and for each time step, the tractive force needed on the wheel is determined. ... is a methodology described, for determining the vehicle mass in the concept phase. .... sonably used in vehicles with lower engine power, or high-performance ... the table, we assume that for certain, especially small cars, the integration of a ...
Description of the modelling style and parameters for electric vehicles in the concept phase Dr.-Ing. Stephan Matz, Institute of Automotive Technology, TU Munich Dipl.-Ing. Lorenz Horlbeck, Institute of Automotive Technology, TU Munich Dipl.-Ing. Andrea Ficht, Institute of Automotive Technology, TU Munich Dr.-Ing. Johannes Fuchs, Institute of Automotive Technology, TU Munich Dr.-Ing. Peter Burda, Institute of Automotive Technology, TU Munich Dipl.-Ing. Richard Eckl, Institute of Automotive Technology, TU Munich Prof. Dr.-Ing. Markus Lienkamp, Institute of Automotive Technology, TU Munich
1 Introduction New drive technologies and mobility concepts, as well as the development of unexploited and the transformation of traditional markets, lead to an ever greater variety of options in the automotive industry. The number of vehicle models and derivatives, as well as the opportunities for differentiation in the equipment, has rapidly increased in recent years [Ren07 pages 9-48]. The starting point of today's (classic) vehicle development process are requirements of the future users, the longer-term corporate strategy as well as experiences drawn from competition and predecessor vehicles. Based on this, target characteristics for the new vehicle are then defined in the concept phase. To, on one hand ensure the subsequent availability of these target characteristics during the concept elaboration and, on the other hand, to not give away potential at an early stage, it is necessary to continuously monitor the expected characteristics of the vehicle. This is done partially through assessments by experienced experts or through the use of highly simplified calculation models. While established auto-mobile manufacturers can rely on their wealth of experience when it comes to conventionally powered vehicles, in new technologies, such as the electrical powertrain, the model-based approach is moving to the spotlight more and more. One advantage of a model-based approach is the automation capacity and therefore the possibility of its use in concept optimizers [Kuc11, Wie12, Mat13]. A challenge in calculation of characteristics in the concept development phase is the fact, that very little information about the future vehicle is known yet. The vehicle modelling must be limited to the essential components and must display these at an appropriate degree of abstraction [Lin09, p.8].
1.1 Motivation Electrical energy storage in the form of high-voltage battery systems, electric drive units, power-electronic components such as traction converters, DC-DC converter and charging current converter, as well as fuel cell systems and hydrogen storages constitute new vehicle components, from the perspective of the automotive industry. These core components as well as the underlying technologies are still at the initial stage of their development for the large-scale use in motor vehicles. Series production experience with modern electric road vehicles and their drive and storage components are still very limited in most car manufacturers.
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The design of future vehicle concepts must therefore consider the foreseeable developmental dynamics of core technologies - largely in terms of drive systems and energy storage. An estimate of the technological potential of these core components is essential in the early concept phase, in order to allow vehicle projects, already, about five years before production starts, to design suitable vehicle architectures (Figure 1).The latter are also subject to a developmental dynamics, which are in strong interaction with the technical characteristics of the individual components used. This aspect gains additional importance in the context of strategic corporate decisions: vehicle platforms and building sets are usually used for several model series and generations [Fuc14a, p.22].
-55
-40
Planning phase
-25
Definition phase
Months 0 before SOP
-8
Implementation phase Production phase
Concept design
Project start
Conceptdefinition
Series development
Design decision
0-series Start of production (SOP)
Figure 1: Automotive development process [after LIE12 p.118]
1.2 Component Selection This paper outlines a component selection, which is specific for electrification, and an appropriate modelling depth for the described application. The focus lies on the prediction of energy consumption for purely electrically powered vehicles. This is calculated in a longitudinal dynamics simulation for a given driving cycle. Here, the cycle is divided into discrete time steps and for each time step, the tractive force needed on the wheel is determined. This is, according to [Bra13, p.51] the sum of the inertial force to be overcome 𝐹B , the rolling resistance force 𝐹B , the air drag force 𝐹L and the slope force 𝐹St: 𝐹X = 𝐹B + 𝐹R + 𝐹L + 𝐹St .
1–1
The acceleration resistance 𝐹B can be calculated, according to [Hei11, p.45], from the vehicle mass, the rotating mass plus-factor and the current longitudinal acceleration. In [Fuc14] there is a methodology described, for determining the vehicle mass in the concept phase. In chapter 9 of this paper, a simple modelling of the wheels and an associated parameter setting are described. The modelling of air and gradient resistance are described in [Hei 11, p.43f]. Chapter 8 treats a variant for estimating the air drag coefficient 𝑐w in the concept phase. However, the focus of this paper is not the calculation of the driving resistances, but the component models that enable calculating the vehicle energy consumption from the tractive force 𝐹X . Figure 2 shows the components of the powertrain, of a BEV, relevant for this.
2
Potential values
Components
Flow values AC charging current
AC-mains voltage Charger Battery voltage
DC charging current High-voltage battery
Battery voltage
Discharging current Inverter
Induced voltage
Current
E-machine Machine speed
Machine torque Transmission & differential
Wheel torque
Wheel speed Wheel Vehicle speed
Circumferential force
Figure 2: Powertrain components
Analogously, this paper is divided in the components battery system, range extender, inverter and electrical machine, hydrogen storage, fuel cell, gearbox, aerodynamics as well as tyres.
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2 Battery System For the vehicle concept design, a complex simulation of the electrical behaviour of the battery does not make sense, because a simulation of current loads cannot be yet carried out in cycle, at a high enough resolution, and detailed cell parameters are not available. Instead, the focus on the sensible choice of suitable battery parameters is essential for the present requirements, because there are batteries available, which are optimized for different operating conditions. The simulation of the battery as a power source with (temperature-dependent) internal resistance and given capacity allows for a parameterization with parameters for different cells, available in literature and on data sheets. It thus allows a fast assessability of different cell types. The most important characteristic parameters of the energy storage are:
Energy density volumetrically in Wh/ m 3 and gravimetric in Wh/kg
Max. discharge rate C in kW/kWh
Cycle stability (number of cycles up to 80% capacity)
Costs in €/kWh
For the concept design there are three classes of energy storages being defined. A storage optimized for maximum energy content, based on 18650 cells from the field of consumer electronics, a storage optimized for very high discharge power from cells, which already being used in hybrid vehicles as well as a storage built under VDA standard with typical "automotive" lithium-ion cells. Averaged values of typical available cells are used as parameters. Normally, for the proportions by weight of the secondary components of the pack, 50% of the total mass of the energy storage is indicated [Wag10, p 2208]. For proportions by volume, of the secondary components of the pack, a mean value of 25% of the total volume is assumed, based on own investigations. Based on the normally lower total energy content of the high-performance energy storages, most frequently used in hybrid cars, the secondary components have a higher proportion by weight here. Higher currents and the resulting design of the electrical components lead to a further increase. Table 1.1.: Characteristics of typical vehicle batteries High-energy (18650)
Cell
Standard (VDA BEV)
Cell
High-current (Pouch)
Cell
Energy density in Energy density Discharge rate
Cycle stability 1. 2. 3. 4. 5. 6. 7.
Data and extrapolation according to fig. 1.1 2700-3350 mAh, 45-48 g [Pan10; Pan13; Pan12] Volume 18650: 0.016 liter Extrapolated according to development of Wh/kg Tesla Roadster S [Tes13; Hei13; IAV14, p.9] Own investigations on MUTE Incl. internal cooling, without cooling units
8. 9. 10. 11. 12. 13.
Vol. from fig. BMW i3 pack (reference value cell) [Bim13] Cell: VDA BEV2 [Lam12, p.10] Optimization cell+pack structure Optimization cell+pack structure [FAZ13; IAV14, p.6] Very small energy storage for hybrid vehicles
Available electric vehicles show corresponding energy densities: about 75 Wh/kg (18 kWh at 240 kg [Vol13]) for the VW E-Up, 156 Wh/kg (85 kWh at 544 kg [Tes13; Hei13; IAV14, p.9]) for the Tesla Model S, 82 Wh/kg (18.8 kWh at 230 kg [FAZ13; IAV14, p.6]) for the BMW i3. 4
In the first design of the energy storage for an electric vehicle, when selecting the cells, it needs to be considered that the targeted high-energy and high-performance cells differ with regard to their internal resistance. Higher capacities at the same cell volumes are normally (with the same cell chemistry) achieved through a thicker coating of the electrodes, resulting in higher internal resistances of the cells .Therefore, before the cell selection, at least one power and coverage requirement must be known. With the help of formula 2-1, the internal resistance of the entire battery can be roughly calculated. With a known performance requirement now, the voltage drop can be estimated at maximum performance requirement or when the maximum permissible current must be reduced by the battery management system. The goal of cell selection should be that the BMS has to limit the current only at low SOC. Voltage drops that are too high can possibly be compensated by parallel connection of additional cells: 𝑅Batterie = 𝑠
1 + 𝑅w 1 𝑝 𝑅 Zelle + 2 𝑅Kontaktierung
2–1
with 𝑠 = Number of serial strands, 𝑝 = Number of parallel strands, 𝑅Zelle = Internal resistance (DC) of the cell used, 𝑅Kontaktierung= Resistance of a bonding point and 𝑅w = Additional resistances i.e. for wiring, contactors, etc. The "Technology Roadmap Energy Storage for Electric Mobility 2030" of the Fraunhofer ISI [Fra12] does not distinguish between packs of dedicated high-energy cells, as they are reasonably used in vehicles with lower engine power, or high-performance storages for use in hybrid vehicles. These literature values are thus used for a "standard pack" 'of cells under VDA standard. The batteries of the BMW i3 and the VW E-Up serve as a base. The values for high energy packs were taken for 2014 from the data of the electric vehicle Tesla Model S, available in the market and the results of the MUTE project, and extrapolated accordingly. Analogically, the values for high-performance packs are based on typical available energy storages for hybrid vehicles. In the case of cycle stability, there is a significant improvement to be foreseen with the high-energy cells. As for standard and high-performance cells the cycle stability achievable today may be considered sufficient, the probable development focus lies on increasing the energy content at constant cycle stability. Similarly, for high-performance cells there is no increase in the maximum discharge rate to be expected, because here, bonding and design of the HV wiring system already represent more limiting factors. Figure 3 shows the development of the energy densities of 18650 cells using the example of Sanyo / Panasonic.
5
Energy density in Wh/kg
Year Figure 3: Development of the capacity of lithium-ion cells using the example of 18650 cells from Sanyo/Panasonic company [Kin09, p.12] [San10] [Pan10] [Pan13]
For current and projected costs of energy storages, refer to [Koc14].
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3 Range Extender Range extenders are always provided in electric vehicles, when a greater range, than the one possible by the main electric storage, has to be achieved. It is desirable to design the vehicle as cost-effective as possible. Since the battery storage is the most expensive component, it should be kept as small as possible. So in this case, the storage battery merely covers the common required ranges .Longer journeys that occur rarely, are to be covered with the range extender. State of the art in the automotive industry in this case is the combustion engine as a range extender. Vehicles such as the BMW i3 and the Opel Ampera are equipped with such range extenders. Several suppliers have meanwhile recognized this trend and have made their own developments. A selection is presented in Table 3.1.To determine the values of specific performance (volumetric and gravimetric) and the specific energy content (volumetric and gravimetric) complete systems are always assumed. These include, besides of the engine, also the generator, the tank, the fuel and exhaust systems. Since the manufacturers usually only provide information on the motor weight (possibly with generator), matching weights and volumes are assumed for the missing components. The specific energy contents are always calculated with 10 litres of fuel and the respectively presumed maximum efficiency.
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Table 3.1: Range extender comparative data Name Engine design
2 cylinders
Wankel engine
OTTO 4-stroke OTTO 4-stroke OTTO 4-stroke Diesel 4-stroke Wankel 4-stroke
Arrangement (cylinder/discs) Spec. power in Wh/kg Spec. power in W/l Spec. energy content in Wh/kg for tank capacity 10l Spec. energy content in Wh/l for tank capacity 10l
Power (max.) in kW Volume in l Engine volume in l Engine weight in kg Weight incl. tank, fuel, generator and exhaust system in kg Efficiency (concept related) Relative costs 6 1
2
3
4
5
Because the sources only specify engine volumes, 40 l will be added for tank (10l), generator and exhaust system. Because the sources only specify volumes of engines together with the generator, 30 l are added for tank (10l) and exhaust system. Because the sources only specify engine weights, 40 kg are added for tank (10l), fuel, generator and exhaust system. Because the sources only specify engine weights together with the generator, 20 kg are added for tank (10l) and exhaust system. 6 7 8 9 10 [Her13] [DLR12] [Tur10] [Gum10] [AVL10] [Kub14]
It can be seen that the specific gravimetric energy content, being 279-468 Wh/kg of the considered range extender, is indeed considerably higher than that of battery storage systems with up to 200 Wh /kg, but the difference will decrease in the future. Based on the values from the table, we assume that for certain, especially small cars, the integration of a range extender is not worthwhile. Instead, it will be increasingly attractive to increase the main energy storage. We expect no major improvements in gravimetric and volumetric energy density with combustion engines. These two values will, however, be improved for battery storage systems with about 7% per year. 8
4 Inverter and electrical machine For the design of an electrical machine, plus the associated power electronics, in the early stage of designing the powertrain, approximate measures can be assumed at first. The characteristic values of electrical machines for automotive applications are:
The volumetric power density in kW/l
The gravimetric power density in kW/kg
The overload capacity of the machine, non-dimensional
There is a need here to discern which type of machine should be used. Basically, the selection can be currently made from three different types of machines, which are all used by different manufacturers in series production:
Asynchronous machine (ASM)
Permanent synchronous machine (PSM)
Separately excited synchronous machine (FSM)
In direct comparison to each other, all machines have pros and cons that must be weighed. They are presented below. Thereby characteristic values can be considered for each type of machine. The forecast values used come from a separate database and are also aligned with the values of the International Energy Agency [IEA10].The collected data show a fundamental agreement with the predictions of the IEA and are therefore used as a basis for the modelling of the electrical machine. A first efficiency characteristic map of the electrical machine is created using a database. Used as input parameters are machine type, the rated power, the maximum speed as well as some of the setpoint values of the vehicle to be constructed, such as elasticity values or torque requirements for the curbstone crossing. For quick rough calculations of the energy balance in the vehicle, a fixed efficiency of the power electronic drive machine unit is set alternatively, of 80% for the motor operation and 70% for the generator operation. These values are determined experimentally in the NEDC driving cycle, for a current electric vehicle of the middle class. Based on these setpoint values, the database is searched for similar types of machines. Because, in most cases, the desired machine does not already exist, the calculation tool approximates the characteristics map of an electrical machine, which enables the desired driving performance. If the speed or torque ranges of the machine to be calculated machine are outside the values that are available in the database, then there will be extrapolated starting from the next known values. The extrapolation is done through the gradient between the last two known measuring points of an existing characteristic map. In principle, it should be noted that the different machine types have different maximum efficiencies. Of all types, PSM usually have the best maximum efficiency, followed by the FSM and the ASM. The best operating points are also restricted to different operating ranges. PSM and FSM show very good efficiencies at moderate speeds and high loads. The ASM, on the other hand, has its best values at high speeds and medium loads. 9
With regard to price, asynchronous machines are cheaper than permanently excited and separately excited synchronous machines, which cause extra costs mainly because of the installed permanent magnets or the additional regulation of the rotor circuit costs [KOC 14].Furthermore, asynchronous machines are capable of higher overload with a maximum factor of 4, due to higher admissible rotor temperature. Permanently excited machines, which are limited here by the maximum temperature of their magnets, reach approximately twice the overload compared to the rated power. FSM are estimated with a factor of 2.5. The maximum duration of the overload is approximately 30 s. Then the power of the machine must be throttled back to the rated power, to prevent thermal overload. As a guide values for gravimetric rated power density for PSM, FSM and ASM, up to 2 kW/kg, 1.25 kW/kg and 0.9 kW/kg are assumed. The volumetric power density at rated power can be set for the PSM to max. 5.80 kW/l, the FSM to max. 4 kW/l and the ASM with 3.70 kW/l [MAR11]. These values are improving, the more powerful the machine must be. For the future, until the year 2030, an improvement of both the volumetric and gravimetric power density is expected. So it can be assumed that the gravimetric power density can be increased , until 2030, in all types of machines by about 50% [IEA10].This is due to a variety of factors. These include, for instance an optimized machine layout, increased utilisation and improved use of existing material, perhaps with the help of improved slot fill ratios. By using, for example, improved flow barriers, perturbations can be further minimized, and the efficiency of the machines can be further increased, and they can be built to be more powerful. In addition, further progress in the machine design is to be expected, such as the development of new winding techniques, which may lead to a further increase in performance. The focus of optimization is primarily limited to the gravimetric power density, because the installation space required for electrical machines is now already considerably smaller, compared to other components such as, for example, the battery. Due to the above improvement of the gravimetric power density, the increase of the volumetric power density will not turn to the same extent. Nevertheless, there is still a significant improvement to be expected here also. By the year 2030 this will be increased by a maximum of 30%.There is less potential here, because by improving the material utilization and increasing the power, there is less potential for a more compact design. For the inverter, in case of a rough design, a blanket efficiency of 0.95 can be assumed over all operating points within a random cycle. The gravimetric and volumetric power density reaches values of 10.8 kW/kg and 8.7 kW/l [IEA10].These key figures are also to experience further improvement in the course of future developments, so by 2030, values of around 15 kW/kg or 15 kW/l can be expected here. The same applies to possibly installed chargers. ASM (rated power) kW/l kW/kg Overload
2015 3.7 0.9 4
2030 1.1
PSM (rated power) kW/l kW/kg Overload
LE kW/l kW/kg Overload
2015 12.5 10.8 1.5
2030 20 20
FSM (rated power) kW/l kW/kg Overload
2015 5.8 2.0 2 2015 4.0 1.2 2.5
2030 2.5
2030 1.8
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5 Hydrogen storage The data used come from scientific publications in the field, as well as some target values communicated by the US Department of Energy [DOE11].The latter also frequently serve as a cited reference in scientific works, so it is not rare, for a "circular reference" of information on technical characteristics of hydrogen storage, to occur in scientific works. Two physical quantities have been identified as characteristic parameters for describing hydrogen storages:
Hydrogen mass density relative to the storage medium, in kgH2/m3 and gH2/l
Mass fraction of hydrogen in the storage system weight, in wt%
Specific energy based on the storage system weight, in kWh/kg
The last two parameters can be transformed into each other according to the formula 5-1. In it, 𝐸H2 is the energy of the hydrogen, 𝑚H2,system the storage system weight and 𝑚H2,sp the mass fraction of hydrogen in the storage system weight. The calorific value 𝐻U of hydrogen is assumed to be 33.33 kWh/kg: 𝐸sp =
𝐸H2 𝑚System
=
𝐻u . 100 − 1 𝑚H2,sp
5–1
Based on the target values published by the US Department of Energy (DOE), technologyindependent values can be interpolated for random time steps (e.g. linear).To estimate the above mentioned characteristic values for specific technology alternatives, the following storage concepts are being considered:
Pressure accumulator (C-H2), 35 MPa and 70 MPa
Cryogenic pressure accumulator (Cc-H2)
Liquid storage (LH 2)
Mass density of the stored hydrogen
gH2/l
C-H2 35 MPa 23
Mass fraction of hydrogen in the storage system weight
wt %
4.2
Specific energy based on the storage system weight
kWh/kg 1.46
C-H2 70 MPa 39
Cc-H2
L-H2
71
71
4.8 5.5 7.5 (DOEtarget value) 1.68 1.94 2,70 (DOEtarget value)
7 24 (freeform container) 2.51 10.53 (freeform container)
The state of the art is represented by pressure tanks of the 70 MPa class. Liquid and cryogenic pressure accumulators are also being investigated by various OEMs and suppliers and implemented prototypically. Other variants, such as hydride storages and organic structures are currently still in the laboratory stage and are therefore not included in the data collection. For
11
the above mentioned storage technologies, scientific publications from system suppliers, vehicle manufacturers and research institutions have been analysed [Bar05, p. 390; DOE11, p. 48; Eic10, p. 120-121; Fic08, p. 7; Kun11, p. 3, 5; Pas11, p. 14539; Rei06, p. 4; Str08, p. 22].
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6 Fuel cell The data used come from scientific publications in the field, as well as some target values communicated by the US Department of Energy [DOE12].The latter also frequently serve as a cited reference in scientific works, so it is not rare for a "circular reference" of information on technical characteristics of fuel cell systems, to occur in scientific works. The availability and validity of forecasts on future developments is very limited. The physical quantities of fuel cell system are depending to a large extent on the particular system design and can be difficult to generalize. Two quantities are nevertheless viewed as characteristic values at the level of vehicle concept design:
Specific output based on the fuel cell system [Eic10, p 227; Dil05, p.73] in kW/kg
System efficiency at the nominal operating point
The forecasts published by the US Department of Energy (DOE) show merely technologyindependent target values. Since the supporting points of the DOE forecasts don't show improvement in the above mentioned parameters after the year 2020, a saturation of the two target quantities is assumed. More detailed statements require constant observation of the actual industrial development of fuel cell technology for high-volume production automotive applications, also in the coming years [DOE12, p. 3.4-17].
Specific output based on the fuel cell system
kW/kg
0.40 – 0.65
System efficiency at the nominal operating point
-
0.50 – 0.60
The polymer electrolyte membrane fuel cell (PEM, including: Proton Exchange Membrane Fuel Cell) is considered to be the favourite option for automotive use, among the different models. The research and development activities of the automotive and supplier industry focus to a large extent on this type.
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7 Transmission The transmission of an electric vehicle is much simpler than that of a conventional vehicle. In most cases it cannot be shifted and has no clutch. The installation of the drive machine is always axially parallel or concentric to the drive axle, so that no angular gearbox is required. In this paper, the considerations are limited to axially parallel installation, because this is by far the most common. The gear ratio is, depending on the machine type and wheel dimensions, in the range of 10. For acoustic reasons, a two-stage spur gearbox is therefore mostly used. In the concept phase, the three characteristics mass, efficiency and costs are of interest. The rotational inertia of the two spur gear stages is neglected because of its low impact, as compared to the inertia of the comparably heavy wheels and the inertia of the high-speed rotor of the drive machine. The modelling of the mass is described in [Fuc14a], that of the costs in [Koc14], so that this paper covers only the efficiency. The occurring losses can be grouped [Lin00, p.387] into gearing losses, bearing losses, seal losses, and other losses such as the splashing of oil. While gearing losses and bearing losses scale with speed and load, seal losses and losses due to oil splashing are only speed-dependent. To break down the individual losses accurately, they either have to be measured on the existing transmission or be calculated based on the geometry and material data. For an estimate of the total power loss in the concept phase, a comparison with existing transmissions of the same design can be drawn. Table 7.1 shows the mechanical efficiency of an electric powertrain with 30 kW "peak" power and two-stage gearbox at different operating points. The values for the transmission efficiency derived from the simulation model featured in [Hoe12] .In contrast to the cited transmission model, there is a lower gearing quality assumed here, which corresponds more to the current state of technology. This impairs the efficiency by 2%. In addition, a percent efficiency is being calculated for the losses occurring in the constant velocity joints of the driveshafts. By linear interpolation between the support points, this efficiency characteristic map can be used to determine the total vehicle energy consumption in a longitudinal dynamics simulation. Although the efficiency strongly declines at high speeds and low loads, this has hardly any influence on the energy balance, due to the low transmitted power. With 30 kW of power, this example represents the lower limit of the design spectrum. Because economies of scale lead to efficiency being generally better in larger transmission, the mentioned values can be used as a conservative estimate. Table 7.1: Characteristics map of the mechanical efficiency of an electrical powertrain (transmission and driveshaft losses taken into account, wheel bearings disregarded)
Torque in % from mmax
Speed in % from nmax
According to [Hoe12]
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8 Aerodynamics According to [Bra13, p.54] the air resistance of a car can be calculated by equation (8.1): 1 2
𝐹L = 𝜌L 𝑐w 𝐴St 𝑣 2.
8–1
In the concept phase, the end face 𝐴St and the 𝑐w value are usually not yet known. To be nevertheless able to make statements about future energy consumption, these values have to be estimated. For the 𝑐w value, an empirical model of [Fuc14, p.53] is used. In case of this model, the 𝑐w value is linearly correlated with the vehicle length .For each of the construction types hatchback, sedan and fastback there are correlation formulas used: cwSteilheck = 𝑃1 ⋅ 𝐿103 + 𝑃2,
8–2
cwLimousine = 𝑃3 ⋅ 𝐿103 + 𝑃4 und
8–3
𝑐wSchrägheck = 𝑃5 ⋅ 𝐿103 + 𝑃6,
8–4
with 𝐿103 = vehicle length in m. The printed equations are each valid for a windscreen angle of 40 °.In case of a different angle a corrected value [Fuc13] is calculated with the help of 8–5 𝑐wkorrigiert = 𝑐𝑤 (𝛼 𝑃7 + 𝑃8)
P 1 to P 8 are to be taken from the publications [Fuc14, p.53] and [Fuc13] and are in addition filed in the Annex. The improvement of the 𝑐w -value, due to lower engine compartment and brakes flow, in electric vehicles, is taken into consideration by [Fuc13] through a correction factor of 0.9 based on [Bos10, p 857]. According to [Hak11 p.153] the end face can be approximated from the vehicle width, the vehicle height, and a factor which takes into consideration ground clearance, tyre width, lateral roof indentation and the vehicle's tail: 𝐴 ≈ 0,81 ⋅ 𝑊103 ⋅ 𝐻100
8–6
with W 103 = vehicle width in m and H 100 = vehicle height in m. This assessment may be replaced by an exact value once geometry data of the vehicle are present.
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9 Wheels/Tyres With simulation models for tyres, different tyre properties can be mapped. These are, for example, models for adhesion, slip, rolling resistance, wear, noise emissions or inertial properties. Adhesion and slip properties play a crucial role in situations of danger, but can be neglected when considering the energy consumption, because the time portion of these situations is negligible. The calculation of the noise emissions for the accounting of energy consumption is not required. All these properties change over the service life of the tyres. Taking into account the influence of tyre wear on the rolling resistance in the overall energy consumption would be desirable, however, is usually not possible, due to lack of underlying data. The most important factor influencing the energy consumption is the rolling resistance. The rolling resistance force FR is according to [Bra13, p.50]: 𝐹𝑅 = 𝐶RR 𝑚 𝑔.
9–1
The rolling resistance coefficient CRR is dependent on the rubber compound and construction of the tyre, as well as the operating conditions. These include the contact force, the tyre pressure, the ambient temperature and the driving speed. According to ISO-standard referred to [ISO09] is the tyre rolling resistance usually calculated for 80% of the maximum contact force, a tyre pressure of 2.1 bar, measured at an ambient temperature of 25 ° C and a constant speed of 80 km/h. If the rolling resistance is required for other operating conditions, it can be calculated using the empirical formula suggested in [ISO09]: 𝑝 𝛼 𝑍 𝛽 𝐶RR = 𝐶RR,iso ( ) ( ) . 𝑝iso 𝑍iso
9–2
Figure 4 shows according to [Bra13, p.50] the velocity dependence of the rolling resistance coefficient.
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Rolling resistance coefficient f
Speed v Figure 4: rolling resistance coefficient as a function of vehicle speed for different tyres
The velocity dependence is not modelled in this paper for two reasons. The design relevant driving cycles like the NEDC [EEC 70 p.]772ff], FTP-72 [Bar 09 p.31], FTP-75 [Bar 09 p.32] or the Artemis urban cycle [Bar 09 p.129] are mostly in a speed range below 100 km/h, in which the rolling resistance coefficient is usually approximately constant .The additional modelling effort would not lead to appreciably better results. The second reason is the lack of underlying data, as is the case with tyre wear. Since November 1st, 2012 tyre manufacturers must display an energy efficiency label for each tyre, according to the stipulations of the EU regulation on the labelling of tyres [Rat09].The fuel efficiency class of a tyre allows conclusions to be drawn upon its rolling resistance coefficient [Rat09 p51]. Table 9.1 shows the state of the art with respect to energy efficiency, for the manufacturers Bridgestone, Continental and Michelin. Table 9.1: Tyres database Name
Dimension
Mass tyres & wheels in kg
Moment of inertia in kg m2
Rolling resistance coefficient in kg/t
Rough calculation according to formula 9.4
Based on these reference tyres, a value of 6.5 kg/t is set as a realistic rolling resistance coefficient for the conception of future electric vehicles.
17
The specified rolling resistance coefficient corresponds to the value that has been measured in accordance with precisely defined operating conditions according to ISO standard. This also stipulates that the tire is warmed up on the test stand for at least 30 minutes. During this time it is ensured that the operating temperature of the tyre is achieved in the measurement. Only if this is the case, does the rolling resistance achieve its minimal, constant value. Thus it can be assumed that the tyre adopts a higher rolling resistance coefficient during warm-up. This would then, for instance, also apply if the NEDC is gone through. In order to take the transient effects of the rolling resistance into account, a thermal rolling resistance model as in [Fic15] can be used. In addition to the rolling resistance, the inertial properties of the wheel are passed on into energy consumption during the acceleration phases. [Fuc14, p.39] derives a correlation of the wheel mass 𝑚Rad with the wheel diameter 𝐷Radand the tyre width𝑏Reifen : 𝑚Rad = 𝑃9 𝐷Rad 𝑏Reifen + 𝑃10.
9–3
The parameters 𝑃9and 𝑃10are to be taken from [Fuc14, p.39] and are also printed in the appendix. A distinction between steel and aluminium wheel is not carried out due to the usually negligible weight difference. Because wheels whose are rotating components, their rotational inertia must also be taken into account. The analytical calculation of it can be performed as described in [Wie12] with the assumption that 100% of the wheel mass is spread around the circumference. Since this is not the case in reality, but also there isn't any reference data available, the assumption is made that 80% of the mass are spread on the shell surface and the remaining 20% are distributed homogeneously on the cylinder volume. The moment of inertia 𝐽Rad the wheel is then 2 𝐽Rad = 𝑚Rad 𝑟Rad (0,8 +
0,2 ). 2
9–4
18
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Kunze, C.: Crycomp. In: National Innovation Programme for Hydrogen and Fuel Cell Technology - Assembly, Berlin, 2011
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Lamm, A.: "Entwicklungen auf dem Batteriesektor aus Sicht eines Automobilherstellers" [Changes in the battery sector from the perspective of an auto-mobile manufacturer], presentation, May 2012
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Lienkamp, M.: "Fahrzeugkonzepte: Entwicklung und Simulation" [Vehicle concepts: development and simulation]. Garching, Technical University of Munich, Department of Vehicle Engineering, lecture notes, 2012
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Linke, H.: "Stirnradverzahnung" [Spur gear teeth). 2nd revised edition, Carl Hanser Verlag Munich Vienna, ISBN 978-3-446-41464-8, 2000
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Lindemann, U.: "Methodische Entwicklung technischer Produkte" [Methodological development of technical products], 3rd edition, Berlin, Springer, ISBN 978‑3‑642‑01422‑2, 2009
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21
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22
11 Appendix P 1 = - 2,49 ⋅ 10-5/m P 2 = 0,42 P 3 = - 2,93 ⋅ 10-5/m P 4 = 0,41 P 5 = - 3,94 ⋅ 10-5/m P 6 = 0,44 P 7 = 0,0013/deg P 8 = 0,9479 P 9 = 2,764 ⋅ 10-4 kg/m2 P 10 = - 4,682 ⋅ 10-1 kg
23
12 Quantities 𝑏Reifen 𝐶RR 𝐶RR,iso
Unit m2 mm -
𝑐w 𝐷Rad 𝐸 𝐹B 𝐹L 𝐹R 𝐹R,iso 𝐹St 𝐹X 𝑔 𝐽Rad 𝐻 𝐻𝑢 𝐿 𝑚Fzg 𝑚Rad 𝑃 𝑝 𝑝 𝑝iso 𝑅 𝑟Rad 𝑠 𝑣 𝑊 𝑍 𝑍iso 𝛼 𝛼 𝛽 𝜌L
mm J N N N N N N m/s² kg/m² mm kWh/kg mm Kg Kg 1/mm, bar bar Ω mm m/s mm N N ° kg/m3
𝐴St
Frontal Area Tyre Width Rolling Resistance Coefficient ISO- Rolling Resistance Coefficient Drag Coefficient Wheel Diameter Energy Content Intertial Force Aerodynamic Drag Force Rolling Resistance Force ISO- Rolling Resistance Force Downhill Force Traction Force Gravity Acceleration Tyre Inertia Height Lower Heat Value Length Vehicle Mass Wheel Mass Correlation Values Cells in Parallel Tyre Pressure ISO- Tyre Pressure Electrical Resistance Wheel Radius Cells in Series Velocity Width Tyre Load ISO- Tyre Load Windscreen Angle Tyre Specific Constant Tyre Specific Constant Air Density
24
