Resource Efficient Vehicles Conference14 – 16 June 2021

Optimising tyre wear and exploring its conflict with comfort

Georgios Papaioannou1,2*, Jenny Jerrelind1,2 and Lars Drugge1,2

1Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden2The Centre for ECO2 Vehicle Design, KTH Royal Institute of Technology, Stockholm, Sweden*Corresponding author. Email: papaioa@kth.se

The automotive industry is shifting its focus on energy efficient driving to tackle rising environ-mental issues. In this direction, as exhaust particle emissions continuously decrease, the attentionis turned on non-exhaust traffic related sources in ground vehicles, such as the interaction betweentyre and roads and the tyre wear. Given that the tyres are costly for the vehicle owner and wear cre-ates large waste of old tyres, the modelling and the minimisation of tyre wear have been of greatinterest recently. The tyre wear is mainly caused by inner (tyre structure and shape) and external(suspension configuration, speed, road surface, etc.) factors. So, this work presents a sensitivityanalysis of both inner and external factors, and then explores the optimisation of tyre and sus-pension parameters for minimising tyre wear and enhancing comfort. More specifically, initiallythe inner factors are investigated regarding their impact on tyre wear, while external factors, i.e.,vehicle loading, velocity and road type, which can be different daily regarding the purpose of theride, are studied regarding both comfort and tyre wear outlining the conflicting relation betweenthese two objectives. Finally, informed by the results, the optimum tyre and suspension design fora passenger vehicle are sought to both minimise tyre wear, enhance comfort and improve vehiclestability in normal loading conditions while the vehicle drives in a city road (Road Class A) withnormal speed.

© 2021 by the authors. Published by the Resource Efficient Vehicles Conference.This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

1. Introduction

The automotive industry is shifting its focus on energy efficient driving hoping to tackle risingenvironmental issues. In this direction, as exhaust particle emissions continuously decrease, the at-tention is turned on non-exhaust traffic related sources in ground vehicles, such as the interactionbetween tyre and roads and the tyre wear. Regarding the latter, where this work focuses, it was es-timated around 300,000 tonnes in few European countries in 2013 [1]. A significant percentage ofthese are within PM10 fraction [2], ending up in air, water, soils etc. and leading to increasing envi-ronmental pollution. Hence, the need to develop more environmentally friendly vehicle systems thatcan decrease tyre wear has risen.

Tyre wear is categorised, according to Huang et al. [3], into two types normal and abnormal. Thenormal wear is responsible for uniform wear along the tyre circumference and over its width, whilethe abnormal is defined by uneven and irregular wear. Uneven wear mostly describes the non-uniformwear distribution over the tyre width, whereas the irregular wear mainly considers the circumferentialwear. The total amount of wear is mainly caused because of inner (tyre design and manufacturing)and external (vehicle, road, driving condition and circumstances) factors. Considering these, thiswork investigates the sensitivity of tyre wear with regards to the majority of these factors, and also

© 2021 by the authors. Published by the Resource Efficient Vehicles Conference.This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Resource Efficient Vehicles Conference – rev2021

the relation of tyre wear with occupants comfort. Even though the modeling of tyre wear has beenstudied extensively both analytically [4, 5] and experimentally [6, 7], very few works have consideredthe optimisation towards tyre wear minimisation. This has led to a non clear understanding so farregarding the trade-off between important vehicle performance aspects and wear. Recently Andersonet al. [8] investigated the trade-off between wear performance and handling. However, to the authors’knowledge no emphasis has been given with regards to comfort and wear relation. In this direction,this work considers the optimisation of both tyre and suspension parameters for minimising wear andenhancing comfort on a passenger vehicle. Significant conclusions regarding how tyre wear behaveswith regards to important tyre parameters and to passenger comfort are extracted.

To sum up, this paper is organised as follows: firstly, all the models (vehicle, tread and wear) aredescribed, and the road excitations used are displayed; secondly, the sensitivity analysis is presented;thirdly, the formulation of the multi-objective optimisation and its results are displayed; and finally,conclusions are extracted.

2. Methods and materials

The simulation model (Fig. 1a) considers four basic subsystems of the vehicle: the chassis, thesuspension systems, the unsprung mass and the tyres. The chassis is considered as a rigid bodyof mass (ms = 1301/4 kg), and it is connected with the unsprung mass (mu = 43 kg) through thesuspension system, which is modelled as spring and damper (Ku = 25000 N/m andCu = 2500 Nm/s).Regarding the tyres, a more detailed modelling is applied compared to the common quarter car model.Firstly, the tyre sidewall is modelled as spring and damper (KT = 0.8 ∗Kt and CT = 508 Nm/s) andconnects the unsprung mass with the tyre tread (mt), whose mass is varying dynamically accordingto analytical equations. Finally, the tread element consists of linear springs and dampers (Kt andCt = 2508 Nm/s), which receive the unevenness of the road profile (zR) as an excitation (Fig. 1b). Thetreat element stiffness (Kt) is evaluated according to the tread model and is described in the followingsections. The detailed governing equations of the vehicle model can be found in the literature [9].

(a) Quarter Car Model

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2.1 Tread model

This model considers the tread as a cuboid element with a, b and h being its length, width andheight respectively. Regarding the first two, they are evaluated according to empirical equations (Eq.(1)) extracted from the literature [10, 11], which consider tyre dimensions, i.e. the outside radius(d [m]) and the crown thickness (b0 [m]), and the tyre deformation (δ [m]):

a = 4d

(δ

2d

)s, b = b0(1 − e−ψ), δ =

α1Fz2P

+

√(α1Fz2P

)2

+ α2Fz (1)

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where ψ (=115) and s (=0.67) are empirical coefficients, α1 is 1/2πdrw, with rw (m) being the tyrechordwise curvature radius; α2 (=3.70 ∗ 10−8) is a constant for car tyre; P (kPa) is the tyre pressure.Finally, the mass of the tread element can be derived by Eq. (2), where ρ (=1156 kg/m3) is density:

mt = abhρ (2)

while Fz is the wheel load, and when the wear model is coupled with the vehicle model it is evaluatedaccording to Eq. (3),where FZ0 is the static load applied.

Fz = FZ0 + Ct(zt − zR) +Kt(zt − zR) (3)

(a) Tread element modeled as a cuboid

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Figure 2: The modeling of the tread element (mt) and the force-deflection curves according Eq. (1).

According to the tyre deformation (δ-Eq. (1)), the tread deformation is related with the pressure-P(Fig. 2b), the tyre radius-d and chordwise radius-rw. Therefore, during the sensitivity analysis and theoptimisation studied in this work, Kt is evaluated according to these values. More specifically, theforce-deflection curve is evaluated based on Eq. (1) for each potential combination of P , d and rwwith Fz varying from 500 N to 7000 N . Then, having obtained the force-deflection curve, the Kt isevaluated as the slope at the linear region, while the sidewall stiffness (KT ) is evaluated by 0.8 ∗Kt.

2.2 Tyre wear quantity

The frictional or wear energy, Ew [Nm/m2] per unit area is evaluated according to Eq. (4), whilethe wear energy per contact area can be related with the mass loss according to Eq. (5), which isderived by Lupker et al. [12] from experiments:

Eyw =

a

2Cxtan

2φb2(1 − q)2 +µatanφ

2Fz[3(1 − q)4 − 4(1 − q)3 + 1] (4)

∆m = f1Ef2 (5)

where Cx(=3.57 107) is the transverse tread elastic coefficient; φ the sideslip angle; µ (=1) is thefriction coefficient; q = Cxba2

6µFzφ; f1 and f2 (=1.5106) are constants at a given temperature. The mass

loss (∆m) evaluated at each time step is used to calculate the mt dynamically. As an extension ofEq. (5), Yong et al. [9], incorporated in these two constants the effect of temperature according toEq. (6), where f0 (=2.0 10−10) is f1 at T0 (=60o) and Tt is defined as the steady state tread temperatureaccording to Eq. (7) where V [m/s] is the vehicle velocity; r (= 0.229 m) is the rim radius; c (=0.235 m) is the tyre width; γ (=0.12) is the tyre hysteresis coefficient; β (=1.40) is the correctioncoefficient; T∞ is the ambient temperature.

∆m = f0 1.02Tt−T0 Ef2 (6)

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Tt =0.0447γ (3.6 ∗ V )0.16 Fz d

−0.5 δ0.5

πβ [2dc+ 0.4(d2 − r2) + 0.4(d2 + dr + r2) − 0.6r(d+ r)]+ T∞ (7)

where the velocity (V ) and the slip angle (φ) are extracted from simulations from IPG CARMAKER8.0, while the vehicle drives over an S-path (Fig. 3) on which the various roads are assigned (Fig. 1b).

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The total wear quantity caused by the mass loss (Eq. (6)), is defined as the height change (∆h):

∆h =∆m

ρab(8)

Finally, the total wear is defined:

W (t) = W (t− t0) + ∆h (9)

where W (t − t0) is the total tread wear before the first tyre revolution; t0 (=2πrr/V ) is the rotatingperiod and rr the rolling radius. In this work, the maximum value of W (t) (max(W (t)) is consideredas the index of wear levels.

3. Sensitivity analysis

As mentioned previously, this work illustrates initially a sensitivity analysis of both inner andexternal factors. More specifically, the inner factors are investigated regarding their impact on tyrewear, while external factors, which can be different daily regarding the purpose of the ride, are studiedregarding both comfort and tyre wear. Regarding the comfort, it is assessed by using the root meansquare value of vertical acceleration measurements at the vehicle sprung mass (zs). The sensitivityanalysis conducted with regards to various inner factors is displayed in Fig. 4, while with regards tothe external factors in Fig. 5.

Regarding the inner factors, four case studies are considered. In each of the case studies, both thetyre pressure (P ) and one inner factor (d, c, rw and b0) are varied in order to capture their relation withtyre wear (TW ). Their values are presented in the corresponding plots for each case study (Fig. 4a-4d). Regarding the results, according to Fig. 4, the relation of TW with P is clear and as P increasesthe TW is decreased. Similar behaviour is illustrated in the rest of the inner factors (d, c and rw)except the crown thickness (b0), where its increase leads to an increase in TW . Moreover, the mostdominant impact on TW is identified on b0, which reaches up to ∼ 40% increase when it changesfrom 0.15 to 0.23 m. The next is the impact of P being ∼ 25% when P varies from 150 to 350 kPa,while this change is consistent whatever inner factor is varied. At the same time, d, c and rw illustratethe smallest impact being ∼ 2%, ∼ 3%, ∼ 1% for changes from 0.27 to 0.35 m, 0.19 to 0.23 m and0.14 to 0.18 m, respectively.

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(a) Tyre pressure with regards to tyre radius

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Figure 4: Sensitivity analysis of tyre wear with regards to inner factors related with the tyre structure.

As far as the external factors are concerned, three case studies are considered. In each of the casestudies, both the tyre pressure (P varying from [150,350] kPa) and one external factor (road classes,masses and velocities) are varied in order to capture their relation with tyre wear (TW ). In Fig. 5c-5b, the tyre wear and comfort levels are presented, displaying the conflicting relations of wear withcomfort. Regarding the wear behaviour, according to Fig. 5, the relation of TW with the externalfactors is less consistent compared to the previous analysis. At the same time, the different pressuresoutline for each external factor highlight the conflicting relation between wear and comfort. Morespecifically for each external factor, the mass analysis (Fig. 5a) presents uniformity with regards tothe TW increase at each mass increase, illustrating an overall change ∼ 30% when varying from 250to 450 kg. Similarly, the analysis with regards to the velocity (Fig. 5b) presents an increase ∼80% inTW whenever the vehicle velocity is increased by 5 km/h. This is also depicted in the slip angles asexpected (Fig. 6a), which have a constant increase with every velocity increase. On the other hand, theTW variations for different road classes are not consistent, where greater TW increases are identifiedwhen the class changes from B to C. The is because of the impact that the different road classes has onthe slip angles, as illustrated in Fig. 6. According to Fig. 6, the vibration in the slip angles from classB to C are increasing significantly. However, this might be because of the power spectral densitiesselected to design the random road classes, leading to a bad class C profile.

4. Optimisation

4.1 Configuration

As mentioned previously, the second part of this work considers the optimisation of tyre andsuspension parameters for minimising tyre wear, but also enhancing comfort and improving vehicle

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(a) Tyre wear vs. comfort for different sprung masses.

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Figure 5: Sensitivity analysis of tyre wear vs. comfort with regards to external factors.

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Figure 6: The slip angles used in the sensitivity analysis for different road classes and velocities.

stability. Therefore, the appropriate metrics to represent these objectives are the maximum wearquantity (F1 = max(W (t))), described in Section 2.2, the root mean square value of the sprungmass accelerations (F2 = rms(zs)) and the root mean square value of the tyre deflections (F3 =rms(zu− zR)), respectively. The design variables selected are C3, K3, P, c, d, b0 and rw, while theupper and lower bounds selected for them are illustrated in Table 1 and are according to the sensitivityanalysis. Also, Kt and KT are considered indirect design variables as they are evaluated based on thedesign variables according to Section 2.1. The optimisation is conducted for the vehicle model being

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excited by a Class A random road profile. The MATLAB 2017b GAMULTIOBJ toolbox is used.

Table 1: Lower and upper bounds for the design variables.

Design Variables BoundsLower Upper

C3 [N/m] 500 5000 Suspension ParametersK3 [N/m] 15000 60000P [KPa] 150 350

Tyre Parametersc [m] 0.14 0.22d [m] 0.27 0.35b0 [m] 0.12 0.19rw [m] 0.12 0.20

4.2 Results

Regarding the optimisation results, they are illustrated in Fig. 7, where the objectives of the op-timal solution are plotted. More specifically, Fig. 7a is illustrating the relation between comfort andhandling for the optimal solutions provided by the optimisation process, while Fig. 7b presents theirrelation with regards to their comfort and tyre wear objectives.

According to Fig. 7, the conflicting relation between comfort and handling are accurately captured,which proves the validity of the optimisation results. Also, the optimisation has converged to a well-shaped pareto front (Fig. 7a) due to the correct optimisation configuration for the given problem (i.e.population size at 200, elite count at 5) and also due to the simple excitation studied (class A roadprofile). As far as comfort and tyre wear are concerned, they display the same conflicting relation withcomfort and handling (Fig. 7a) according to Fig. 7b. However, most of the solutions have converged tothe same area of tyre wear values (∼ 2−3∗10−5). The solutions at the lower part of pareto front, whichare the ones providing the most comfortable suspension and tyre design (RMS(zs)=[0.36, 0.38]),increase wear more than ∼ 100%.

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Figure 7: The pareto fronts obtained for the optimisation problem described in Section 4.1.

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5. Conclusions

To sum up, this work illustrated initially a sensitivity analysis of both inner and external factors,and then explored the optimisation of tyre and suspension parameters for minimising tyre wear andenhancing comfort. The results outlined the conflicting relation between wear and comfort boththrough the sensitivity analysis and the optimisation. At the same time, handling illustrates a linearrelation with wear, i.e the increasing tyre deflections increase wear. Regarding the inner factors,tyre pressure and crown thickness were highlighted as the most dominant with regards their impacttowards wear levels providing 25% and 40% changes within the range of study. As far as the externalfactors are concerned, all the ones studied (vehicle mass and velocity, and road class) illustrated greatimpact on wear levels, affecting comfort significantly at the same time.

6. Acknowledgements

The authors would like to thank the Centre for ECO2 Vehicle Design, funded by the SwedishInnovation Agency Vinnova (Grant Number 2016-05195), for financial support.

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