*Article* **On the Impact of Maximum Speed on the Power Density of Electromechanical Powertrains**

#### **Daniel Schweigert 1,\*, Martin Enno Gerlach 2, Alexander Ho**ff**mann 2, Bernd Morhard 1, Alexander Tripps 1, Thomas Lohner 1, Michael Otto 1, Bernd Ponick <sup>2</sup> and Karsten Stahl <sup>1</sup>**


Received: 30 May 2020; Accepted: 17 June 2020; Published: 25 June 2020

**Abstract:** In order to achieve the European Commission's ambitious climate targets by 2030, BEVs (Battery Electric Vehicles) manufacturers are faced with the challenge of producing more efficient and ecological products. The electromechanical powertrain plays a key role in the efficiency of BEVs, which is why the design parameters in the development phase of electromechanical powertrains must be chosen carefully. One of the central design parameters is the maximum speed of the electric machines and the gear ratio of the connected transmissions. Due to the relationship between speed and torque, it is possible to design more compact and lighter electric machines by increasing the speed at constant power. However, with higher speed of the electric machines, a higher gear ratio is required, which results in a larger and heavier transmission. This study therefore examines the influence of maximum speed on the power density of electromechanical powertrains. Electric machines and transmissions with different maximum speeds are designed with the state-of-the-art for a selected reference vehicle. The designs are then examined with regard to the power density of the overall powertrain system. Compared to the reference vehicle, the results of the study show a considerable potential for increasing the power density of electromechanical powertrains by increasing the maximum speed of the electric machines.

**Keywords:** E-Mobility; powertrain design; high-speed; electric machine design; transmission design; gearbox

#### **1. Introduction**

In 2011, the EU Commission for Energy, Climate change and Environment published ambitious plans for the future climate and energy policy framework. By 2030, greenhouse gas emissions have to be lowered by at least 40% in comparison to 1990. Furthermore, the energy efficiency of products should, at the same time, increase by at least 32.5%. Limit values for CO2 emissions of newly registered cars of each manufacturer are also part of this initiative. The average emissions of a manufacturer's fleet in 2021 must, for example, be lower than the limit of 95 grams of CO2 per 100 km [1]. If manufacturers exceed the limit values for CO2 emissions, they are expected to pay substantial fines. In order to achieve the ambitious goals, set for the protection of the environment and to avoid heavy fines, the mobility behavior has to change significantly.

The electrification of the automotive powertrain is expected to play an important role in this change. A combination of battery electric vehicles (BEVs) and electricity from renewable energy sources can enable a CO2 neutral and largely pollutant-free usage phase and thus make a significant

contribution to reducing greenhouse gas emissions in the future. Furthermore, the tank-to-wheel efficiency of electromechanical powertrains in BEVs, which is significantly higher than that of internal combustion engines (ICE), is intended to make a contribution to the increase of efficiency of mobility [1].

The electromechanical powertrain of a BEV typically consists of power electronics, a drive motor or electric machine and a transmission. While the power electronics are responsible for the conversion of electrical power to control the electric motor, the transmission's gear ratio is used to adapt the electric machine's speed and torque to the required values at the drive axle. An important parameter in the design process of an electromechanical powertrain is the maximum speed of the electric machines in combination with the gear ratio of the transmission to reach the desired maximum speed of the vehicle. A higher speed of the electric machine leads to a lower required torque at constant power, which means that more compact and lighter electric machines can be designed. However, a transmission with an increased input speed needs a higher gear ratio to reach the same output speed and must therefore be designed larger and heavier. Nevertheless, there is a trend towards increasing speeds of electric machines in a BEV. The positive influence of increased speeds of the electric machine on the power density of the whole powertrain has been proven in various studies [2,3]. This positive influence may play an important role in the achievement of ultimate efficiency and climate goals by 2030.

This study presents a detailed analysis of the influence of maximum speed of the electric machine on the power density of an electromechanical powertrain. For this purpose, conceptual designs of electric machines with various maximum speeds and transmissions with suitable overall gear ratios have been developed. The considered speeds are set from *n* = 12, 000 min−<sup>1</sup> to *n* = 50, 000 min<sup>−</sup>1. While the speed increases and thus the torque of the electric machines decreases, the gear ratio has to increase to remain a constant output torque and vehicle speed. These boundary conditions are based on the parameters of the BMW i3 (120Ah) as reference vehicle. Table 1 shows the parameters of the electric machine and transmission relevant for this study. The voltage level of the battery is increased to satisfy the demands of the high-speed electric machine.


**Table 1.** Relevant parameters and view of the BMW i3 reference vehicle (120Ah). Data from [4].

The electric machine of the reference vehicle is designed as a permanent magnet synchronous machine (PMSM) with a rated power of 75 kW and a peak power of 135 kW. Furthermore, the electric machine has a rated torque of 150 Nm and a peak torque of 250 Nm and reaches a maximum speed of 11,400 1/min. The gear ratio determines the corresponding parameters on the drive axle. All of the designed electric machines and transmissions for every considered maximum speed and overall gear ratio result in a large number of electromechanical powertrains. All of these designs represent potential drivetrains for the reference vehicle and will be analyzed with regard to mass, volume, volumetric and gravimetric power density. This is intended to make a statement regarding the potential of increase of the maximum speed in electromechanically powertrains to increase power density.

After applying the state of the art to design parameters of high-speed electric machines and transmissions in Sections 2–4 present the conceptual design process of the electric machines and transmissions used in this study. The results of the study will be shown in Section 5, followed by a discussion and an outlook of the results in Section 6.

#### **2. State of the Art Considerations for Higher Shaft Speeds**

The following section will cover the key aspects of current developments in the field of electrical machines and transmissions with regard to high speeds. After discussing the current technological driver in this field, this section will close with a summary of current and future generation powertrains.

#### *2.1. Electric Machines*

In the context of electrical machines, the term high-speed refers to the surface speed of the rotor *vs* and not to the synchronous shaft speed

$$m\_0 = \frac{f\_1}{p},\tag{1}$$

where *f*<sup>1</sup> is the fundamental electric stator frequency and *p* is the number of pole pairs. It is therefore important to understand the relation

$$
v\_{\text{rot}} = 2\pi r\_{0,2} n\_{\prime} \tag{2}$$

where *ro*,2 is the outer radius of the rotor, because the surface speed *v*rot is in fact the variable on which the mechanical boundaries depend in the first place. The variable on which the electrical boundaries depend in the first place is the fundamental electric stator frequency *f*1. With the importance of these two quantities in mind, subjects such as rotor topologies, winding technologies and materials will be discussed in the context of PMSMs [5].

#### 2.1.1. Rotor Topologies

Rotors for PMSMs are subdivided into two categories, surface type rotors and interior type rotors. The definition is based on the location of the permanent magnet relative to the outer contour of the rotor iron, as shown in Figure 1. Depending on the desired maximum surface speed, surface PM rotors are preferable to interior PM rotors [6].

**Figure 1.** Two different rotor topologies for PMSMs.

The mechanical stresses introduced on the rotor iron due to rotation are proportional to the square of the rotational speed and the square of the outer radius *ro*,2. Due to this strongly non-linear relationship, the mechanical stress on the rotor iron requires special consideration. The introduction of so-called pockets for the permanent magnets has the consequence of weakening the material, which further increases the mechanical stresses [7]. For fast rotating electric machines, it is common to reinforce the rotor with a so-called bandage or sleeve. Such reinforcement is applied on the outer radius and prevents the expansion of the rotating rotor. The insertion of a bandage thus has the consequence of increasing the magnetically effective air gap. A larger magnetic air gap acts like an increased magnetic resistance and reduces the magnetic flux, which has an influence on a number of important parameters of the electric machine. The use of a bandage must therefore be weighed against other possibilities and the influence on all requirements must be checked. This includes the selection of the bandage itself. Different materials will be discussed in a later section. Decisions are usually made by evaluating results from finite element simulations [8].

#### 2.1.2. Rotor Materials

To go into more detail, an overview of materials is presented for the three basic components (besides the shaft) of a PMSM rotor, electrical steel sheets, permanent magnets and bandage material. An example for a high-speed PMSM rotor is shown in Figure 2.

**Figure 2.** Exploded view of an PMSM rotor assembly.

#### 2.1.3. Electrical Steel Sheets

While industrially used induction machines usually have a laminated rotor, PMSMs do not require a laminated rotor. However, the use of electric sheet metal has a positive effect on the losses of the rotor due to eddy currents and therefor on the rotor temperature. Electrical steel is the most common material seen in electrical machines; with increasing demands on efficiency and power density, electrical steel with cobalt is gaining interest. However, the cost of cobalt electrical steel is considerably higher. High strength steel is particularly interesting for the rotors electrical machines with high speeds [9]. The yield strength of such sheets is higher than that of electrical steel sheets but returns less favorable magnetic properties. Recent developments in electrical steel have resulted in high-strength electrical steel, which aims to close the gap between conventional electrical steel and structural optimized steel [10].

#### 2.1.4. Permanent Magnets

In addition to the different materials for permanent magnets (AlNiCo, NdFeB and SmCo), a variety of different segmentation strategies exist. Segmentation of permanent magnets is performed in order to reduce eddy currents inside of the permanent magnets and to avoid overheating of the rotor assembly [11]. If the rotor in a PMSM reaches unconsidered temperatures, a loss of torque at the shaft

and permanent damage due to demagnetization can occur. Currently, permanent magnet segmentation can be performed with a layer thickness of as low as 500 μm in thickness and a <20 μm insulation between the layers [12]. In general, segmentation can be in axial or in tangential direction of the rotor. The selection of suitable permanent magnet shapes and the placement within the rotor are most often aided by magnetostatic simulations using the finite-element-method [13].

#### 2.1.5. Sleeve and Bandage Materials

Materials for sleeves and bandages can be differentiated into steel-based sleeves and composite-based sleeves. Materials for steel sleeves are high strength steels with alloying elements such as chromium, molybdenum and nickel. For steel-based sleeves, the highest tensile strength is given at 700 N/mm2 for 2.461 NiMo16Cr16Ti; in comparison, the well-known 1.7225 42CrMo4 achieves a tensile strength of 550 N/mm2 according to the manufacturer's data [14,15]. Both have a good strength to weight ratio and are considerably stronger and harder than standard steels. A side-by-side comparison of the values for tensile strength, density and electrical resistivity shows that the composite-based sleeves are more suitable for high-speed electrical machines than sleeves made of steel. It should be said, that the properties of the fiber and the finished composite sleeve depend heavily on the fabrication process. Therefore, the given data in Table 2 is for bare fiber and is presented to provide a starting point for further analysis.

**Table 2.** Bare fibers for composite-based sleeve materials. Data from [16].


#### 2.1.6. Winding Technologies

In the field of traction motors, two different types of distributed windings can be observed for electrical machines. The random winding, consisting of randomly distributed round shaped conductors, and the form wound winding, which is composed of so-called hairpins. Hairpins in the context of windings are solid copper conductors with rectangular shape, are formed into the shape of a conventional hairpin by bending. By connecting several hairpins trough welding, the actual winding is created. Hairpin windings are favored by car manufacturers because the manufacturing process can be fully automated [17]. But this does not mean that all traction motors for electric cars are equipped with hairpin windings. Both winding technologies are still on the market. In the context of high-speed electric machines, hairpin windings have concrete disadvantages. The cross-sectional area of a hairpin must not fall below a certain value, otherwise processing becomes more difficult. Since the winding resistance has a great influence on efficiency, and since the phase current in high-speed electrical machines can reach higher frequencies than in conventional designs, the frequency dependence of the winding resistance has to be considered for the selection of the winding technology. Finally, Figure 3 shows an example of the phase resistance for the two mentioned winding technologies as a function of frequency. The displayed data is acquired via direct measurements at electrical machines. It can be seen that the resistance of the hairpin wound winding is already greater by a factor of 10 at a frequency of 1000 Hz due to current displacement effects. This factor has a direct linear effect on the power loss in the winding [18].

**Figure 3.** Comparison of the phase resistance of a hairpin winding with a conductor diameter of 0.5 mm and a random wound winding with a conductor width of 3.2 mm and a height of 1.6 mm (Phase resistance is related to DC resistance).

#### *2.2. Technologies for High-Speed Transmissions*

High-speed electromechanical powertrains as scope of recent research history [19–24] promise an increased power density of the whole powertrain. Indeed, the required torque and speed at the wheels cause the transmission to be designed with a higher total gear ratio that on the first glance causes increased weight, installation space and cost of the transmission itself. Still, the conglomerate of high-speed electrical machines and high-speed transmissions is able to demonstrate its benefits. To meet the high-level requirements of BEVs concerning range, comfort and operability new technologies have to support and enable transmissions to operate within this high-speed approach.

#### 2.2.1. Improved Efficiency for Maximized Range

As the available range of BEVs is reduced by the power losses of the whole powertrain, the efficiency of the powertrain in general and of the transmission in particular is of prime importance. The power loss of a transmission and hence the efficiency is determined by gear power losses, bearing power losses, sealing power losses and other power losses, e.g., caused by oil pumps. Both, gear power losses and bearing power losses are separated into load-dependent and no-load power losses. In order to reduce the power losses of the transmission, and more precisely the load-dependent gear power losses, low-loss gear geometries and water-containing gear fluids with coefficients of friction smaller than 0.01 [25] (which is referred to as superlubricity [26]) can be used in electromechanical powertrains. As both technologies reduce the frictional losses, they can also be seen as a compensation for the rising sliding speeds with higher input speeds, usually causing a higher risk of scuffing. The low-loss gear geometry concentrates the path of contact to a minimum around the pitch point. As sliding speed rises with increasing distance to the pitch point, high sliding speeds are avoided this way, resulting in reduced load-dependent gear power losses [27]. Hinterstoisser et al. [28] outline in experiments the significant impact of the low-loss gear geometry on the efficiency. With an extreme low-loss gear design, the power losses can be reduced by about 79% compared to a conventional gear design. In order to reduce the mean gear coefficient of friction, water-containing gear fluids promise a significant improvement of the efficiency. Yilmaz et al. [29] demonstrate on the FZG gear efficiency test rig the reduction of the mean gear coefficient of friction and hence of the load-dependent gear power losses by water-containing fluids (cf. Figure 4). Using those fluids, the mean gear coefficient of friction is reduced by up to 82%.

**Figure 4.** Mean gear coefficient of friction μmz determined on the FZG gear efficiency test rig at a load pC of 1723 N/mm<sup>2</sup> for a mineral oil (MIN), polyalphaolefine oils (PAO) and water-containing polyalkylenglycols (PAGW) according to Yilmaz et al. [25].

Concerning bearings, investigations with water-containing gear fluids on the FZG bearing power loss test rig show reduced no-load bearing losses and increased load-dependent bearing losses with higher rotational speeds of roller bearings [30] which additionally supports the approach of high speeds and low loads on the input of high-speed transmissions. The authors mention that hybrid bearings with Si3N4 ceramic cylindrical rollers, cronidur races, and polyether ether ketone (PEEK) cages were used to avoid incompatibilities with the investigated water-containing gear fluids [30]. As the presence of hydrogen is suspected to cause white edge cracks (WECs), or at least to support its formation, causing premature failure of the bearings [31–33], WECs have to be considered when using water-containing fluids. As the water content strongly improves its caloric properties, water-containing gear fluids are possible to use as coolant. By this, the whole powertrain including power electronics, electrical machines and the transmission can be cooled and lubricated by one circuit. This holistic thermal management promises further improvement of efficiency of the powertrain as e.g., injection lubrication in the transmission can be used without additional oil pumps.

#### 2.2.2. Improved Acoustics for Increased Comfort

As the internal combustion engine is cut in BEVs, its masking sound is not present anymore. Consequently, the customer faces noise of the transmission in BEVs which can be felt as uncomfortable, particularly because of its tonal character. Furthermore, in comparison to conventional powertrains in ICE, the drive speeds are already higher in BEV series solutions, which leads to new spectral compositions of the noise emissions. In particular, the high-frequency components of the spectrum can be perceived as disturbing by the human ear. The increase in speed in comparison to BEV series solutions, which is carried out in the context of this study to achieve higher power densities, further aggravates this problem [34].

In addition, increasing speeds make it more difficult to operate the transmission subcritically over the entire operating range. The subcritical operating range is the range with a mesh frequency f lower than the torsional natural frequency *fn* of the meshing. Especially in the critical operating range with reference speeds (*f*/ *fn*) from 0.85 to 1.15, significant additional dynamic forces and thus vibrations and noise emissions occur in the meshing, as stated in Figure 5. Therefore, the critical operating range is typically avoided in ICE by operating the transmission in the subcritical range with low dynamic forces [31,35,36].

**Figure 5.** Dynamic factor as a function of resonance ratio.

In case of the first stage of the high speed transmissions of this study, subcritical operating will not be possible over the entire operating range with increasing speed of the electric machines. Hence, special precautions are needed to optimize the acoustical behavior of high-speed transmissions. The basis for this optimization is a precise knowledge of acoustically critical operating ranges of all meshes. For powertrains with double-e-architectures, this knowledge can be used to split the required power and torque between two non-identical power-paths and therefore avoid those areas. If there is only one power path available, resonance areas should be positioned in an area which can be passed [35].

#### 2.2.3. Operability of High-Speed Transmission

The high circumferential speeds caused by the high rotational speeds on the rotor and input shaft cause stricter requirements the bearings and sealings must fulfill in order to ensure the reliability needed.

That is why the bearings of the input shaft and the rotor of high-speed electrical machines need to be designed for high-speeds. The limiting speed of bearings is given by the speed factor ndm consisting of the maximum speed n [min<sup>−</sup>1] and the mean diameter of the bearing dm [mm]. In the work of Deiml et al. [37] it is mentioned that common SKF bearings are designed with a maximum speed factor of 0.7 <sup>×</sup> 106 mm/min, but for their high-speed approach sealed bearings with a speed factor of 1.6 <sup>×</sup> 106 were designed. Usually, spindle bearings (super precision angular ball bearings) according to DIN 628-1 [38] are used in machine tools, reaching highest rotational speeds. With oil lubrication, the bearing manufacturer SCHAEFFLER mentions that spindle bearings are suitable for a speed factor of up to over 3.0 <sup>×</sup> 106 mm/min [39]. The bearing manufacturer SKF outlines, that hybrid bearings with ceramic balls are superior to all steel bearings in terms of operating speed, as ceramic balls are lighter which causes reduced centrifugal forces leading to reduced losses and heat development [40].

To ensure the operability of the transmission fluid leakage and dirt entry via the input and output shaft have to be avoided by appropriate sealing. Rotary shaft lip seals according to ISO 6194-1 [41], as a part of contact seals and commonly used in automotive sector, operate at circumferential speeds beneath 40 m/s as the frictional losses cause unnecessary high temperatures harming those seals at higher speeds. Contactless seals like labyrinth seals overcome the limiting circumferential speeds as only negligible frictional losses are acting, enabling the operation at highest circumferential speeds [42]. In terms of sealing itself, contactless seals, being more precisely labyrinth seals, are disadvantageous as they are not able to completely seal the transmission, causing leakage [43]. In order to overcome these disadvantages, new sealing technologies have to be used within the high-speed approach. One promising sealing technology is the gas-lubricated mechanical face seal applied on transmissions. The working principle is that the primer ring and mating ring move apart at rotation of the shaft as a consequence of gas flow (usually air) caused by the aerodynamically optimized surface structure of the mating ring [44]. These seals are characterized by reduced frictional losses, enabling the operation at highest rotational speeds.

#### 2.2.4. Research on the High-Speed Transmission of Speed4E

In the joint research project Speed4E [45] a hyper-high-speed powertrain for electric vehicles is developed, designed, and investigated. The goals of Speed4E include the development of an innovative powertrain for BEVs with rotational speeds of the electrical machines of up to 50,000 min<sup>−</sup>1, the integration into a test vehicle, and a holistic thermal management based on a water-containing gear fluid also used for lubrication of the transmission. Different aspects are considered, such as efficiency optimization, mass and cost reduction as well as the power density increase by the high input speeds. In the transmission of the research project Speed4E among other things, the mentioned low-loss gear geometry, NVH-optimized gears, water-containing gear fluids, holistic thermal management, high-speed spindle and hybrid bearings as well as contactless, lifting seals are investigated with respect to input speeds.

#### *2.3. Series and Future Axle Drive Systems*

A survey on current single axle drive systems for personal BEV shows, that the peak power is around 150 kW and the peak speed is below *n* = 20, 000 min<sup>−</sup>1. Depending on which components are included in the axle drive system the weight is at around 80 kg. All shown drive systems in Table 3 aim for a high level of integration and combine the main major parts of a drive system: the electric machine, the inverter of power electronics and the transmission.


**Table 3.** Overview of current axle drive systems from automotive suppliers.

#### **3. Conceptual Design of High-Speed Electric Machines**

In this section, the design process is introduced for electric machines. Four machines with a rated power of *P*<sup>N</sup> = 75 kW and different maximum speeds are designed, as it can be seen in Table 4. The PMSM-B1 and PMSM-B2 machines have interior bar magnets and the PMSM-S1 and PMSM-S2 machines have surface mounted magnets with a bandage. The field weakening behavior of machines with interior magnets is better than with surface mounted magnets. Thus, the rated speed of the PMSM-B1 and PMSM-B2 machines is chosen smaller in relation to the maximum speed, than for the PMSM-S1 and PMSM-S2 machines. The geometry, mass, volume, volumetric and gravimetric power density are determined and presented later.


**Table 4.** Speeds and power requirements for the machine designs.

#### *3.1. Design Process of Active Parts*

To design an electric machine, different fundamental equations can be used to estimate the size and the geometry of the machine. Therefore, input parameters such as power, speed and voltage have to be provided and assumptions regarding certain machine parameters and boundary conditions have to be specified to start the design process.

Each machine is designed for one specific operating point in the torque speed diagram, i.e., the rated operation, as can be seen in Figure 6. In this case, this point is set to be the point of rated power *P*<sup>N</sup> and rated speed *n*<sup>N</sup> at which the machine's supply voltage *U*<sup>1</sup> reaches the maximum output voltage of the inverter *U*max and the maximum continuous torque *M*cont is provided. The machine's induced voltage

$$
\Box I\_1 \propto \Box w, \,\, \hat{\Phi} \,, \, n, \, p, \tag{3}
$$

which almost matches the supply voltage, is proportional to the magnetic flux φˆ, the speed *n*, the number of pole pairs *p* and the number of series turns per phase *w*. The torque is proportional to the torque-forming part *I*<sup>q</sup> of the current *I*1. Using the dq-plane, the current *I*<sup>1</sup> can be displayed as the q-axis current *I*<sup>q</sup> and the magnetizing d-axis current *I*<sup>d</sup> [50]. Since the induced voltage reaches the voltage limit *U*max, for speeds above the rated speed, the current *I*<sup>d</sup> is increased to provide field weakening and decrease the magnetic flux in the machine. Dividing the current *I*<sup>1</sup> by the number of parallel branches per phase *a*, the number of conductors per slot *z* and the conductors cross sectional area of copper *A*co, the current density

$$S\_1 = \frac{I\_1}{A\_{\rm co} \cdot a} \tag{4}$$

in the slot can be calculated [18]. Depending on the cooling system, the current density *S*1,cont at which the machine can be operated continuously and the maximum current density *S*1,max is given. The machine geometry is therefore mainly determined by the magnetic flux φˆ, the current density *S*1,cont, and the maximum voltage *U*max.

**Figure 6.** Schematic torque speed diagram.

The design process can be seen in Figure 7. First, the main dimensions of the machine such as bore diameter and length are specified. Then the electric quantities and the main parameters of the machine are calculated and determined. From thereon, the geometry of the lamination and the magnets is calculated, based on the magnetic circuit in the stator and the rotor lamination. The machine design is completed, specifying the winding quantities and the slot geometry. The design process of the machine is followed by a general design of the housing. Finally, the volume and mass of the housing and the machine are calculated and the volumetric and gravimetric power density are determined.

**Figure 7.** Design process of electric machines.

#### 3.1.1. Main Dimensions

The first step of the design process is a first assessment of the main dimensions of the machine. The bore diameter and the length determine the provided torque of the machine. The torque

$$T = \frac{2\pi}{8} \, d\_{i,1}^2 \, l\_1 \hat{B}\_{\text{mp}} \hat{A}\_p \tag{5}$$

is calculated using the spatial fundamental of the electric loading *A*ˆ*<sup>p</sup>* and the spatial fundamental of the magnetic flux density of the magnet in the rotor *B*ˆ mp [18]. Estimating these two quantities, *A*ˆ*<sup>p</sup>* and *B*ˆ mp, the bore volume

$$\frac{2\pi}{8}\,d\_{i,1}^2\,l\_i = \frac{P\_{\rm N}}{2\pi\,n\_{\rm m}\,\mathcal{B}\_{\rm mp}\mathcal{A}\_p} \tag{6}$$

can be calculated, if the rated power *P*<sup>N</sup> and speed *n*<sup>N</sup> are given. By setting the ratio of length and bore diameter to *li di*,1 = 1.3, the length and the diameter are determined. This ratio is set accordingly to other traction drives. The electric loading *A*ˆ*<sup>p</sup>* and magnetic flux density *B*ˆ mp are chosen according to the maximum speed, (cf. Table 4). For higher speeds, the electric loading *A*ˆ*<sup>p</sup>* is chosen smaller. The calculated lengths and diameters of the four machine designs are shown in Table 5.

The parameters need to be validated concerning their maximum surface velocity *v*rot. The PMSM-B1 and PMSM-B2 machine designs have interior magnets. Their surface velocity should not exceed *v*rot,max = 120 m/s [6]. The surface mounted magnets of PMSM-S1 and PMSM-S2 are kept by a bandage. The bandage leads to a bigger magnetic air gap, but allows to increase the maximum surface velocity to *v*rot,max = 250 m/s [5]. The air gap for the designs with interior magnets is assumed to be δ = 1 mm. For the PMSM-S1 surface mounted rotor, the bandage height is set to 2 mm and, for the PMSM-S2, the bandage height is set to 4 mm.

The surface velocity of the machine designs

$$
v\_{\rm rot} = 1.1 \cdot \pi \cdot n\_{\rm max} \cdot d\_{o,2} \tag{7}$$

is calculated for an overspeed of 10% of the maximum speed. The results for these machines are listed in Table 5 and do not exceed the limits of the surface velocity. The PMSM-B1 and PMSMS-S1 machine designs show low mechanical utilization compared to the limits. By increasing the bore radius and though the surface velocity, the machine would become larger and heavier.

**Table 5.** Main dimensions, electric loading and magnetic flux density of the magnet.


#### 3.1.2. Electric Quantities

To distinguish the rated current *I*<sup>N</sup> of the machine at rated power *P*N, the apparent power

$$S\_{\rm N} = \frac{P\_{\rm N}}{\eta\_{\rm N} \cdot \cos(\phi\_{\rm N})} \tag{8}$$

is calculated. The rated phase current

$$I\_{\rm N,str} = \frac{S\_{\rm N}}{m\_1 \cdot \mathcal{U}\_{\rm str,max}} \tag{9}$$

is then determined using the maximal phase voltage *U*str,max provided by the inverter. *m*<sup>1</sup> is the number of phases. To determine the current and the apparent power the efficiency η<sup>N</sup> and the power factor cos(φN) at rated operation must be assumed reasonably. In this case η<sup>N</sup> and cos(φN) are set to η<sup>N</sup> = 0.95 and cos(φN) = 0.9. With the maximum phase voltage of *U*str,max = 230 V, the rated current of *I*N,str = 127.67 A is calculated. The maximum current deliverable by the inverter is *I*max,str = 205 A.

The maximum operating frequency

$$f\_{\text{max}} = \frac{n\_{\text{max}}}{p} \tag{10}$$

is determined based on the number of pole pairs *p*. The number of pole pairs is kept small to keep the hysteresis and eddy current losses low. The number of stator slots *N*<sup>1</sup> is chosen to feature a high fundamental winding factor and a good compromise between reasonable slot dimensions and a low harmonic leakage factor. The resulting number of slots per pole and phase is accordingly set to *q* = 2. The pole pitch <sup>τ</sup>*<sup>p</sup>* <sup>=</sup> *di*,1<sup>π</sup> <sup>2</sup>*<sup>p</sup>* and the stator slot pitch <sup>τ</sup><sup>N</sup> <sup>=</sup> *di*,1<sup>π</sup> *<sup>N</sup>*<sup>1</sup> are then defined. The results are shown in Table 6.

**Table 6.** Electric quantities and main parameters.


#### 3.1.3. Magnetic Quantities and Geometry of the Magnetic Circuit

The geometry of the stator and the rotor lamination, as well as the magnet geometry, are initially based on the estimation of the magnetic flux density in the air gap *B*ˆp at rated speed and rated power. This flux density is defined by the coupling between the stator and rotor flux and is accordingly higher than the flux density just due to the magnet, that was defined in Section 3.1.1. This effect is higher for the machines with interior magnets since their air gap is much smaller than for the machines with surface mounted magnets. The assumptions of the flux density for the four designs can be seen in Table 7. The magnetic flux per pole

$$
\hat{\phi} = l \cdot \tau\_p \cdot \frac{2}{\pi} \cdot \mathcal{B}\_\mathbb{P} \tag{11}
$$

is calculated based on this assumption. By knowing the magnetic flux per pole, the tooth width and the height of the stator and the rotor yoke can be calculated by specifying the permissible magnetic flux density in the teeth *B*ˆt, in the stator yoke *B*ˆ y,1 and in the rotor yoke *B*ˆ y,1 for rated operation. These values are set different for the four machine designs. The machine designs with the lower operating frequency *f* can be operated with higher flux densities. This is due to eddy-current losses in the iron that depend on the flux density and the frequency. For higher speed, the permissible magnetic flux density should be set lower to limit the eddy-current losses. The chosen permissible magnetic flux is shown in Table 7. To determine the yoke height

$$h\_{\rm y,i} = \frac{\hat{\phi}}{\mathcal{B}\_{\rm y,i} \cdot l \cdot 2},\tag{12}$$

the magnetic flux must be divided by the length of the machine *l* the permitted magnetic flux density and a factor of 2, since the magnetic flux splits up in the two directions of the yoke [18]. The index i stands for either stator *i* = 1 or rotor *i* = 2.

The tooth width is calculated by multiplying the slot pitch with the ratio of the magnetic flux density in the air gap and the allowed magnetic flux density in the teeth as

$$w\_{\rm t,1} = \tau\_{\rm N} \frac{\hat{B}\_{\rm mp}}{\hat{B}\_{\rm t,1}}.\tag{13}$$

The results for the four machine designs are shown in Table 7.

**Table 7.** Magnetic quantities and geometry. Data from [18].


**Figure 8.** Schematic B-H and J-H diagram.

The size of the magnet, i.e., the width *w*m and the height *h*m, are set according to the flux density in the air gap and the *B*-*H* diagram of the magnet (cf. Figure 8) [50]. The flux density of the magnet in rated operation is determined from the estimated flux density in the air gap by

$$B\_{\rm m} = \frac{\vec{B}\_{\rm mp}}{\frac{\bf A}{\pi}}.\tag{14}$$

To take into account the drop of magnetic voltage in the iron, in comparison to the drop of voltage over the air gap, a saturation factor of *<sup>k</sup>*sat <sup>=</sup> *<sup>V</sup>*Fe+*V*<sup>δ</sup> *<sup>V</sup>*<sup>δ</sup> is defined and set to *<sup>k</sup>*sat = 1.6. To take into account the slotting of the stator, the carter factor *k*c is used. *k*c is set to 1.1 [18]. The magnetic motive force of the magnet

$$
\delta\theta\_{\rm m} = k\_{\rm sat} k\_{\rm c} \delta \frac{B\_{\rm m}}{\mu\_0} \tag{15}
$$

is calculated regarding these phenomena. The magnetic field strength of the magnet *H*m is determined from the *B*-*H* diagram of the magnet, as depicted in Figure 9. The height of the magnet is then defined by the magnetic motive force θ<sup>m</sup> and the determined magnetic field strength *H*<sup>m</sup>

$$h\_{\rm m} = \frac{\theta\_{\rm m}}{H\_{\rm m}}.\tag{16}$$

**Figure 9.** Machine geometry.

Since the machine shall be short-circuit-resistant, the height of the magnet needs to be validated after finalizing the winding configuration.

For a PMSM with interior magnets the width of the magnet

$$w\_{\rm m} = \sin\left(\frac{\pi}{2\,p}\right) d\_{\rm i,1} \cdot 0.85$$

is set to 85% of the side length of the equilateral triangle of one rotor pole pitch. For a PMSM with surface mounted magnets the width of the magnet is defined by the pole pitch

$$w\_{\mathfrak{m}} = \tau\_{\mathfrak{p}} = \frac{\pi \, d\_{\mathfrak{i},1}}{2 \, \mathfrak{p}}.\tag{18}$$

The bore diameter defines the magnetic flux in the machine and must be chosen accordingly.

Knowing the size of the magnet and the rotor yoke height, the rotor geometry can be completed. For a surface magnet rotor, the inner radius of the rotor is determined by

$$d\_{i,2} = d\_{o,2} - 2 \text{ h}\_{\text{m}} - 2 \text{ h}\_{y,2} \tag{19}$$

If the magnets are interior in a bar shape, the depth is considered by multiplying the magnet height by a factor β to determine the inner radius:

$$d\_{i,2} = d\_{o,2} - 2 \, \beta \, h\_{\text{m}} - 2 \, h\_{y,2}. \tag{20}$$

The factor is set to β = 3 for the machines with interior magnets. The magnet parameters are shown in Table 8.


#### **Table 8.** Magnetic quantities.

#### 3.1.4. Winding Quantities

The maximum number of series turns per phase is determined for the operating point at rated speed *n*<sup>N</sup> and rated power *P*N. The magnetic flux per pole φˆ at this point has already been estimated with the magnetic flux density in the air gap (see Equation (9)). Assuming the winding factor ξ*<sup>p</sup>* = 0.92 the maximum number of turns per phase

$$w\_{\rm calc} = \frac{\sqrt{2} \mathcal{U}\_{\rm str,max}}{2\pi \cdot n\_{\rm N} \cdot p \cdot \xi\_p \cdot \hat{\phi}} \tag{21}$$

can be calculated [18]. The number of turns can be achieved with different winding configurations. The number of conductors per slot *z*, the number of slots per pole and phase *q* and the number of parallel branches *a* determine the winding configuration and the winding layout. The number of series turns per phase is set by these winding parameters to

$$w = \frac{z \cdot q \cdot p}{a} \tag{22}$$

and should be close to the value determined. The chosen values for the winding quantities are listed in Table 9. This winding configuration also determines the previously estimated spatial fundamental of the electric loading, calculated by

$$\mathcal{A}\_p = \sqrt{2} \,\, \xi\_p \frac{m \, w \, I\_{\rm N,str}}{\pi \frac{d\_{i,1}}{2}}. \tag{23}$$

After setting the winding parameters, the geometry of the slot can be determined. The cross-sectional area of the conductors

$$A\_{\rm co} = \frac{I\_{\rm N,str}}{S\_{1,\rm cont}}\tag{24}$$

is calculated from the rated current *I*N,str and the current density *S*1,cont. The machines are supposed to have a water jacket. The current density is accordingly assumed at *S*1,cont = 12 A/mm2.

Depending on the type of winding and the manufacturing process, the copper fill factor *k*co must be estimated. In this case for an automated round wire winding, it is set to *k*co = 0.36 [50]. The area of the slot is then determined by

$$A\_{\rm slot} = z \frac{A\_{\rm co}}{k\_{\rm co}}.\tag{25}$$

In the case of a round wire winding, the slot can be designed as a trapezium. The width of the slot at the bore radius is set by the width of the tooth and the bore radius to

$$b\_{\text{slot, i}} = \frac{\pi \, d\_{i,1}}{N\_1} - b\_t. \tag{26}$$

The width of the slot at the bottom of the slot *b*slot,u and the corresponding slot height *h*slot are calculated with the relation

$$h\_{\text{slot}} = \frac{2 \cdot A\_{\text{slot}}}{(b\_{\text{slot}, \text{ } l} + b\_{\text{slot}, \mu})} \tag{27}$$

and the width of the trapezium at the bottom of the slot with

$$b\_{\rm slot,o} = \frac{2\pi \cdot r\_{\rm i,1} + 2 \,\, h\_{\rm slot}}{N\_1} - b\_{\rm t.} \tag{28}$$

Using the height of the slot, the outer radius of the stator is calculated as

$$d\_{\rm O,1} = d\_{\rm i,1} + 2 \, h\_{\rm slot} + 2 \, h\_{\rm I,V} \,. \tag{29}$$

#### **Table 9.** Winding configuration.


*Vehicles* **2020**, *2*

Finally, the design needs to be validated to determine if it is short-circuit-resistant. This is done by calculating the magnetic motive force

$$
\hat{\theta}\_{\text{sc}} = 4\pi \frac{m}{2} 4 \sqrt{2} \, I\_{\text{N,str}} \, w \frac{\xi\_{\text{w}}}{2p} \tag{30}
$$

in case of a sudden short circuit from rated operation occurs [51]. The calculation is based on the maximum short-circuit current. The winding attempts to keep the magnetic flux constant while the rotor keeps rotating. The short-circuit current is assumed to be 4 times the current at rated power. In the worst case, the magnetic flux is directed opposite to the magnetization direction of the magnet. The magnetic field strength of the winding, in case of the sudden short circuit, leads to a decrease of the magnetic polarization *J* of the magnet (cf. Figure 9). If the magnetic motive force of the winding is higher than the product of coercive field strength *H*cJ and the height of the magnet *h*m, the magnet will be demagnetized, leading to the requirement

$$h\_{\rm m} \geq \frac{\Theta\_{\rm sc}}{H\_{\rm cf}}.\tag{31}$$

The resulting heights of the magnets are listed in Table 10 for the four machine designs. All machine designs are short circuit resistant.

**Table 10.** Short circuit resistant magnet height.


The active parts, i.e., rotor and stator lamination, winding and magnets, of the machine designs are shown in Figure 10. It can be noticed, that the machine size decreases with increased maximum speed, as expected.

**Figure 10.** Final design of PMSM-B1, PMSM-B2, PMSM-S1 and PMSM-S2.

#### *3.2. Housing Design*

The housing consists of four components as depicted in Figure 11: The shaft, the water jacket and the two end shields. The components are designed as simple geometric bodies with dimensions set according to the machine designs.

**Figure 11.** Housing components.

The shaft and the water jacket are approximated as hollow cylinders. The inner diameter of the shaft is set to

$$d\_{\rm i,shaff} = \frac{d\_{\rm i,2}}{1.8}.\tag{32}$$

The outer diameter is equal to the inner diameter of the rotor. The inner diameter of the water jacket is set to the outer diameter of the stator and the outer diameter is approximated by

$$d\_{0,\mathcal{E}} = d\_{0,1} \cdot 1.1.\tag{33}$$

The length of the housing

$$l\_{\text{housäng}} = 1.5 \cdot l\_1 \tag{34}$$

includes space for the end windings and the winding protection of the machine. The housing is closed with the end shields, that are approximated as cylinders, on both sides. The outer diameter of the end shields is equal to the outer diameter of the water jacket and the height of the end shields is set to 20 mm.

#### *3.3. Electric Machine Design Results*

Finally, the volume and the mass of the housing and the machine are calculated. The volume of the components is determined based on the derived geometric quantities. The weight is calculated based on material densities, shown in Table 11.

**Table 11.** Volume of the machine designs and volumetric power density.


#### *Vehicles* **2020**, *2*

For the housing a weight of 60% of the housing weight is added, to consider additional components, i.e., bearings, retaining rings and screws. To calculate the volume of the winding and the winding protection, the end windings need to be considered. For the PMSM-S1 and the PMSM-S2 machine designs, the volume of the end winding and winding protection is assumed to be the same size, as in the active part. For the machine design PMSM-B1 and PMSM-B2, it is assumed to be 60% of the active part. The machine designs PMSM-S1 and PMSM-S2 have a larger end winding, due to the smaller number of pole pairs *p*.

The weight, the volume and the volumetric and gravimetric power density, in case of maximum power, of the four designs are listed in Table 12. The results are discussed in Section 5, together with the results of the transmission.



#### **4. Conceptual Design of High-Speed Transmissions**

After the introduction of the design process for the high-speed electric machines in Section 3, this section will give an overview of the design process for the associated high-speed transmissions. Like the electric machines, the transmissions are designed to match the reference vehicle's requirements for a rated power of 75 kW (cf. Table 1). In order to obtain comparable transmission designs, all systems feature the same speed and torque on the drive axle. The workflow in Figure 12 shows the design process for the transmission with the desired maximum input speed of the electric machine. After selecting the maximum speed, the necessary overall gear ratio follows directly by considering the data of the reference vehicle. The next step is the selection of the desired transmission configuration. This study considers two- and three-stage helical gear units and a combination of a planetary and helical gear set in axial parallel configurations. In the next steps, the wheel set of the transmission, including the gearings, wheel bodies, shafts and bearings is generated with the software GAP [52]. This program is able to generate transmission designs automatically and can additionally optimize the structure with regard to a large number of target variables [53]. In order to design the gearing, practical gear parameters are specified as optimization goals. To ensure comparability of the gearings, uniform target values were defined for safety factors in the load capacity calculation. The actual design of the toothing is carried out with the software STplus [54] in accordance with DIN ISO 6336 [55]. GAP also contains a structure generator for the rapid design of wheel bodies, shafts and bearings. After using the GAP structure generator, a draft of the wheel set is available that can be used to generate a model of the transmission housing. Finally, this process results in a complete concept of a transmission based on the selected configuration and overall gear ratio suitable for the reference vehicle. The following subsection will explain the individual steps of the design process in more detail.

**Figure 12.** Transmission design process.

#### *4.1. Calculation of Transmission Input Data*

The first step of the design process is the calculation of the required input data (power, speed and torque) of the transmission. In order to obtain comparable powertrains for the reference vehicle, the transmission output parameters (see Section 1) on the drive axle are kept constant. With the maximum speed on the drive axle *nmax*,*out* and the maximum speed of the considered electric machine *n*max, the required overall gear ratio *i* follows.

$$i = \frac{n\_{\text{max}}}{n\_{\text{max},out}}.\tag{35}$$

The overall gear ratio *i* of the transmission together with the known maximum torque of the reference vehicle on the drive axle *Tmax*,*out* lead to the maximum torque at the transmission input.

$$T\_{\text{max}} = \frac{T\_{\text{max},out}}{i}.\tag{36}$$

In addition to the peak parameters at the transmission input, the rated input parameters are important for the design process. The rated *Pn* power of the electric machines is 75 kW and can be used to calculate the rated torque of each transmission.

$$T\_n = \frac{P\_N}{2 \cdot \pi \cdot n\_N}.\tag{37}$$

Using these simple formulas, the required gear ratio and input torque can be determined for each considered input speed of the transmission.

#### *4.2. Transmission Configurations*

In the course of this study, three different transmission layouts in axial parallel configurations are considered. Figure 13 shows the transmission configurations, which are from left to right a two- (2ST) and three-stage (3ST) helical gear unit and a combination of a planetary and helical gear set (PLST). Helical gear sets with one stage are not considered, since the high gear ratios, which are considered in this study, lead to very high volumes. In case of the PLST, the first stage is the planetary gear set, since a planetary gear set on the drive axle would lead to complicated designs. Due to the small rotor diameter for higher speeds, a coaxial transmission configuration with a drive shaft guided through the rotor is not considered, as there would not be enough installation space.

**Figure 13.** Considered transmission configurations.

#### *4.3. Transmission Design with GAP*

After the selection of the transmission configuration, the next step is to design the transmission system using the GAP software. The software is suitable for the rapid generation of transmission designs including the gearings, shaft dimensioning and calculation of the bearing loads. It is possible to define target functions such as minimal mass, volume or maximum efficiency and load capacity to optimize the design [56]. Since the study focuses on the power density of the powertrain, the transmissions are optimized to reach minimal mass. Therefore, the first step of the actual design process is the splitting of the overall gear ratio *i* into the transmissions' partial gear ratios.

#### 4.3.1. Determination of the Transmissions Partial Gear Ratios

The overall gear ratio *i* of a transmission is generally made up of the transmission's stage gear ratios *ik*, which are in series. Bansemir [57] developed an approach with a parameterized power function for determining the stage gear ratios of the *kmax* stages, taking into account an exemplary shaft mass.

$$i\_k = a\_k \cdot i^{y\_k} \qquad\qquad\text{for } k < k\_{\text{max}} \tag{38}$$

$$\dot{\mathbf{a}}\_{k\_{\max}} = \frac{\dot{\mathbf{i}}}{\prod\_{k=1}^{k\_{\max}-1} \dot{\mathbf{i}}\_{k}} \tag{39}$$

The index *k* identifies the current number of the considered stage and *kmax* accordingly for the number of stages of the transmission. The parameters *ak* and *bk*, which control the splitting of the overall gear ratio into the stage gear ratios, are the result of an optimization for each transmission configuration and will be shown in Section 4.4.

#### 4.3.2. Gear Dimensioning and Design

With the partial gear ratios of the transmission, the actual design of the gearings are calculated with the STplus software [54]. This software includes the load capacity calculation according to DIN ISO 6336 [55] and additional content regarding the geometrical design and machining of spur gear stages. The starting point of the design process are uniform values of the safety factors for all transmissions

that lead to comparable gearing designs regarding the load carrying capacity. Table 13 shows the minimal safety factors for the load carrying capacity calculation. *SF*,*min* stands for the minimal safety factor against tooth root breakage, *SH*,*min* against pitting and *SB*,*min* represents the minimal required safety against scuffing. In addition to the safety factor that should be achieved, the considered load cases play an important role in gear dimensioning.

**Table 13.** Safety factors for the load carrying capacity calculation. **Safety Factors** *SF*,*min* 1.3

*SH*,*min* 1.1 *SB*,*min* 1.3


**Table 14.** Load cases for the gearing design.


To receive comparable gearing designs, uniform values for central gear parameters and other design parameters are also specified. Table 15 shows important design factors according to DIN ISO 6336 [55] and design targets for the gear design optimization. The dynamic factor *KV* considers additional forces in the tooth contact due to dynamic effects. The load factors *KH*<sup>α</sup> and *KH*<sup>β</sup> represent the influence of an uneven load distribution over the profile and width of the flank. Furthermore, in order to control the gear design process, design targets for the contact ratios εα and εβ as well as the width-to-diameter ratio b/d of the wheel bodies are defined. The selected design values are suitable for the practical preliminary design of gearings, but would have to be determined more precisely with higher-quality methods for detailed designs.

**Table 15.** Design factors and design targets for the gear design process.


#### 4.3.3. Structure Generator

To complete the transmission wheel set, the shafts, wheel bodies and bearing are generated in the next step. The shaft length follows from the numbers of bearings and wheel bodies, which are located on the shaft. Each element on the shaft is associated with an individual section. For these sections, an equivalent stress according to Niemann et al. [42] is calculated from the torsional and bending moments *T* and *Tb* to define the minimum shaft diameter *dV*,*a*,*min*(Equation (38). The allowable stress σ*b*,*all* is derived from the fatigue strength σ*<sup>w</sup>* of the material, which is 20MnCrS5 in case of the shafts.

$$d\_{V\rho,\min} = 2.17 \cdot \sqrt{\frac{T \cdot 1000 \cdot \sqrt{a\_b^2 + 0.4}}{\sigma\_{b\,\mu\text{ll}}}} \text{ with } a\_b = \frac{T\_b}{T} \quad \text{and} \quad \sigma\_{b\,\mu\text{ll}} = \frac{\sigma\_w}{S} \tag{40}$$

Furthermore, Parlow's [53] approach for designing a hollow shaft is used, which calculates the minimum outer diameter *dHW*,*a*,*min* and maximum inner diameter *dHW*,*i*,*min* to achieve the identical moment of resistance as the solid shaft. While the shafts of the spur gear sets are solid shafts, the design of the planetary gear set requires a hollow shaft for the planet carrier.

Figure 14 illustrates the simplified approach to determine the length of the transmissions' shafts. When calculating the shaft length, the input variables are the tooth widths *bw*, the distances between the wheel bodies *dww*, the distances between the wheel bodies and bearings *dwb* and bearing widths *bb*. The distances are fixed at a value of *dwb* = *dww* = 10 mm, the toothing widths *bw* are a result of the gear dimensioning and the bearing widths are changed depending on the torque at the specific shaft. Arrangements with a locating and a non- locating bearing, using a cylindrical roller and a deep groove ball bearing are used for all shafts. Since the loads on the output shafts are very similar for all transmission designs, a uniform bearing concept was chosen. The bearing sizes and weights of the remaining bearings were scaled from the design with the maximum input speed according to the torque and speed.

**Figure 14.** Schematic structure for definition of the shaft length.

Finally, the wheel body structures are calculated in the structure generator. Figure 15 shows the geometry of the wheel bodies. The geometry depends on the root diameter *df* and the tooth width *b* parameters, where the web width is *bs* = 0.25·*b*. The thickness of the gear rim follows the recommendations of the ISO6336 standard, in which a minimum ring gear thickness of three times the module *mn* is required. Therefore, the diameter results in *drim* = *df* − 6·*mn*. The hub geometry of the wheel body is defined by the inner and outer hub diameters *dih* and *doh* and the hub width, which is the tooth width. The inner hub diameter is equal to the outer shaft diameter, and the wheel hubs have a thickness of three times the module according to the procedure in case of the gear rim.

**Figure 15.** Schematic geometry of the wheel bodies.

4.3.4. Optimization of Transmission Design for Minimal Mass

With the conclusion of the structure generator, a first draft of a complete wheel set for the considered configuration and gear ratio is available. Since this study primarily looks at the power density of the system, the next step is to optimize the transmission to find an optimal design regarding systems minimal mass. The optimization used in the study is based on the simulated annealing algorithm [53,58], which is part of GAP and provides values for the parameters *ak* and *bk*; this is introduced in Section 4.4 for the splitting of the gear ratio. Table 16 shows the optimized factors in case of the three considered transmission configurations. In case of the PLST configuration, an additional requirement for a sufficient center distance was introduced to ensure the installation space for the drive axle.

**Table 16.** Parameters for splitting of overall gear ratio to reach minimal mass.


#### 4.3.5. Generation of Simplified Housing Geometry

Analogous to the design of the electric machines, the housing structure is also considered for the transmissions. To do this, an envelope curve is placed around the wheelset, the shaft angles being adjusted to reach a minimum base area of the housing. Figure 16 shows the base area of the considered three-stage configuration 3ST, which can be described by simple geometric shapes (circular sectors and trapezoid). When calculating the housing volume, a distance of at least 10 mm from all rotating components to the housing wall and a constant wall thickness of 5 mm is assumed.

**Figure 16.** Exemplarily generation of a simplified housing geometry for 3ST.

Considering the maximum axis angles without collision of wheel bodies, the shaft angles α and β were optimized for each transmission design to achieve a minimum base area of the housing and thus a minimum volume and mass. A common transmission-housing alloy, AlSi9, with a density of ρ*AlSi*<sup>9</sup> = 2.65 kg/dm<sup>3</sup> was assumed as material. In addition, stiffening structures and variable wall thicknesses of the housing are considered according to Linke [59] by a correction factor of *fh*= 1.5, which is multiplied with the housing mass derived from the described optimization.

#### *4.4. Transmission Design Results*

With the designed wheelset and the simplified housing geometry, the transmission design with the desired maximum input speed and gear ratio are finalized. An overview of the results of the masses and volumes of the designed transmissions is given in this section. Figure 17 shows the transmission masses of the three configurations and total gear ratios from 5 to 50 with the associated maximum speed of the electric machines. The PLST configuration shows the lowest transmission mass over the entire range of input speeds and gear ratios, whereby the mass increases with increasing gear ratios. As expected, ST3 has the largest overall transmission mass due to the additional shaft and wheel bodies, whereby a decreasing transmission mass with increasing gear ratio can be found. The reason for the decreasing mass in case of ST3 is the decreasing torque with increasing maximum speed of the electric machine and thus a smaller possible size of the gears and shafts. The ST2 configuration is between PLST and ST3, whereby ST2 becomes heavier than ST3 for gear ratios larger than i = 40.

**Figure 17.** Transmission masses for the three considered configurations over the gear ratio.

Figure 18 shows the resulting volumes of the three transmission configurations. Again, the PLST configuration achieves the lowest values for the entire values of the volumes for the entire evaluation range. In case of the two-stage ST2 configuration, the large required wheel diameters quickly lead to a large overall system volume. The three-stage ST3 configuration shows the smallest increase in volume with increasing gear ratios and its total is in between the compact PLST and larger ST2 configuration.

**Figure 18.** Transmission volume for the three considered configurations over the gear ratio.

#### **5. Merged Design of High-Speed Powertrain**

In this chapter, the results of the electric machine and transmission designs from Sections 3 and 4 are combined and presented. A total of four different electric machines with various maximum speeds but identical power values were designed, as described in Section 3. Analogously, suitable transmissions were designed in Section 4, which adapt the maximum speed of the electric machine with constant output parameters by adjusting the total gear ratio. In order to make a statement about characteristics of the whole powertrain, the transmissions that exactly match the designed electric machines were selected and combined. Through this procedure, twelve possible powertrain systems for the BMW i3 reference vehicle (cf. Chapter 1) will be presented, which differ in maximum speeds of the electric machine and transmission design. Based on these powertrain designs, the system is examined for total mass and volume and thus the power density of the electromechanical powertrain.

Figure 19 (left) shows the masses of the resulting powertrain designs over the gear ratio, respectively the maximum speed of the electric machines. The total masses show a clear decrease in powertrain mass for all transmission configurations. Since PLST achieves the lowest transmission masses, the powertrain system with this transmission configuration has the lowest overall mass, too. The increase of the maximum speed of the electric machines from 12,000 to 50,000 min−<sup>1</sup> reduces the weight for the PLST configuration from 55.0 to 32.4 kg, which is 22.6 kg or a mass reduction of 41.1%. In case of the two-stage 2ST configuration, the mass reduction is 24.2 kg from 63.4 to 39.2 kg or 38.2%, whereas for the three-stage 3ST configuration this is 27.1 kg from 66.7 to 39.6 kg or 40.7%. The weight of the electric machine is reduced by 57.6% from 44.1 to 18.7 kg by increasing the maximum speed of the electric machine. The diagram on the right in Figure 19 further clarifies the composition of the total mass from the electric machine and the transmission for the PLST configuration. It shows a significantly increasing share of the transmission mass in the total mass of the powertrain due to the rapidly decreasing weight of the electric machine. However, the transmission mass is not increased by the same extent as the weight of the electric machine is decreased, which makes it possible to strongly reduce the overall weight of the powertrain.

In addition to the powertrain design of this study, the diagram in Figure 20 (left) also shows the powertrain mass of the reference vehicle including the electric machine and transmission. The transmission of the reference vehicle has a gear ratio of 9.665 and a mass of 23.2 kg. Together with the electric machine, the reference powertrain achieves a total mass of 73.1 kg [60]. This value is close to the data point of this study with a gear ratio of 8.2.

Figure 20 shows similarly to Figure 19 the volumes of the powertrain designs with the four electric machines and the three different transmission configurations. Here, the increase of maximum speed from 12,000 to 50,000 min−<sup>1</sup> reduces the volume for the PLST configuration from 11.3 dm<sup>3</sup> to 9.2 dm3, which is 2.09 dm<sup>3</sup> or a reduction of 18.5%. In case of the two-stage 2ST configuration, the volume reduction results in 1.8 dm3 from 14.0 dm3 to 12.2 dm3 or 13.1%. The largest volume reduction can be found for the ST3 configuration with 3.3 dm<sup>3</sup> from 14.1 dm3 to 10.8 dm<sup>3</sup> or 23.6%. The volume of the electric machines decreases equivalently as the mass.

**Figure 19.** Powertrain masses (**left**) and its split into transmission and electric machine (**right**).

**Figure 20.** Powertrain volumes (**left**) and its split into transmission and electric machine (**right**).

In contrast to the total mass, the increase in the maximum speed from 30,000 to 50,000 min−<sup>1</sup> in the case of the PLST and ST2 configurations already shows an increasing total volume. The volume of these transmission configurations increases to a greater extent than the electric machine decreases its volume because of the large wheel diameters. While the share of the transmission mass for PLST in the total mass at 50,000 min−<sup>1</sup> is 42.3% (cf. Figure 20), the share for the volume is 62.3%, which is higher than the electric machine volume.

Figure 21 (left) shows the gravimetric power density of the powertrain designs and an increasing power density with increasing maximum speed of the electric machines in all three transmission configurations. Since PLST achieves the lowest masses, this configuration achieves the highest power density. The increasing difference between the PLST, ST2 and ST3 configurations, respectively with increasing gear ratio is due to the increasing share of the transmission mass to the total mass. In addition, the gravimetric power density of the reference vehicle's powertrain of 1.85 kW/kg is supplemented into the diagram. In comparison with the PLST configuration at maximum speed of 50,000 min<sup>−</sup>1, the gravimetric power density can be increased by 125.7% to 4.17 kW/kg.

**Figure 21.** Gravimetric power density of powertrain (**left**), electric machine and transmission (**right**).

Figure 21 (right) shows the evolution of the gravimetric power density of the electric machine and the transmission PLST with increasing gear ratio. While there is a large gap between the very high value for the transmission and the low value of the power density of the electric machine at a low gear ratio, this gap is becoming lower and the values converge with increasing gear ratio.

When looking at the results of the volumetric power density in Figure 22, the effect of the disproportionately increasing transmission volume becomes apparent. Even at a gear ratio of 21, which equals the maximum speed of 30,000 min<sup>−</sup>1, the electric machine has a higher volumetric power density than the transmission and expands the distance to the transmission with further increase of the maximum speed. Like in the case of the powertrain mass, the transmission shows higher volumetric power densities for lower gear ratios. A balanced ratio of the volumetric power density can be expected in the range of the overall gear ratio between 14 and 21.

**Figure 22.** Volumetric power density of powertrain (**left**), electric machine and transmission (**right**).

#### **6. Conclusions**

This study investigated the influence of maximum speed of the electric machine on the power density of electromechanical powertrains. For this purpose, powertrains with an electric machine and suitable transmission were designed for different maximum speeds of the electric machines. An increase in the speed of the electric machine results in a higher required gear ratio of the transmission to reach the same transmission output conditions. Four different electric machines with maximum speeds from 12,000 min−<sup>1</sup> to 50,000 min−<sup>1</sup> were designed. This defined four powertrain designs, which are completed by suitable transmissions with three different configurations. The machines and

transmissions were calculated based on conceptual design. Further investigations and adaptions may be necessary to meet all requirements of a detailed design.

The results of the powertrain designs show that the mass of the electric machines decrease significantly with increasing maximum speed. Contrarily, the mass of the transmissions increases, whereby the increase of mass is less than the reduction in mass for the electric machines. As a result, the gravimetric power density can be increased significantly by increasing the maximum speed of the electric machines. Compared to the reference vehicle, which has a maximum speed of 11,400 min<sup>−</sup>1, the gravimetric power density could be increased by 125.7% from 1.85 to 4.17 kW/kg by increasing the maximum speed up to 50,000 min<sup>−</sup>1. In addition to the mass, the volume of the powertrains can also be reduced, whereby the reduction is smaller due to a disproportionately increase of the transmission volume.

For both parameters, the gravimetric and volumetric power density, a convergent growth could be found. In case of the volumetric power density, a peak can be determined between 20,000 min−<sup>1</sup> and 30,000 min<sup>−</sup>1, while the peak of the gravimetric power density lies above the maximum speed of 50,000 min−<sup>1</sup> of the fastest electric machine considered in this study. The results of this study clearly show the potential of increasing both the gravimetric and volumetric power density of electromechanical powertrains significantly by increasing the maximum speed of the electric machine.

#### **7. Outlook**

In addition to the power density of electromechanical powertrains, there are other important parameters whose behavior for increasing maximum speed should be investigated in future studies.

The increasing speed limits the bore volume, due to mechanical stress in the rotor and bend critical speeds. Consequently, the output power of the machine is limited [5]. These limits have not been exceeded in the presented machines. Thus, the increase of the output power at high maximum speed will lead to a limitation in the power of the electric machine. Further investigation needs to be carried out to distinguish these limits. Furthermore, effects such as field weakening behavior in case of the electric machines or the manufacturing need to be discussed further on.

One crucial aspect in the design process of electromechanical powertrains is the efficiency behavior of the overall powertrain with increasing maximum speed that determines the size of the battery or the range of the car. In the electric machine, the hysteresis and eddy-current losses rise due to the higher frequency. Furthermore, the frequency dependent ohm's losses need to be investigated in depth to make a statement about the efficiency of the electric machine. For the transmission, the impact of the higher speeds on the losses has to be investigated. Concerning the no-load losses, higher speeds of the bearings and gearings are expected to have an impact towards higher losses. Optimizing the oil supply and oil flow as well as low viscosity fluids in the transmission can reduce the increase of these losses. In case of load-dependent losses, the increased speed causes reduced normal force on the tooth flanks due to the reduced torque and therefore reduced bearing loads, reducing the load-dependent losses. Also, high circumferential speeds can support fluid film lubrication regime of tribological contacts. Further investigations on the efficiency are to be carried out to describe the interdependency of higher circumferential speeds and the reduced forces acting in transmissions and powertrains with increasing maximum speed. In addition, the potential of low-loss gears and innovative base oils like water-containing gear fluids have to be evaluated, also in the context of holistic thermal managements.

Another aspect is the NVH-behavior of the transmission and the electric machine. Even though the eigenfrequencies of the electric machine are increasing, due to the more compact design, the frequency range of the exiting forces' waves increases as well with the maximum speed. For the transmission, it becomes more difficult to operate the first stages subcritically over the entire operating range. The interaction of the electric machine with its larger frequency range can also lead to a more complex excitation behaviour for the transmission and powertrain system, which should be examined in detail.

Furthermore, the increase of the maximum speed result in the use of new technologies, which currently may be not present or lead to increased costs of the powertrain system. For the electric

machine, one technology leap is the use of surface mounted magnets and the fixation with the bandage onto the rotor. The bandage material is quite expensive and the shrinkage on the rotor a challenging process. Furthermore, the amount of magnet material increases to keep the magnetic flux density in the air gap high with increasing size of the air gap. To achieve the high rotor speeds, bearings with higher accuracy and special materials to limit the centrifugal forces are needed. The lower torque leads to smaller sizes of the gearings, which means that influences from manufacturing errors are more important. Therefore, the quality of the gearings may be increased in order to obtain a sufficient load capacity and acoustical behaviour of the meshes under load.

**Author Contributions:** Conceptualization: D.S. and M.E.G.; methodology, D.S. and M.E.G.; software, D.S., A.T. and M.E.G.; validation, D.S., A.T., and M.E.G.; investigation, B.M., A.H.; resources, Institute of Machine Elements (TUM, Munich), Institute for Drive Systems and Power Electronics (LUH, Hannover); data curation, D.S. and M.E.G.; writing—original draft preparation, D.S., B.M., M.E.G. and A.H.; writing—review and editing, T.L., M.O., K.S. and B.P.; visualization, D.S. and M.E.G.; supervision, T.L., M.O., K.S. and B.P.; project administration, K.S.; All authors have read and agreed to the published version of the manuscript.

**Funding:** Supported by: Federal Ministry of Economic Affairs and Energy on thebasis of a decision by the German Bundestag.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


#### *Vehicles* **2020**, *2*


© 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/).

## *Article* **Benchmarking of Dedicated Hybrid Transmissions**

#### **Christian Sieg \* and Ferit Küçükay**

Institute of Automotive Engineering, Technische Universität Braunschweig, 38106 Brunswick, Germany; f.kuecuekay@tu-braunschweig.de

**\*** Correspondence: c.sieg@tu-braunschweig.de; Tel.: +49-531-391-2641

Received: 20 December 2019; Accepted: 10 February 2020; Published: 13 February 2020

**Abstract:** For many manufacturers, hybridization represents an attractive solution for reducing the energy consumption of their vehicles. However, electrification offers a wide range of possibilities for implementing powertrain concepts. The concepts can differ regarding their mechanical complexity and the required power of the electrical machines. In this article, drive concepts that differ in their functionality and drive train topology are compared. Based on requirements for the C, D, and E segment, the mechanical and electrical effort of the concepts is analyzed. The results show that the mechanical effort in the C segment can be reduced as long as the electrical effort is increased. In case of higher vehicle segments, the electrical effort can increase considerably, making concepts with increased mechanical complexity more suitable. The driving performance and efficiency in hybrid operation are evaluated via simulation. The results show that the difference of acceleration times in hybrid operation between a charged and discharged battery is lower for mechanically complex concepts. At the same time, they achieve lower CO2 emissions. Therefore, these concepts represent a better compromise regarding performance and efficiency. Despite lower transmission efficiencies in hybrid operation, they achieve conversion qualities similar to simpler concepts and lower emissions with lower electrical effort.

**Keywords:** dedicated hybrid transmission; benchmarking; hybrid electric vehicle; efficiency; topology optimization; drive train optimization; powertrain concepts

#### **1. Introduction**

To reduce the energy consumption, electrification of the drive train represents a suitable solution. Since one or more electric machines (EM) can be integrated into the drive train at different positions, a large number of possible drive concepts for hybrid electric vehicles (HEV) can be realized. The possible drive trains differ in their characteristics and operating modes. On the one hand, powertrains of conventional vehicles can be electrified, resulting in comparatively complex mechanical concepts. On the other hand, it is possible to implement transmissions that are dedicated for use in HEV and have a much simpler design.

Due to this diversity, the question which kinds of drive train concepts represent suitable solutions in which vehicle segment needs to be answered. It is of interest to be able to make a statement whether the mechanical effort of a transmission can be reduced in low vehicle segments without having to accept a loss of driving performance or efficiency. At the same time, the question should be answered whether higher vehicle segments require an increase in the mechanical complexity of the transmission. The aim of this article is to answer these questions. A detailed analysis regarding the influence of multi-speed transmissions on various basic dedicated hybrid transmission (DHT) concepts is carried out by [1]. However, coaxial multi-mode DHT (MM-DHT) with several planetary gear sets (PGS), which enable parallel as well as power-split operating modes, are not included in the considerations.

For these reasons, this article compares drive train concepts with different mechanical and electrical complexity. Several add-on concepts as well as DHT are considered. Furthermore, similar concepts with different mechanical complexity are analyzed. Based on equal driving performance requirements for all concepts, it is shown which EM power is necessary to meet the requirements for plug-in hybrid electric vehicles (PHEV) in the C, D, and E segments. The results confirm the correlation between the concept's mechanical and electrical complexity identified by [1]. They show that a reduction of the mechanical complexity is only possible in connection with a simultaneous increase of the electrical power. Based on the results, it can be derived which concepts can be used in which segment. Furthermore, characteristic properties of the considered concepts are derived.

Within the scope of a concept comparison for vehicles in the C segment, the concepts are evaluated regarding their efficiency in hybrid operation and driving performance. Apart from these factors, especially costs for mechanical and electrical components as well as the necessary installation space have a major influence on the concept decision. However, the costs depend on the quantities of produced transmissions. In addition, they may be influenced by using existing components from either previous or other vehicle models so that the costs of a powertrain concept are manufacturer-specific. Furthermore, not every component is produced by vehicle manufacturers so that the transmission costs also depend on the suppliers. To assess the required installation space, a detailed design of the transmission is necessary. Therefore, the mechanical components such as gears, bearings, shafts, and the transmission housing need to be dimensioned regarding worst-case scenarios, which are unknown for new concepts in early development phases and can only be estimated. In addition, the available installation space depends on a specific vehicle model. In early concept phases, it is unknown in which segment or vehicle a powertrain concept will be used. Considering the legislation, it can be expected that the energy consumption of vehicles needs to be reduced even further in the future. Thus, it is a major influencing factor when comparing powertrain concepts. For these reasons, this paper focuses on efficiency and driving performance.

The results show that concepts with high mechanical effort offer a good compromise between driving performance and efficiency. The advantage of these concepts is that in hybrid operation there are minor differences in acceleration times when the battery can be discharged or needs to be charged. If the concepts are simpler, a higher share of the power of the internal combustion engine (ICE) must be transmitted via the EM, resulting in higher losses and thus lower driving performance.

#### **2. Drive Train Concepts**

In this article, different powertrain concepts for hybrid vehicles are compared. The topologies differ considerably regarding their structure, the number of EM, the power flows occurring in the drive train and the operating modes. The mechanical and electrical complexity of the concepts is another important distinguishing feature.

Hybrid powertrains can be divided into two main categories. In addition to so-called add-on hybrids based on conventional powertrains, this article examines DHT especially designed for use in hybrid vehicles. Furthermore, hybrid drive trains can be divided into parallel hybrids, series-parallel hybrids, power-split hybrids, and multi-mode DHT (MM-DHT).

#### *2.1. Parallel Hybrid Concepts*

Due to their high market share, two parallel hybrids are analyzed in this article. They are based on a conventional drive train and differ with respect to the positioning and the number of EM. In addition to the P2 topology, explained in Section 2.1.1, a P1P4 topology, shown in Section 2.1.2, with two EM is investigated. In both concepts, an 8-speed transmission with a wet dual-clutch is used.

#### 2.1.1. P2 HEV

The drive train topology of a P2 hybrid is shown in Figure 1. In this configuration, an EM is positioned between the ICE and the transmission. Furthermore, there is a separating clutch between EM and ICE, so that the ICE can be disconnected from the drive train. Thus, the vehicle can be driven either electrically without ICE drag losses or by the combustion engine solely or in hybrid mode.

**Figure 1.** P2 drive train topology.

The transmission of this add-on topology is a wet 8-speed dual-clutch transmission (DCT). Consequently, it offers eight hybrid and eight electric driving modes.

Since P2 HEV are based on conventional drive trains, they are characterized by a high number of mechanical components compared to other concepts considered in this paper. To estimate and compare the mechanical effort of different concepts, the number of relevant mechanical components can be totaled. In the P2 HEV from Figure 1, the relevant components include the double clutch at the transmission input, the separating clutch between ICE and EM, the final drive (FD) at the front axle and the eight gears. This results in a total mechanical effort of 11.

#### 2.1.2. P1P4 HEV

Apart from P2 HEV, vehicles with an electrified rear axle, so-called P4 hybrids, show a high market share. Thus, a parallel hybrid with an electrified rear axle is investigated in this paper, see Figure 2. To enable battery charge at standstill and to start the ICE quickly and comfortably while driving, the drive train additionally comprises an electric motor between ICE and transmission. Since there is no disconnect clutch, electric driving is only possible by using the rear axle.

**Figure 2.** P1P4 drive train topology.

Because of the positioning of the electric motor on the rear axle, the P1P4 topology offers temporary all-wheel drive. To avoid over-speeding of the rear electric motor, a disconnect device is installed between the EM and the reduction gear on the rear axle. The concept comprises the same 8-speed DCT as the P2 HEV concept. It offers an electric driving mode and 16 hybrid modes since the vehicle can be driven in eight gears with or without the rear axle.

Similar to the P2 hybrid, the P1P4 hybrid has a high mechanical complexity. Both the eight gears of the transmission and the FD on the front axle are identical to the P2 concept. Differences result from the fact that there is no separating clutch between the ICE and the P1 EM and that the EM is connected to a second FD at the rear axle via a reduction gear with a disconnect device. This results in a higher mechanical effort of 13 compared to the P2 HEV.

#### *2.2. Series-Parallel DHT*

Another topology suitable for HEV is the powertrain shown in Figure 3. On the one hand, it enables a serial operating mode in which there is no mechanical connection between the ICE and the wheel, and the EM can transmit the power electrically. On the other hand, the ICE and the wheel can be connected by closing a separating clutch so that the ICE drives the vehicle at higher wheel powers. When the clutch is open, an electrical mode is possible. The shift matrix of the concept is shown in Table 1.

**Figure 3.** Drive train topology of the series-parallel DHT.

**Table 1.** Shift matrix of series-parallel DHT.


The series-parallel concept differs greatly from the other concepts in this article in terms of its design, operating modes, and mechanical complexity.

The mechanically relevant components include the two reduction gears, the separating clutch and the FD, so that the mechanical effort of 4 is lower compared with most other concepts.

#### *2.3. Power-Split DHT Concepts*

In addition to add-on hybrids, the Toyota Prius' power-split hybrid drive system has established itself on the market. In addition to a variant known from the Prius, a drive system based on the same concept and supplemented by a 4-speed transmission is considered. This allows determination of the influence of increased mechanical complexity on Power-Split-DHT (PS-DHT).

#### 2.3.1. Power-Split DHT

An important DHT concept with a high market share is the power-split concept introduced by Toyota in 1997. In this paper, the transmission structure of the 4th generation of Toyota's power-split concept, introduced in [2], is investigated. The drive train structure is shown in Figure 4.

The most important component of the transmission is a PGS. The ICE is connected to the planet carrier C. One EM is connected to the sun gear S and one to the ring gear R. The EM connected to the ring gear is connected to the driven axle via a reduction gear. Furthermore, a one-way clutch (OWC) is connected to the PGS so that the vehicle can be driven by both EM in electric driving. Without the OWC, EM1 would need to be controlled so that the planet carrier would be stationary to turn off the ICE.

**Figure 4.** PS-DHT drive train topology with planetary gear set—R: ring gear, C: planet carrier, S: sun gear.

Apart from electric driving, the PS-DHT offers a hybrid mode with a continuously variable gear ratio. This can be realized by controlling the speed of EM1 so that the mode can also be called electronic continuously variable transmission (eCVT) mode. In this operating mode, the speed and torque of the ICE can be chosen freely.

The concept is comparatively simple regarding the mechanical effort. In addition to the planetary gear set, the relevant components include the OWC, the reduction gear for EM2 and the FD. This results in a mechanical effort of 4.

#### 2.3.2. Power-Split DHT with 4-Speed Transmission

The PS-DHT structure can be combined with a 4-speed transmission. A similar concept is introduced in [3,4]. Figure 5 shows a modified structure with an OWC between ICE and the planet carrier so that both EM can operate during electric driving. The 4-speed transmission is positioned between EM2 and the FD so that the speed of EM2 and the ring gear can be changed. Thus, it influences the power flow between the energy converters but does not add an output-split or compound-split operating mode. Instead, four input-split eCVT modes and four electric driving modes can be selected.

**Figure 5.** Drive train topology of PS-DHT enhanced by 4-speed transmission—R: ring gear, C: planet carrier, S: sun gear.

The 4-speed transmission consists of two PGS and four shifting elements. By controlling two clutches C1 and C2 and two brakes B1 and B2, four gear ratios can be selected. The shift matrix is shown in Table 2.


**Table 2.** Shift matrix of PS-DHT with 4-speed transmission.

Compared to the PS-DHT without the 4-speed transmission, the powertrain is more complex. The increased mechanical effort directly results from the 4-speed transmission. For the quantification of the mechanical effort, three PGS, 5 shifting elements and the FD must be taken into account. Thus, the mechanical complexity can be estimated with 9.

#### *2.4. Multi-Mode DHT Concepts*

MM-DHT represent another category of hybrid transmission. They differ from PS-DHT since they do not only have an input-split eCVT mode in addition to electrical operation, but also offer additional functions. Depending on the structure of the concepts, several parallel or additional power-split modes, such as compound-split modes, can be implemented. This paper analyzes two concepts that are used in production vehicles. These include the concept from the second-generation Chevrolet Volt, introduced in [5] and the concept from the Cadillac CT6 PHEV, introduced in [6]. The influence of increased mechanical complexity compared to the basic concept can also be determined for the MM-DHT.

#### 2.4.1. Multi-Mode-DHT with two PGS

Figure 6 shows the structure of the MM-DHT with two PGS and two active shifting elements. The concept shown, corresponds to the drive system of the Chevrolet Volt 2, see [5]. The ICE is connected to the ring gear of the first PGS and can drive the vehicle. The sun gears of the PGS are each connected to EM, while the planet carriers form a common output. The sun gear of the first PGS can be connected to the second one via a clutch C. In addition, the ring gear of the second PGS can be stationary, when brake B is actuated. With the PGS and three shifting elements, the concept enables two electric, two power-split, and one parallel operating mode. The corresponding shift matrix is shown in Table 3.

**Figure 6.** Drive train topology of MM-DHT with two planetary gear sets—R: ring gear, C: planet carrier, S: sun gear.


**Table 3.** Shift matrix of MM-DHT with two PGS.

In mode eCVT 1st there is an input-split power flow while in mode eCVT 2nd there is a compound-split power flow. The shift matrix in Table 3 shows that in mode electric 1st both EM can drive the vehicle, while in mode electric 2nd only EM2 can operate.

With the two PGS, three shifting elements and the axle drive, the mechanical effort for the concept can be quantified to 6. This results in a complexity between the PS-DHT and the PS-DHT with 4-speed transmission.

#### 2.4.2. Multi-Mode-DHT with three PGS

An extension of the MM-DHT with two PGS is the MM-DHT with three PGS, see Figure 7. Up to the third PGS, the design is identical. The drive system is derived from the Cadillac CT6 PHEV, see [6]. The planet carrier of the first two PGS no longer forms the transmission output but is connected to the sun gear of the third PGS. The EM2 is connected to the ring gear of the third PGS via a clutch C2. The ring gear R is stationary when brake B2 is actuated. The output is the planet carrier of the third PGS.

**Figure 7.** Drive train topology of MM-DHT with three planetary gear sets—R: ring gear, C: planet carrier, S: sun gear.

With the three PGS and five shifting elements, 11 operating modes can be implemented. These include four electrical operating modes in which either one or both EM can operate. In addition, four eCVT modes are available in which either an input-split or compound-split power transmission occurs. In addition, three parallel modes with a constant gear ratio between ICE and wheel can be selected. The shift matrix of the concept is shown in Table 4.


**Table 4.** Shift matrix of MM-DHT with three PGS.

Compared to the MM-DHT with two PGS, the MM-DHT with three PGS is more complex. An additional PGS and two additional shifting elements increase the mechanical complexity from 6 to 9.

#### **3. Vehicle Parameters**

One aim of this paper is to show that there is a connection between the total electrical power required to meet the driving performance requirements and the mechanical effort of a concept. For this purpose, the three high-volume vehicle segments C, D, and E are considered. For all concepts, equal driving performance requirements are defined within a segment. Table 5 shows the vehicle parameters of the three segments.


**Table 5.** Vehicle parameters for C, D, and E segment vehicle.

This paper examines concepts suitable for use in PHEV. For this reason, typical vehicle parameters are defined. The vehicle mass of the C segment is assumed 1600 kg. It increases to 1700 kg for the D segment and 1900 kg for the E segment. The maximum payload in the C segment is 500 kg, 550 kg in the D segment and 650 kg in the E segment. The wheelbase increases from 2.65 m for the C segment over 2.8 m in the D segment to 2.95 m in the E segment. Another important parameter is the center of gravity of the vehicles. In the unloaded case, the vehicles in the C and D segments are front-loaded with a weight distribution of 60:40, while the vehicle in the E segment has a balanced weight distribution. If the vehicles are loaded by their maximum payload, the center of gravity of the vehicle changes. In case of the C and D segments, a balanced weight distribution results. The vehicle of the E segment has a weight distribution of 45:55 when fully loaded.

Another important difference between the segments is the maximum power of the ICE. For the C segment vehicle, a naturally aspirated engine with a maximum output of 100 kW is considered. The D segment is based on a supercharged engine with 150 kW, while the E segment is based on a supercharged engine with a maximum power of 225 kW. For all concepts within a segment, the equal combustion engine is used to determine the effects of a certain drive train structure on important properties such as performance and efficiency. It should be noted that it is neglected that the ICE can be optimized for some concepts.

As the reference vehicle is a PHEV and there are no requirements for the electrical range, the battery capacity is 10 kWh.

The driven axle also influences the driving performance requirements. In the C and D segments, the vehicles are front-wheel-drive (FWD) and in the E segment rear-wheel-drive (RWD).

The residual brake force describes an additional driving resistance resulting from residual braking torques of the wheel brake and wheel bearing friction.

#### **4. Driving Performance Requirements**

In hybrid drive trains, multiple energy storages and energy converters are present. Depending on their interaction, the power available on the wheel may vary. Therefore, several drive train states should be taken into account when defining driving performance requirements. According to [1], there can be several ways in which the energy can be provided by either the battery or the ICE in case of HEV. In this article, three corresponding states are taken into account when defining driving performance requirements. In hybrid mode, the battery can either be charged by the ICE or provide additional power to drive the vehicle. In addition to hybrid operation, it is also possible to define driving performance requirements for electrical operation. The power available at the wheel varies as a result of the power provided by the energy converters. This is shown in Figure 8 for different drive states.

6SHHGY

**Figure 8.** Traction force at wheel level for different drive train states.

The number of defined driving performance requirements should be as low as possible to be able to consider many possible variants within a parameter variation. At the same time, it needs to be ensured that a sufficient number of driving situations, i.e., tractive forces at a certain speed, are taken into account. Therefore, there is a conflict between the number of requirements and the required computation time. In this paper, driving performance requirements for different drive states are defined at a small number of vehicle speeds, so that there are several requirements per drive state

in order to keep the computing time as short as possible. The requirements are distributed over the entire speed range of the vehicle to ensure that the resulting delivery maps contain realistic driving situations. It should be noted that the specified driving performance requirements represent minimum requirements, which all variants of each concept must meet. The requirements within one segment are the same for all concepts to enable a fair comparison. In addition, the designed concepts may exceed the minimum requirements. Table 6 summarizes the requirements.


**Table 6.** Drive train state specific driving performance requirements for C, D, and E segment vehicle.

It should be noted that the requirements in hybrid operation for charging or discharging the battery refer to the transmission input. The requirement at wheel level is calculated for a powertrain efficiency of 90%.

In hybrid operation, when the battery is discharged, all variants, irrespective of the segment, must reach the traction force limit of the fully loaded vehicle in a speed range up to at least 10 km/h to ensure sufficient gradeability. In all DHT concepts considered, one of the EM is responsible for providing sufficient torque on wheel level until the traction force limit is reached. Since EM can deliver their maximum torque over a wider speed range, there are delivery maps in which the traction force limit is reached at speeds higher than 10 km/h. It is, therefore, sufficient to require the concepts to reach the traction force limit at least in a speed range between 0 km/h and 10 km/h.

For the medium speed range at 80 km/h, it is required that the variants must achieve a certain traction force. To be able to quantify this traction force, ICE operation without discharging the battery is the starting point. For hybrid operation with battery discharge, a boost power is defined that must be applied in addition to the maximum ICE power. For vehicles in the C segment, 140 kW of power must be available at the transmission input. This power results from a nominal ICE power of 100 kW in combination with a boost power of 40 kW. Taking into account a drive train efficiency of 90%, the necessary power or traction force can thus be calculated at wheel level. For the other segments, there is a differentiation due to a higher ICE maximum power as well as a higher boost power.

To define a driving performance requirement in the higher speed range and to limit the demand map of the vehicles, the variants in the C segment are required to achieve a maximum speed of 200 km/h in hybrid operation when the battery is discharged. In the D and E segment, the maximum speed is 225 km/h and 250 km/h, respectively.

In addition to discharging the battery, hybrid operation while charging the battery is a relevant drive train state since less power is available on the wheel. The approach to determine the corresponding tractive force is identical to hybrid operation while discharging the battery. The only difference is that no additional power is provided, but is reserved for charging the battery. In the C and D segment, a reserve of 10 kW is defined, while in the E segment the maximum ICE power is reduced by 20 kW. This does not mean that the battery is charged with the specified power, but takes into account the fact that some concepts in eCVT mode or serial mode require the battery to be charged in a certain speed range, resulting in increased losses. In the driving performance calculation of the simulation model, see Section 5, no charging power of the battery is specified. The model only ensures a negative battery power. In hybrid operation while charging the battery, the requirements are identical to the drive train state in which the battery is discharged.

It is characteristic for PHEV that they can achieve higher distances in electrical operation due to their battery capacity. Compared to mild or full hybrids, the driving performance requirements for electrical operation are therefore becoming more important. For the vehicles of all segments, it is specified that they must reach the traction force limit when the vehicle is fully loaded. The only exception is the P1P4 topology with an electric all-wheel drive. In electric operation, this vehicle would have RWD and would therefore offer a considerably higher traction potential than vehicles with FWD in the C and D segment. This would lead to significantly higher tractive forces required for electrical operation and would contradict a fair comparison of concepts. Therefore, the variants of the P1P4 topology are required to reach the traction force limit of a FWD vehicle in electrical operation.

To define a driving performance requirement in the medium speed range, an acceleration time from 60 km/h to 100 km/h is used as a distinguishing feature. It is assumed that below 60 km/h there are minor differences regarding the acceleration time between different vehicle segments. Therefore, the acceleration time between 60 km/h and 100 km/h can be used to determine an average longitudinal acceleration at 80 km/h. This acceleration requirement directly corresponds to a traction force requirement. It should be noted that the acceleration time only servers as an orientation for deriving an average acceleration or traction force and does not represent a requirement to be achieved.

For the variants in the C segment, the acceleration time is 6 s, in the D segment it declines to 5 s and in the E segment to 4 s.

In electrical operation, the requirement for the maximum vehicle speed in the C segment is based on the speed profile of the Worldwide harmonized Light Duty Test Cycle (WLTC). To ensure that the cycle can be fully completed in electrical operation, a maximum speed of 135 km/h must be reached. So that vehicles in higher segments differ from those of the C segment, the maximum speed in the D segment is 145 km/h and 160 km/h in the E segment.

#### **5. Simulation Model**

A modular simulation model developed by [1] makes a significant contribution to the results in this paper. The structure and the essential functionality are explained in this section. Explanations that are more detailed can be found in [1].

An essential feature of the simulation model is that the calculation of operating points and the efficiency of drive concepts is coupled with a driving performance calculation. Based on the possible driving performance, i.e., the delivery maps of a drive train concept, an efficiency calculation can be carried out in any speed profile. Therefore, the model can be used on the one hand for estimating driving performance and thus for determining appropriate drive train variants. On the other hand, it enables the simulation of almost any drive topology in cycle or customer operation.

A schematic structure of the model is shown in Figure 9. Based on driving resistances due to the vehicle parameters, operating points of the drive train components and energy converters are calculated backwards through the drive train. Based on efficiency maps of the energy converters, the vehicle's energy consumption can be determined.

**Figure 9.** Schematic structure of the modular simulation model developed and inspired by [1].

A central component of the model is a modular transmission calculation, which calculates the associated speeds and torques within the transmission based on all possible operating points of the energy converters. The calculation has a modular structure so that a wide variety of transmission concepts can be calculated within a short time with little parameterization effort. In addition to the calculation of conventional transmissions, it is possible to simulate concepts in which several EM are integrated into the transmission. This feature is particularly necessary for the simulation of complex DHT with several EM.

To calculate the transmission losses, two approaches can be selected. In addition to a simplified approach, which describes the efficiency depending on the output power of the transmission, mode-specific efficiency maps can be implemented. In this paper, however, the simplified approach is used to reduce the calculation time.

Two primary energy converters can be positioned outside the transmission. They can be connected to the transmission module via a launch element. The primary energy converters include ICE, fuel cells and EM.

In addition to the modules for calculating driving performance and efficiency, driving performance requirements can be defined. With the help of the performance calculation, it is then possible to determine which variants of a drive train concept can meet the requirements. Within the scope of parameter variations, fractional or full factorial scaling plans can be considered.

To select the most efficient operating points, two operation strategy approaches are implemented. In addition to a globally optimal control strategy, presented in [7,8], there is a locally optimal operating strategy based on the equivalent consumption minimization strategy (ECMS) [9,10]. This local optimal approach is used in the following considerations.

#### **6. Dimensioning of Electric Motors**

The simulation tool described in Section 5 is used to determine powertrain designs that meet the requirements described in Section 4. For each concept considered in this paper, a range of design parameters is defined. These include upper limits for the maximum power of the EM. Furthermore, intervals are defined in which ratios of PGS, the FD or the reduction gears are varied.

The driving performance calculation allows determination of which variants meet the requirements. The variants whose total EM power is minimal are of particular importance. Designs with a significantly higher total power are of less importance as they are oversized regarding the requirements. Based on

the driving performance requirements and the drive train concepts, the above-mentioned relationship between mechanical and electrical effort can be confirmed. Furthermore, the investigations allow drawing of conclusions about the suitability of concepts in different vehicle segments.

Figure 10 shows the minimum required power of the EM which is necessary to meet the requirements. Furthermore, the mechanical effort quantified by a figure, see Section 2, is compared.

**Figure 10.** Concept-specific minimal required EM power to meet the driving performance requirements in the C, D, and E segment in comparison with the estimated mechanical effort of the concepts.

#### *6.1. Analysis of Total Necessary EM Power for C Segment Requirements*

In the C segment, the minimum required EM power for the P2 HEV is 80 kW. Due to the eight gears of the DCT, the necessary EM power does not result from the requirements in hybrid operation, but is due to the requirement in electric operation at 80 km/h. Reaching the traction force limit at full load can also be ruled out as a cause since the first gear already enables a high gear ratio. A power of 80 kW is therefore not required to reach the traction force limit.

The total necessary electrical power of the P1P4 HEV increases to 125 kW. This consists of 15 kW for the P1-EM and 110 kW for the P4-EM. It should be noted that a power of 15 kW has been defined for the P1-EM for all variants of the P1P4 and in all segments. Compared to the P2 HEV, the higher power of the EM results from the fact that there is only a constant gear ratio between EM and wheel and that the EM can only be separated from the drive train when its speed limit is reached. To reach the maximum speed in electrical operation, the reduction gear ratio for the EM must not exceed a certain value. The P4-EM must therefore provide a sufficiently high torque to allow the vehicle to reach the traction force limit when launching with full load.

The total necessary electrical power in case of the series-parallel DHT increases considerably compared to the add-on concepts. In total, 270 kW of electrical power must be installed in the drive train to meet the requirements in the C segment. This high power demand results from the requirements in hybrid operation when charging the battery. In this case, the concept offers two operating modes. In parallel mode, the ICE can only provide the required wheel power in a certain speed range since there is a constant gear ratio between ICE and wheel. In case the ICE cannot provide enough power to meet the requirement, the serial mode needs to be selected. In this mode, the ICE provides power to drive the vehicle and EM1, see Figure 10, needs to have a similarly high power to be able to transmit the power electrically so that EM2 can drive the vehicle. EM2 therefore at least needs to have a power which is similar to the power of EM1.

To reach the traction force limit, EM2 must provide a high torque during charging of the battery in hybrid operation and during electric driving. There is a similar correlation as with the P4-EM, so that a high torque requirement results in a correspondingly high power for EM2.

The PS-DHT requires a lower total EM power than the series-parallel concept. In the C segment, a total power of 190 kW is required. In this case, EM1 needs to have a power of 60 kW and EM2 is required to provide 130 kW. The significantly higher power of EM2 is needed since the traction force limit must be reached in electric and hybrid operation. Compared to the PS-DHT concept from [4], the minimum required power of EM1 is higher, since high requirements have been defined for hybrid operation with simultaneous charging of the battery.

If a 4-speed transmission is added to the PS-DHT, the minimum power required is reduced to a total amount of 80 kW. This results in an electrical effort comparable to the P2 HEV. The 4-speed transmission, see Figure 5, allows adjustment of the operating point of the EM2 and the speed of the ring gear. This reduces the torque required for EM2 to reach the traction force limit. Furthermore, the speed of the ring gear influences the power flow in power-split mode, so that the power of EM1 can also be reduced.

The required power of the EM of the MM-DHT with two PGS increases to 120 kW. Compared to the PS-DHT, the power is 70 kW lower. Due to a higher number of possible operating modes, including two power-split eCVT modes and a parallel mode, more degrees of freedom are available in hybrid operation when the battery is discharged.

The MM-DHT with three PGS requires as much electrical power as the P2 HEV and the PS-DHT with 4-speed transmission. By increasing the number of available operating modes, including four eCVT modes and three parallel modes, it is possible to install a lower total electrical power than in the similar concept with two PGS.

It can be concluded that with the EM maps used and the requirements applied, the minimum electrical power required in the C segment is 80 kW.

#### *6.2. Analysis of Total Necessary EM Power for D and E Segment Requirements*

Due to the higher requirements in the D segment, the total electrical power required for all concepts increases. However, a comparison between the concepts shows that the increase differs among the concepts. For example, the P2 HEV's and the P1P4 HEV's output increases by 20 kW. It should be noted that the increase for the P1P4 HEV only affects the P4-EM, as it was specified that the P1-EM should have an output of 15 kW in all segments.

A higher increase results in case of the series-parallel DHT. For this concept, the electrical effort increases by 80 kW to 350 kW. This corresponds to an increase of approx. 29.6%. On the one hand, the increase in power can be explained by the higher traction force limit due to the vehicle parameters. On the other hand, the increased electrical power requirement results from hybrid operation when the battery is charged. In this case, only the ICE is available as a power source. The power provided by the ICE is received by EM1, see Figure 3. As a result of this dependency, the power of EM1 is directly dependent on the power of the ICE.

The power of EM1 is also dependent on the power of the ICE in case of the PS-DHT. When charging the battery with low power, however, a portion of the power provided by the ICE can be transferred mechanically to the wheel. Therefore, the EM1 of the PS-DHT does not have to receive the maximum power of the ICE. As a result, the total electrical power required for the PS-DHT increases by approx. 21% compared to the C segment. The total required power of the EM is 230 kW.

The 4-speed transmission allows adjustment of the operating point of EM2 and the speed of the ring gear. This reduces the total electrical power required compared to the PS-DHT without a multi-speed transmission. Therefore, in hybrid operation with discharged battery less power must be transmitted via the EM in the case of split power mode, which directly reduces the power requirement of the EM. As a result of this, an electrical effort of 100 kW is required in the D segment.

#### *Vehicles* **2020**, *2*

A total electrical power demand of 140 kW results for the MM-DHT with two PGS in the D segment. Compared to the C segment the increase of approx. 16.7% is lower. In comparison to the PS-DHT, less electrical power is required because two eCVT modes and one parallel mode are available.

If the MM-DHT with two PGS is supplemented by an additional PGS, 100 kW of electrical power are required in the D segment. As in the C segment, this concept has a similar electrical effort as the P2 HEV and the PS-DHT with 4-speed transmission.

In the E segment, the total electrical power required for all concepts increases as a result of increased requirements. The P2 HEV, PS-DHT with 4-speed transmission, and MM-DHT with three PGS continue to have the lowest electrical effort. However, there are slight differences between these concepts in the E segment. The total necessary EM power for the series-parallel DHT increases to 580 kW. The relative increase is even higher for the PS-DHT, but with 440 kW less electrical power is required in total. Compared to the PS-DHT, the required EM power of the MM-DHT with two PGS in the E segment increases to a comparatively lower value of 170 kW.

#### *6.3. Relationship between Mechanical and Electrical E*ff*ort*

In addition to the total electrical power required, Figure 10 shows an estimate of the mechanical effort for the considered concepts. If this is compared with the required electrical power, a correlation between electrical and mechanical effort is shown.

The results show that the concepts with high mechanical effort require a comparatively low electrical effort in all vehicle segments. The P2 hybrid has a mechanical effort of 11 and is the concept with the second highest mechanical complexity according to the estimation used in this paper. In all segments, the P2 HEV requires the lowest total electrical power.

Due to the additionally driven rear axle, the mechanical effort of the P1P4 HEV rises to 13. Compared to the P2 HEV, a higher overall EM power is required in all segments. Therefore, no linear relationship between the mechanical effort and the electric effort can be shown. However, a clear trend can be identified based on the results. For future considerations, however, a different parameter should be used to estimate the mechanical effort to be able to describe a clearer relationship.

The PS-DHT with 4-speed transmission and the MM-DHT with three PGS also are concepts with a high mechanical effort. Each of these concepts is a mechanically more complex variant of a basic concept. In the C and D segment, they have a similarly low necessary EM power as the P2 HEV, but with lower mechanical effort. Although there are differences in the E segment, the overall EM power is significantly lower compared to the other concepts with lower mechanical complexity.

If the mechanical effort of the concepts is significantly reduced, the required power of the EM increases significantly. Both the series-parallel DHT and the PS-DHT have a comparatively simple design with a mechanical effort of 4. At the same time, these concepts require the highest EM power compared to the other concepts. The difference is particularly high in the E segment.

#### *6.4. Application of Powertrain Concepts in Di*ff*erent Vehicle Segments*

Based on the results in Figure 10, it can be concluded which concepts should be used in which vehicle segment. For this purpose, the ratio of electrical and mechanical effort can provide a helpful orientation. It should be noted that the assessment of the suitability of drive train concepts in different segments depends on the underlying requirements to a considerable extent. For example, a reduction of the requirements in hybrid operation while charging the battery would lead to significantly reduced EM power. Especially concepts with low mechanical effort would benefit from this. Nevertheless, it can be expected that mechanically complex concepts would still have the lowest power demand for electrical power.

However, based on the driving performance requirements in this paper, the use of the concepts for segments C, D, and E can be assessed.

The E segment shows considerable differences between the total electrical power required by the concepts. The largest difference with 440 kW is between the P2 HEV and the series-parallel DHT. The difference between P2 HEV and PS-DHT is 300 kW. In comparison to the MM-DHT with two PGS, the difference decreases to 130 kW. This leads to the conclusion that the series-parallel DHT as well as the PS-DHT in the E segment do not represent the most favorable solutions. For the MM-DHT with two PGS it is shown that the electrical effort can be reduced considerably compared to concepts with higher complexity. Thus, the required power output decreases by 120 kW in case of the MM-DHT with three PGS and by 100 kW in case of the PS-DHT with 4-speed transmission if the mechanical effort is increased by 3. Therefore, it can be concluded that the MM-DHT with two PGS should not be used in the E segment either. Instead, concepts with a mechanical complexity of 9 or higher represent promising solutions.

In the D segment, the series-parallel DHT as well as the PS-DHT require significantly lower EM power compared to the E segment. However, regarding a good compromise between electrical and mechanical effort, other concepts lead to a better solution. Compared to the PS-DHT, the electrical effort of the MM-DHT with two PGS is reduced by almost 100 kW with a moderate increase of the mechanical complexity. This leads to the conclusion that the MM-DHT with two PGS is a better concept than the PS-DHT and the series-parallel DHT in the D segment. Concepts that are mechanically more complex have a lower electrical power requirement. To be able to assess the applicability with sufficient quality in these cases, further criteria such as costs or required installation space need to be taken into consideration.

Compared to the D segment, the difference between the series-parallel DHT and the PS-DHT is similarly large in the C segment. The difference in the D segment between the series-parallel DHT compared to the P2 hybrid is about 338%, while in the C segment it is 350%. For PS-DHT, there are relative differences of 230% in the D segment and about 238% in the C segment. Although the difference between the concepts is similar, the absolute required power decreases, so that the series-parallel DHT should not be excluded from application in the C segment. However, it becomes apparent that the PS-DHT as well as the MM-DHT with two PGS represent a better compromise between mechanical and electrical effort. For the mechanically more complex concepts, less clear statements can be made, since although a low total electrical power is required, criteria such as cost, scalability, or modularity play an important role and are not considered in this paper.

#### **7. Benchmark Analysis**

The approach described in Section 6 allows identification of the minimal required EM power which needs to be installed in the considered concepts to meet the performance requirements. Furthermore, the simulation model provides requirement-compliant transmission ratios, which are varied within a parameter variation. The gear ratios include the FD ratio for the P2 and P1P4 hybrids. In the case of the series-parallel DHT, the gear ratios of the reduction gear for EM2 and the FD are varied. In case of the PS-DHT and MM-DHT concepts, the PGS ratios, the gear ratio of the FD and, if available, the gear ratio of the reduction gear for EM2 are varied.

For the concepts considered in this paper, the parameter variations result in a high number of different drive train variants. These can differ from each other in terms of driving performance and efficiency. To be able to make a statement which concepts and which dimensioning represent promising solutions, the concepts are compared with each other with regard to their driving performance in hybrid operation and in electric operation as well as their efficiency in charge sustaining operation.

The analysis of the minimum required EM power shows that all considered concepts require a low electrical effort in the C segment compared to higher segments. Additionally, the differences between the concepts are smaller than in the D or E segment. Therefore, the question arises whether a high mechanical effort should be realized in the C segment to reduce the required electrical power. By comparing the driving performance and efficiency, it can be analyzed whether a high mechanical complexity results in advantages regarding driving performance and efficiency. Furthermore, the results can indicate whether concepts with high electrical effort should not be used in the C segment. For these reasons, the following considerations are limited to the results of the C segment.

To compare the efficiency of the concepts, the CO2 emissions in the WLTC for charge sustaining operation are calculated. During charge sustaining operation, it is ensured that the state of charge (SOC) of the battery is almost identical at the beginning and end of the cycle to allow a fair comparison of the concepts. To evaluate the driving performance, the acceleration times from 0 km/h to 100 km/h in hybrid as well as in electric operation are calculated. For these calculations, the simulation model presented in Section 5 is used. A locally optimal operating strategy based on the ECMS is used.

Since it can be assumed that realistic drive trains are not over-dimensioned with regard to their driving performance requirements, variants that are in the range of the minimum required total electrical power are selected for the concept comparison. Table 7 shows the selected EM power for all concepts.


**Table 7.** EM-specific and total EM power selected for C segment drive train concepts.

In addition to the driving performance and the efficiency of the concepts, this article also evaluates the conversion quality defined by [11]. The concepts are compared regarding this benchmark parameter. Based on these results, important concept-specific properties are identified.

#### *7.1. Analysis of E*ffi*ciency in WLTC and Driving Performance*

In this section, the concepts in the C segment are compared regarding their efficiency in charge sustaining operation in the WLTC as well as their hybrid and electric driving performance. In hybrid operation, a distinction is made between driving performance with fully charged and discharged battery. In this case, the SOC-neutral CO2 emissions are not affected by the battery's state of charge, since the simulation ensures a SOC of 50% at the beginning and end of the cycle.

#### 7.1.1. Evaluation of Efficiency and Driving Performance in Hybrid Driving while Discharging the Battery

The simulation results in case the battery can be discharged are shown in Figure 11. It should be noted that the emissions in charge sustaining mode do not correspond to the combined CO2 emissions, since the electrical energy consumption must also be analyzed and weighted to determine the combined CO2 emissions.

The P2 HEV variants achieve acceleration times of approx. 6.4 s from 0 km/h to 100 km/h in hybrid operation while the battery is discharged. Furthermore, CO2 emissions of about 111 g/km to 111.6 g/km are achieved. Compared to the other concepts, the P2 HEV variants achieve both good acceleration times and low CO2 emissions.

As a result of electrifying the rear axle with a P4-EM with an output of 110 kW or 120 kW, considerably lower acceleration times can be achieved due to the electric all-wheel drive. Depending on the power of the EM on the rear axle, the variants achieve acceleration times in a range between 4.1 s and 4.4 s. Thus, the difference compared to the P2 HEV is about 2 s or 2.3 s. It should be noted that the simulation model allows a serial power flow in case of full-load acceleration for the P1P4 hybrid. If

the front axle of the vehicle reaches the traction force limit, the P1-EM can transmit excess torque to the P4-EM positioned on the rear axle.

**Figure 11.** Comparison of charge sustaining efficiency in WLTC and hybrid driving performance for drive train concepts compliant with C segment requirements.

In contrast to the P2 HEV, however, the CO2 emissions of the variants of the P1P4 concept are significantly higher. Depending on the dimensioning, the emissions range between 115 g/km and 118.5 g/km. The higher CO2 emissions result from the fact that the P4-EM, which can be used during electric operation, is connected to the wheel via a constant gear ratio. Therefore, the operating point of the EM cannot be changed by a gearshift during electric driving or recuperation. In addition, due to its lower power output than the P2 HEV, the P1-EM allows the load point of the ICE to be increased to a lesser extent. This can have a less positive effect on the efficiency of the ICE. Furthermore, operating states may occur in which the load point of the ICE is increased via the P4-EM on the rear axle, which may result in high transmission losses.

With the series-parallel DHT, hybrid operation shows a comparatively good acceleration time of approx. 5.9 s due to the powerful EM. This means that all variants of this concept reach the traction force limit up to at least 100 km/h.

However, the variants of the concept show high differences in CO2 emissions. They range between 113 g/km and 117.1 g/km. The transmission ratio between the ICE and the wheel has a major influence, since with increasing the gear ratio, the ICE is operated at higher speeds and lower torques. As a result, a higher amount of load point increase is carried out to improve ICE efficiency. The energy obtained by load point increase must later be used for electric driving or load point decrease to ensure SOC neutrality. The energy available for electrical operation is therefore generated under high losses compared to energy gained from recuperation. Thus, the CO2 emissions are increased. Furthermore, the high power of the EM has a negative effect on CO2 emissions as well. Due to the high power, the EM are operated at a low average power and thus at low efficiencies. As a result, their efficiency during electric driving and recuperation is lower compared to other concepts. This means that fewer driving situations can be covered in electric operation.

Compared to the series-parallel concept, the acceleration times of the PS-DHT variants increase. Depending on the variant, acceleration times between approx. 6.1 s and 6.3 s are possible. In contrast to the series-parallel DHT, the driving performance is slightly reduced, because EM2 has a lower maximum power and torque. Therefore, the variants of the PS-DHT do not reach the traction force limit up to speeds of 100 km/h.

The CO2 emissions of the PS-DHT are between approx. 115.7 g/km and 117.5 g/km. Therefore, the PS-DHT has a lower efficiency in WTLC compared to the series-parallel DHT. Although the ICE can operate at high efficiencies due to the eCVT mode, the powertrain efficiency during electric driving and during recuperation is lower compared to the series-parallel DHT. This means that less electrical energy is available from recuperation in the traction phase and a higher amount of energy is required for electric driving. This means that the ICE operates more frequently and must provide additional energy by increasing the load point. In addition, powerful EM are necessary for the PS-DHT to meet the driving performance requirements. Thus, they operate at low average loads and have a low average efficiency.

If the PS-DHT is supplemented by a 4-speed transmission, the driving performance and CO2 emissions are reduced. The variants achieve acceleration times between 6.3 s and 6.6 s and CO2 emissions between 110.2 g/km and 111 g/km. Due to the lower total electrical power of the EM, the acceleration time increases slightly compared to the PS-DHT. However, four electrical and four power-split operating modes allow adaptation of the operating points of the energy converters to the driving situation. Especially in hybrid operation, this leads to the fact that less power of the ICE must be transmitted via the electrical branch by adjusting the speed of the ring gear. This increases the transmission efficiency and reduces CO2 emissions. Furthermore, the efficiency of the EM in both traction and thrust phase is positively influenced, which also has a positive effect on energy consumption.

The variants of the MM-DHT with two PGS achieve acceleration times between 6.3 s and 7.1 s in hybrid operation. This results in similar driving performance as the PS-DHT with a 4-speed transmission or P2 HEV.

Due to an additional eCVT mode and a parallel mode, the MM-DHT concept with two PGS achieves lower CO2 emissions than the PS-DHT. Although the transmission losses are higher because the concept is mechanically more complex, the additional degrees of freedom regarding the choice of operating points have a positive effect on efficiency. This results in CO2 emissions between 111.2g/km and 114.2g/km. Compared to the P2 HEV, the CO2 emissions are similarly good.

If the MM-DHT concept is enhanced by an additional PGS, the driving performance and efficiency are reduced compared to the concept with two PGS. The acceleration times are in a range between 6.6s and 7.3s and the CO2 emissions are between 109.4 g/km and 111.8 g/km. Compared to the concept with two PGS, the number of operating modes increases, so that more efficient operating points of the energy converters can be selected in WLTC. On the one hand, the concept offers four modes in electrical operation in contrast to the concept with two PGS with two modes. On the other hand, more degrees of freedom are also available in hybrid operation with three parallel and four eCVT modes.

The results in Figure 11 show that mechanically complex concepts offer a higher efficiency in the C segment due to additional operating modes. At the same time, they show only slightly increased acceleration times compared to concepts with more powerful EM. Therefore, the concepts P2, MM-DHT with two PGS, PS-DHT with 4-speed transmission and MM-DHT with three PGS offer a better compromise in terms of performance and efficiency in hybrid operation. A higher mechanical complexity leads to a better efficiency.

However, it should be noted that the differences in efficiency and driving performance are small. For example, the best variants of the series-parallel DHT have good CO2 emissions, which are about 1.7 g/km to 2 g/km higher than the best variants of P2 HEV or MM-DHT with two PGS. In addition, the concepts have to meet high performance requirements in hybrid operation. For example, the concepts must reach the traction force limit between 0 km/h and 10 km/h even when loaded, while the battery is being charged or the vehicle is driven purely electrically. This leads to a comparatively high total EM power for the PS-DHT and the series-parallel DHT, see Section 6. Due to the high requirements, these two concepts show a lower efficiency and driving performance. It can be assumed that different results are obtained if the driving performance requirements are reduced.

Furthermore, other important factors such as the required installation space and the costs influence the evaluation of the drive concepts. As these two important variables are not considered in this paper, the concepts are only assessed in terms of efficiency and driving performance.

7.1.2. Comparison of Efficiency in Hybrid Driving and Driving Performance in Electric Operation

In addition to the driving performance in hybrid operation, this paper also examines the driving performance in electric operation. Figure 12 shows the CO2 emissions in hybrid operation versus the acceleration time from 0 km/h to 100 km/h in electric operation.

**Figure 12.** Comparison of charge sustaining efficiency in WLTC and electric driving performance for drive train concepts compliant with C segment requirements.

It can be seen that concepts with a high total electrical power achieve lower acceleration times in electrical operation. The variants of the PS-DHT and series-parallel DHT have acceleration times of approx. 6 s to 6.5 s, as the EM have total outputs of 170 kW–190 kW and 270 kW–290 kW, respectively. It should be noted that the variants of the PS-DHT have lower acceleration times, although less EM power is installed. The reason for this is that with the PS-DHT, both EM can drive the vehicle in electric mode because of the OWC between the ICE and PGS. In contrast, in series-parallel DHT only the EM2 can drive the vehicle.

The lower the power available in electrical operation, the higher the acceleration time. Therefore, the acceleration time of the MM-DHT with two PGS is between 6.6 s and 7.5 s. In addition, the results show that two different total EM powers are considered. In case of the P1P4 concept, the acceleration time increases to 7.9 s or 8.4 s. For mechanically more complex concepts, EM powers of 80 kW to 90 kW are required. For the P2 hybrid, this results in an acceleration time of about 10.1 s. For the PS-DHT with 4-speed transmission, the acceleration time increases to 9.8 s to 10.3 s. The largest differences are found in the MM-DHT with three PGS. The variants of this concept achieve acceleration times between 9.7 s and 11 s.

In comparison to hybrid operation with a charged battery, these acceleration times therefore differ by approx. 3.1 s in case of the MM-DHT with three PGS and 3.8 s for the P2 HEV. For the P1P4 the difference is also 3.8 s. Furthermore, the difference is considerably smaller for the mechanically simple concepts with high total electrical power. The MM-DHT with two PGS offers a good compromise between the acceleration time in hybrid operation and in electrical operation. For this concept, the acceleration time in electrical operation is 0.5 s higher.

The results in Figure 12 therefore show that the mechanically complex concepts have lower driving performance in electrical operation than the concepts with a simpler mechanical design because of their lower total electrical power. However, it should be noted that no requirement regarding the acceleration time was specified for electrical operation. In this case, it can be assumed that the mechanically more complex concepts would achieve this acceleration time with a lower total electrical power.

7.1.3. Comparison of Hybrid Driving Performance with Charged and Discharged Battery

In addition to electrical operation, the consistency of the acceleration behavior also plays a role in the evaluation of the concepts. Therefore, the concepts in this section are examined regarding the difference between charged and discharged battery in hybrid operation. For this purpose, Figure 13 shows the corresponding acceleration times from 0 km/h to 100 km/h. A solid black line shows the range of equal driving performance with fully charged and discharged battery in hybrid mode. To the right of this line, the driving performance is better with a discharged battery than with a charged battery. Furthermore, isolines indicate a constant time difference between the operation with charged and discharged battery.

**Figure 13.** Comparison of acceleration time from 0 km/h to 100 km/h in hybrid operation in case of charging or discharging the battery.

The highest difference between hybrid operation with charged and discharged battery occurs in case of the P1P4 HEV. At high SOC, additional drive power is available at the rear axle of the vehicle resulting in a good traction potential. However, in case of a low SOC, drive power is only available at the front axle. Thus, the difference in acceleration time is more than 4 s. Therefore, the concept has disadvantages regarding the similarity of driving performance. Furthermore, Figure 13 shows that some variants of the P1P4 HEV have a shorter acceleration time at low SOC than the variants of the P2 HEV. This is due to the possibility to transfer a part of the drive power in series mode to the rear axle of the vehicle. The P1-EM works as a generator, while the P4-EM can provide its power at the rear axle with losses. In the low speed range, when the traction force limit of the front axle is reached, the P1P4 concept can thus offer advantages over the P2 HEV.

A smaller difference results in case of the series-parallel DHT and the PS-DHT. Their acceleration times differ by more than 3 s and less than 4 s. The P2 hybrid can be rated slightly better. A disadvantage of the series-parallel DHT is that the drive power of the ICE must be transmitted in series mode in a certain speed range, depending on the gear ratio between ICE and wheel. This can result in high conversion losses, so that the transmission efficiency declines and less drive power is available at the wheel.

A slightly better compromise than P2 HEV is offered by the MM-DHT variants with two PGS. With this concept the difference in acceleration time of the hybrid operation at high and low SOC is less than 3 s. Compared to the PS-DHT, the two eCVT modes as well as the parallel mode have a positive effect on the acceleration time, since less drive power has to be transmitted via the EM. This means that a higher proportion of the drive power is transmitted to the wheel mechanically, resulting in lower power losses.

If additional mechanical components are added to the PS-DHT, the difference between high and low SOC is reduced. The 4-speed transmission enables transmission of a higher share of the drive power mechanically in eCVT mode, resulting in shorter acceleration times compared to the PS-DHT. For the MM-DHT with two PGS there are similar acceleration times and differences between the two states of charge.

The lowest difference in acceleration time is shown by the MM-DHT variants with three PGS. Depending on the dimensioning, the difference is slightly higher than 2 s and in the best case only about 1.5 s. Since this concept offers the highest number of operating modes, the difference in driving performance is the lowest.

The results in Figure 13 therefore lead to the conclusion that the increase in mechanical effort in the transmission leads to less difference in driving performance in hybrid operation at high and low SOC. The additional operating modes provided by additional mechanical components can lead to a higher share of the drive power provided by the ICE being transferred mechanically to the wheel, resulting in better driving performance at low SOC. As a result, the difference in hybrid operation is lower and the driving performance is better. It should be noted that the MM-DHT with three PGS and the PS-DHT with 4-speed transmission offer better performance in comparison to the P2 HEV in case of a low SOC. This is due to the four eCVT modes offered by both concepts. Compared to the P2 HEV with 8-speed DCT, they provide better adaptation to the traction force hyperbola, resulting in lower acceleration times. In addition, there are variants of the MM-DHT with two PGS, which offer advantages compared to the P2 HEV.

An increase in performance in hybrid operation at low SOC would only be possible in concepts with low mechanical effort if the EM could achieve better efficiencies or if the ICE offered a higher maximum power.

It should be noted that no explicit requirements were made for a small difference in acceleration times. In this case, the required total electrical power of the concepts would differ from the results shown in this paper.

#### *7.2. Evaluation of Conversion Quality and Transmission E*ffi*ciency*

For further evaluation of the concepts in hybrid operation, the average transmission efficiency and the average conversion quality in WLTC are calculated. The conversion quality is introduced in [11] and describes the ratio of the theoretical optimum efficiency of the ICE to the actual efficiency of the ICE. The parameter thus describes the ability of a transmission to operate an energy converter at its power-specific optimum efficiency.

Figure 14 shows the average conversion quality and the average transmission efficiency in hybrid operation in the WLTC. There are differences between add-on hybrid concepts and DHT on the one hand and between mechanically simple and complex concepts on the other hand.

**Figure 14.** Comparison of average conversion quality of the ICE and average transmission efficiency in hybrid operation in WLTC.

The variants of the PS-DHT achieve very good transmission efficiencies of around 97% in hybrid operation. A positive effect is that the transmission is mechanically simple, so that mechanical losses are low. In addition to a good transmission efficiency, all variants of the PS-DHT achieve high conversion qualities of over 99.5%. This is due to the eCVT operating mode, which allows infinite variation of the transmission ratio, so that the ICE can operate at its power-specific optimum efficiency operating point.

Compared to the PS-DHT, the variants of the series-parallel DHT have lower transmission efficiencies in hybrid operation. Although this concept also has a simple mechanical design and thus low mechanical losses, the EM are much more powerful. Since the conversion losses in the EM are taken into account in the transmission efficiency in case of serial operation, the efficiency is lower compared to the variants of the PS-DHT. In addition, the transmission efficiency in hybrid operation depends on the wheel power in which the hybrid operation occurs. It is thus possible that hybrid operation in case of PS-DHT takes place at higher wheel power, whereby the transmission efficiency tends to be better, since load-independent losses cause a smaller share of the losses.

In contrast to the PS-DHT, the variants of the series-parallel DHT have lower conversion qualities in hybrid operation. Compared to the other concepts, there are greater differences. In the best case, the conversion quality is over 99.5% and in the worst case less than 97.5%. This variation results from the scaling of the FD ratios. An increase in the FD ratio leads to a lower conversion quality, since the ICE is operated at higher speeds and lower torques due to the constant gear ratio to the wheel. Thus, load point increase of the ICE is necessary to increase the efficiency of the ICE. Since the load point increase does not lead to an increased efficiency in all areas, the average conversion quality decreases. Furthermore, an increase in the FD ratio means that lower speeds can be achieved in parallel mode. Therefore, there may be variants in which the serial mode must be selected at high speeds. Since in serial mode both the speed and the torque of the ICE can be chosen freely, the conversion quality is positively influenced in serial mode.

Compared to the mechanically simple DHT, the P2 HEV and P1P4 HEV add-on hybrids achieve lower average transmission efficiency. In case of the P2 HEV it is over 94% and in case of the P1P4 it is around 93.5%. The reason for this is that mechanical losses are higher due to the more complex design.

Regarding the average conversion quality, there are greater differences. The P2 HEV variants achieve similarly good conversion qualities as PS-DHT of over 99.5%. On the one hand, the combination of gear ratios and ICE efficiency map has a positive effect on the conversion quality. On the other hand, *Vehicles* **2020**, *2*

with the P2 HEV it is possible to operate the ICE in more favorable efficiency ranges by increasing the load point.

In contrast, the extent of load point increase is limited for the P1P4 HEV. On the one hand, the P1-EM only has a power of 15 kW. On the other hand, the load point increase via the P4-EM is associated with high losses. For this reason, the FD ratio of the P1P4 HEV variants also has a strong influence on the average conversion quality. As with the series-parallel DHT, an increase of the FD ratio leads to a reduction of the conversion quality of the ICE.

A good compromise between conversion quality and transmission efficiency in hybrid operation is offered by the mechanically complex DHT. The variants of the MM-DHT with two PGS achieve transmission efficiencies between approx. 95% and 96.1% in hybrid operation with conversion qualities of 98.7% to 99.6%. With a higher mechanical complexity as with the MM-DHT with three PGS, the transmission efficiency declines to a range between 94.6% and 95.3%. However, the number of operating modes gained through the higher mechanical complexity leads to an increase in the conversion quality compared to the MM-DHT with two PGS. It lies between approx. 98.7% and 99.7%.

The extension of the PS-DHT by a 4-speed transmission has a negative effect on the average transmission efficiency in hybrid operation. It lies between 94.6% and 95% and is significantly lower than in case of the PS-DHT. The conversion quality is also reduced compared to the PS-DHT. However, it is still high with about 99.3% to 99.7%. It should be noted that the local optimal operation strategy approach always achieves an optimal compromise between high conversion quality of the ICE and low losses in the EM. Therefore, a lower conversion quality of the ICE does not directly lead to higher CO2 emissions, see Figure 11.

The results in Figure 14 show characteristic differences between different types of hybrid transmission concepts. For example, mechanically simple DHT such as PS-DHT or series-parallel DHT in hybrid operation show very high transmission efficiencies. The concepts have a low mechanical complexity, so that mechanical losses are reduced. In addition to a high transmission efficiency, these concepts can achieve high conversion qualities of over 99%. However, as the minimum required total EM power in Figure 10 shows, powerful EM are necessary. DHT with increased mechanical complexity have lower transmission efficiencies in hybrid operation, but these concepts can achieve comparably high conversion qualities as mechanically simpler concepts, so that with reduced total EM power, lower CO2 emissions are achieved in SOC-neutral operation. Therefore, especially MM-DHT are a good solution. Although add-on-HEV concepts can also achieve high conversion qualities, their transmission efficiency is lower due to the higher mechanical effort.

#### **8. Summary**

The electrification of the drive train creates considerable degrees of freedom in the design of drive trains. Depending on the number and positioning of EM, there may be significant differences regarding the topology and functionality of the concepts. On the one hand, additional EM can supplement conventional drive trains. Common solutions to add-on concepts are P2 HEV as well as electrified all-wheel drive systems such as P1P4 HEV. In addition, it is also possible to implement DHT. These transmissions are dedicated to HEV and allow different operating modes than parallel hybrids. Depending on the structure, DHT can be of varying complexity.

In this paper, various powertrain concepts, which differ in their design and operating modes, are examined. These include parallel hybrids, series-parallel DHT, PS-DHT, and MM-DHT with different mechanical complexity. In this paper, the concepts are briefly described regarding their structure and operating modes. Furthermore, the mechanical complexity of the concepts is estimated and quantified by considering mechanically relevant components.

To compare powertrain concepts driving performance requirements in different speed ranges are defined for a C, D, and E segment vehicle. These include reaching the traction force limit in the low speed range, requirements in the medium speed range, which are quantified by boost or charge power, and maximum speed requirements.

#### *Vehicles* **2020**, *2*

A comparatively small number of requirements is defined to allow for short computing times while at the same time allowing for a high number of powertrain variants. Therefore, a full factorial scaling plan can be used so that the system behavior can be identified.

The consideration of different speed ranges also ensures that the delivery maps of the concepts match realistic demand maps of the drive concepts.

The requirements are defined for different drive train states to take into account the interaction of ICE and battery. In hybrid operation, a distinction is made as to whether the battery can be discharged or needs to be charged. In addition, requirements for electrical operation are defined.

Using a modular simulation environment described in this paper, variants that meet the requirements can be identified based on a driving performance simulation. Differences arise especially regarding the required EM power. This differs between the segments, since the tractive forces resulting from the requirements depend on vehicle and drive train parameters. Furthermore, concept-specific differences regarding the required EM power are analyzed. This electrical effort is compared to the quantified mechanical effort.

The results show that a reduction in the number of mechanical components requires comparatively high EM power. Responsible for this is a constant gear ratio between the EM, which in most situations operates as a motor. This EM must, on the one hand, reach the maximum speed of the vehicle in hybrid operation and, on the other hand, enable reaching the traction force limit both in hybrid operation and electric driving. Therefore, this EM must have a comparatively high torque and thus a high power output. In addition, due to their structure, the concepts with low mechanical effort must transmit a high share of the drive power electrically. In case of the series-parallel DHT, the serial mode must be selected in a certain speed range when the battery is discharged. In this case, the drive power is only provided by the ICE and transmitted via both EM. Depending on the gear ratio, the PS-DHT also needs to transmit a certain share of the drive power via the EM. The fact that an EM must receive the power of the ICE and therefore operate as a generator results in a dependency on the maximum power of the ICE.

For these reasons, the required EM power of the mechanical simple concepts increases distinctly with higher vehicle segments or higher requirements. In these cases, an increase in the mechanical complexity of the transmission is advisable. Additional components allow transmission of higher shares of the drive power mechanically, which can reduce the required EM power. In addition, several gears may be available for the EM, which is usually operating as a motor. Mechanically complex concepts are therefore better suited for use in higher vehicle segments. Depending on the segment and the EM used, they do not require significantly more EM power than concepts with one EM, such as P2 HEV.

The comparison of the required EM power shows that in the C segment there are the least differences between the drive concepts. For this reason, hybrid operation is examined within a benchmark analysis. This paper focuses on efficiency and performance since both costs and the required installation space can only be evaluated with comparably high uncertainty in early concept phases. To assess the efficiency, the SOC-neutral CO2 emissions in the WTLC are considered. To compare the driving performance, the acceleration time from 0 km/h to 100 km/h for hybrid operation and electric driving is analyzed. The results show that mechanically complex concepts offer a good compromise between driving performance and efficiency in hybrid operation. On the one hand, they achieve low CO2 emissions. On the other hand, they show small differences between the acceleration times of hybrid operation with charged and discharged battery.

In contrast, the CO2 emissions of the mechanically simpler concepts increase. Regarding hybrid operation, they therefore do not represent more attractive solutions in the context of these investigations. However, it should be noted that due to the higher electrical power, the driving performance in electric operation increases. In addition, there are only minor differences in the acceleration time during hybrid operation with a charged battery and electric operation.

To be able to derive concept-specific properties, the average transmission efficiency and the conversion quality in the WLTC are also investigated in hybrid operation. The results show that mechanically simple concepts such as PS-DHT or series-parallel DHT can provide both good transmission efficiency and high conversion quality. However, the PS-DHT offers advantages due to the eCVT mode and can achieve higher conversion qualities.

With mechanically more complex DHT such as MM-DHT with two or three PGS or a PS-DHT with a 4-speed transmission, the average transmission efficiency and conversion quality decline slightly. Compared to the mechanically simpler concepts, however, considerably less electrical power must be installed in the drive train. Therefore, these concepts offer the best compromise between transmission efficiency and conversion quality.

The results also show that the considered parallel hybrids have the lowest average transmission efficiencies in hybrid operation. In case of the P2 HEV, however, a very high conversion quality can be achieved with lower required EM power.

**Author Contributions:** C.S. and F.K.; methodology, C.S.; software, C.S.; validation, C.S., F.K.; formal analysis, C.S.; investigation, C.S. and F.K.; resources, C.S.; data curation, C.S.; writing—original draft preparation, C.S.; writing—review and editing, C.S.; visualization, C.S.; supervision, F.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 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/).
