Article

Parametric Modeling of Mass and Volume Effects for Battery Electric Vehicles, with Focus on the Wheel Components

Abstract and Figures

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.
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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.
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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;
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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”.
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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.
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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.
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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).
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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)
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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
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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.
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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
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Introduction Starting from the beginning, this book explains the development process of all parts related to the topics tire, wheel and tire pressure monitoring system. This is continued by the modern project management methods in the development process of the parts and the necessary tests to build up this safety relevant components. Modern methods for simulations are described.
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In order to perform optimisation of parametric vehicle designs in the conceptual design phase of vehicle development, before detailed design information and styling are defined, it is necessary to estimate the mass of significant vehicle subsystems and the resulting total vehicle curb mass as accurately as possible. This work develops estimation relationships for a number of subsystems and assesses the resulting correlations to actual vehicle subsystem and curb mass data. The mass estimation relationships have been intentionally developed using a minimal set of vehicle parameters (overall length, width, height, wheelbase and engine power) to simplify the process and increase the speed of optimisation iterations. Several of the subsystem estimations can also be used in determining vehicle centre of gravity location. Separate mass relationships for steel and aluminium have been developed for Body in White and closure mass estimation. Additional mass relationships for hybrid vehicles will be included in future work.
Book
This textbook is appropriate for senior undergraduate and first year graduate students in mechanical and automotive engineering. The contents in this book are presented at a theoretical-practical level. It explains vehicle dynamics concepts in detail, concentrating on their practical use. Related theorems and formal proofs are provided, as are real-life applications. Students, researchers and practicing engineers alike will appreciate the user-friendly presentation of a wealth of topics, most notably steering, handling, ride, and related components. This book also: Illustrates all key concepts with examples Includes exercises for each chapter Covers front, rear, and four wheel steering systems, as well as the advantages and disadvantages of different steering schemes Includes an emphasis on design throughout the text, which provides a practical, hands-on approach.
Article
The U.S. Environmental Protection Agency (EPA) has several methods in use to determine the overall fuel economy of a vehicle which is one of the mandatory fields on the Monroney sticker (better known as window sticker) of new cars and trucks. The fuel economy of a typical vehicle depends on many design properties physically known as the inertial-, wind- and rolling resistance. Each of these resistive forces is determined by several key design parameter (such as mass, frontal area, drag coefficient and rolling resistance coefficient) which are predetermined quite early in the design process. These design parameters, to a large extent, cannot freely be determined, are considerably co-dependent and have a large amount of interaction with other vehicle properties including overall vehicle costs. To optimize the design, careful consideration of the cost/benefit analysis for each of the design parameters must be made. A simplified model was developed to calculate various vehicle driving cycles and to study the sensitivity of assorted key design parameters on the fuel economy estimates. Different vehicles representing different categories (a typical light-duty pick-up truck, a mid-size sedan, and an all-electric vehicle) were benchmarked and vehicle parameter sensitivities with regard to the various driving cycles have been determined. Furthermore, fuel economy improvements through energy regeneration (braking) have been addressed.