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

^{*}

## Abstract

**:**

## 1. Introduction

_{2}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 CO

_{2}/km [1]. BEVs represent an efficient way to reduce the average fleet consumption since they do not cause any local CO

_{2}emissions and are accounted as 0 g CO

_{2}/km [2].

- Estimate the resulting SWCs;
- Estimate the SVC of the single components caused by the PWC and triggered SWCs;
- Estimate the SVC on the vehicle installation spaces caused by the components SVCs.

## 2. Materials and Methods

#### 2.1. Employed Databases and Methods

#### 2.2. Brake Model

#### 2.2.1. Volumetric Model

_{veh max}and the maximum attainable speed v

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

_{veh 0–100}from 0 to 100 km/h is a suitable vehicle characteristic for modeling the brake disc diameter.

_{brake}for the vehicles contained in Appendix Table A1, Table A2 and Table 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.

_{brake}= 238.345 mm + (0.053 mm/kg) × m

_{veh max}− (5.631 mm/s) × t

_{veh 0–100}

^{2}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

_{brake}for each of the vehicles in Appendix Table A1, Table A2 and Table A3. The resulting regression model describing the correlation between D

_{brake}and m

_{brake}is shown in Equation (2):

_{brake}= −12.870 kg + (0.069 kg/mm) × D

_{brake}

^{2}of 91.33%, an MAE of 0.52 kg, and an nMAE of 6.42%.

#### 2.3. Rim Model

#### 2.3.1. Minimum Rim Diameter

_{rim min ADAC}. With these data, we calculate the minimum radial clearance D

_{rim clearance}, as shown in Equation (3):

_{rim clearance}= D

_{rim min ADAC}− D

_{brake}

#### 2.3.2. Weight Model

_{rim}, we develop a regression model, which correlates m

_{rim}with the rim diameter D

_{rim}(expressed in inches). Equation (4) shows the resulting linear regression model:

_{rim}= −13.063 kg + (1.405 kg/inch) × D

_{rim}

^{2}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

_{tire}, the nominal aspect ratio, h

_{%}, and the section width, w

_{tire}, 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

_{tire}, 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):

_{tire}= 0.25 × π × w

_{tire}× (D

_{tire}

^{2}− D

_{rim}

^{2})

_{88%}), and the loaded weight for the 100% rule (m

_{100%}).

_{F,88%}and l

_{F,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):

_{tire88%}= (m

_{88%}× (l − l

_{F, 88%}))/(2 × l × 0.88)

_{tire100%}= (m

_{100%}× (l − l

_{F,100%}))/(2 × l)

_{tireSL}, allowing a standard-load tire to carry a given load, L

_{tire}(in kg), is defined by Equation (8):

_{tireSL}= −13462233.892 mm

^{3}+ (87651.102 mm

^{3}/kg) × L

_{tire}

^{2}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 R

^{2}of 98.82% and an nMAE of 2.63%:

_{tireEL}= −13548645.429 mm

^{3}+ (77990.623 mm

^{3}/kg) × L

_{tire}

_{rim}(in mm), with every possible nominal aspect ratio and section width combination and derive the tire diameter, as shown in Equation (10):

_{tire}= D

_{rim}+ (2 × w

_{tire}× h

_{%})/100

#### 2.4.2. Weight Model

_{tire}, based on the tire diameter and its section width. The regression is derived from the evaluation of the vehicles in Appendix Table A1, Table A2 and Table A3 and shown in Equation (11):

_{tire}= −16.890 kg + (0.023 kg/mm) × D

_{tire}+ (0.054 kg/mm) × w

_{tire}

^{2}of 85.85%, an MAE of 0.71 kg, and an nMAE of 6.63%.

#### 2.5. Wheelhouse Model

_{wheelhouse}. Given the wheelhouse width, the position of the side roll rail can be identified. Then, knowing the vehicle width at the front axle (W106) and the width of the side roll rail w

_{srr}, we estimate the available space at the front axle, w

_{available}, as shown in Equation (12):

_{available}= (W106 − 2 × w

_{wheelhouse}+ w

_{srr})

_{available}can be compared with the actual space required by the powertrain components, w

_{required}, to test the vehicle concept feasibility. Figure 3 illustrates the above-cited measures.

_{srr}as constant, since our focus is on the wheelhouse dimensions. A change in the wheel dimensions leads to a variation of w

_{wheelhouse}, which depends on the tire diameter, the tire section width, and the maximum wheel steering angle, δ

_{max}. 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):

_{wheelhouse}= 0.5 × w

_{tire}× cos δ

_{max}+ 0.5 × D

_{tire}× sin δ

_{max}+ 0.5 × w

_{tire}

_{max}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 δ

_{max}from the vehicle turning radius (R

_{turning}), wheelbase (L101), front overhang (L104), maximum width (W103), and track width (W101):

_{max}= atan(L101/(–W103 × 0.5 + (R

_{turning}

^{2}− (L101 + L104)

^{2})

^{0.5}− W101 × 0.5))

## 3. Model Evaluation and Results

#### 3.1. Model Evaluation

^{2}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.

^{2}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.

#### 3.2. Quantification of the Secondary Effects on the Wheel Components

_{available}(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)

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

#### 3.2.3. Influence on the w_{available} (SVC on Vehicle Level)

_{available}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 w

_{srr}constant. Figure 9 shows the loss, in percentage, of w

_{available}, using the initial w

_{available}as reference.

_{available}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 w

_{available}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%).

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

_{available}. 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.

_{available}, 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).

_{BIW}, can be modeled from the vehicle volume, V

_{veh}, as presented in Equation (15) [6] (p. 40):

_{BIW}= (37.45 kg/m

^{3}) × V

_{veh}− 66.38 kg

_{veh}, 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):

_{veh}= (0.5 × L104 + 0.75 × L105 + L101) × W103 × H100

_{veh}, thus influencing m

_{BIW}. 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.

_{available}, it also causes further SWC in other parts of the vehicle. These SWCs can, in turn, cause additional SVCs.

## 4. Discussion and Conclusions

^{2}, 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.

_{available}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.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

- 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).

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 |

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 |

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 |

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 |

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 |

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 |

Symbol | Description | Unit |
---|---|---|

m_{veh max} | Vehicle gross weight | kg |

v_{veh max} | Maximum vehicle speed | km/h |

t_{veh 0–100} | Acceleration time from 0 to 100 km/h | s |

D_{brake} | Brake disc diameter | mm |

m_{brake} | Brake disc weight | kg |

D_{rim min ADAC} | Smallest rim diameter in a model series | mm |

D_{rim clearance} | Rim radial clearance | mm |

m_{rim} | Rim weight | kg |

D_{rim} | Rim diameter | mm or inches |

D_{tire} | Tire diameter | mm |

h_{%} | Nominal aspect ratio | / |

w_{tire} | Tire section width | mm |

V_{tire} | Tire volume | mm^{3} |

m_{88%} | Loaded vehicle weight according to the 88% rule | kg |

m_{100%} | Loaded vehicle weight according to the 100% rule | kg |

l_{F, 88%} | Distance between the center of mass and the front axle for the 88% rule | mm |

l_{F,100%} | Distance between the center of mass and the front axle for the 100% rule | mm |

L_{tire88%} | Tire load according to the 88% rule | kg |

L_{tire100%} | Tire load according to the 100% rule | kg |

L_{tire} | Tire load | kg |

V_{tireSL} | Tire volume allowing a standard-load tire to carry a given load | mm^{3} |

V_{tireEL} | Tire volume allowing an extra-load tire to carry a given load | mm^{3} |

m_{tire} | Tire weight | kg |

w_{wheelhouse} | Wheelhouse width | mm |

W106 | Vehicle width at the front axle | mm |

w_{srr} | Width of the side roll rail | mm |

w_{available} | Available space at the front axle | mm |

w_{required} | Space required by the powertrain components | mm |

δ_{max} | Maximum wheel steering angle | deg |

R_{turning} | Vehicle turning radius | mm |

L101 | Vehicle wheelbase | mm |

L104 | Vehicle front overhang | mm |

W103 | Vehicle maximum width (without side mirrors) | mm |

W101 | Vehicle front track width | mm |

m_{BIW} | BIW weight | kg |

V_{veh} | Vehicle volume | m^{3} |

L105 | Vehicle rear overhang | mm |

H100 | Vehicle height | mm |

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 |

## References

- 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). - 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).
- 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. [Google Scholar] [CrossRef] - 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).
- 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).
- 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 4 June 2020).
- 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. [Google Scholar] [CrossRef]
- Mau, R.J.; Venhovens, P.J. Parametric vehicle mass estimation for optimization. Int. J. Veh. Des.
**2016**, 72, 1–16. [Google Scholar] [CrossRef] - 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. [Google Scholar] [CrossRef]
- 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. [Google Scholar] [CrossRef] [PubMed] - Wiedemann, E.; Meurle, J.; Lienkamp, M. Optimization of Electric Vehicle Concepts Based on Customer-Relevant Characteristics. SAE Tech. Pap. Ser.
**2012**. [Google Scholar] [CrossRef] - Wiedemann, E. Ableitung von Elektrofahrzeugkonzepten aus Eigenschaftszielen. Ph.D. Thesis, Technical University of Munich, Munich, Germany, 2014. [Google Scholar]
- Fuchs, S.; Lienkamp, M. Parametric Modelling of Mass and Efficiency of New Vehicle Concepts. ATZ Worldw.
**2013**, 115, 60–66. [Google Scholar] [CrossRef] - Angerer, C.R. Antriebskonzept-Optimierung für Batterieelektrische Allradfahrzeuge. Ph.D. Thesis, Technical University of Munich, Munich, Germany, 2020. [Google Scholar]
- 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. [Google Scholar] [CrossRef]
- 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. [Google Scholar] [CrossRef] - Leebmann24.de. BMW Online Shop. Originalprodukte Online Kaufen—Leebmann24.de. Available online: https://www.leebmann24.de/## (accessed on 15 May 2020).
- Continental AG. Reifen von Continental. Available online: https://www.continental-reifen.de/autoreifen/reifen?cartype=car&season=summer## (accessed on 20 April 2020).
- A2mac1. a2mac1 Automotive Benchmarking. Available online: https://portal.a2mac1.com/de/home-2/## (accessed on 1 February 2020).
- ADAC. Allgemeine Deutsche Automobilclub. Available online: https://www.adac.de/## (accessed on 14 March 2020).
- 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).
- 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. [Google Scholar]
- 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).
- Reif, K. Bremsen und Bremsregelsysteme; Vieweg+Teubner Verlag: Wiesbaden, Germany; GWV Fachverlage GmbH: Wiesbaden, Germany, 2010; ISBN 978-3-834-81311-4. [Google Scholar]
- Duval-Destin, M.; Kropf, T.; Abadie, V.; Fausten, M. Auswirkungen eines Elektroantriebs auf das Bremssystem. ATZ Automob. Z
**2011**, 113, 638–643. [Google Scholar] [CrossRef] - 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. [Google Scholar] [CrossRef]
- 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%3A42015X1222%2801%29 (accessed on 30 May 2020). - 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. [Google Scholar] [CrossRef]
- 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_Elektromobilitaet/8a_Oekobilanzierung_von_Elektrofahrzeugen_Netzwerk_E-Mobilitaet_RLP.pdf## (accessed on 1 June 2020).
- Breuer, B. Bremsenhandbuch: Grundlagen, Komponenten, Systeme, Fahrdynamik; Vieweg Verlag: Wiesbaden, Germany, 2004; ISBN 978-3-322-99536-0. [Google Scholar]
- 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).
- 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).
- 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**. [Google Scholar] [CrossRef] - Leister, G. Passenger Car Tires and Wheels: Development—Manufacturing—Application; Springer International Publishing: Cham, Switzerland, 2018; ISBN 978-3-319-50117-8. [Google Scholar]
- Jazar, R.N. Vehicle Dynamics: Theory and Application; Springer International Publishing: Cham, Switzerland, 2017; ISBN 978-3-319-53440-4. [Google Scholar]

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

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

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 | - |

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 |

© 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/).

## Share and Cite

**MDPI and ACS Style**

Nicoletti, L.; Romano, A.; König, A.; Schockenhoff, F.; Lienkamp, M.
Parametric Modeling of Mass and Volume Effects for Battery Electric Vehicles, with Focus on the Wheel Components. *World Electr. Veh. J.* **2020**, *11*, 63.
https://doi.org/10.3390/wevj11040063

**AMA Style**

Nicoletti L, Romano A, König A, Schockenhoff F, Lienkamp M.
Parametric Modeling of Mass and Volume Effects for Battery Electric Vehicles, with Focus on the Wheel Components. *World Electric Vehicle Journal*. 2020; 11(4):63.
https://doi.org/10.3390/wevj11040063

**Chicago/Turabian Style**

Nicoletti, Lorenzo, Andrea Romano, Adrian König, Ferdinand Schockenhoff, and Markus Lienkamp.
2020. "Parametric Modeling of Mass and Volume Effects for Battery Electric Vehicles, with Focus on the Wheel Components" *World Electric Vehicle Journal* 11, no. 4: 63.
https://doi.org/10.3390/wevj11040063