and oversteer, sharper and than then the understeer, and oversteer again. The peaks in the second cycle were bigger and sharper than the understeer,ones in the firstand cycle.oversteer again. The peaks in the second cycle were bigger and sharper than the onesSymmetry in the2020 first, 12, 1334cycle. 28 of 33 ones in the first cycle.

Figure 37. Lateral acceleration in the 80 km/h single sinusoidal steering input test. Figure 37. Lateral acceleration in the 80 km/h single sinusoidal steering input test. FigureFigure 37. 37. LateralLateral acceleration acceleration in in the the 80 80 km/h km/h single single sinusoidal sinusoidal steering steering input input test. test.

Figure 38. Yaw velocity in the 80 km/h single sinusoidal steering input test. FigureFigure 38. YawYaw velocity in the 80 km/h km/h single sinusoidal steering input test. Figure 38. Yaw velocity in the 80 km/h single sinusoidal steering input test.

Figure 39. Roll angle in the 80 km/h km/h single sinusoida sinusoidall steering input test. Figure 39. Roll angle in the 80 km/h single sinusoidal steering input test. Figure 39. Roll angle in the 80 km/h single sinusoidal steering input test.

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Figure 40. Steering characteristic in the 80 km/h single sinusoidal steering input test. Figure 40. Steering characteristic in the 80 km/h single sinusoidal steering input test. Table 18 summarized the time of stabilization in the 80 km/h single sinusoidal steering input test, whichTable was the18 summarized time after steering the time turn of completed stabilization to the in timethe 80 vehicle km/h stabilized.single sinusoidal The stabilization steering input time ditest,fferences which between was the the time cases after with steering AARB and turn without completed AARB to for the lateral time acceleration, vehicle stabilized. yaw velocity, The rollstabilization angle, steering time differences characteristic, between and the the total cases stabilization with AARB time and were without8.99%, AARB10.84%, for 8.43%, lateral − − − acceleration,10.56%, and yaw8.43%, velocity, respectively. roll angle, The steering total stabilization characteristic, time wasand to the choose total stabilizationthe longest time time within were − − each−8.99%, case. −10.84%, The time −8.43%, of stabilization −10.56%, for and yaw −8.43%, velocity respectively. had bigger The diff totalerence stabilization between the time cases was with to AARBchoose and the without longest AARB, time within which eachwas around case. The –10.84%. time of The stabilization difference for for roll yaw angle velocity stabilization had bigger time wasdifference the relatively between smallest the cases one. with AARB and without AARB, which was around –10.84%. The difference for roll angle stabilization time was the relatively smallest one. Table 18. Stabilization time comparison for 80 km/h single sinusoidal steering input test. Table 18. Stabilization time comparison for 80 km/h single sinusoidal steering input test. Lateral Acceleration Yaw Velocity Roll Angle Steering Total Stabilization Time StabilizationLateral Time Stabilization Stabilization CharacteristicSteering Stabilization Yaw Velocity Roll Angle Total Stabilization Acceleration(s) Time (s) Time (s) StabilizationCharacteristic Time (s) Time (s) Stabilization Stabilization Stabilization WithoutTime AARB (A)Stabilization 3.45 2.86 3.56Stabilization 2.84 3.56 Time (s) Time (s) Time (s) With AARB (B)Time 3.14 (s) 2.55 3.26Time 2.54 (s) 3.26 WithoutDifference AARB 3.458.99% 2.8610.84% 8.43%3.56 10.56%2.84 8.43%3.56 (BA)(A)/A 100 (%) − − − − − × With AARB (B) 3.14 2.55 3.26 2.54 3.26 Difference Figure 41 shows the−8.99% tire force and− the10.84% body force distribution−8.43% at the−10.56% 16th second for the−8.43% cases (B−A)/A×100 (%) with and without AARB. These two cases were very similar, with very minor differences in the body deformation and stress distribution. However, the body structure with AARB did have little more Figure 41 shows the tire force and the body force distribution at the 16th second for the cases bodywith getand deformed without AARB.to distribute These the two loads cases passed were on. very That similar, helped with the system very minor to stabilize differences a little in faster. the bodyTable deformation 19 summarized and stress the distribution. total stabilization However, time the in body the single structu sinusoidalre with AARB steering did input have tests.little Theremore wasbody no get significant deformed di ff toerence distribute in the the 40 loadskm/h and passed 60 km on./h That cases. helped In the the 80 km system/h case, to duestabilize to the a activelittle faster. anti-roll bar intervention, the vehicle rolling dynamic was controlled, and the time of stabilization was reduced. The danger of the inner wheel lifting was also inhibited.

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Figure 41. Tire force and bodybody forceforce distributiondistribution in the 80 kmkm/h/h singlesingle sinusoidalsinusoidal steering input test (t = 16s).16 s).

Table 19. Comparisons of the total stabilization time of the single sinusoidal steering input tests. Table 19 summarized the total stabilization time in the single sinusoidal steering input tests. There was no significant differenceV = 40 in km the/h Total 40 km/h andV = 6060 km/h km/h Totalcases. In theV 80= 80km/h km/ hcase Total, due to Total Stabilization Time the active anti-roll bar intervention,Stabilization the Time vehicle (s) rollingStabilization dynamic Time was (s) controlledStabilization, and Timethe time (s) of stabilizationWithout was AARB reduced (A). The danger 0.97 of the inner wheel lifting 1.09 was also inhibited. 3.56 With AARB (B) 0.97 1.06 3.26 TableDiff 19.erence Comparisons of the total stabilization time of the single sinusoidal steering input tests. 0 2.75 8.43 (B A)/A 100 (%) − − − × V = 40 km/h V = 60 km/h V = 80 km/h Total Total Total Total As can be seenStabilization in Figure 42, although there is no significant change in the yaw velocity at the Stabilization Stabilization Stabilization medium and low speed,Timethere is a difference in the yaw angle between before the turn signal input Time (s) Time (s) Time (s) (first fifteen seconds) and the end of the test (at 30 s), as recorded in Table 20. The yaw angle differences Without AARB in percentage between with AARB and without0.97 AARB for the1.09 cases of 40, 60, and3.56 80 km/h are increased Symmetry 2020, 12, x FOR PEER(A) REVIEW 32 of 34 by 16.7%, decreased by 10%, and decreased by 14.6%, respectively. With AARB (B) 0.97 1.06 3.26 Difference 0 −2.75 −8.43 (B−A)/A×100 (%)

As can be seen in Figure 41, although there is no significant change in the yaw velocity at the medium and low speed, there is a difference in the yaw angle between before the turn signal input (first fifteen seconds) and the end of the test (at 30 s), as recorded in Table 20. The yaw angle differences in percentage between with AARB and without AARB for the cases of 40, 60, and 80 km/h are increased by 16.7%, decreased by 10%, and decreased by 14.6%, respectively.

Figure 42. The yaw angle changes in the single sinusoidal steering input tests. Figure 41. The yaw angle changes in the single sinusoidal steering input tests.

Table 20. Comparisons of the yaw angle before and after the single sinusoidal steering input tests.

V = 40 km/h V = 60 km/h V = 80 km/h Yaw angle Yaw Angle Yaw Angle Yaw Angle (deg) (deg) (deg) Without AARB −0.6 +4.0 +26.0 (A) With AARB (B) −0.7 +3.6 +22.2 Difference +16.7% −10% −14.6% (B−A)/A×100 (%)

5. Conclusions The objective of this research is to improve the handling performance of a medium-size electric bus by establishing a flexible multi-body dynamic simulation model with the proposed control strategy used to adjust the stiffness of the anti-roll bars. The control strategy is based on the steer characteristics. When huge oversteer occurred, the strategy is used to increase the front rolling stiffness, reducing load shifting to the front outer wheel, and increasing the front inner tire traction. When the vehicle is understeer too much, the strategy is to increase the rear rolling stiffness, reducing load shifting to the rear outer wheel, increasing the rear inner tire traction, increasing the rear slip angle. This research used HyperMesh and MotionView software under the Hyperworks computer engineering analysis system to build a rigid-flexible coupling medium-size electric bus model. Two types of open-loop testing method, namely a step steering input test and single sinusoidal steering input test, were established according to ISO7401 and ISO/TR8725, respectively. Under the same steering signal, the simulation test was performed at speeds of 40, 60, and 80 km/h to observe the vehicle dynamic and to improve the handling characteristic based on the proposed control strategy with active anti-roll bar system (AARB). The following results could be obtained by the simulation test of this research: (1) In the step steering input test, for this medium-size electric bus, understeering occurred at 40 km/h and oversteering occurred at 60 and 80 km/h in both the original case without AARB and the improved case with AARB. In the original case, the time of stabilization for 40 km/h was 6.23 s. The time of stabilization for 60 km/h was 33.67 s. However, for a speed of 80 km/h, the steering characteristic continued changing and was unstable, where the inner wheel lifting occurred which is unwanted unsteady situation. (2) In the single sinusoidal steering input test of the original vehicle model, the time of stabilization increased with the increase of the vehicle speed. In the 80 km/h test, the steady

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Table 20. Comparisons of the yaw angle before and after the single sinusoidal steering input tests.

V = 40 km/h V = 60 km/h V = 80 km/h Yaw Angle Yaw Angle (deg) Yaw Angle (deg) Yaw Angle (deg) Without AARB (A) 0.6 +4.0 +26.0 − With AARB (B) 0.7 +3.6 +22.2 − Difference +16.7% 10% 14.6% (B A)/A 100 (%) − − − ×

5. Conclusions The objective of this research is to improve the handling performance of a medium-size electric bus by establishing a flexible multi-body dynamic simulation model with the proposed control strategy used to adjust the stiffness of the anti-roll bars. The control strategy is based on the steer characteristics. When huge oversteer occurred, the strategy is used to increase the front rolling stiffness, reducing load shifting to the front outer wheel, and increasing the front inner tire traction. When the vehicle is understeer too much, the strategy is to increase the rear rolling stiffness, reducing load shifting to the rear outer wheel, increasing the rear inner tire traction, increasing the rear slip angle. This research used HyperMesh and MotionView software under the Hyperworks computer engineering analysis system to build a rigid-flexible coupling medium-size electric bus model. Two types of open-loop testing method, namely a step steering input test and single sinusoidal steering input test, were established according to ISO7401 and ISO/TR8725, respectively. Under the same steering signal, the simulation test was performed at speeds of 40, 60, and 80 km/h to observe the vehicle dynamic and to improve the handling characteristic based on the proposed control strategy with active anti-roll bar system (AARB). The following results could be obtained by the simulation test of this research: (1) In the step steering input test, for this medium-size electric bus, understeering occurred at 40 km/h and oversteering occurred at 60 and 80 km/h in both the original case without AARB and the improved case with AARB. In the original case, the time of stabilization for 40 km/h was 6.23 s. The time of stabilization for 60 km/h was 33.67 s. However, for a speed of 80 km/h, the steering characteristic continued changing and was unstable, where the inner wheel lifting occurred which is unwanted unsteady situation. (2) In the single sinusoidal steering input test of the original vehicle model, the time of stabilization increased with the increase of the vehicle speed. In the 80 km/h test, the steady state restored within three to four seconds after the turn signal ended, and the unsteady situation of the inner wheel lifting also occurred. (3) After the improvement made with the active anti-roll bar system designed by this research, most of the data changed during the step steering input test. In the 40 km/h step steering input test, the yaw velocity reduced 0.002 rad/s, which was about 0.60%; the understeering characteristic was effectively suppressed by 0.12 degree, which is about 3.91%; and the total time of stabilization increased by 0.61 s, which is about 9.79%. In the 60 km/h case, the yaw velocity reduced 0.009 rad/s, which was about 3.63%; the oversteering characteristic was effectively suppressed by 0.45 degree, which was about 22.5%; and the total stabilization time reduced 18.21 s, which is about 54.08%. In the 80 km/h case, the phenomenon of the inner wheel lifting, occurred in the original vehicle, was effectively suppressed and altered the original unstable and dangerous condition to stable. Since the original vehicle is not stable in the 80 km/h step steering input test, an average mean of each performance value was calculated for comparison. In comparison with the mean of original design, the design with active anti-roll bar had a lower yaw velocity than the original one by 1.09%. The diameter of the circle path was reduced by 2.65%. (4) With the active anti-roll bar design, there was no significant difference from the original one in the yaw velocity and the total stabilization time for the 40 km/h single sinusoidal steering input test. The yaw angle changed between the steering turned and the end of test. In the original design, Symmetry 2020, 12, 1334 32 of 33

the change of yaw angle was 0.6 degree, while it was 0.7 degree in the proposed design, increased 0.1 degree, which was about 16.7% to the baseline value. In the test of 60 km/h, there was no significant difference in the yaw velocity and the total stabilization time. In the original design, the change of yaw angle was 4.0 degrees, while it was 3.6 degrees in the proposed design, reduced by 0.4 degrees, which was about 10%. In the test of 80 km/h, the time of stabilization was reduced by 8.43%. In the original design, the change of yaw angle was 26.0 degrees, while it was 22.2 degrees in the proposed design, reduced by 3.8 degrees, which was about 14.6%.

The proposed control strategy with active anti-roll bar helped to improve the handling performance of the medium-size electric bus. The vehicle can have better control in terms of direction and a shorter stabilization time in response to the steering input, especially preventing from the dangerous unstable condition. Further enhancement study including other types of suddenly turning or driving behaviors can be carried out in the near future.

Author Contributions: Conceptualization, H.-Y.H.; methodology, T.-S.L.; software, H.-Y.H. and J.-S.C.; validation, J.-S.C. and T.-S.L.; investigation, H.-Y.H.; project administration, J.-S.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

References

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