Content uploaded by Lorenzo Nicoletti

Author content

All content in this area was uploaded by Lorenzo Nicoletti on Nov 16, 2020

Content may be subject to copyright.

World Electric Vehicle Journal 2020, 11, 63; doi:10.3390/wevj11040063 www.mdpi.com/journal/wevj

Article

Parametric Modeling of Mass and Volume Effects for

Battery Electric Vehicles, with Focus on the

Wheel Components

Lorenzo Nicoletti *, Andrea Romano, Adrian König, Ferdinand Schockenhoff and

Markus Lienkamp

Institute for Automotive Technology, Technical University of Munich, Boltzmannstr. 15, 85748 Garching,

Germany; ge73fir@mytum.de (A.R.); adrian.koenig@ftm.mw.tum.de (A.K.);

schockenhoff@ftm.mw.tum.de (F.S.); lienkamp@ftm.mw.tum.de (M.L.)

* Correspondence: nicoletti@ftm.mw.tum.de; Tel.: +49 89 289 10495

Received: 13 August 2020; Accepted: 1 October 2020; Published: 2 October 2020

Abstract: Defining a vehicle concept during the early development phase is a challenging task, since

only a limited number of design parameters are known. For battery electric vehicles (BEVs), vehicle

weight is a design parameter, which needs to be estimated by using an iterative approach, thus

causing weight fluctuations during the early development phase. These weight fluctuations, in turn,

require other vehicle components to be redesigned and can lead to a change in their size (secondary

volume change) and weight (secondary weight change). Furthermore, a change in component size

can impact the available installation space and can lead to collision between components. In this

paper, we focus on a component that has a high influence on the available installation space: the

wheels. We model the essential components of the wheels and further quantify their secondary

volume and weight changes caused by a vehicle weight fluctuation. Subsequently, we model the

influence of the secondary volume changes on the available installation space at the front axle. The

hereby presented approach enables an estimation of the impact of weight fluctuations on the wheels

and on the available installation space, which enables a reduction in time-consuming iterations

during the development process.

Keywords: battery electric vehicles; secondary volume changes; secondary weight changes

1. Introduction

The CO2 emission limits for manufacturer fleets set by the European Union (EU) have become

increasingly restrictive in recent years: In 2021, the tank-to-wheel limit will be lowered to 95 g CO2/km

[1]. BEVs represent an efficient way to reduce the average fleet consumption since they do not cause

any local CO2 emissions and are accounted as 0 g CO2/km [2].

However, for BEVs, there are currently neither established platforms nor predecessor vehicles

on which the development can be based. Therefore, during the developing process of BEVs, many

design parameters have to be estimated [3]. The parameter weight plays a key role because of the low

energy density of lithium-ion-batteries compared to diesel or gasoline fuels. This can be shown by

comparing an internal combustion engine vehicle (ICEV) and a BEV of the same model series (Table

1). To increase the range by 100 km, the Golf TSI (Table 1) would need an extra 4.1 L tank capacity,

which results in approximately 3 kg additional weight. For the same range increase, the e-Golf would

have to store 12.7 kWh more energy in the traction battery, which would result in a weight increase

of approximately 127 kg, considering its actual energy density for the battery pack [4].

Correspondingly, the required battery volume increase is approximately 78 L.

World Electric Vehicle Journal 2020, 11, 63 2 of 24

Table 1. Comparison between the internal combustion engine vehicle (ICEV) [5] and the battery

electric vehicle (BEV) [5] variants of the Golf model series.

Vehicle characteristic VW Golf 1.0 TSI BMT VW Golf (VII) e-Golf Delta

Length 4258 mm 4270 mm 12 mm

Width 1799 mm 1799 mm 0 mm

Height 1492 mm 1482 mm 10 mm

Curb weight (with driver) 1026 kg 1615 kg 589 kg

Power 63 kW 100 kW 37 kW

Top speed 180 km/h 150 km/h 30 km/h

Range 1219 km 231 km 988 km

Energy consumption 4.1

L/100 km 12.7

kWh/100 km -

The weight increase caused by a larger traction battery does not only affect vehicle consumption

but also impacts other vehicle components. If a component becomes heavier or a new one is added

during the development process, it leads to a primary weight change (PWC) [6] (p. 9). Using the

above-cited example, the 127 kg of added battery weight is the PWC. A PWC, in turn, may require

the resizing of other vehicle components. For example, to ensure the same driving performance, the

drivetrain components must be adapted. The sum of the weight increases caused by this adaptation

is the secondary weight change (SWC). On the other hand, the 78 L of battery increase represents the

secondary volume change (SVC). Furthermore, the PWC, can also impact on further components,

such as the wheels. A greater vehicle weight requires a greater tire volume and therefore new tire

dimensions. The increase in tire volume can, in turn, impact on the available space at the front axle

(SVC on the vehicle).

The modeling of vehicle weight in the early development design has already been researched

by various authors. Yanni et al. [7], Mau et al. [8], and Felgenhauer et al. [9] present various empirical

equations for vehicle weight estimation. However, these authors do not model SWC.

Alonso et al. [10] derive an empirical weight model by dividing the vehicle in modules and

quantifying the SWC of each module. The results are further used to evaluate the effects of SWC on

vehicle consumption. Nevertheless, the model considers only ICEVs.

Wiedemann et al. [11,12] develop a more detailed method for estimating BEVs weight. They

derive a basis weight for the vehicle using the model of Yanni and further add to the basis weight the

weight of the electric powertrain, which comprises traction battery, electric machine, power

electronics, and transmission. The weight of these components is estimated by using empirical

models. The Wiedemann model can estimate the SWCs, but only for the powertrain components.

Fuchs [6,13] creates a weight model for BEVs, dividing the vehicle into modules, which are, in

turn, subdivided into their subcomponents. The weight of each subcomponent is modeled

empirically or semi-physically. The method can estimate all SWCs.

Angerer et al. [14,15] and Del Pero et al. [16] focus on the influence of weight on BEVs

consumption. Angerer uses the model of Fuchs to estimate the influence of weight fluctuations on

vehicle dynamics and consumption. Del Pero and al. also focus on the effects of weight reduction on

vehicle consumption. However, the model of Del Pero et al. simply consists of a longitudinal

simulation and does not contain any weight modeling.

The above-cited authors mainly focus on the SWCs, without considering that a redesign of the

components due to a PWC can trigger a change in the component volumes (i.e., a SVC). The SVC can

further impact on the available installation space. This requires a check to ensure that the package of

the vehicle remains feasible.

To our knowledge, no automatized method exists to simultaneously estimate both SWCs and

SVCs. Thus, we aim to extend the existing SWC models with a package model that is capable of

estimating the SVC triggered by PWC and SWC. With this method, it is possible, given a PWC, to do

the following:

Estimate the resulting SWCs;

Estimate the SVC of the single components caused by the PWC and triggered SWCs;

World Electric Vehicle Journal 2020, 11, 63 3 of 24

Estimate the SVC on the vehicle installation spaces caused by the components SVCs.

To show exemplary how this scope can be achieved, we present, in this paper, the developed

model for the vehicle wheels. We focus on the wheels at the front axle, since it is the primary steering

axle, and, therefore, the wheels greatly influence the available installation space for the powertrain

components. Therefore, the SVCs triggered by the wheels are particularly relevant.

2. Materials and Methods

We subdivide the wheel into three subcomponents: brake discs (Section 2.2), rims (Section 2.3),

and tires (Section 2.4). To describe these subcomponents (Figure 1), we employ empirical models,

which require creating a components database (Section 2.1). After explaining how subcomponent

models operate (Sections 2.2 to 2.4), we combine them to describe the entire wheel and conduct an

evaluation of the wheel model (Section 3.1). This allows an estimation of SWCs and SVCs of the

wheel, thus enabling a quantification of the SVC on the installation space at the front axle (Section

3.2).

Figure 1. Overview of the subcomponent models, based on References [17,18].

2.1. Employed Databases and Methods

Due to the limited number of BEVs, it is necessary to include hybrid (HEVs) and plug-in hybrid

vehicles (PHEVs) in the database. To ensure a homogeneous and up-to-date state of technology, we

consider only vehicles built between 2010 and 2019.

To derive the parametric models for the wheel components, we employ two databases: A2Mac1

[19] and the catalog of the Allgemeine Deutsche Automobil-Club (ADAC) [20]. A2Mac1 is an

automotive benchmarking service provider and offers precise and detailed component

documentation for the vehicles of leading manufacturers. The ADAC is Europe's largest automobile

club [20], and its online catalog offers an extensive database with 96 current and discontinued brands

and a complete list of their vehicles. The catalog assigns a map to each vehicle, which contains

information on the overall vehicle level.

We use the A2Mac1 database to acquire data regarding the dimensions and weights of the wheel

components. For the modeling of these components, a required variable is the vehicle weight. In this

paper, we distinguish between vehicle curb weight (VCW) and vehicle gross weight (VGW). The

difference between the two terms is explained below. In the automotive sector, the terms weight and

vehicle weight are established definitions [6] (p. IV), which are used as synonyms for “mass”.

World Electric Vehicle Journal 2020, 11, 63 4 of 24

Therefore, in the scope of this paper, we employ the term weight when referring to the mass of the

vehicle or one of its components.

A model series, for example, the Audi e-tron, contains different model variants: quattro,

advanced quattro, and S line Quattro [21]. Each model variant has a different weight, which depends

on its equipment. We dimension the brakes and tires so that they can withstand the weight of the

heaviest model variant of the model series. This ensures that the dimensioned brakes and tires are

compatible with all model variants within the model series. The vehicle models contained in A2Mac1

are not necessarily the heaviest variant of the model series, and therefore their VCW cannot be used

to dimension the wheel’s components. For this reason, we link each vehicle model of the A2Mac1

database with the corresponding ADAC model series. This step enables us to link the VCW of the

corresponding heaviest model variant to each model documented in A2Mac1. An overview of the

database can be found in Appendix Tables A1, A2 and A3. In the next sections, when referring to the

VCW, we mean the weight of the heaviest model variant of the model series in the vehicle empty

state as defined by Reference [22].

Following §34 StVZO [23], the VGW is defined as the weight that must not be exceeded,

considering the material stress, engine power, and emergency and long-lasting brake applications.

The VGW is calculated from the sum of the VCW and the maximum vehicle payload, which depends

on the equipment level and, therefore, on the model variant within a single model series. In this

paper, when referring to the VGW, we mean the weight of the heaviest model variant of the model

series.

The following subsections (Sections 2.2 to 2.5) describe the developed parametric models for

estimating the volume and weight of the wheel components. The content of these subsections is

required to understand the results presented in Section 3.

2.2. Brake Model

Two types of wheel brakes are used in passenger cars: drum and disc brakes [24] (p. 64). In

today's vehicles, only front brakes are fitted with disc brakes, and drum brakes are used less often

nowadays for rear-wheel brakes, which often use disc brakes instead [24] (p. 64). Therefore, in this

paper, we will only focus on disc brakes.

BEVs, PHEVs, and HEVs can recuperate their kinetic energy during deceleration and store it in

the traction battery [25]. During recuperation, the electric machine works like a generator: a

deceleration of up to 0.3 g can be achieved without using the friction brakes [26]. Thus, most car

journeys can be carried out without actuating the wheel brakes. This concept suggests the possibility

of downsizing the brake system, which could reduce weight and costs [26]. However, for safety

reasons, BEVs, PHEVs, and HEVs are tested for braking by using the same criteria as ICEVs [26].

Recuperation is completely disabled during the performance tests because, when the battery is fully

charged or cold, the maximum regeneration potential is not available [27] (p. 29). The vehicle must

always ensure maximum braking performance [26] under such conditions.

To provide long-range driving capability, BEVs are equipped with a large battery that can reach

a considerable weight (in the case of the Audi e-tron, almost 700 kg [28]). As a result, BEVs are usually

heavier than ICEVs with comparable exterior dimensions (see Table 1) [29] (p. 8). Moreover, HEVs

and PHEVs are heavier than comparable ICEVs, due to the higher number of required components

for the powertrain. Therefore, to comply with legal requirements, the brakes on these vehicles must

be larger because the kinetic energy is higher compared to that of a similar ICEV traveling at the same

speed [26] (p. 663). Thus, we do not include ICEVs in our database.

2.2.1. Volumetric Model

For the brake disc dimensions, we derive a linear regression model, which correlates the

diameter of the brake disc (dependent variable) to the vehicle characteristics (independent variables).

In order to identify the vehicle characteristics, which are suitable for modeling the brake disc

dimensions, we must identify the central design focus for dimensioning this component.

World Electric Vehicle Journal 2020, 11, 63 5 of 24

To ensure safe driving, wheel brakes must be able to withstand heavy operating conditions. An

important design criterion for braking systems is the thermal design. The thermal mass of the brake

disc plays an important role in thermal stability: Larger and heavier brake discs have more heat-

storage capacity and cooling properties. They are, therefore, better able to absorb the kinetic energy

of the vehicle that is converted into heat during braking [30] (p. 72). The maximum value of the kinetic

energy is calculated by considering the vehicle VGW mveh max and the maximum attainable speed vveh

max. The VGW and its top speed are, hence, suitable variables for estimating the brake disc diameter.

The thermal load of the brake discs is also determined by the time it takes to allow the brakes to

cool down between two consecutive brake applications. This amount of time relates to the

acceleration capability of the vehicle. The faster the vehicle can accelerate, the shorter the time

available for brake cooling. This is particularly critical for cases like the AMS consumer test, which

tests the braking performance of the vehicle [31]. For this reason, the acceleration time tveh 0-100 from 0

to 100 km/h is a suitable vehicle characteristic for modeling the brake disc diameter.

We extract from A2Mac1 the brake disc diameter Dbrake for the vehicles contained in Appendix

Tables A1, A2, and A3. The acceleration time and the VGW are obtained from the ADAC database.

We correlate both variables to the brake disc diameter, thus deriving the linear regression model in

Equation (1). A list of the symbols used in Equation (1) and the following equations can be found in

Appendix Table A4.

Dbrake = 238.345 mm + (0.053 mm/kg) × mveh max – (5.631 mm/s) × tveh 0-100 (1)

With this variable choice, we can model the thermal load of the vehicle, using the acceleration time,

and the kinetic energy, using the VGW. For the modeling, we only consider ventilated discs, since all

vehicles of the database mount ventilated discs as front brakes. The developed model achieves an R2

of 87.3%, a mean absolute error (MAE) of 9.94 mm. The corresponding normalized mean absolute

error (nMAE) is 3.22%.

2.2.2. Weight Model

The weight of a brake disc is mainly related to its diameter and its thickness. However, our

statistical evaluation showed that the thickness is not a significant variable for weight modeling.

We extract the disc diameter and its weight mbrake for each of the vehicles in Appendix Tables

A1, A2, and A3. The resulting regression model describing the correlation between Dbrake and mbrake

is shown in Equation (2):

mbrake = – 12.870 kg + (0.069 kg/mm) × Dbrake (2)

The developed model achieves an R2 of 91.33%, an MAE of 0.52 kg, and an nMAE of 6.42%.

We also model the weight of the brake calipers and brake pads. In both cases, it was not possible

to set up a regression model to link the component’s weight to the vehicle’s characteristics; thus, we

use constant values for the modeling. We extract for the vehicles in Appendix Tables A1, A2, and A3

the weight values for the front brake calipers and the brake pads from A2Mac1. We derive a mean

value of 5.46 kg for the brake calipers and a standard deviation equal to 1.70 kg. We derive a mean

value of 1.02 kg and a standard deviation of 0.31 kg for the weight of each pair of front brake pads.

2.3. Rim Model

To model the rims, we use the nominal rim diameter, which is specified in inches by the

manufacturer. It is not possible to create an empirical model, which estimates the rim diameter from

dimensions of other components such as the tire diameter. Due to its importance as a design element,

the rim and its dimensions do not depend exclusively on the tire diameter, but rather on the specific

design strategy the manufacturer specifies. Therefore, we choose to use the rim diameter as the model

input.

World Electric Vehicle Journal 2020, 11, 63 6 of 24

2.3.1. Minimum Rim Diameter

Since the rim diameter is an input for this model, we do not need to model the rim dimensions.

Nevertheless, it must be guaranteed that the input rim diameter is compatible with the brake disc,

i.e., that no collision occurs between the brake caliper and rim. To model this effect, we derive a

minimum radial clearance, which must be maintained between brake and rim to avoid a collision.

The minimum radial clearance must be calculated, taking as reference the smallest rim offered

in the model series, since this rim size represents the worst-case scenario. However, the vehicles

documented in A2Mac1 are not necessarily the model variant with the smallest rim diameter.

Therefore, we link each model variant of A2Mac1 with the corresponding model series in ADAC and

extract from ADAC the smallest rim diameter offered inside the model series Drim min ADAC. With these

data, we calculate the minimum radial clearance Drim clearance, as shown in Equation (3):

Drim clearance = Drim min ADAC – Dbrake (3)

We calculate the radial clearance for the vehicles in Appendix Tables A1, A2, and A3 and derive a

mean value of 122.24 mm, with a standard deviation of 27.25 mm.

2.3.2. Weight Model

To calculate the rim weight mrim, we develop a regression model, which correlates mrim with the

rim diameter Drim (expressed in inches). Equation (4) shows the resulting linear regression model:

mrim = – 13.063 kg + (1.405 kg/inch) × Drim (4)

The model achieves an R2 of 88.48%, an MAE of 0.64 kg, and an nMAE of 5.56%. Initially, we also

tried to employ the rim material (aluminum or steel) as an independent variable, but it was

categorized as statistically irrelevant. The same effect has also been observed by Fuchs [6] (p. 42).

2.4. Tire Model

The European Tire and Rim Technical Organization (ETRTO) defines a tire as a flexible element

made of rubber and reinforcement materials [32] (p. G2). The significant tire parameters are the tire

diameter, Dtire, the nominal aspect ratio, h%, and the section width, wtire, which are described in the

ETRTO manual [32] (pp. G2–G13). In this paper, when referring to the tire diameter, we mean the

outer diameter of the wheel. The tires have a great impact on vehicle design [33], and their diameter

also depends on the design strategy of the individual manufacturer. Thus, we decide to implement

the tire diameter as model input.

2.4.1. Volumetric Model

The volumetric model is implemented as follows: First, the axle load is calculated, thus deriving

the required tire load capacity. Subsequently, the tire volume is estimated, empirically, according to

the required tire load capacity. Finally, using the rim diameter and tire diameter inputs, the

empirically estimated volume is corrected, and the further tire dimensions’ section width and aspect

ratio are derived. The exact implementation of these steps is explained below.

The tire volume, Vtire, is defined as the volume of gas contained between the rim and tire under

pressure. Given the tire diameter, the corresponding volume can be calculated by using Equation (5):

Vtire = 0.25 × π × wtire × (Dtire2 - Drim2) (5)

To dimension the tire, engineers select the appropriate section width and aspect ratio, which can

provide the air volume needed to support the VGW and is compatible with the desired rim diameter.

Wider tires provide better traction when accelerating: A large contact area helps powerful vehicles

reduce tire slippage when accelerating from standstill and improve acceleration time. Therefore, we

set minimal values for the tire width, depending on the vehicle’s power and drivetrain (front-wheel

drive, rear-wheel drive, or all-wheel drive) according to Reference [34] (p. 22).

World Electric Vehicle Journal 2020, 11, 63 7 of 24

The required tire volume depends on the required tire load capacity, which is the maximum

load a tire can carry under specified conditions of use [32] (p. G5) and is coded by the load index.

Depending on the structure of the tire, we need to distinguish between standard and extra-load tires.

Tires with the additional "extra-load" marking are designed for loads and inflation pressures higher

than the standard version [32] (p. G10).

The required tire load capacity depends on the load at the axle. To calculate the axle load and to

select the appropriate tire dimensions, the ETRTO manual defines two loading conditions: the 88%

rule and the 100% rule [32] (pp. P15–P17). The manual further prescribes for each loading condition

the number of passengers aboard and the load stowed in the luggage compartment. Starting with the

VCW, the vehicle must be loaded with the prescribed number of passengers and luggage load, thus

yielding the loaded weight for the 88% rule (m88%), and the loaded weight for the 100% rule (m100%).

By applying the described loading conditions and knowing the positions of the rows of seats,

the position of the luggage compartment, and the axle load distribution of the empty vehicle, it is

possible to compute the new axle distribution according to the 100% and 88% rules. We can then

derive the distances lF,88% and lF,100% between the center of mass and the front axle for both load cases.

Finally, by using l to denote the vehicle wheelbase, we can calculate the tire load (in kg) according to

the 88% rule, using Equation (6):

Ltire88% = (m88% × (l – lF, 88%)) / (2 × l × 0.88) (6)

Using the same method, we calculate the tire load for the 100% rule (Equation (7)):

Ltire100% = (m100% × (l – lF,100%)) / (2 × l) (7)

For the following tire dimensioning, we consider the loading condition, which generates the highest

tire load. We then derive a regression that correlates the required tire volume (dependent variable)

to the occurring tire load (independent variable). The data needed for this purpose are collected from

the ETRTO manual [32]. The ETRTO lists for every tire contained in the manual the corresponding

volume and the maximum tire load capacity (in kg), which allows us to set up calculate a regression

linking these two variables. For the modeling, we consider all the standard- and extra-load tires listed

in the manual section “Passenger car tires”. The tire volume, VtireSL, allowing a standard-load tire to

carry a given load, Ltire (in kg), is defined by Equation (8):

VtireSL = – 13462233.892 mm3 + (87651.102 mm3/kg) × Ltire (8)

The developed model achieves an R2 of 98.68% and an nMAE of 2.83%. For extra-load tires, the tire

volume is calculated according to Equation (9). The developed model achieves an R2 of 98.82% and

an nMAE of 2.63%:

VtireEL = – 13548645.429 mm3 + (77990.623 mm3/kg) × Ltire (9)

The main drawback of the empirical models in Equations (8) and (9) is that, although they

estimate a minimum required tire volume, they do not ensure that the resulting volume is realistic.

In fact, the tire volume cannot assume arbitrary values, since the tire dimensions have specific

proportions regarding section width and nominal aspect ratio, which are documented in the ETRTO

manual. Regarding the tire section width, the manual prescribes values ranging between 125 and 355

mm. The tire section width is always expressed as a multiple of five but not ten, with an interval of

10

mm between two consecutive values. For the nominal aspect ratio, the manual prescribes values

between 25% and 80%. The aspect ratio is always expressed as a multiple of five with an interval of

5% between two consecutive values. Therefore, the tire volumes resulting from the regression models

have to be corrected to ensure that the volume can be generated from admissible values of tire width

and aspect ratio. Figure 2 shows the correction method, which is divided into three steps.

In the first step (Figure 2), we combine the input rim diameter, Drim (in mm), with every possible

nominal aspect ratio and section width combination and derive the tire diameter, as shown in

Equation (10):

Dtire = Drim + (2 × wtire × h%) / 100 (10)

World Electric Vehicle Journal 2020, 11, 63 8 of 24

The result is a tire diameter matrix (Figure 2) containing all the possible diameters that are

compatible with the input rim size. From this matrix, we use Equation (5) to derive the matrix for the

corresponding volumes (volume matrix, Figure 2).

In the second step (Figure 2), the diameter and volume matrices are compared with the input

tire diameter and the minimum tire volume from Equations (8) and (9). Based on this comparison,

we generate two matrices that describe the percentual deviation from the single elements of the

diameter matrix or volume matrix to the input tire diameter or minimum tire volume.

Finally, in the third step (Figure 2), we choose from the two deviation matrixes the tire that has

the smallest deviation from the calculated volume and the desired diameter. This results in the final

values for the tire diameter and volume, as well as the aspect ratio and width. After this step, the

dimensions of the tire are fully defined.

Figure 2. Overview of the correction method for the tire dimensions.

2.4.2. Weight Model

For the weight analysis, we implement a regression model that estimates the tire weight, mtire,

based on the tire diameter and its section width. The regression is derived from the evaluation of the

vehicles in Appendix Tables A1, A2, and A3 and shown in Equation (11):

mtire = – 16.890

kg + (0.023

kg/mm) × Dtire + (0.054

kg/mm) × wtire (11)

The developed model has an adjusted R2 of 85.85%, an MAE of 0.71 kg, and an nMAE of 6.63%.

2.5. Wheelhouse model

Given the tire dimensions, we can estimate the wheelhouse dimensions. In this paper, we focus

on the wheelhouse width, wwheelhouse. Given the wheelhouse width, the position of the side roll rail can

World Electric Vehicle Journal 2020, 11, 63 9 of 24

be identified. Then, knowing the vehicle width at the front axle (W106) and the width of the side roll

rail wsrr, we estimate the available space at the front axle, wavailable, as shown in Equation (12):

wavailable = (W106 – 2 × wwheelhouse + wsrr) (12)

In the further steps of the product specification, wavailable can be compared with the actual space

required by the powertrain components, wrequired, to test the vehicle concept feasibility. Figure 3

illustrates the above-cited measures.

Figure 3. Overview of the relevant measures at the front end of the vehicle, based on Reference [3].

In the later sections, we consider the wsrr as constant, since our focus is on the wheelhouse

dimensions. A change in the wheel dimensions leads to a variation of wwheelhouse, which depends on

the tire diameter, the tire section width, and the maximum wheel steering angle, δmax. If we simplify

the model by assuming that the wheel steers at its center (located at the half of the tire width), the

wheelhouse width can be derived according to Equation (13):

wwheelhouse = 0.5 × wtire × cos δmax + 0.5 × Dtire × sin δmax + 0.5 × wtire (13)

The δmax is usually reached when driving slowly or during parking. For this scenario, we assume

an Ackermann characteristic for the steering [35] (pp. 379–380). The inner wheel steering angle is

always bigger than that of the outer wheel and thus determines the width of the wheelhouse.

Therefore, in Equation (14), we can estimate the δmax from the vehicle turning radius (Rturning),

wheelbase (L101), front overhang (L104), maximum width (W103), and track width (W101):

δmax = atan(L101/(–W103 × 0.5 + (Rturning2 – (L101 + L104)2)0.5 – W101 × 0.5)) (14)

By combining the result of Equation (14) with the wheel dimensions (Section 2.4), it is possible

to estimate the wheelhouse width using Equation (13).

3. Model Evaluation and Results

In the first part of this section, we carry out an evaluation based on a vehicle database, to assess

the accuracy of the wheel model. In the second section, we apply a parameter variation to the model

in order to quantify the SWC on the wheel and SVC on the wheel and on the vehicle.

3.1. Model Evaluation

To model the SVCs, the accuracy of the estimation of the tire volume and the tire width must be

tested. To reach this scope, we first need to create an evaluation database.

World Electric Vehicle Journal 2020, 11, 63 10 of 24

We set up the evaluation database, using A2Mac1, ADAC, and the ETRTO manual. We extract

from the A2Mac1 database the following information: vehicle axle distribution, the position of the

rows of seats, position of the luggage compartment, and the tire load index. The ETRTO manual lists

every available tire dimension and the related load indexes. Therefore, using the load indexes, we

link the A2Mac1 database with the ETRTO manual, thus identifying which model variants of the

A2Mac1 database mount a standard and which an extra load tire. We further link the A2Mac1 models

with the corresponding model series in ADAC, thus identifying the VCW of the heaviest model

variant for each A2Mac1 model and the exact dimensions of the tires. It was not possible to conduct

the above-cited linking for all the vehicles of Appendix Tables A1, A2, and A3 because some

information was missing for some vehicles, or no ADAC model series could be found. Appendix

Table A5 shows an overview of the evaluation database.

To evaluate the tire volume model, we assign as inputs the vehicle empty axle load, the tire

diameter, the rim diameter, the vehicle's outer dimensions, the VCW, and the vehicle payload. With

these inputs, we calculate the VGW for each vehicle of the database. We then calculate the tire load

as in Equations (6) and (7), using the positions of the row of seats and the luggage compartment. We

suppose that the axle distribution for the heaviest model variant corresponds to the axle distribution

given in A2Mac1. Subsequently, we estimate the required tire volume according to the mounted tire

type, using Equations (8) and (9). Finally, we conduct the correction method shown in Figure 2. The

results are presented in Figure 4.

The X-axis in Figure 4 presents the tire volume resulting from the model, and the Y-axis shows

the real tire volume. The resulting estimation has an R2 of 91.0%. For most of the vehicles, the volume

is slightly underestimated. This depends on the fact that the different manufacturers use safety

factors, dimensioning the tire by using loads, which are higher than the real load. With this strategy,

it is possible to compensate for weight estimation errors that can occur in the later specification phase.

The volume is overestimated for the BMW 5-Series, the Jaguar I-Pace, and the Kia Niro. Regarding

the BMW and the Kia, the error can be attributed to slightly inaccurate load-distribution data, which

lead to an overestimation of the required tire volume. The reason for overestimating the Jaguar is

explained in the tire-model-width-evaluation section.

Figure 4. Whole-model plot for the tire-volume evaluation.

We use the same database to evaluate the precision of the tire width estimation. Our wheel

model calculates the tire dimensions that fulfill the conditions given on the required tire diameter,

the calculated tire volume, and the desired rim diameter, according to the method described in

Section 2.4.1. The tire width is calculated for each vehicle listed in Appendix Table A5 and compared

e-tron (GE)

2er-Reihe (F45) Active Tourer

5er-Reihe (G30) Limousine

i3

X5 (F15)

IONIQ (AE) Hybrid

Kona (OS) Elektro I-Pace (X590)

Niro (DE)

Outlander (III) Plug-In

Leaf (ZE1)

Ampera-E

Cayenne (9YA)

Zoe

Auris (E18)

C-HR (X10)

Prius (XW5) Plug-In

Prius (XW3) Plug-In

RAV4 (XA5)

Golf (VII) e-Golf

up! e-up!

XC60 (U)

XC90 (L)

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Real tire volume in l

Calculated tire volume in l

World Electric Vehicle Journal 2020, 11, 63 11 of 24

with the real values (Figure 5). The tire width model achieves a R2 of 77.0%. The tire width is

overestimated for the BMW 5-er (G30), the Jaguar I-Pace (X590), and the Kia Niro (DE). The slightly

overestimated tire volume leads to an overestimated tire width for the BMW and the Kia. The

required tire volume would be estimated correctly for the Jaguar; however, the calculated value for

the tire width of 265 mm is higher than the real one (245 mm). This result is caused by the constraint

on the minimal tire width, which is set equal to 255 mm due to the high power of this car’s drivetrain.

For the same reason, the resulting volume is also overestimated.

Figure 5. Whole-model plot for the tire-width evaluation.

Another cause of deviations from the real tire width values is that our model calculates the tire

dimensions only in dependency on the vehicle weight and power without considering lateral

dynamic requirements. We do not have enough data to model the lateral dynamic requirements;

therefore, we cannot consider this influence.

3.2. Quantification of the Secondary Effects on the Wheel Components

In this section, we apply the wheel model to four reference vehicles, each belonging to a different

segment. We intend to evaluate the SVCs and SWCs resulting from a stepwise increase in the VCW,

which is denoted in the following sections as the PWC. The reference vehicles are shown in Table 2;

the data are collected from the ADAC catalog. Table 2 shows the initial VCW and the tire and rim

diameter, which are simulated. The further vehicle data required for implementing Equations (12) to

(14) are collected from the A2Mac1 database and are not shown in the table.

Table 2. Reference vehicles used for analyzing secondary effects on the wheel components

Vehicle model

(model series) Initial VCW Min–Max diameter

rim variants

Mean outer tire

diameter

Renault Zoe 22 kWh

(Zoe (06/13-09/19)) 1547 kg 16"–17" 621 mm

Nissan Leaf 40 kWh

(Leaf (ZE1) (from 01/18)) 1580 kg 16"–17" 640 mm

Audi e-tron 55 quattro

(e-tron (GE) (from 03/19)) 2565 kg 19"–21" 765 mm

Jaguar I-Pace

(I-Pace (X590) (from 10/18)) 2208 kg 18"–22" 759 mm

VCW = vehicle curb weight.

e-tron (GE)

2er-Reihe (F45) Active Tourer

5er-Reihe (G30) Limousine

i3

X5 (F15)

IONIQ (AE) Hybrid

Kona (OS) Elektro

I-Pace (X590)

Niro (DE)

Outlander (III)

Plug-In

Leaf (ZE1)

Ampera-E

Cayenne (9YA)

Zoe

Auris (E18)

C-HR (X10)

Prius (XW5) Plug-In

Prius (XW3) Plug-In

RAV4 (XA5)

Golf (VII) e-Golf

up! e-up!

XC60 (U)

XC90 (L)

145

155

165

175

185

195

205

215

225

235

245

255

265

275

285

295

305

315

325

145 155 165 175 185 195 205 215 225 235 245 255 265 275 285 295 305 315 325

Real tire width in mm

Calculated tire width in mm

World Electric Vehicle Journal 2020, 11, 63 12 of 24

Regarding the tire diameter, it can vary of a few mm inside a model series, depending on the

chosen rim. For the simulation, we take for each reference vehicle the mean value of all the offered

tire diameter of the corresponding model series. Therefore, our method dimensions the tire so that

the resulting diameter is as close as possible to the diameter shown in Table 2.

In our analysis, we dimension the tires considering the maximum rim size inside of the model

series (Table 2). If the diameter is kept constant, a bigger rim reduces the tire sidewall and requires a

wider tire to fulfill the volume requirement. Furthermore, the wheel equipped with the biggest rim

is the heaviest wheel variant. Therefore, focusing on the maximum rim size allows us to consider the

worst-case scenario for both volume and weight analysis. Nevertheless, the minimum rim size cannot

be ignored, since the more the PWC increases, the bigger the brake disc diameter becomes, which

could cause incompatibility between the minimum rim size and the brake disc. We discuss this

subject in the next section.

We do not consider the limitation on the minimal tire width, due to the vehicle’s power (Section

2.4.1), in order to highlight the effects of the weight increase alone.

We subdivide the quantification of the secondary effects in four steps. In the first step (Section

3.2.1), we analyze the influence of the PWC on the wheel volume, thus quantifying the SVC of the

wheel. In the second step (Section 3.2.2), we quantify the influence of the PWC on the wheel, thus

estimating the SWC. In the third step (Section 3.2.3), we combine the SVC of the wheel with the

wheelhouse model (Section 2.5) and the dimensional chain presented in Equation (12) and Figure 3.

This allows an estimation of the SVC on the wavail able (Section 2.5). Finally, in the last step (Section

3.2.4), we invert Equation (12) to simulate a strategy, where the SVC of the wheel is compensated by

increasing the vehicle width.

3.2.1. Influence on the Wheel Volume (SVC on Component Level)

An increased PWC leads to a greater tire load, which requires a redesign of the tire, thus affecting

its volume (Figure 6). The X-axis in Figure 6 represents the PWC (in %) with respect to the initial

VCW. For example, for the Audi e-tron, a PWC of 5% with respect to the initial VCW of 2565 kg (see

Table 2) corresponds to a weight increase of approximately 128 kg. The steps in Figure 6 represent

the points where the PWC requires a redesign of the tire, i.e., causes a SVC.

As the model also dimensions the brake disc sizes (Section 2.2.1), we can test if the smallest rim

size offered for the vehicles of Table 2 has enough radial clearance from the brake disc. This is

particularly interesting for the case of the Audi e-tron. The increment of the brake disc diameter

caused by a PWC of approximately 0.7% (corresponding to a VCW increase of 17 kg) causes an

incompatibility with the given minimum rim size of 19", as the minimum radial clearance (see

Equation (3)) is not fulfilled. To overcome this problem, we distinguish between two possible

strategies.

In the first strategy (Audi e-tron 55, two rim variants), the rim size of 19" is simply excluded

from the model series, which means that the customer can configure the vehicle with only two rim

sizes (20" and 21"). With this strategy, the minimum rim size changes to 20", thus avoiding the

collision between the brake disc and rim. The tire volume does not have to be changed until a PWC

of around 8% (Figure 6). The maximum rim size remains unchanged (21").

In the second strategy (Audi e-tron 55, three rim variants), we impose the requirement that,

despite the unfulfilled radial clearance, the vehicle must be configurable by using three rim variants.

Such a strategy could be imposed for design reasons or to offer a high product range to the customer.

Therefore, since the 19" rim is incompatible with the brake disc after a PWC of 0.7%, it is necessary to

start from a minimum rim of 20" and also offer the variants 21" and 22", shifting the maximum rim

size from 21" to 22". Increasing the maximum rim diameter leads to a decrease in tire volume (because

the tire diameter remains constant), which requires a change of the tire section width and nominal

aspect ratio in order to comply with the minimum volume requirement. In this particular case, it is

possible to find a section width and aspect ratio combination that comes closer to the minimum

required volume than the previous one, which explains the slight volume reduction at 0.7% (Figure

World Electric Vehicle Journal 2020, 11, 63 13 of 24

6). Nevertheless, this tire combination has a greater section width than the initial one. The effects

caused by this redesign are shown in Section 3.2.3.

Regarding the other vehicles, the same effect as the Audi e-tron occurs also for the Nissan Leaf

at a PWC of around 6.5% (corresponding to a weight increase of 102 kg). For the sake of simplicity,

we do not distinguish between two cases for this vehicle and suppose that a strategy corresponding

to the “Audi e-tron 55, three rim variants” is applied, i.e., the number of offered rim variant does not

change.

The remaining volume changes, such as the step at 5.2% for the Renault Zoe or the step at 5.8%

for the Jaguar I-Pace, are caused by an increase of the tire section width, which is required to

compensate for the increase of the minimum required tire volume.

Figure 6. Interdependency between secondary volume change (SVC) of the wheel and the primary

weight change (PWC).

3.2.2. Influence on the Wheel Weight (SWC on Component Level)

For each PWC, we recalculate the dimensions of the brake disc (Section 2.2.1), rim (Section 2.3.1),

and tire (Section 2.4.1). The hereby calculated dimensions can be further employed for the weight

models of Sections 2.2.2, 2.3.2, and 2.4.2, thus allowing an estimation of the total wheel weight. Figure

7 shows the SWC of the wheel caused by the PWC.

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

012345678910

Calculated tire volume in l

PWC (VCW increase) in %

Renault Zoe 22 kWh

Nissan Leaf 40 kWh

Jaguar I-Pace EV 400

Audi e-tron 55, three rim variants

Audi e-tron 55, two rim variants

World Electric Vehicle Journal 2020, 11, 63 14 of 24

Figure 7. Interdependency between SWC of the wheel and PWC.

The small steps are related to an increase of the brake disc diameter, while the bigger ones are

caused by an increase of the tire width. The great SWC at 0.7% for the strategy “Audi e-tron three rim

variants” results from the change in the maximum rim size needed to offer the same number of rim

variants: Both the weights of tire and rim change significantly. Figure 7 shows how limiting the

maximum rim diameter on the Audi e-tron to 21" allows a wheel weight reduction of approximately

3 kg (for a VCW increase of 6%) with respect to the 22" variant. Reducing the number of rim variants

from two to one would also avoid the step at 6.5% for the Nissan Leaf.

In conclusion, if we do not consider the cases of the Audi e-tron and the Nissan Leaf, where the

rim size must be changed, we can conclude that the SWC caused by a PWC of 6% is comprised in a

range between 0.5 and 1.5 kg per wheel. If we further assume that the vehicles mount the same wheel

components at the front and rear axles, this corresponds to a total SWC between 2 and 6 kg.

3.2.3. Influence on the wavailable (SVC on Vehicle Level)

The outer tire diameter is an input of the model and remains constant regardless of PWC. The

maximum rim diameter also remains constant as long as no collision between the brake disc and base

rim occurs. Therefore, to compensate for the volume increase shown in Section 3.2.1, the tire must

necessarily become wider. A change in the tire dimensions leads to a variation of the wheelhouse

width as shown in Section 2.5 and Equation (13). Figure 8 shows the increase of wheelhouse width in

mm, using the initial wheelhouse width as reference.

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

5,5

0 1 2 3 4 5 6 7 8 9 10

SWC of the wheel in kg

PWC (VCW increase) in %

Renault Zoe 22 kWh

Nissan Leaf 40 kWh

Jaguar I-Pace EV 400

Audi e-tron 55, three rim variants

Audi e-tron 55, two rim variants

World Electric Vehicle Journal 2020, 11, 63 15 of 24

Figure 8. Interdependency between wheelhouse width and PWC.

Finally, using the results shown in Figure 8, we evaluate the variation of wavailable caused by the

PWC. We apply to the four vehicles the dimensional chain depicted in Equation (12). For this

calculation, we only model the wheelhouse width variation caused by the PWC, while keeping the

values W106 and wsrr constant. Figure 9 shows the loss, in percentage, of wavailable, using the initial

wavailable as reference.

For the reference vehicles, a PWC of approximately 6% leads to a loss in wavailable of up to 12%.

Regarding the Nissan Leaf, it is clearly shown that keeping the same number of rim variants is not a

good strategy, since it can lead to a loss in wavailable greater than 10%. Limiting the Audi e-tron number

of rim variants to two can avoid loss of approximately 6% at the front end (for a PWC above 8%).

Figure 9. Interdependency between the SVC at vehicle front end and the PWC.

0

5

10

15

20

25

30

35

40

45

50

55

0 1 2 3 4 5 6 7 8 9 10

Increase of the wheelhouse width in mm

PWC (VCW increase) in %

Renault Zoe 22 kWh

Nissan Leaf 40 kWh

Jaguar I-Pace EV 400

Audi e-tron 55, three rim variants

Audi e-tron 55, two rim variants

0

1

2

3

4

5

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6 7 8 9 10

w

available

loss in %

PWC (VCW increase) in %

Renault Zoe 22 kWh

Nissan Leaf 40 kWh

Jaguar I-Pace EV 400

Audi e-tron 55, three rim variants

Audi e-tron 55, two rim variants

World Electric Vehicle Journal 2020, 11, 63 16 of 24

3.2.4. Influence on the Vehicle Outer Dimensions (SVC on Vehicle Level)

As shown in the previous section, the PWC greatly influences the wavailable. The size of the

powertrain components can be only roughly estimated due to the lack of known design parameters

during early development design. Therefore, it is advisable to reserve some extra space for these

components, thus enabling more freedom in the later course of the development.

For this reason, if the manufacturer does not want to accept a loss of wavailable, another possibility

is to increase the vehicle width. While inverting the dimensional chain shown in Equation (12), the

increase in wheelhouse width (Section 3.2.2) can be compensated by increasing vehicle width (W106).

This inevitably increases the vehicle outer dimensions (Figure 10).

Although this strategy counters the SVC of the wheel, it has a major drawback. The increase in

the vehicle outer dimensions directly impacts the VCW. This can be shown by using the empirical

model presented by Fuchs [6] (p. 40) for estimating the weight of the body in white (BIW). The BIW

weight, mBIW, can be modeled from the vehicle volume, Vveh, as presented in Equation (15) [6] (p. 40):

mBIW = (37.45 kg/m3) × Vveh − 66.38 kg (15)

To model the Vveh, Fuchs distinguishes among different body frames. For example, for the

“hatchback” body frame, the volume can be modeled by using the vehicle width (W103), the front

and rear overhangs (L104, and L105), the vehicle height (H100), and its wheelbase (L101) as in

Equation (16) [6] (p. 39):

Vveh = (0.5 × L104 + 0.75 × L105 + L101) × W103 × H100 (16)

It can be seen that a percentual increase in the W103 causes the same percentual increase in the

Vveh, thus influencing mBIW. By applying the model for the three rim variants of the Audi e-tron, a 4%

increase of the W106 would correspond to a VCW increase of 20 kg based solely on the BIW.

In conclusion, although this strategy avoids a loss of wavailable, it also causes further SWC in other

parts of the vehicle. These SWCs can, in turn, cause additional SVCs.

Figure 10. Interdependency between the vehicle width and the PWC.

4. Discussion and Conclusions

The presented model enables us to quantify the SWC and SVC of the wheels and to further

model the triggered SVC at the front end of the vehicle. It further allows us to estimate the effects of

various design strategies.

0

1

2

3

4

5

6

7

012345678910

Vehicle width increase in %

PWC (VCW increase) in %

Renault Zoe 22 kWh

Nissan Leaf 40 kWh

Jaguar I-Pace EV 400

Audi e-tron 55, three rim variants

Audi e-tron 55, two rim variants

World Electric Vehicle Journal 2020, 11, 63 17 of 24

After introducing the subcomponent models (Sections 2.2 to 2.5), we combine them to create a

complete wheel model and further evaluate it (Section 3.1). For the subcomponent models, such as

brake disc weight and dimensions, no evaluation is required, since the performance of the model is

already described by the R2, nMAE, and MAE, which are listed in the corresponding model section.

Regarding the evaluation of the wheel volume and width, the deviations from the real values mainly

depend on the employed tolerances from the manufacturers, which we are not able to estimate.

Additional errors may also be caused by the fact that we do not know the exact position of the center

of gravity (and therefore the axle distribution) of the heaviest model variant, and we have to suppose

that it corresponds to the distribution of the model variant given in A2Mac1.

The model shows that, depending on the vehicle and the applied design strategy, the SWC on

the wheels is contained in a range between 2 and 6 kg. If the design strategy is poorly chosen, the

SWC can increase up to 20 kg (as in the case we simulated for the Nissan Leaf). These SWC are still

too low to trigger further SVCs. Nevertheless, it must be considered that the wheels are not the only

components that are affected by SWCs. The same tendency will be observable for components such

as the electric machine, body in white, axles, and, most importantly, the traction battery. The sum of

the SWCs of these components can, in turn, cause further SWCs [10] and SVCs. Furthermore, an

increase in the wheel weight impacts on its inertia, which can lead to higher vehicle consumption.

This, in turn, can require a higher battery capacity and generate further SWCs. These effects can be

only modeled by coupling the weight model with a longitudinal dynamic simulation. This topic will

be addressed in further publications.

While the SWC is relatively low, the SVC on the vehicle shows great relevance. A PWC

corresponding to 6% of the initial VCW can cause a loss in wavailable of up to 12%, depending on the

applied strategy and on the vehicle characteristics. These results highlight the importance of a SVC

estimation in early development, most of all for BEV, which are particularly subject to weight

fluctuations. The SVC on the vehicle is highly dependent on the vehicle segment, the design strategy,

and the VCW. Nevertheless, the presented methodology is capable of taking into account all of these

effects and can be employed to identify SVC already in the early development phase. The approach

is developed by following the actual dimensioning methods used by the manufacturers, which enable

integration in the manufacturer developing process and can thus minimize the errors and reduce the

number of iterations and costs.

In conclusion, in this paper, we quantify the SVC and SWC caused by the wheels and propose

an effective approach for addressing the problems they cause. In future publications, we will apply

the presented method to further vehicle components, thus expanding the SWC estimation to all the

relevant vehicle components. This will allow precise modeling of SWCs and SVCs on other vehicle

areas, such as the rear end and the installation space for the battery.

Author Contributions: As first author, L.N. defined the approach for the development of the presented model,

identified the relevant components, and detailed the method and the data evaluation. A.R. supported during his

semester thesis with the creation of the database, the derivation of the regression models, and the evaluation.

A.K. and F.S. supported by the definition of the concept and proofread the paper. M.L. made an essential

contribution to the conception of the research project. He revised the paper critically for important intellectual

content. M.L. gave final approval of the version to be published and agrees to all aspects of the work. As a

guarantor, he accepts responsibility for the overall integrity of the paper. All authors have read and agreed to

the published version of the manuscript.

Funding: The research of L.N. was funded by the AUDI AG and the Technical University of Munich. The

research of A.K. and F.S. is accomplished within the project “UNICARagil” (FKZ 16EMO0288). A.K. and F.S.

acknowledge the financial support for the project by the Federal Ministry of Education and Research of Germany

(BMBF).

Acknowledgments: The author L.N. would like to thank the colleagues of the AUDI AG in the persons of

Maximilian Heinrich, Martin Arbesmeier, and Alois Stauber, who provided support during concept

development. The authors would like to thank A2Mac1 EURL, in the person of Pir Ivedi, for the access to the

A2Mac1 automotive benchmarking database.

World Electric Vehicle Journal 2020, 11, 63 18 of 24

Conflicts of Interest: The authors declare no conflicts of interest, and the funders had no role in the design of

the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision

to publish the results.

Appendix A

This appendix presents the database we used for developing our parametric models. Tables A1,

A2, and A3 give an overview of the database. For each vehicle model, the brand, the ADAC model

series, the production year, and the drivetrain type are listed. The ADAC Model Series column is

empty for the vehicles not sold in Germany. The “Wheel model” column specifies the parametric

model for which each vehicle was used.

For simplicity’s sake, we use the following abbreviations to identify the parametric models:

All: the vehicle is used for all models;

BV: brake volume (Section 2.2.1);

BW: brake weight (Section 2.2.2);

RD: minimum rim diameter (Section 2.3.1);

RW: rim weight (Section 2.3.2);

TW: tire weight (Section 2.4.2).

Table A1. Database overview, part 1.

Brand Vehicle Model ADAC Model Series Production

Year

Wheel

Model

Audi e-tron 55 quattro e-tron (GE) (from 03/19) 2019 All

Audi A3 Sportback e-tron A3 (8V) Sportback e-tron

(01/15-05/16) 2015 BV, RD

BAIC EX360 Fashion - 2018 BW, TW, RW

BMW 2 Series Active Tourer

225 xe Luxury

2-er Reihe(F45) Active

Tourer (09/14-02/18) 2016 All

BMW 5 Series 530e

iPerformance

5-er Reihe (G30) Limousine

(from 02/17) 2018 All

BMW i3 Range Extender

Urban Life i3 (11/13-08/17) 2014 All

BMW i3 Range Extender i3 (from 11/17) 2018 BV, RD

BMW X1 xDrive 25Le - 2018 BW, TW, RW

BMW X5 2.0 xDrive40e X5 (F15) (11/13-07/18) 2016 BV, RD

BYD E6 Jingying Ban - 2015 BW, TW, RW

BYD Song DM 1.5 comfort - 2017 BW, TW, RW

BYD Tang 2.0 Ultimate - 2015 BW, TW, RW

BYD Tang EV 600D

ChuangLing - 2019 BW

BYD Yuan EV 360 Cool - 2017 BW, TW, RW

Chevrolet Malibu Eco 2.4 - 2011 BV

Chevrolet Volt 1.4 Voltec Volt (11/11-08/14) 2011 All

Chevrolet Volt 1.5 Premier - 2015 BV

World Electric Vehicle Journal 2020, 11, 63 19 of 24

Citroen DS5 Hybrid4 So Chic DS 5 (03/12-05/15) 2012 All

Ford C-Max Energi SEL 2.0 C-MAX (II) (11/10-05/15) 2013 BV

Denza EV Executive - 2014 BW, TW, RW

Gac Ne Aion S Max 630 - 2019 BW

Geely Emgrand EV300 elite - 2015 BW, TW, RW

Geometry A Standard range

power edition - 2019 BW

Honda CR-V 2.0 Hybrid

Comfort CR-V (V) (from 10/18) 2019 All

Hyundai Ioniq 1.6 Plug-in IONIQ (AE) Hybrid (10/16-

07/19) 2017 All

Hyundai Kona electric Executive

64 kWh

Kona (OS) Elektro (from

08/18) 2018 All

Jaguar I-Pace EV 400 I-Pace (X590) (from 10/18) 2018 All

All = the vehicle is used for all models; BV = brake volume; BW = brake weight; RD = minimum rim

diameter; RW = rim weight; TW = tire weight.

Table A2 Database overview, part 2.

Brand Vehicle Model ADAC Model Series Production

Year

Wheel

Model

Kia Niro 1.6 GDi HEV

Active Niro (DE) (09/16-05/19) 2016 All

Lexus GS 450h F-Sport GS (L10) (06/12-08/15) 2012 All

Maxus EG10 Luxury 2017 BW, TW, RW

Mercedes EQC 400 4MATIC 1886

Edition EQC (293) (from 06/19) 2019 All

Mercedes GLE 550e 3.0 4Matic GLE (166) (08/15-10/18) 2016 BV, RD

Mitsubishi I-Miev i-MiEV (12/10-04/14) 2011 RD

Mitsubishi Outlander PHEV

Business Nav Safety

Outlander (III) Plug-In

Hybrid (05/14-10/15) 2014 All

Mitsubishi Outlander PHEV GT S-

AWC

Outlander (III) Plug-In

Hybrid (10/15-08/18) 2017 BV, RD

Nio ES8 Base - 2019 BW, TW, RW

Nio ES8 founding - 2019 TW, RW

Nissan Leaf 24 Leaf (ZE0) (04/12-06/13) 2011 All

Nissan Leaf 30 Leaf (ZE0) (06/13-11/17) 2016 BV, RD

Nissan Leaf Tekna 40 Leaf (ZE1) (from 01/18) 2018 All

Opel Ampera-e Ampera-E (07/17-06/19) 2017 All

Porsche Cayenne e-Hybrid Cayenne (9YA) (from 11/17) 2018 All

World Electric Vehicle Journal 2020, 11, 63 20 of 24

Porsche Cayenne S-Hybrid Cayenne (958) (10/14-12/17) 2014 BV, RD

Renault Kangoo Maxi Z.E. 33 Kangoo (II) Z.E. Rapid (from

05/13) 2017 BW

Renault Zoe R135 Edition One Zoe (from 10/19) 2019 BW

Renault Zoe ZE Intens Zoe (06/13-09/19) 2013 All

Roewe 550 1.5 Plug-in hybrid - 2016 BW, TW, RW

Roewe ei5 Topline - 2018 BW, TW, RW

Roewe Marvel X AWD - 2018 BW, TW, RW

Roewe RX5 1.5 plug-in Hybrid - 2017 BW, TW, RW

Roewe RX5 EV400 - 2017 BW, TW, RW

Tesla Model-S 60 kWh Model S (08/13-04/16) 2013 BV, RD

Tesla Model-X P90D Model X (from 06/16) 2016 BV, RD

Toyota Auris 1.8 HSD Dynamic

nav. comfort Auris (E18) (01/13-08/15) 2013 All

Toyota Camry Hybrid No match found in ADAC 2018 BV

Toyota C-HR 1.8 Hybrid C-HR (X10) (10/16-11/19) 2018 All

Toyota Corolla 1.8 Hybrid elite Corolla (E17) (12/16-12/18) 2017 All

Table A3. Database overview, part 3.

Brand Vehicle Model ADAC Model Series Production

Year

Wheel

Model

Toyota Corolla 2.0 Hybrid

Collection Corolla (E21) (from 04/19) 2019 All

Toyota Levin 1.8 Hybrid CVT

Zunxiang No match found in ADAC 2018 BW, RW

Toyota Prius 1.8 Hybrid Four

Touring Prius (XW3) (04/12-02/16) 2015 BV

Toyota Prius 1.8 PHV Prius (XW5) Plug-In (from

03/17) 2017 All

Toyota Prius 1.8 Plug-in

Hybrid

Prius (XW3) Plug-In (10/12-

12/16) 2012 BV, RD

Toyota Prius 1.8 VVT-i Hybrid

Lounge Prius (XW5) (from 03/16) 2016 All

Toyota RAV4 2.5 Hybrid

Lounge RAV4 (XA5) (from 01/19) 2019 All

Volkswagen Golf VII e-Golf 85 kW Golf (VII) e-Golf (03/14-

10/16) 2014 All

Volkswagen Golf VII e-Golf 100 kW Golf (VII) e-Golf (04/17-

05/20) 2018 BV

Volkswagen Golf VII GTE Golf (VII) GTE (12/14-10/16) 2015 All

World Electric Vehicle Journal 2020, 11, 63 21 of 24

Volkswagen Jetta Hybrid 1.4 Jetta IV (01/11-08/14) 2013 BV, RD

Volkswagen Up! e-Up! up! e-up! (04/13-06/16) 2013 All

Volvo XC60 2.0 T8 Twin

Engine AWD R-Design XC60 (U) (from 07/17) 2018 All

Volvo XC90 T8 Inscription XC90 (L) (from 01/15) 2015 BV, RD

Weltmeister EX5 500 Extra No match found in ADAC 2019 BW, TW, RW

Zotye E200 No match found in ADAC 2016 BW, TW, RW

Table A4. List of employed symbols.

Symbol Description Unit

mveh max Vehicle gross weight kg

vveh max Maximum vehicle speed km/h

tveh 0-100 Acceleration time from 0 to 100 km/h s

Dbrake Brake disc diameter mm

mbrake Brake disc weight kg

Drim min ADAC Smallest rim diameter in a model series mm

Drim clearance Rim radial clearance mm

mrim Rim weight kg

Drim Rim diameter mm or inches

Dtire Tire diameter mm

h% Nominal aspect ratio /

wtire Tire section width mm

Vtire Tire volume mm3

m88% Loaded vehicle weight according to the 88% rule kg

m100% Loaded vehicle weight according to the 100% rule kg

lF, 88% Distance between the center of mass and the front axle for the

88% rule mm

lF,100% Distance between the center of mass and the front axle for the

100% rule mm

Ltire88% Tire load according to the 88% rule kg

Ltire100% Tire load according to the 100% rule kg

Ltire Tire load kg

VtireSL Tire volume allowing a standard-load tire to carry a given

load mm3

VtireEL Tire volume allowing an extra-load tire to carry a given load mm3

mtire Tire weight kg

wwheelhouse Wheelhouse width mm

W106 Vehicle width at the front axle mm

wsrr Width of the side roll rail mm

wavailable Available space at the front axle mm

wrequired Space required by the powertrain components mm

δmax Maximum wheel steering angle deg

Rturning Vehicle turning radius mm

World Electric Vehicle Journal 2020, 11, 63 22 of 24

L101 Vehicle wheelbase mm

L104 Vehicle front overhang mm

W103 Vehicle maximum width (without side mirrors) mm

W101 Vehicle front track width mm

mBIW BIW weight kg

Vveh Vehicle volume m3

L105 Vehicle rear overhang mm

H100 Vehicle height mm

BIW = body in white.

Table A5. Database for the evaluation of the wheel model.

Brand ADAC Model Series VCW in kg VGW in kg

Audi e-tron (GE) (from 03/2019) 2565 3130

BMW 2er-Reihe (F45) Active Tourer (09/14-02/18) 1735 2180

BMW 5er-Reihe (G30) Limousine (from 02/17) 1845 2440

BMW i3 (11/13-08/17) 1415 1755

BMW X5 (F15) (11/13-07/18) 2305 2980

Hyundai IONIQ (AE) Hybrid (10/16-07/19) 1580 1970

Hyundai Kona (OS) Elektro (from 08/18) 1760 2170

Jaguar I-Pace (X590) (from 10/18) 2208 2670

Kia Niro (DE) (09/16-05/19) 1594 2000

Mitsubishi Outlander (III) Plug-In Hybrid (05/14-10/15) 1945 2310

Nissan Leaf (ZE1) (from 01/18) 1707 2140

Opel Ampera-E (07/17-06/19) 1691 2056

Porsche Cayenne (9YA) (from 11/17) 2370 3030

Renault Zoe (06/13-09/19) 1575 1954

Toyota Auris (E18) (01/13-08/15) 1420 1915

Toyota C-HR (X10) (10/16-11/19) 1460 1930

Toyota Prius (XW5) Plug-In (from 03/17) 1605 1855

Toyota Prius (XW3) Plug-In (10/12-12/16) 1500 1840

Toyota RAV4 (XA5) (from 01/19) 1795 2185

VW Golf VII e-Golf (03/14-10/16) 1585 1980

VW up! e-up! (04/13-06/16) 1215 1500

Volvo XC60 (U) (from 07/17) 2223 2660

Volvo XC90 (L) (from 01/15) 2384 3010

World Electric Vehicle Journal 2020, 11, 63 23 of 24

References

1. The European Parliament and the Council of the European Union. Regulation (EU) 2019/631 of the

European Parliament and of the Council of 17 April 2019 setting CO2 emission performance standards for

new passenger cars and for new light commercial vehicles, and repealing Regulations (EC) No 443/2009

and (EU) No 510/2011. Off. J. Eur. Union 2019, 111, 13–53. Available online: https://eur-lex.europa.eu/legal-

content/EN/TXT/?uri=CELEX%3A32019R0631 (accessed on 13 June 2020).

2. The International Council on Clean Transportation. CO2 Emission Standards for Passenger Cars and Light-

Commercial Vehicles in the European Union; ICCT: Washington, DC, USA, 2019. Available online:

https://theicct.org/sites/default/files/publications/EU-LCV-CO2-2030_ICCTupdate_201901.pdf (accessed

on 21 June 2020).

3. Nicoletti, L.; Mayer, S.; Brönner, M.; Schockenhoff, F.; Markus, L. Design Parameters for the Early

Development Phase of Battery Electric Vehicles. WEVJ 2020, 11, 47, doi:10.3390/wevj11030047.

4. ADAC, VW e-Golf (04/17–05/20): Technische Daten, Preise. Available online: https://www.adac.de/rund-

ums-fahrzeug/autokatalog/marken-modelle/vw/golf/vii-facelift/266575/## (accessed on 7 June 2020).

5. ADAC, VW Golf 1.0 TSI BMT Trendline (03/17–08/18). Available online: https://www.adac.de/rund-ums-

fahrzeug/autokatalog/marken-modelle/vw/golf/vii-facelift/266199/## (accessed on 7 June 2020).

6. Fuchs, S. Verfahren zur parameterbasierten Gewichtsabschätzung neuer Fahrzeugkonzepte: Ein Werkzeug

zur Spezifikation von effizienten Antriebstopologien für Elektrofahrzeuge. Ph.D. Thesis, Technical

University of Munich, Munich, Germany, 2014. Available online: https://mediatum.ub.tum.de/1207264

(accessed on ).

7. Yanni, T.; Venhovens, P.J.T. Impact and Sensitivity of Vehicle Design Parameters on Fuel Economy

Estimates. In Proceedings of the SAE 2010 World Congress & Exhibition, Detroit, MI, USA, 13–15 April

2010, doi:10.4271/2010-01-0734.

8. Mau, R.J.; Venhovens, P.J. Parametric vehicle mass estimation for optimization. Int. J. Veh. Des. 2016 72, 1–

16, doi:10.1504/IJVD.2016.079202.

9. Felgenhauer, M.; Nicoletti, L.; Schockenhoff, F.; Angerer, C.; Lienkamp, M. Empiric Weight Model for the

Early Phase of Vehicle Architecture Design. In Proceedings of the 2019 Fourteenth International Conference

on Ecological Vehicles and Renewable Energies (EVER), Monte-Carlo, Monaco, 8–10 May 2019,

doi:10.1109/EVER.2019.8813530.

10. Alonso, E.; Lee, T.M.; Bjelkengren, C.; Roth, R.; Kirchain, R.E. Evaluating the potential for secondary mass

savings in vehicle lightweighting. Environ. Sci. Technol. 2012, 46, 2893–2901, doi:10.1021/es202938m.

11. Wiedemann, E.; Meurle, J.; Lienkamp, M. Optimization of Electric Vehicle Concepts Based on Customer-

Relevant Characteristics. SAE Tech. Pap. Ser. 2012, doi:10.4271/2012-01-0815.

12. Wiedemann, E. Ableitung von Elektrofahrzeugkonzepten aus Eigenschaftszielen. Ph.D. Thesis, Technical

University of Munich, Munich, Germany, 2014, 9783954047895.

13. Fuchs, S.; Lienkamp, M. Parametric Modelling of Mass and Efficiency of New Vehicle Concepts. ATZ

Worldw. 2013, 115, 60–66, doi:10.1007/s38311-013-0034-6.

14. Angerer, C.R. Antriebskonzept-Optimierung für batterieelektrische Allradfahrzeuge. Ph.D. Thesis,

Technical University of Munich, Munich, Germany, 2020; ISBN 3843943885.

15. Angerer, C.; Krapf, S.; Buß, A.; Lienkamp, M. Holistic Modeling and Optimization of Electric Vehicle

Powertrains Considering Longitudinal Performance, Vehicle Dynamics, Costs and Energy Consumption.

In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and

Information in Engineering Conference, Quebec City, QC, Canada, 26–29 August 2018,

doi:10.1115/DETC2018-85430.

16. Del Pero, F.; Berzi, L.; Antonacci, A.; Delogu, M. Automotive Lightweight Design: Simulation Modeling of

Mass-Related Consumption for Electric Vehicles. Machines 2020, 8, 51, doi:10.3390/machines8030051.

17. Leebmann24.de. BMW Online Shop. Originalprodukte online kaufen—leebmann24.de. Available online:

https://www.leebmann24.de/## (accessed on 15 May 2020).

18. Continental AG. Reifen von Continental. Available online: https://www.continental-reifen.de/autoreifen/

reifen?cartype=car&season=summer## (accessed on 20 April 2020).

19. A2mac1. a2mac1 Automotive Benchmarking. Available online: https://portal.a2mac1.com/de/home-2/##

(accessed on 1 February 2020).

20. ADAC. Allgemeine Deutsche Automobilclub. Available online: https://www.adac.de/## (accessed on 14

March 2020).

World Electric Vehicle Journal 2020, 11, 63 24 of 24

21. ADAC. Audi e-tron 1.Generation: Technische Daten, Preise. Available online: https://www.adac.de/rund-

ums-fahrzeug/autokatalog/marken-modelle/audi/e-tron/1generation/## (accessed on 27 May 2020).

22. German Institute for Standardization. DIN 70020-3:2008-03. Road Vehicles—Automotive Engineering—Part 3:

Testing Conditions, Maximum Speed, Acceleration and Elasticity, Mass, Terms, Miscellaneous; German Institute

for Standardization: Berlin, Germany, 2008.

23. Bundesministerium der Justiz und für Verbraucherschutz. Straßenverkehrs-Zulassungs-Ordnung

(StVZO): §34 Achslast und Gesamtgewicht. Available online: https://www.gesetze-im-internet.de/stvzo_

2012/__34.html## (accessed on 20 April 2020).

24. Reif, K. Bremsen und Bremsregelsysteme; Vieweg+Teubner Verlag: Wiesbaden, Germany; GWV Fachverlage

GmbH: Wiesbaden, Germany, 2010; ISBN 978-3-834-81311-4.

25. Duval-Destin, M.; Kropf, T.; Abadie, V.; Fausten, M. Auswirkungen eines Elektroantriebs auf das

Bremssystem. ATZ Automob. Z 2011, 113, 638–643, doi:10.1365/s35148-011-0148-3.

26. Wagner, D.; Hoffmann, J.; Lienkamp, M. Downsizing potential of wheel brakes in electric vehicles. In

Proceedings of the 8th International Munich Chassis Symposium, Munich, Germany, 20 – 21 June 2017; pp.

661–691, doi:10.1007/978-3-658-18459-9_47.

27. UN/ECE. Regulation No 13-H of the Economic Commission for Europe of the United Nations (UN/ECE)—

Uniform provisions concerning the approval of passenger cars with regard to braking. Off. J. Eur. Union

2015, 335, 1–84. Available online: https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A42015X

1222%2801%29 (accessed on 30 Mai 2020).

28. Doerr, J.; Ardey, N.; Mendl, G.; Fröhlich, G.; Straßer, R.; Laudenbach, T. The new full electric drivetrain of

the Audi e-tron. In Der Antrieb von Morgen 2019; Springer Vieweg: Wiesbaden, Germany, 2019; pp. 13–37,

doi:10.1007/978-3-658-26056-9_2.

29. Dietz, J.; Helmers, E.; Türk, O.; Beringer, F.; Brand, U.; Walter, J. Ökobilanzierung von Elektrofahrzeugen.

Available online: https://www.stoffstrom.org/fileadmin/userdaten/dokumente/Netzwerk_Elektromobili

taet/8a_Oekobilanzierung_von_Elektrofahrzeugen_Netzwerk_E-Mobilitaet_RLP.pdf## (accessed on 1

June 2020).

30. Breuer, B. Bremsenhandbuch: Grundlagen, Komponenten, Systeme, Fahrdynamik; Vieweg Verlag: Wiesbaden,

Germany, 2004; ISBN 978-3-322-99536-0.

31. Textar Brake Technology. Benchmark Testing: Ams-Test: The Test: Do the Pads Perform When Hot and

Cold? Available online: https://textar.com/en/ams-test/## (accessed on 15 July 2020).

32. European Tyre and Rim Technical Organisation (ETRTO). Standards Manual: ETRTO—The European Tyre

and Rim Technical Organisation. 2014. Available online: https://www.etrto.org/Publications/Available/

Standards-Manual (accessed on 22 May 2020.)

33. Luccarelli, M.; Lienkamp, M.; Matt, D.; Spena, P.R. Automotive Design Quantification: Parameters

Defining Exterior Proportions According to Car Segment. SAE Tech. Pap. Ser. 2014, doi:10.4271/2014-01-

0357.

34. Leister, G. Passenger Car Tires and Wheels: Development—Manufacturing—Application; Springer International

Publishing: Cham, Switzerland, 2018; ISBN 978-3-319-50117-8.

35. Jazar, R.N. Vehicle Dynamics: Theory and Application; Springer International Publishing: Cham, Switzerland,

2017; ISBN 978-3-319-53440-4.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access

article distributed under the terms and conditions of the Creative Commons Attribution

(CC BY) license (http://creativecommons.org/licenses/by/4.0/).