applied sciences

Article On the Influence of Suspension Geometry on Steering Feedback

Emanuele Bonera * , Marco Gadola , Daniel Chindamo , Stefano Morbioli and Paolo Magri Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy; [email protected] (M.G.); [email protected] (D.C.); [email protected] (S.M.); [email protected] (P.M.) * Correspondence: [email protected]; Tel.: +39-0303715552



Received: 31 March 2020; Accepted: 16 June 2020; Published: 23 June 2020


Abstract: Feedback through the steering wheel is known as the most important source of information to the driver. The so-called steering feeling, composed of self-aligning actions coming from tyres and suspension geometry all the way through mechanical linkages to the driver’s hands, provides vital communication for intuitive driving, and it is therefore utterly important for safety and for a pleasant driving experience as well. Subtle forces and vibrations, due to the interaction between the tyre contact patch and the road surface texture, also play a role, provided they are not heavily filtered or cancelled by the power steering system. Human perception is guided by experience in order to establish correlations between steering feedback and vehicle motion in terms of straight-line stability, cornering speed, tyre adhesion and available friction, vehicle balance, and so on. A front-wheel drive car is potentially a critical vehicle from this point of view, especially when the powertrain can deliver large torque figures, and even more so if a limited-slip differential (LSD) or a similar active device is present in order to improve traction capabilities. Any difference between the two wheels in terms of tractive force can result into the so-called torque steer issue, that is to say, a “pulling” sensation on the steering wheel or a shifting of the vehicle from the desired trajectory. This paper analyses the torque steer phenomenon on an all-wheel-drive, full electric sportscar where a significant portion of the torque is transferred to the front axle. The effects of suspension kinematics and the load variation at tyre contact patch level are taken into account. For evaluating the impact of steering feedback, the VI-grade® simulation software is adopted and a test campaign on the professional driving simulator available at the University of Brescia has been carried out in order to understand the impact of steering feedback on driver perception and performance.

Keywords: steering feeling; torque steer; electric cars

1. Introduction As stated by the authors in [1,2], the steering system and geometry have a primary impact on the tactile feel perceived by the driver through his hands acting on the steering wheel. This perception —often called “steering feel”— is considered to be vital because steering is the driver’s main line of communication with the car; distortion in this guidance channel makes every other perception more difficult to comprehend [3]. Friction in the steering line, for instance, must be accurately calibrated in order to prevent stick and slip effects that could heavily affect returnability and the on-centre feel, while providing enough damping at the same time [2]. According to [4], steering feel or steering torque feedback is widely regarded as an important aspect of the handling quality of a vehicle, as it is known to help the driver in reducing path-following errors. Some authors even suggest that, apart from eyesight, the driving action is mainly based on feedback communication through the steering system [5]. Therefore, any interaction between the steering system on one side, and the effects of

Appl. Sci. 2020, 10, 4297; doi:10.3390/app10124297 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 21

Appl.system Sci. 2020[5]. , Therefore,10, 4297 any interaction between the steering system on one side, and the effects2 of 21of power delivery, braking torque, load transfer and road surface irregularities on the other, should be very carefully handled in order not to alter such a vital feedback. The disturbance related to unequal power delivery, braking torque, load transfer and road surface irregularities on the other, should be braking forces on the two sides is called “brake pull”, while the disturbance induced by uneven very carefully handled in order not to alter such a vital feedback. The disturbance related to unequal tractive forces on the front axle is known as “torque steer” [6,7]. They are both undesirable because braking forces on the two sides is called “brake pull”, while the disturbance induced by uneven tractive they upset the correlation between lateral acceleration (hence cornering speed), steering angle and forces on the front axle is known as “torque steer” [6,7]. They are both undesirable because they upset steering effort. the correlation between lateral acceleration (hence cornering speed), steering angle and steering effort. Standard front-wheel drive (FWD) cars are normally equipped with a so-called open or free Standard front-wheel drive (FWD) cars are normally equipped with a so-called open or free differential delivering torque in equal amounts to the wheels on both sides. Therefore, torque steer differential delivering torque in equal amounts to the wheels on both sides. Therefore, torque effects can be a consequence of rarely found non-symmetrical designs between the left and right half- steer effects can be a consequence of rarely found non-symmetrical designs between the left and shaft geometry, such as different shaft length, rotational inertia and inclination angle [8]. Transient right half-shaft geometry, such as different shaft length, rotational inertia and inclination angle [8]. phenomena like powertrain movements over elastic mountings and large roll angles also play a role, Transient phenomena like powertrain movements over elastic mountings and large roll angles also while minor effects can be due to suspension geometry tolerances, tyre conicity and wear and play a role, while minor effects can be due to suspension geometry tolerances, tyre conicity and asymmetric mass distribution as a consequence of vehicle loading [9]. Finally, whenever occasional wear and asymmetric mass distribution as a consequence of vehicle loading [9]. Finally, whenever wheelspin occurs under heavy acceleration, inertia effects can also induce unpleasant self-steering occasional wheelspin occurs under heavy acceleration, inertia effects can also induce unpleasant transients. self-steering transients. Where present, a limited-slip differential (LSD) can help to mitigate traction problems in cars Where present, a limited-slip differential (LSD) can help to mitigate traction problems in cars featuring a high torque-to-weight ratio or on low-friction surfaces. The LSD can also be tuned to featuring a high torque-to-weight ratio or on low-friction surfaces. The LSD can also be tuned to improve improve handling and stability by generating a yaw moment influencing the handling characteristics handling and stability by generating a yaw moment influencing the handling characteristics [10–13]. [10–13]. However, relevant torque steer problems were encountered when limited-slip differentials However, relevant torque steer problems were encountered when limited-slip differentials first first appeared in front-wheel drive rally cars in the early 1970s, given the large asymmetry in terms appeared in front-wheel drive rally cars in the early 1970s, given the large asymmetry in terms of of torque and tractive force generated under certain conditions [14,15]. Peculiar geometries have been torque and tractive force generated under certain conditions [14,15]. Peculiar geometries have been designed with the aim of minimising these effects. For example, the McPherson suspension with designed with the aim of minimising these effects. For example, the McPherson suspension with separate steering axis found in sporty Honda cars (see Figure 1) is aimed at reducing the wheel center separate steering axis found in sporty Honda cars (see Figure1) is aimed at reducing the wheel center arm (KO, see chapter 2). The very same concept can be found on the so-called RevoKnuckle® Ford arm (KO, see chapter 2). The very same concept can be found on the so-called RevoKnuckle® Ford geometry [16]. geometry [16].

Figure 1.1. Special McPherson front suspension with separateseparate steeringsteering axisaxis (courtesy(courtesy ofof HondaHonda Press).Press). It should also be stated that it is not possible to eliminate the asymmetry of driving or braking It should also be stated that it is not possible to eliminate the asymmetry of driving or braking torque applications completely. As a matter of fact, the resultant forces exchanged between the tyre torque applications completely. As a matter of fact, the resultant forces exchanged between the tyre and the ground can move laterally across the contact patch, especially on uneven road surfaces and and the ground can move laterally across the contact patch, especially on uneven road surfaces and with wide tyres, thus inducing torque steer or brake pull [6]. with wide tyres, thus inducing torque steer or brake pull [6]. High-performance or special application vehicles can feature active differentials or torque vectoring High-performance or special application vehicles can feature active differentials or torque devices aimed at extending the performance and stability envelopes by further enhancing yaw motion vectoring devices aimed at extending the performance and stability envelopes by further enhancing control [17–28]. Where a passive LSD or these advanced devices are adopted on the front axle, the yaw motion control [17–28]. Where a passive LSD or these advanced devices are adopted on the front control of torque steer phenomena should be taken into account from the very early design stages. axle, the control of torque steer phenomena should be taken into account from the very early design Electric power-assisted steering (EPAS) systems also offer the opportunity to cancel out torque steer by stages. Electric power-assisted steering (EPAS) systems also offer the opportunity to cancel out torque means of suitable control strategies [29] steer by means of suitable control strategies [29] It is, however, where the torque can be controlled independently on each wheel that the torque It is, however, where the torque can be controlled independently on each wheel that the torque vectoring concept can be taken to new heights [30]. On electric vehicles with a multiple-motor vectoring concept can be taken to new heights [30]. On electric vehicles with a multiple-motor powertrain, for instance, the torque vectoring can be achieved with individual wheel torque control. Appl. Sci. 2020, 10, 4297 3 of 21

This feature can significantly enhance the cornering response, driving stability, performance and active safety whilst improving vehicle dynamic properties and/or the fun-to-drive attitude of the car. Torque vectoring can also increase energy efficiency through the appropriate design of the reference understeer characteristics and the calculation of the wheel torque distribution providing either the desired total wheel torque and a direct yaw moment [31–33]. Today, the evolution of the automotive world towards electrification means that a variety of hybrid and electric cars with different powertrain/transmission architectures can be found on the market. In the specific case of an electric or hybrid car, one or two independent electric motors can be installed on a driving axle. Therefore, it is possible to use the control system of these motors to deliver different torques to the left and right wheel. A front driving axle with independent motors therefore raises the bar of the torque steer challenge. Furthermore, in the case of an electric powertrain, the very fast response times related to a driver input could generate sudden torque peaks on the steering wheel, thus making feedback even worse than traditional FWD cars equipped with an LSD or an actively controlled differential. This paper is aimed at providing an insight on the torque steer phenomenon in light of the shift towards full electric vehicles even in the high-performance market segment, in order to understand which geometric parameters of the car it is directly connected to, starting with a comprehensive theoretical background. Examples of suspension kinematic re-design are proposed to minimise the torque steer effects with the help of a specific software. Such a tool has been self-developed within the Automotive Engineering Group of Brescia University by the authors of this work. The development process is reported in [34]. A thorough validation was carried out by comparing results with commercial tools, like Lotus Suspension Design (Shark®) by Lotus Engineering and with the Adams multi-body package. This proprietary tool:

enables the design and analysis of all kinds of suspension geometries (from swing arm to full • multi-link to typical racecar layouts), including kinematics of the complete steering line; allows any kind of user to quickly perform a ground-up design; • can plot all the relevant suspension characteristics; • can overlay results coming from incremental design steps; • features a specific setup mode to simulate the effects of suspension adjustability; • features the direct export of suspension kinematics towards professional simulation packages like • CarSim® and VI-CarRealTime®; has been successfully employed in some previous works [35,36]. • Finally, a simulation campaign is carried out on VI-grade’s VI-CarRealTime® (VI-CRT) simulation environment with standard sine steer and track laps. The results will be reported.

2. Materials and Methods First, the torque steer theory has been analysed with particular focus on the geometric parameters. The main steering geometry parameters are defined in Figure2. Appl. Sci. 2020, 10, 4297 4 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 21

FigureFigure 2.2. Steering geometry parameters inin orthographicorthographic projectionprojection (SAE(SAE vehiclevehicle axisaxis system).system).

InIn particular, the the scrub scrub radius radius (SR) (SR) is isdefined defined as asthe the distance distance between between the tyre the tyrecontact contact patch patch mid- mid-pointpoint and the and intersection the intersection between between the steering the steering axis and axis the and road the surface road surface projected projected onto the onto yz theplane, yz plane,the caster the castertrail (CT) trail (CT)is the is same the same distance distance projec projectedted onto onto the the xz xzplane plane and and the the wheel wheel center center arm or kingpinkingpin ooffsetffset (KO)(KO) isis thethe distancedistance betweenbetween thethe steeringsteering axisaxis andand the wheel center, projectedprojected ontoonto thethe horizontalhorizontal planeplane (see(see toptop leftleft ofof FigureFigure2 2).). AA simplesimple case case of drivingof driving along along a straight a straight line at constantline at constant speed is takenspeed as is a reference.taken as Consideringa reference. theConsidering front left the wheel front and left analysing wheel and the analysing equilibrium the equilibrium around the around spindle the point spindle S, a fewpoint simplified S, a few configurationssimplified configurations will be used will to be explain used to the explai balancen the ofbalance forces of and forces moments and moments acting acting on the on front the wheelfront wheel assembly. assembly. 2.1. Case 1 2.1. Case 1 The first simplified case considers a vertical steering axis passing through point S and a half shaft The first simplified case considers a vertical steering axis passing through point S and a half aligned along the Y-axis (Figure3). The longitudinal force driving the vehicle under power is Fx. shaft aligned along the Y-axis (Figure 3). The longitudinal force driving the vehicle under power is In order to consider it as applied at the tyre contact patch, a balance force must be applied at S, thus Fx. In order to consider it as applied at the tyre contact patch, a balance force must be applied at S, generating moments M1 and M2, while the vertical load is balanced through the spring unit, and as thus generating moments M1 and M2, while the vertical load is balanced through the spring unit, and such, it is not relevant. as such, it is not relevant. Appl. Sci. 2020, 10, 4297 5 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 21

FigureFigure 3.3. SimplifiedSimplified casecase 1:1: vertical steering axis.

TheThe reactionreaction forcesforces are:are: X ⇒ ∑F(axisF(axis x)x)= = FxFx − Rx = 00 RxRx == FxFx (1) (1) − ⇒ X∑F(axis y), F(axis z) = 0 (2) F(axis y), F(axis z) = 0 (2) ∑Mxy (S) = −Fx∙SR +M1 ⇒ M1 = Fx∙SR (3) X Mxy∑Mxz (S) (S)= =Fx −FxSR∙r + MM12 ⇒ MM21 == FxFx∙r SR(4) (3) − · ⇒ · X Since the steering axis is vertical,Mxz the (S) only= Fx cormponent+ M2 Mof 2the= Fxmomentr responsible for the torque (4) steer is proportional to the scrub radius. − · ⇒ · Since the steering axis is vertical, the only component of the moment responsible for the torque steer2.2. Case is proportional 2 to the scrub radius.

2.2. CaseIn the 2 second case, the steering axis is inclined by the so-called kingpin angle λ, while the half shaft is still horizontal and transverse (Figure 4). In the second case, the steering axis is inclined by the so-called kingpin angle λ, while the half shaft is still horizontal and transverse (Figure4). Appl. Sci. 2020, 10, 4297 6 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 21

Figure 4. Case 2: kingpin angle > 0. Figure 4. Case 2: kingpin angle > 0. The arm at wheel center height is: The arm at wheel center height is: KO = SR + r tan(λ) (5) KO = SR + r∙tan(· λ) (5) WithWith a anon-zero non-zero kingpin kingpin angle, angle, the the moment moment components components around around the the steering steering axis axis are: are:

M1∥ = M1∙cos(λ) = Fx∙KO∙cos(λ) (6) M1 = M1 cos(λ) = Fx KO cos(λ) (6) k · · · M2∥ = M2∙sin(λ) = −Fx∙r∙sin(λ) (7) M2 = M2 sin(λ) = Fx r sin(λ) (7) k · − · · 2.3.2.3. Case Case 3 3 TheThe third third case case introduces introduces the the half-shaft half-shaft inclination inclination ξ ξinin the the transverse transverse plane plane (Figure (Figure 5):5): Appl. Sci. 2020, 10, 4297 7 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 21

Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 21

Figure 5. Case 3: inclined half shaft. Figure 5. Case 3: inclined half shaft. In a FWD car with an independent suspension system, the differential output is not necessarily In a FWD car with an independent suspension system, the differential output is not necessarily alignedaligned with with the wheelthe wheel axis. axis. In In any any case,Figure case, it it 5. is is Case usually usually 3: inclined connected half shaft. to to the the spindle spindle by bymeans means of a ofhalf a halfshaft shaft (or driveshaft)(or driveshaft) and and two two constant constant velocity velocity (CV)(CV) joints, joints, with with an an inclination inclination angle angle ξ. Givenξ. Given the nature the natureof In a FWD car with an independent suspension system, the differential output is not necessarily of thethe CV CV joints, joints, the the driving drivingtorque torque remainsremains constant constant along along the the half half shaft. shaft. A secondary A secondary torque torque (Mp, (Mp, aligned with the wheel axis. In any case, it is usually connected to the spindle by means of a half shaft FigureFigure6) is established6) is established as a as function a function of of the the angle angle of of inclination inclination of the the axle axle half half shaft shaft ξ. ξ. (or driveshaft) and two constant velocity (CV) joints, with an inclination angle ξ. Given the nature of WithWith reference to to the the S Spoint, point, the the power power balance balance is: is: the CV joints, the driving torque remains constant along the half shaft. A secondary torque (Mp, Figure 6) is established as a function of theM angle2∙ωhub of = inclinationCm∙ωm of the axle half shaft ξ. (8) M ω = C ω (8) With reference to the S point, the power balance2 hub is: m m where ωhub is the angular velocity at the· wheel hub· and ωm and Cm are the angular velocity and output torque at the differential. where ωhub is the angular velocity at the wheelM2∙ωhub hub = Cm and∙ωm ωm and Cm are the angular velocity(8) and And again, due to the nature of the CV joint: output torquewhere at ω thehub is di thefferential. angular velocity at the wheel hub and ωm and Cm are the angular velocity and Andoutput again, torque due at tothe the differential. nature of the CV joint:ωm = ωhub (9) So:And again, due to the nature of the CV joint: ωm = ωhub (9) ωm = ωhub (9) M2 = Cm (10) So: So:

MM2 =2 =C Cmm (10) (10)

Figure 6. Power balance and secondary torque. Appl. Sci. 2020, 10, 4297 8 of 21

Appl. Sci.The 2020 vector, 10, x notationFOR PEERis REVIEW usedin order to establish the entity of Mp, which is the vector sum of8 of M 212 on the two sides of the joint: Figure 6. Power balance and secondary torque. → → → → → → Mp = M2 i + M2 cos(ξ) i + M2 sin(ξ) j = M2 [cos(ξ) 1] i + M2 sin(ξ) j (11) The vector notation− is used· in order to establis· h the entity· of Mp,− which is the· vector sum of M2 on theThe two module sides of is: the joint:

Mp ⃗= - Mq2 i ⃗ + M2∙cos(ξ) i ⃗ + M2∙sin(ξ) j ⃗ = M2∙(cos(ξ) − 1) qi ⃗ + M2∙sin(ξ) j ⃗ (11) 2 2 2 Mp = M2 [cos (ξ) + 1 2cos(ξ)] + M2 sin(ξ) = M2 2[1 cos(ξ)] (12) The module is: − − Now, the secondary component Mp is projected on the steering axis, which is inclined by an angle |Mp| = √[M22 (cos2 (ξ) +1 − 2cos(ξ) ) + M22 sin(ξ)] = M2 √[2(1-cos(ξ))] (12) λ, and as such it is identified by the unit vector: Now, the secondary component Mp is projected on the steering axis, which is inclined by an angle λ, and as such it is identified by →theu = unitsin( vector:λ)→i + cos(λ)→j (13) u ⃗= sen(λ) i ⃗ + cos(λ) j ⃗ (13) The scalar product is: The scalar product is:

→ → → → → Mpu ⃗= Mp u⃗ =⃗ M2 sin2 (λ) [cos(ξ) 1] i +⃗ M2 2cos(λ)sin(ξ) j⃗ (14) Mpu = Mp· ∙u = M· ∙sin(λ·)∙(cos(ξ)− − 1) i + M· ∙cos(λ)sin(ξ) j (14) q 2 2 2 |Mpu| = M2 √[(sin (λ)(cos (ξ) + 1 − 2cos(ξ) ) + cos (λ)sin(ξ)] (15) 2 2 2 Mpu = M2 sin (λ)cos (ξ) + 1 2cos(ξ) + cos (λ)sin(ξ) (15) − 2.4. Case 4 The fourth and last case features the same configurationconfiguration as case 3. However, the caster angle on plane xz is now non-zero (Figure(Figure7 7).).

FigureFigure 7.7. Case 4:4: kingpin and caster angles > 0.

The equations are the same as case 3, but the M1 component in the xz plane now changes to:

M1c = M1∙cos(ν) = Fx∙KO∙cos(ν) (16) On the xy plane: Appl. Sci. 2020, 10, 4297 9 of 21

The equations are the same as case 3, but the M1 component in the xz plane now changes to:

M = M cos(ν) = Fx KO cos(ν) (16) 1c 1· · · On the xy plane: M1 = M1c cos(λ) = Fx KO cos(ν)cos(λ) (17) k · · · Then the torque module on the steering axis is:

MSA = M1 + Mpu p| | k| | (18) = Fx [KO cos(ν) cos(λ) + r sin2 (λ)[cos2 (ξ) + 1 2 cos(ξ)] + cos2 (λ)sin(ξ)] · − From the formulas above, therefore, the moment around the steering axis is a function of the longitudinal force at ground, the inclination angle of the half shafts ξ and the typical parameters of the steering geometry, such as the kingpin (λ) and caster angles (ν), as well as the kingpin offset (KO). Now, considering the complete front axle of the car, the two sides are connected by the steering rack. In a straight-line driving condition at constant speed, the Fx forces, as well as the M1 moments on both sides, are equal in module but opposite in direction, so the contribution to the torque steer is zero. The moment M2 does not cause any torque steer at all if the torque transmitted by the differential is the same on both sides, as it is the case for an open differential, and if the geometry is symmetric in terms of steering axis position (caster and kingpin angles) and half shaft inclination angle ξ. If an LSD is installed and there is a torque difference transmitted across the differential, this contribution can become relevant. A torque vectoring system (TV) is based on a purposely designed delivery of the drive torques to each individual wheel. It is well known as a powerful tool to improve the balance and stability of the vehicle as the difference in terms of longitudinal force at ground level can be used to generate a moment controlling yaw, i.e., rotation around the vertical axis. However, when TV is applied on the front axle, the effects in terms of torque steer can be seen as similar to those caused by the action of a self-locking differential.

2.5. Analysis of the Torque Steer Effects In order to better understand the problem, the lumped element, model-based, vehicle dynamics simulation software VI-CarRealTime® (VI-CRT) was used. The sportscar model was selected among the original vehicle models provided within the software database and retained its original steering geometry. The powertrain model was converted to full electric vehicle (FEV) in an all-Wheel drive (AWD) configuration, where a significant portion of the torque is transferred to the front. To analyse the vehicle reaction in terms of steering response, a sine steer sweep input with 45◦ amplitude at the steering wheel was chosen, with a frequency increasing from 0.5 to 4 Hz. Vehicle speed is 60 km/h. At the front, the “passive” reference vehicle features a free differential (usually referred to as an “open diff”), hence the torque distribution left to right is always even, if not for negligible inertia effects in transients. Therefore, there is virtually no torque steer at all. The steering wheel torque (often referred to as steering effort) is basically a function of the steering geometry design, and it is proportional to tyre forces exchanged with the ground due to accelerations, load transfers, and so on. This usually results in a self-aligning steering torque in phase with the driver’s hand motion, hence in an intuitive feedback the vehicle is stable because releasing the hand action from the steering wheel will just realign the vehicle back to straight line running.

2.6. Suspension Kinematics and Its Effects The correlation between steering geometry and the torque steer effects have been investigated by means of a self-developed software tool for suspension kinematic design and analysis (see Figure8). Appl. Sci. 2020, 10, 4297 10 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 21

Figure 8. The software tool created by the authors for the design of suspension and steering FigureFigure 8.8.The The software software tool tool created created by the by authors the authors for the designfor the of design suspension of suspension and steering and kinematics. steering kinematics.kinematics. The reference geometry in Figure9 is taken from the vehicle model. It appears suitable for a The reference geometry in Figure 9 is taken from the vehicle model. It appears suitable for a high-performanceThe reference sportscar, geometry as in it isFigure a little 9 extreme,is taken givenfrom the highvehicle value model. of the It casterappears angle. suitable Camber for isa high-performance sportscar, as it is a little extreme, given the high value of the caster angle. Camber kepthigh-performance to zero for simplicity. sportscar, Additionally, as it is a little the extreme, overall steeringgiven the ratio high (steering value of wheelthe caster angle angle./wheel Camber angle, is kept to zero for simplicity. Additionally, the overall steering ratio (,steering wheel angle/wheel is kept to zero for simplicity. Additionally, the overall steering ratio (,steering wheel angle/wheel Sa/angle,Wa) is Sa/Wa) fairly direct,is fairly hence direct, it hence can be it classifiedcan be classified as “sporty” as “sporty” or “reactive”, or “reactive”, see Table see 1Table. 1. angle, Sa/Wa) is fairly direct, hence it can be classified as “sporty” or “reactive”, see Table 1.

FigureFigure 9. 9.Schematic Schematic front front view view (yz (yz plane)plane) ofof the original front front axle axle pick-up pick-up points. points. Upper Upper wishbone wishbone is is shown in red, lower wishbone in blue, upright in green, tie rod in light blue, spring is shown as a pink shownFigure in9. red,Schematic lower wishbonefront view in (yz blue, plane) upright of the in original green, tie front rod axle in light pick-up blue, points. spring Upper is shown wishbone as a pink is line with grey coil, the green horizontal line shows the chassis lower plane, rim offset is shown by the lineshown with in greyred, lower coil, the wishbone green horizontal in blue, upright line shows in green the chassis, tie rod lower in light plane, blue, rim spring offset is shown is shown as bya pink the vertical purple line. verticalline with purple grey coil, line. the green horizontal line shows the chassis lower plane, rim offset is shown by the vertical purple line. The first modification, called EB0, was aimed at making the geometry more representative of a The first modification, called EB0, was aimed at making the geometry more representative of a wider range of cars, and therefore with less aggressive caster and kingpin settings. This in turn allows widerThe range first of modification, cars, and therefore called with EB0, less was aggressive aimed at making caster and the kingpin geometry settings. more Thisrepresentative in turn allows of a for the kingpin offset (KO) to be halved (Figure 10 and Table 1). According to the formulas in chapter forwider the range kingpin of ocars,ffset and (KO) therefore to be halved with (Figureless aggressive 10 and Table caster1). and According kingpin to settings. the formulas This in in turn chapter allows 2, 2, all these three parameters have a large influence on torque steer, as shown later. allforthese the kingpin three parameters offset (KO) have to be a halved large influence (Figure 10 on and torque Table steer, 1). According as shown later.to the formulas in chapter 2, all these three parametersTable have 1. EB0 a large suspension influence compared on torque with the steer, original as shown one. later. Table 1. EB0 suspension compared with the original one. Name Caster[deg]Table Kingpin[deg] 1. EB0 suspension SR[mm] compared withCT[mm] the original KO[mm] one. Sa/Wa[deg/deg] OriginalName Caster10.2 [deg] Kingpin 14.2 [deg] SR 16.1 [mm] CT 29.0 [mm] KO 102 [mm] Sa/Wa 15.7 [deg /deg] NameOriginalEB0 Caster[deg] 10.25 Kingpin[deg] 14.2 3.7 SR[mm] 16.129.2 CT[mm]12.5 29.0 KO[mm]51.4 102 Sa/Wa[deg/deg] 15.5 15.7 OriginalEB0 10.2 5 3.7 14.2 29.2 16.1 12.529.0 51.4102 15.5 15.7 EB0 5 3.7 29.2 12.5 51.4 15.5 Appl. Sci. 2020, 10, 4297 11 of 21

Appl.Appl. Sci. Sci. 2020 2020, ,10 10, ,x x FOR FOR PEER PEER REVIEW REVIEW 1111 of of 21 21

FigureFigure 10. 10. Schematic Schematic front front view view (yz (yz plane) plane) of of the the EB0 EB0 suspension, suspension, KO KO (Kingpin (Kingpin OOffset) Offset)ffset) isis is halved.halved. halved.

Figure 11 shows a comparison between the steering effort required for a sine steer sweep FigureFigure 1111 showsshows aa comparisoncomparison betweenbetween thethe steersteeringing efforteffort requiredrequired forfor aa sinesine steersteer sweepsweep manoeuvre with the passive vehicle equipped with the original and EB0 front axle geometries, with the manoeuvremanoeuvre with with the the passive passive vehicle vehicle equipped equipped with with th thee original original and and EB0 EB0 front front axle axle geometries, geometries, with with latter requiring reduced effort and driver involvement. However, the phase and shape are unaltered, thethe latterlatter requiringrequiring reducedreduced efforteffort andand driverdriver involvement.involvement. However,However, thethe phasephase andand shapeshape areare thus giving an intuitive, “friendly” feedback in both cases because the steering effort remains on the unaltered,unaltered, thusthus givinggiving anan intuitive,intuitive, “friendly”“friendly” feedbackfeedback inin bothboth casescases becausebecause thethe steeringsteering efforteffort self-aligning side. remainsremains on on the the self-aligning self-aligning side. side.

5050 3535 4040 2525 3030 15 2020 15 1010 55 00 012345678 012345678-5-5 -10-10 -20 -20 -15-15

Steering wheel angle -30 [deg] Steering Steering wheel torque [Nm]

Steeringwheel angle [deg] -30 -25-25 [Nm] torque wheel Steering -40-40 -50-50 -35-35 TimeTime [s] [s] Steering wheel angle original vehicle Steering wheel angle EB0 vehicle

Steering wheelSteering angle wheel torqueSteering original wheel vehicletorque original vehicleSteering wheel torqueSteering EB0 wheel vehicle torque EB0 vehicle

Figure 11. Steering angle and steering torque for passive vehicle with original (blue) and EB0 (red) Figure 11.11. SteeringSteering wheel wheel angle angle for for both both vehicles vehicles (continuous (continuous blue line)blue andline) steering and steering torque fortorque passive for suspension. vehiclepassive withvehicle original with original (dotted blue(dotted line) blue and line) EB0 and (dotted EB0 red(dotted line) red suspension. line) suspension.

2.7.2.7. Torque Torque VectoringVectoring Vectoring andand and ItsIts Its EEffects Effectsffects AA description description of of the the strategy strategy adoptedadop adoptedted for for typical typical torque torque vectoring vectoring (TV) (TV) control control in in itself itself is is beyond beyond thethe scope scopescope of ofof this thisthis paper, paper,paper, and andand so is soso the isis related thethe relatedrelated impact impactimpact on vehicle onon vehiclevehicle balance, balance,balance, handling handlinghandling dynamics, dynamics,dynamics, and stability. andand ® Therefore,stability.stability. Therefore,Therefore, an over-simplified anan over-simplifiedover-simplified open-loop open-loopopen-loop TV logic was TVTV purposelylogiclogic waswas purposely builtpurposely within builtbuilt MATLAB-Simulink withinwithin MATLAB-MATLAB- ® andSimulinkSimulink simulated® and and simulated throughsimulated co-simulation. through through co-simulation. co-simulation. The TV action The The TV TV in ac termsactiontion ofin in torqueterms terms of of di torque fftorqueerence, difference, difference, left to right, left left to isto proportionalright,right, is is proportional proportional to the steering to to the the wheelsteering steering angle wheel wheel and angle angle is directed an andd is is atdirected directed reducing at at reducing understeer.reducing understeer. understeer. That means That That the means means outer wheelthethe outer outer torque wheel wheel is highertorque torque thanis is higher higher the inner than than wheelthe the inner inner torque, wheel wheel so torque, thetorque, torque so so the atthe wheeltorque torque is: at at wheel wheel is: is: C[Nm] = k[Nm/rad] ∙ SW_angle[rad] (19) C[Nm]C[Nm]= = k[Nmk[Nm/rad]/rad] ∙ SW_angle[rad]SW_angle[rad] (19) (19) · FigureFigure 12, 12, obtained obtained by by a a sine sine sweep sweep steer steer test, test, shows shows the the torque torque delivered delivered to to the the left-hand left-hand and and right-handright-handFigure side 12side, obtainedwheels wheels being being by a stro sinestronglyngly sweep differentiated differentiated steer test, showsto to achieve achieve the torquea a yaw yaw moment moment delivered by by to means means the left-hand of of the the torque torque and right-handvectoringvectoring action. action. side wheels being strongly differentiated to achieve a yaw moment by means of the torque vectoring action. Appl. Sci. 2020, 10, 4297 12 of 21

Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 21

800 800 600 600 400 400 200 200 0 0 012345678 -200 012345678 Torque Torque [Nm] -200 Torque Torque [Nm] -400 -400 -600 -600 -800 -800 Time [s] Time [s]

Front left torque at wheel Front right torque at wheel Front left torque at wheel Front right torque at wheel

Figure 12. Front wheel torque at the ground on left (red) and right (blue) sides for vehicle with TV FigureFigure 12. 12.Front Front wheelwheel torquetorque atat the ground on left (red (red)) and and right right (blue) (blue) sides sides for for vehicle vehicle with with TV TV (Torque Vectoring), k = 600. (Torque Vectoring), k = 600. (Torque Vectoring), k = 600. Two valuesvalues of of coe coefficientfficient k (300k (300 and and 600 600 Nm Nm/rad)/rad) were were tested. tested. The vehicleThe vehicle balance balance change change in terms in Two values of coefficient k (300 and 600 Nm/rad) were tested. The vehicle balance change in ofterms the understeerof the understeer reduction reduction is shown is shown in Figure in 13Figure for a 13 90 forstep a 90° steer step test steer at 80 test km at/h. 80 A km/h. higher A value higher of terms of the understeer reduction is shown in Figure 13 ◦for a 90° step steer test at 80 km/h. A higher kvalue results of k in results less understeer in less understeer and a smaller and a cornering smaller cornering radius as radius expected. as expected. value of k results in less understeer and a smaller cornering radius as expected.

2 2 0 0 -80 -70 -60 -50 -40 -30 -20 -10-2 0 10 -80 -70 -60 -50 -40 -30 -20 -10-2 0 10 -4 -4 -6 -6 -8 -8 -10 -10 -12 -12 Distance [m]lateral -14 Distance [m]lateral -14 -16 -16 -18 Distance longitudinal [m] -18 Distance longitudinal [m] Passive vehicle TV k=300 TV k=600 Passive vehicle TV k=300 TV k=600

Figure 13. Trajectory after a 90° step steer for passive vehicle (green), TV k = 300 (blue), TV k = 600 Figure 13. Trajectory after a 90° step steer for passive vehicle (green), TV k = 300 (blue), TV k = 600 Figure(red). 13. Trajectory after a 90◦ step steer for passive vehicle (green), TV k = 300 (blue), TV k = 600 (red). (red). Figure 14 compares the steering wheel torque requiredrequired with the passive vehicle (dotted green Figure 14 compares the steering wheel torque required with the passive vehicle (dotted green line) and with torquetorque vectoringvectoring (k(k == 300 dotted blue line, k = 600 dotted red line), with the standard line) and with torque vectoring (k = 300 dotted blue line, k = 600 dotted red line), with the standard geometry in all cases. geometry in all cases. Appl. Sci. 2020, 10, 4297 13 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 21

50 35 50 35 40 40 25 30 25 30 20 15 20 15 10 10 5 0 5 0 012345678-5 -10 012345678-5 -10 -20 -15 -20 -15

Steering wheel angle-30 [deg] Steering wheel torque [Nm]

Steering wheel angle-30 [deg] -25 -40 -25 Steering wheel torque [Nm] -40 -50 -35 -50 Time [s] -35 Time [s]

Steering wheel angle Steering wheel torque passive vehicle Steering wheel angle Steering wheel torque passive vehicle Steering wheel torque TV vehicle K=600 Steering wheel torque TV vehicle K=300 Steering wheel torque TV vehicle K=600 Steering wheel torque TV vehicle K=300

Figure 14. Steering wheel: angle and torque for passive vehicle (green) and TV vehicle (blue k = 300, Figure 14.14. Steering wheel: angle and torque for passive vehicle (green) and TV vehicle (blue(blue kk == 300, red k = 600). redred kk == 600). It shows that the disequilibrium in terms of to torquesrques and longitudinal forces Fx at the ground It shows that the disequilibrium in terms of torques and longitudinal forces Fx at the ground affectsaffects the the shape, shape, linearity linearity and and phase phase of ofthe the steering steering effort eff ortrequired. required. The adverse The adverse effects eff areects even are more even affects the shape, linearity and phase of the steering effort required. The adverse effects are even more evidentmore evident in the indriver-in-the-loop the driver-in-the-loop simulator: simulator: the TV the coefficient TV coeffi cientk = 600 k = Nm,600 Nm,in particular, in particular, results results in a evident in the driver-in-the-loop simulator: the TV coefficient k = 600 Nm, in particular, results in a surprisingin a surprising and andconfusing confusing feedback, feedback, and and in the in the onset onset of ofsteering steering instability, instability, with with the the phase phase shift surprising and confusing feedback, and in the onset of steering instability, with the phase shift inducing an undesirable self-steering effect effect and jeopardisingjeopardising the driving feeling; the vehicle model inducing an undesirable self-steering effect and jeopardising the driving feeling; the vehicle model becomes literally undriveable. From now on, all simulationssimulations will be performedperformed with kk == 600 because becomes literally undriveable. From now on, all simulations will be performed with k = 600 because this appeared as the most critical case. this appeared as the most critical case. Figure 15 shows the steering effort effort required with torque vectoring applied to the EB0 modifiedmodified Figure 15 shows the steering effort required with torque vectoring applied to the EB0 modified geometry. The reaction is similar to the standard geometrygeometry withwith TVTV andand kk = 300,300, so so the the negative negative effects effects geometry. The reaction is similar to the standard geometry with TV and k = 300, so the negative effects affectingaffecting steeringsteering feedbackfeedback are are somehow somehow mitigated; mitigated; the the phase phase shift shift is reduced,is reduced, but but the the response response is still is affecting steering feedback are somehow mitigated; the phase shift is reduced, but the response is verystill very far from far from the desirablethe desirable curve curve obtained obtained with with the passivethe passive vehicle, vehicle, as it as can it can also also be perceived be perceived in the in still very far from the desirable curve obtained with the passive vehicle, as it can also be perceived in thedriving driving simulator. simulator. the driving simulator.

50 35 50 35 40 40 25 30 25 30 20 15 20 15 10 10 5 0 5 0 012345678-5 -10 012345678-5 -10 -20 -15 -20 -15

Steering Steering wheel angle [deg] -30 Steering wheel torque [Nm]

Steering Steering wheel angle [deg] -30 -25 -40 -25 Steering wheel torque [Nm] -40 -50 -35 -50 Time [s] -35 Time [s]

Steering wheel angle Steering wheel torque passive vehicle Steering wheel angle Steering wheel torque passive vehicle Steering wheel torque TV vehicle original Steering wheel torque TV vehicle EB0 Steering wheel torque TV vehicle original Steering wheel torque TV vehicle EB0

Figure 15. The EB0 sine steer (blue line) compared with TV original (red) and passive vehicle Figure 15. The EB0 sine steer (blue line) compared with TV original (red) and passive vehicle Figure 15. The EB0 sine steer (blue line) compared(green). with TV original (red) and passive vehicle (green). (green).

Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 21

Appl. Sci. 2020, 10, 4297 14 of 21 3.Appl. Results Sci. 2020 , 10, x FOR PEER REVIEW 14 of 21 From here, different suspension geometries have been proposed with the aim of possibly 3.3. ResultsResults restoring a stable and intuitive steering response regardless of the disequilibrium induced by the torqueFromFrom vectoring here, here, di atffdifferenterent the front, suspension suspension while maintaining geometries geometries have at leastha beenve the proposedbeen same proposed overall with the steeringwith aim ofthe ratio, possibly aim and of restoring withoutpossibly aclaimingrestoring stable and to a intuitiveachievestable and a steering definitive intuitive response co steeringnfiguration. regardless response As of a the regardlessmatter disequilibrium of fact, of the the induced disequilibriumrefinement by the of torquethe induced self-aligning vectoring by the atpropertiestorque the front, vectoring given while byat maintaining thethe front,combination while at least maintaining theof tyre same char overall atacteristics least steering the andsame ratio, steering overall and without geometrysteering claiming ratio, would and to certainly achievewithout arequireclaiming definitive more to configuration.achieve insight a and definitive fine As atuning. matter configuration. Additionally of fact, the As refinementa ,matter the compatibility of offact, the the self-aligning refinementwith the design properties of the of self-aligning the given wheel by thegroupproperties combination itself given would of by tyrerequire the characteristics combination further evaluation, and of tyre steering charwher geometryacteristicse the wheel would and group steering certainly is composed geometry require by more would the insight wheel, certainly and the fineupright/brakerequire tuning. more Additionally, insightassembly, and the fine compatibilityCV tuning. joint/driveshaft Additionally with the assembly,, designthe compatibility of etc. the The wheel withsecond group the variation itselfdesign would of (EB1) the require wheel was furtherdesignedgroup itself evaluation, to reducewould whererequirethe kingpin the further wheel offs evaluation,et group (KO) is (Figure composed wher 16e theand by wheel theTable wheel, group 2). the is uprightcomposed/brake by the assembly, wheel, thethe CVupright/brake joint/driveshaft assembly, assembly, the etc.CV Thejoint/driveshaft second variation assembly, (EB1) etc. was The designed second to variation reduce the (EB1) kingpin was odesignedffset (KO) to (Figure reduce 16 theTable and kingpin Table2. New2 offs). EB1et suspension(KO) (Figure compared 16 and with Table the 2). previous ones. Name Caster[deg] Kingpin[deg] SR[mm] CT[mm] KO[mm] Sa/Wa[deg/deg] TableTable 2. 2.New New EB1EB1 suspensionsuspension comparedcompared with with the the previous previous ones. ones. Original 10.2 14.2 16.1 29.0 102 15.7 NameNameEB0 CasterCaster[deg]5 [deg] KingpinKingpin[deg] 3.7 [deg] SRSR[mm] [mm]29.2 CTCT[mm] [mm]12.5 KOKO[mm]51.4 [mm] Sa/Wa[deg/deg] Sa/Wa 15.5[deg/ deg] OriginalOriginalEB1 10.210.25.3 14.2 14.22.1 16.1− 16.11.2 29.030.2 29.0 10211.4 102 15.7 15.0 15.7 EB0EB0 55 3.7 3.7 29.229.2 12.512.5 51.451.4 15.5 15.5 EB1 5.3 2.1 1.2 30.2 11.4 15.0 EB1 5.3 2.1 − −1.2 30.2 11.4 15.0

Figure 16. Schematic front view (yz plane) of the EB1 suspension, KO has been reduced to almost

zero. FigureFigure 16. 16.Schematic Schematic front front view view (yz (yz plane) plane) of theof the EB1 EB1 suspension, suspension, KO hasKO beenhas been reduced reduced to almost to almost zero. Afterzero. the same sine steer sweep test, the steering wheel torque of EB1 is shown in blue in Figure After the same sine steer sweep test, the steering wheel torque of EB1 is shown in blue in Figure 17. 17. Apart from a small phase shift at low frequency, the steering effort is very similar to the reference Apart from a small phase shift at low frequency, the steering effort is very similar to the reference case. case. After the same sine steer sweep test, the steering wheel torque of EB1 is shown in blue in Figure 17. Apart from a small phase shift at low frequency, the steering effort is very similar to the reference case. 50 35 40 25 3050 35 40 15 20 25 1030 5 15 200 10 012345678-5 -10 5 0 -20 -15 012345678-5 -10

Steering Steering wheel angle [deg] -30 -25 Steering wheel torque [Nm] -40-20 -15

Steering Steering wheel angle [deg] -30

-50 -35 Steering wheel torque [Nm] Time [s] -25 -40 -50 -35 Time [s] Steering wheel angle Steering wheel torque passive vehicle Steering wheel torque TV vehicle original Steering wheel torque TV vehicle EB1

Steering wheel angle Steering wheel torque passive vehicle Figure 17. The EB1 Steeringsine steer wheel (blue) torque TVcompared vehicle original with TV originalSteering wheel (red) torque and TV passive vehicle EB1 vehicle (green). Figure 17. The EB1 sine steer (blue) compared with TV original (red) and passive vehicle (green). Figure 17. The EB1 sine steer (blue) compared with TV original (red) and passive vehicle (green). Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 21 Appl.Appl. Sci.Sci. 20202020,, 1010,, 4297x FOR PEER REVIEW 1515 ofof 2121 At this point, further variations were designed with a small, negative KO (−5.6 mm, EB2, Figure At this point, further variations were designed with a small, negative KO (−5.6 mm, EB2, Figure 18) and with a very large negative one (−48.9 mm, EB3, Figure 19 and Table 3). 18) andAt thiswith point, a very further large variationsnegative one were (− designed48.9 mm, withEB3, a Figure small, negative19 and Table KO ( 3).5.6 mm, EB2, Figure 18) − and with a very large negative one ( 48.9 mm, EB3, Figure 19 and Table3). Table 3. New EB2 and− EB3 suspensions compared with the previous ones. Table 3. New EB2 and EB3 suspensions compared with the previous ones. Name Caster[deg]Table 3. New Kingpin[deg] EB2 and EB3 suspensionsSR[mm] comparedCT[mm] with the KO[mm]previous ones. Sa/Wa[deg/deg] Name Caster[deg] Kingpin[deg] SR[mm] CT[mm] KO[mm] Sa/Wa[deg/deg] Original 10.2 14.2 16.1 29.0 102 15.7 OriginalName Caster10.2 [deg] Kingpin 14.2 [deg] SR 16.1 [mm] CT 29.0 [mm] KO 102 [mm] Sa/Wa [deg15.7/ deg] EB0 5 3.7 29.2 12.5 51.4 15.5 OriginalEB0 5 10.2 3.7 14.2 29.2 16.1 12.5 29.0 51.4 102 15.7 15.5 EB1EB0 5.3 5 2.1 3.7 − 29.21.2 30.2 12.5 11.451.4 15.5 15.0 EB1EB1 5.3 5.3 2.1 2.1 −1.21.2 30.2 30.2 11.4 11.4 15.0 15.0 EB2 3.9 −7.8 40.8− 16.4 −5.6 15.3 EB2EB2 3.9 3.9 −7.87.8 40.8 40.8 16.4 16.4 −5.65.6 15.315.3 − − EB3EB3 4.8 4.8 −8.18.1 −0.30.3 19.0 19.0 −48.5 15.015.0 EB3 4.8 −−8.1 −−0.3 19.0 −−48.5 15.0

Figure 18. Schematic front view (yz plane) of the EB2 suspension, with small and negative KO. FigureFigure 18.18. Schematic front viewview (yz(yz plane)plane) ofof thethe EB2EB2 suspension,suspension, withwith smallsmall andand negativenegative KO.KO.

FigureFigure 19.19. SchematicSchematic frontfront viewview (yz(yz plane)plane) ofof thethe EB3EB3 suspension,suspension,with with large large and and negative negative KO. KO. Figure 19. Schematic front view (yz plane) of the EB3 suspension, with large and negative KO. EB3EB3 in in particular particular features features a a larger larger amplitude amplitude in in terms terms of of self-aligning self-aligning torque, torque, as shownas shown in Figure in Figure 20. EB3 in particular features a larger amplitude in terms of self-aligning torque, as shown in Figure Again,20. Again, although although this this is a self-aligningis a self-aligning torque, torque, in the in simulator,the simulator, the amplitudethe amplitude reveals reveals itself itself to be to too be 20. Again, although this is a self-aligning torque, in the simulator, the amplitude reveals itself to be muchtoo much of an of e ffanort, effort, hence hence it is notit is desirablenot desirable and and calls calls for veryfor very small small values values of KO, of KO, which which in turn in turn is in is too much of an effort, hence it is not desirable and calls for very small values of KO, which in turn is agreementin agreement with with vehicle vehicle dynamics dynamics experience experience and and theory. theory. in agreement with vehicle dynamics experience and theory. Appl. Sci. 2020, 10, 4297 16 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 21

50 35 50 35 40 40 25 30 25 30 20 15 20 15 10 10 5 5 0 0 012345678-5 -10 012345678-5 -10 -20 -15 -20 -15

Steering Steering wheel angle [deg] -30 Steering wheel torque [Nm]

Steering Steering wheel angle [deg] -30

-25 Steering wheel torque [Nm] -40 -25 -40 -50 -35 -50 Time [s] -35 Time [s]

Steering wheel angle Steering wheel torque passive vehicle Steering wheel angle Steering wheel torque passive vehicle Steering wheel torque TV vehicle EB2 Steering wheel torque TV vehicle EB3 Steering wheel torque TV vehicle EB2 Steering wheel torque TV vehicle EB3

Figure 20. The EB2 (red) and EB3 (blue) sine steer compared with passive vehicle (green). Figure 20. The EB2 (red) and EB3 (blue) sine steer compared with passive vehiclevehicle (green).(green). For the sake of completeness, in order to verify the global performance of the vehicle, additional For the sake of completeness, in order to verify the global performance of the vehicle, additional offline simulations were carried out on a lap of the Hockenheim short track (Figure 21), a circuit oofflineffline simulationssimulations were were carried carried out out on aon lap a oflap the of Hockenheim the Hockenheim short track short (Figure track 21(Figure), a circuit 21), featuringa circuit featuring either slow and fast corners and quick changes of direction, often considered to be eitherfeaturing slow either and fastslow corners and fast and corners quick changes and quick of direction, changes oftenof direction, considered often to beconsidered representative to be representative for handling evaluations. The original, passive vehicle (without torque vectoring) is forrepresentative handling evaluations. for handling The evalua original,tions. passive The original, vehicle passive (without vehicle torque (without vectoring) torque is compared vectoring) with is compared with the application of TV to the various kinematic variants. Fast laps on the driving thecompared application with of the TV application to the various of TV kinematic to the variants.various kinematic Fast laps onvariants. the driving Fast laps simulator on the were driving also simulator were also performed by an experienced driver in order to assess the performance potential performedsimulator were by an also experienced performed driver by an in experienced order to assess driver the in performance order to assess potential the performance of each solution, potential the of each solution, the subjective feeling and also the consistency of consecutive lap times, the latter subjectiveof each solution, feeling andthe subjective also the consistency feeling and of consecutivealso the consistency lap times, of the consecutive latter often lap being times, considered the latter as often being considered as a meaningful indicator of driving intuitiveness and stability, especially in aoften meaningful being considered indicator ofas drivinga meaningful intuitiveness indicator and of stability, driving especiallyintuitiveness in motorsport.and stability, especially in motorsport. motorsport.

500 500

400 400

300 300

200 200

Distancey [m] 100 Distancey [m] 100

0 0 -500 -400 -300 -200 -100 0 100 200 300 400 -500 -400 -300 -200 -100 0 100 200 300 400 -100 -100 Distance x [m] Distance x [m]

Figure 21. The Hockenheim short track map. FigureFigure 21.21. The Hockenheim short track map.

The steering wheel angle and steering effort in the space domain along the circuit are shown in The steering wheel angle and steering eeffortffort inin thethe spacespace domaindomain along the circuit are shownshown inin Figures 22–26 for all configurations analysed in the previous chapter. The vehicle options are driven Figures 2222–26–26 forfor allall configurationsconfigurations analysedanalysed inin thethe previousprevious chapter.chapter. The vehicle options are drivendriven on a fixed trajectory by VI-grade’s Virtual Driver model, therefore, the subjective driver assessment on aa fixedfixed trajectorytrajectory by by VI-grade’s VI-grade’s Virtual Virtual Driver Driver model, model, therefore, therefore, the the subjective subjective driver driver assessment assessment on on the vehicle balance and optimum racing line is removed from the equation. theon the vehicle vehicle balance balance and and optimum optimum racing raci lineng line is removed is removed from from the the equation. equation. Appl. Sci. 2020, 10, 4297 17 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 21

250 150 250 150 200 200 100 150 100 150 100 100 50 50 50 50 0 0 0 0 500 1000 1500 2000 2500 0 -50 0 500 1000 1500 2000 2500 -50 -50 -100 -50 -100 Steering Steering angle wheel [deg]

-150 Steering wheel torque [Nm]

Steering Steering angle wheel [deg] -100

-150 Steering wheel torque [Nm] -200 -100 -200 -250 -150 -250 Distance [m] -150 Distance [m] Steering wheel angle passive vehicle Steering wheel torque passive vehicle Steering wheel angle passive vehicle Steering wheel torque passive vehicle

Figure 22. The passive vehicle: steering wheel angle (red) and steering wheel torque (blue). FigureFigure 22.22. The passive vehicle: steering wheel angle (red) and steering wheel torque (blue).(blue).

The passivepassive vehiclevehicle behaviour behaviour with with TV TV off andoff standardand standard geometry geometry is shown is shown in Figure in 22 Figure. Steering 22. The passive vehicle behaviour with TV off and standard geometry is shown in Figure 22. Steeringangle and angle steering and wheel steering torque wheel always torque have always the same have sign; the thissame is sign; the desirable this is the situation desirable ofself-aligning situation of Steering angle and steering wheel torque always have the same sign; this is the desirable situation of self-aligningtorque feedback torque to be feedback taken as to a be reference, taken as whicha reference, also makes which driving also makes on the driving simulator on the a naturalsimulator and a self-aligning torque feedback to be taken as a reference, which also makes driving on the simulator a naturalintuitive and process, intuitive as shown process, by as lap shown time consistency.by lap time consistency. natural and intuitive process, as shown by lap time consistency.

80 40 80 40 60 30 60 30 40 20 40 20 20 10 20 10 0 0 0 0 500 1000 1500 2000 2500 0 -20 0 500 1000 1500 2000 2500 -10 -20 -10 -40 -20

Steering wheel angle -40 [deg] -20 Steering wheel torque [Nm] Steering wheel angle [deg] -60 -30 Steering wheel torque [Nm] -60 -30 -80 -40 -80 Distance [m] -40 Distance [m] Steering wheel angle TV original vehicle Steering wheel torque TV original vehicle Steering wheel angle TV original vehicle Steering wheel torque TV original vehicle

Figure 23. The original vehicle with TV: steering wheel angle (red) and steering wheel torque (blue). Figure 23. The original vehicle with TV: steering wheel angle (red) and steering wheel torque (blue). Self-steeringFigure 23. The moment original showed vehicle in with green TV: boxes. steering wheel angle (red) and steering wheel torque (blue). Self-steeringSelf-steering momentmoment showedshowed inin greengreen boxes.boxes. Like in the sine sweep test, torque vectoring on the original vehicle geometry causes a large self- LikeLike in the the sine sine sweep sweep test, test, torque torque vectoring vectoring on on the the original original vehicle vehicle geometry geometry causes causes a large a large self- steering moment in most of the corners (green boxes in Figure 23). This is where the torque and self-steeringsteering moment moment in most in most of the of thecorners corners (green (green boxe boxess in Figure in Figure 23). 23This). Thisis where is where the torque the torque and steering angle have opposite signs. Driving this configuration on the simulator immediately andsteering steering angle angle have have opposite opposite signs. signs. Driving Driving this this configuration configuration on on the the simulator immediatelyimmediately demonstrates how difficult it would be to drive a powerful car at racing pace (i.e., very close to the demonstratesdemonstrates how didifficultfficult it wouldwould be toto drivedrive aa powerfulpowerful carcar atat racingracing pacepace (i.e.,(i.e., veryvery closeclose toto thethe limit of adherence) without the re-assuring self-aligning steering torque a feedback: the driver has to limitlimit ofof adherence)adherence) withoutwithout thethe re-assuringre-assuring self-aligningself-aligning steeringsteering torquetorque aa feedback:feedback: thethe driverdriver hashas toto “fight” the steering all the time. Consecutive lap times are slow and extremely inconsistent (Figure “fight”“fight” thethe steering steering all all the the time. time. Consecutive Consecutive lap lap times times are are slow slow and and extremely extremely inconsistent inconsistent (Figure (Figure 27) 27) because the vehicle behaviour and trajectory are scarcely predictable. because27) because the vehiclethe vehicle behaviour behaviour and and trajectory trajectory are scarcelyare scarcely predictable. predictable. With the EB0 suspension, designed to reduce KO, although still matching wheel assembly WithWith thethe EB0EB0 suspension,suspension, designeddesigned toto reducereduce KO,KO, althoughalthough stillstill matchingmatching wheelwheel assemblyassembly components, the result is better but occasional self-steering peaks are still visible (Figure 24). In the components,components, the resultresult isis betterbetter butbut occasionaloccasional self-steeringself-steering peakspeaks areare stillstill visiblevisible (Figure(Figure 2424).). InIn thethe simulator, this effect can be clearly detected after a few laps. Driving at the limit is still very stressful simulator,simulator, thisthis eeffectffect cancan bebe clearlyclearly detecteddetected afterafter aa fewfew laps.laps. DrivingDriving atat thethe limitlimit isis stillstill very stressful and the pace is inconsistent; the lap time improves after a typical learning cycle, then they tend to and the pace is inconsistent; the lap time improves after a typical learning cycle, then they tend to increase again, this is probably due to the driver’s mental fatigue. increase again, this is probably due to the driver’s mental fatigue. Appl. Sci. 2020, 10, 4297 18 of 21 and the pace is inconsistent; the lap time improves after a typical learning cycle, then they tend to increase again, this is probably due to the driver’s mental fatigue. Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 21

80 40 80 40 60 30 60 30 40 20 40 20 20 10 20 10 0 0 0 0 500 1000 1500 2000 2500 0 -20 0 500 1000 1500 2000 2500 -10 -20 -10 -40 -20

Steering Steering angle wheel [deg] -40 -20 Steering wheel torque [Nm] Steering Steering angle wheel [deg] -60 -30 Steering wheel torque [Nm] -60 -30 -80 -40 -80 Distance [m] -40 Distance [m] Steering wheel angle TV vehicle EB0 Steering wheel torque TV vehicle EB0 Steering wheel angle TV vehicle EB0 Steering wheel torque TV vehicle EB0

Figure 24. The TV vehicle with EB0 suspension: steering wheel angle (red) and steering wheel torque Figure 24. TheThe TV TV vehicle vehicle with EB0 suspension: steering steering wheel wheel angle angle (red) and steering wheel torque (blue). Self-steering moment showed in green boxes. (blue). Self-steering Self-steering moment showed in green boxes. As in the previous section, the most balanced results, i.e., the closest to the reference passive As inin thethe previousprevious section, section, the the most most balanced balanced results, results, i.e., i.e., the the closest closest to the to referencethe reference passive passive case, case, have been obtained with the EB1 geometry (KO = 11.4 mm, Figure 25). case,have have been obtainedbeen obtained with thewith EB1 the geometry EB1 geometry (KO = (KO11.4 = mm,11.4 Figuremm, Figure 25). 25).

90 60 90 60 70 70 40 50 40 50 30 20 30 20 10 10 0 -10 0 500 1000 1500 2000 2500 0 -10 0 500 1000 1500 2000 2500 -30 -20 -30 -20 -50 Steering Steering angle wheel [deg] -50 Steering wheel torque [Nm] Steering Steering angle wheel [deg] -40 -70 -40 Steering wheel torque [Nm] -70 -90 -60 -90 Distance [m] -60 Distance [m] Steering wheel angle TV vehicle EB1 Steering wheel torque TV vehicle EB1 Steering wheel angle TV vehicle EB1 Steering wheel torque TV vehicle EB1

Figure 25. The TV vehicle with EB1 suspension: steering wheel angle (red) and steering wheel torque Figure 25. The TV vehicle with EB1 suspension: steering wheel angle (red) and steering wheel torque (blue).Figure 25. The TV vehicle with EB1 suspension: steering wheel angle (red) and steering wheel (blue).torque (blue). This basically deletes the interaction between the differentiated torque delivery due to TV and This basically deletes the interaction between the differentiated torque delivery due to TV and steering,This thus basically making deletes TV theapplication interaction possible. between Self-steering the differentiated effects torqueare totally delivery removed due to and TV andthe steering, thus making TV application possible. Self-steering effects are totally removed and the steeringsteering, feel thus on makingthe simulator TV application is back to a possible. reassuring Self-steering, natural effort, eff ectshelping are th totallye driver removed to establish and the steering feel on the simulator is back to a reassuring, natural effort, helping the driver to establish the abovementionedsteering feel on the intuitive simulator correlation is back to between a reassuring, cornering natural speed, effort, steering helping angle the driver and steering to establish effort, the abovementioned intuitive correlation between cornering speed, steering angle and steering effort, andabovementioned to perceive vehicle intuitive balance. correlation Lap ti betweenmes are corneringfaster overall speed, and steering consistent. angle and steering effort, and and to perceive vehicle balance. Lap times are faster overall and consistent. to perceiveThe EB3 vehicle geometry balance. (KO Lap= −48.5, times Figure are faster 26) basically overall and amplifies consistent. the self-aligning effect, which is a The EB3 geometry (KO = −48.5, Figure 26) basically amplifies the self-aligning effect, which is a goodThe thing EB3 in geometryitself. However, (KO = it48.5, also Figurerestores 26 the) basically undesirable amplifies interaction the self-aligning between torque effect, whichdelivery is good thing in itself. However, −it also restores the undesirable interaction between torque delivery (undera good power thing in for itself. instance) However, and steering it also restores feel and the driving undesirable on the interaction simulator once between again torque becomes delivery less (under power for instance) and steering feel and driving on the simulator once again becomes less intuitive(under power and more for instance) stressful, and as shown steering by feel the and fairly driving poor lap on thetime simulator consistency. once The again overall becomes steering less intuitive and more stressful, as shown by the fairly poor lap time consistency. The overall steering effort is also harder. effort is also harder. Appl. Sci. 2020, 10, 4297 19 of 21 intuitive and more stressful, as shown by the fairly poor lap time consistency. The overall steering Appl.effort Sci. is 2020 also, 10 harder., x FOR PEER REVIEW 19 of 21

Appl. Sci. 2020, 10, x FOR PEER REVIEW 19 of 21 90 60

7090 60 40 5070 40 3050 20

1030 20 0 -1010 0 500 1000 1500 2000 2500 0 -30-10 0 500 1000 1500 2000 2500 -20

-50-30 -20 Steering Steering angle wheel [deg] -40 Steering wheel torque [Nm] -70-50 Steering Steering angle wheel [deg] -40 Steering wheel torque [Nm] -90-70 -60 Distance [m] -90 -60 Steering wheel angle TV vehicle DistanceEB3 [m] Steering wheel torque TV vehicle EB3

Steering wheel angle TV vehicle EB3 Steering wheel torque TV vehicle EB3 Figure 26. 26. TheThe TV TV vehicle vehicle with with EB3 EB3 suspension: suspension: steering steering wheel wheel angle angle(red) and (red) steering and steering wheel torque wheel Figure(blue).torque (blue).26. The TV vehicle with EB3 suspension: steering wheel angle (red) and steering wheel torque (blue).

Figure 27. Lap time comparison over a 10-lap run on the driving simulator.

Figure 27. LapLap time time comparison comparison over a 10-lap run on the driving simulator. 4. Conclusions 4. Conclusions ConclusionsThis paper aims at describing the application of torque vectoring on the vehicle front axle by meansThis of paper two separate aims at electric describing motors. the application TV can offer of torque potential vectoring benefits on in the terms vehicle of handling front axle and by meansstability ofof at twotwo the separate separateexpense electric ofelectric steering motors. motors. feel, TV andTV can canultimately offer offer potential potential performance, benefits benefits in termsif torque in ofterms handling steer of effectshandling and stabilityare andnot stabilitytakenat the into expense at account the ofexpense steering during of the feel,steering design and ultimatelyfeel, phase. and The ultimately performance, analysis performance,of different if torque suspension/steering steerif torque effects steer are effects not geometries taken are intonot showstakenaccount into that during account the kingpin the during design offset the phase. design(KO) The has phase. analysis a strong The of anal diinfffluenceerentysis of suspension ondifferent torque suspension/steering/ steeringsteer. It geometriesshould be minimised,geometries shows that showsprovidedthe kingpin that the the o ffresultantset kingpin (KO) geometry hasoffset a strong (KO) is compatible has influence a strongon with in torquefluence the des steer. onign torque Itof should the wheelsteer. be minimised, Itassembly. should be provided minimised, the providedresultantFinally, geometrythe it resultant should is compatiblebe geometry stated that is with compatible the the net design force with ex ofchanged thethe wheeldesign between assembly. of the wheelthe rolling assembly. tyre and the road is inevitablyFinally, applied it should to a be point stated wandering that the netwithin force the exchangedex contactchanged patch between area, theespecially rolling ontyre uneven and the surfaces. road is inevitablyTherefore, applied the effective to a point point KO amount wandering wandering is not within within a fixed the the di contact contactstance patch patchand it area, area, is not especially especially possible on onto uneveneradicate uneven surfaces. surfaces. torque Therefore,steer effects thethe completely, eeffectiveffective KO KOespeci amount amountally iswith is not not modern a fixeda fixed distance wide distance tyres. and and it is it not is possiblenot possible to eradicate to eradicate torque torque steer steereffects effects completely, completely, especially especi withally modernwith modern wide tyres.wide tyres. Author Contributions: E.B., D.C., and M.G. conceived the presented idea. E.B. developed the theory and performedAuthor Contributions: the computations. E.B., D.C.,P.M. developedand M.G. conceivedthe software the tool presen usedted for idea. kinematics E.B. developed analysis. D.C.,the theory P.M., and performedS.M. verified the the computations. analytical methods. P.M. developed M.G. encouraged the software E.B. tool to usedinvestigat for kinematicse the subjective analysis. aspects D.C., of P.M., steering and feedback and supervised the findings of this work. All authors discussed the results and contributed to the final S.M. verified the analytical methods. M.G. encouraged E.B. to investigate the subjective aspects of steering manuscript.feedback and supervised the findings of this work. All authors discussed the results and contributed to the final manuscript. Appl. Sci. 2020, 10, 4297 20 of 21

Author Contributions: E.B., D.C. and M.G. conceived the presented idea. E.B. developed the theory and performed the computations. P.M. developed the software tool used for kinematics analysis. D.C., P.M. and S.M. verified the analytical methods. M.G. encouraged E.B. to investigate the subjective aspects of steering feedback and supervised the findings of this work. 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

1. Marchesin, F.P.; Barbosa, R.S.; Gadola, M.; Chindamo, D. High downforce race car vertical dynamics: Aerodynamic index. Veh. Syst. Dyn. 2018, 56, 1269–1288. [CrossRef] 2. Gritti, G.; Peverada, F.; Orlandi, S.; Gadola, M.; Uberti, S.; Chindamo, D.; Romano, M.; Olivi, A. Mechanical steering gear internal friction: Effects on the drive feel and development of an analytic experimental model for its prediction. In Proceedings of the International Joint Conference on Mechanics, Design Engineering & Advanced Manufacturing (JCM), Catania, Italy, 14–16 September 2016. 3. Kim, N.; Cole, D.J. A model of driver steering control incorporating the driver’s sensing of steering torque. Veh. Syst. Dyn. 2011, 49, 1575–1596. [CrossRef] 4. Gillespie, T. Fundamentals of Vehicle Dynamics; Society of Automotive Engineers, Inc.: Warrendale, PA, USA, 1992. 5. Sharp, R.S. Vehicle performance-understanding human monitoring and assessment. In Vehicle Dynamics and the Judgement of Quality; Swets & Zeitlinger: Delft, The Netherlands, 1999; pp. 87–96. 6. Dornhege, J.; Nolden, S.; Mayer, M. Steering torque disturbance rejection. SAE Int. J. Veh. Dyn. Stab. NVH 2017, 1, 165–172. [CrossRef] 7. Wikipedia on the Torque Steer Effect. Available online: https://en.wikipedia.org/wiki/Torque_steer (accessed on 25 February 2020). 8. Woo, S.; Park, S.; Oh, Y. Solution for the torque steer problem of a front-wheel drive car with a high torque engine in vehicle development stages. In Proceedings of the 14th Asia Pacific Automotive Engineering Conference, Hollywood, CA, USA, 5–8 August 2007. 9. Dornhege, J. Torque Steer Influences on McPherson Front Axles. In Proceedings of the 2002 European Adams User Conference, London, UK, 13–14 November 2002; Multi-Body Dynamics: Monitoring and Simulation Techniques-III, 2004; pp. 439–446. 10. Gadola, M.; Chindamo, D.; Lenzo, B. On the Passive Limited Slip Differential for High Performance Vehicle Applications. In Proceedings of the 14th International Symposium on Advanced Vehicle Control (AVEC 18), Beijing, China, 16–20 July 2018. 11. Mastinu, G.; Battistini, E. The influence of limited-slip differentials on the stability of rear-wheel-drive automobiles running on even road with dry surface. Int. J. Veh. Des. 1993, 14, 166–183. 12. Tremlett, A.J.; Assadian, F.; Purdy, D.J.; Vaughan, N.; Moore, A.P.; Halley, M. Quasi steady state linearisation of the racing vehicle acceleration envelope: A limited slip differential example. Veh. Syst. Dyn. 2014, 52, 1416–1442. [CrossRef] 13. Tremlett, A.J.; Massaro, M.; Purdy, D.J.; Velenis, E.; Assadian, F.; Moore, A.P.; Halley, M. Optimal control of motorsport differentials. Veh. Syst. Dyn. 2015, 53, 1772–1794. [CrossRef] 14. Huchtkoetter, H.; Klein, H. The effect of various limited-slip differentials in front-wheel-drive vehicles on handling and traction. In Transmission and Driveline Systems Symposium: Efficiency, Components, and Materials; JAE Paper; JAE: Detroit, MI, USA, 1996; Volume 960717, pp. 131–141. 15. Tremlett, A.J.; Purdy, D.J.; Vaughan, N.; Assadian, F.; Moore, A.P.; Halley, M. The influence of torque and speed sensitive differential characteristics in a FWD vehicle during on limit manoeuvres. In Proceedings of the FISITA 2012 World Automotive Congress, Beijing, China, 27–30 November 2012; Lecture Notes in Electrical Engineering. Springer: Berlin/Heidelberg, Germany, 2013; Volume 193, pp. 79–91. 16. Frantzen, M. Reduktion Störender Lenkmomente, Hervorgerufen Durch Antriebskräfte an Federbein Vorderachsen; Forschungsges. Kraftfahrwesen Aachen: Aachen, Germany, 2008; ISBN 978-3-940374-03-5. 17. Abe, M.; Ohkubo, N.; Kano, Y. A direct yaw moment control for improving limit performance of vehicle handling—Comparison and cooperation with 4WS. Veh. Syst. Dyn. 1996, 25, 3–23. [CrossRef] Appl. Sci. 2020, 10, 4297 21 of 21

18. Kinsey, J. The Advantages of an Electronically Controlled Limited Slip Differential; No. 2004-01-0861; SAE Technical Paper; SAE: Warrendale PA, USA, 2004. 19. Hancock, M.; Williams, R.; Gordon, T.; Best, M. A comparison of braking and differential control of vehicle yaw-sideslip dynamics. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 2005, 219, 309–327. [CrossRef] 20. Cheli, F.; Pedrinelli, M.; Resta, F.; Travaglio, G.; Zanchetta, M.; Zorzutti, A. Development of a new control strategy for a semi-active differential for a high-performance vehicle. Veh. Syst. Dyn. 2006, 44, 202–215. [CrossRef] 21. Morselli, R.; Zanasi, R.; Sandoni, G. Detailed and reduced dynamic models of passive and active limited-slip car differentials. Math. Comput. Model. Dyn. Syst. 2006, 12, 347–362. [CrossRef] 22. Hancock, M.J. Vehicle Handling Control Using Active Differentials. Ph.D. Thesis, Loughborough University, Loughborough, UK, 2006. 23. Hancock, M.J.; Williams, R.A.; Fina, E.; Best, M.C. Yaw motion control via active differentials. Trans. Inst. Meas. Control 2007, 29, 137–157. [CrossRef] 24. Ross, C.; Carey, C.; Schanz, T.; Gaffney, E.; Catalano, M. Development of an Electronically-Controlled, Limited-Slip Differential (Elsd) for Fwd Applications; SAE Paper; SAE: Warrendale, PA, USA, 2007. 25. Assadian, F.; Hancock, M.; Best, M.C. Development of a control algorithm for an active limited slip differential. In Proceedings of the 10th International Symposium on Advanced Vehicle Control (AVEC), Loughborough, UK, 22–26 August 2008; pp. 55–60. 26. De Rosa, R.; Russo, M.; Russo, R.; Terzo, M. Optimisation of handling and traction in a rear wheel drive vehicle by means of magneto-rheological semi-active differential. Veh. Syst. Dyn. 2009, 47, 533–550. [CrossRef] 27. Deur, J.; Ivanovic, V.; Hancock, M.; Assadian, F. Modeling and analysis of active differential dynamics. J. Dyn. Syst. Meas. Control 2010, 132, 61501. [CrossRef] 28. Tremlett, A.J.; Purdy, D.J.; Vaughan, N.; Assadian, F.; Moore, A.P.; Halley, M. The control authority of passive and active torque vectoring differentials for motorsport applications. In Proceedings of the FISITA 2012 World Automotive Congress, Beijing, China, 27–30 November 2012; Lecture Notes in Electrical Engineering. Springer: Berlin/Heidelberg, Germany, 2013; Volume 193, pp. 335–347. 29. Dornhege, J. Torque Steer Compensation Using EPAS; EAEC Congress: Valencia, Spain, 2011. 30. De Novellis, L.; Sorniotti, A.; Gruber, P. Wheel torque distribution criteria for electric vehicles with torque-vectoring differentials. IEEE Trans. Veh. Technol. 2014, 63, 1593–1602. [CrossRef] 31. Chatzikomis, C.; Zanchetta, M.; Gruber, P.; Sorniotti, A.; Modic, B.; Motaln, T.; Blagotinsek, L.; Gotovac, G. An energy-efficient torque-vectoring algorithm for electric vehicles with multiple motors. Mech. Syst. Signal Process. 2019, 128, 655–673. [CrossRef] 32. Sforza, A.; Lenzo, B.; Timpone, F. A state-of-the-art review on torque distribution strategies aimed at enhancing energy efficiency for fully electric vehicles with independently actuated drivetrains. Int. J. Mech. Control 2019, 20, 3–13. 33. Lenzo, B.; Gruber, P.; Sorniotti, A. On the Enhancement of Vehicle Handling and Energy Efficiency of Electric Vehicles with Multiple Motors: The iCOMPOSE Project. In Proceedings of the 26th Symposium of the International Association of Vehicle System Dynamics, IAVSD 2019, Gothenburg, Sweden, 12–16 August 2019; Code 237679. [CrossRef] 34. Bonera, E.; Gadola, M.; Chindamo, D.; Morbioli, S.; Magri, P. Integrated Design Tools for Model-Based Development of Innovative Vehicle Chassis and Powertrain Systems. In Proceedings of the International Conference on Design Tools and Methods in Industrial Engineering, ADM 2019, Modena, Italy, 9–10 September 2019. Code 232769. [CrossRef] 35. Benini, C.; Gadola, M.; Chindamo, D.; Uberti, S.; Marchesin, F.P.; Barbosa, R.S. The influence of suspension components friction on race car vertical dynamics. Veh. Syst. Dyn. 2017, 55, 338–350. [CrossRef] 36. Gadola, M.; Chindamo, D.; Legnani, G.; Comini, M. Teaching automotive suspension design to engineering students: Bridging the gap between CAD and CAE tools through an integrated approach. Int. J. Mech. Eng. Educ. 2019, 47, 23–43. [CrossRef]

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