Benchmark parameters of transmissions

Conversion quality, transmission efficiency and effectiveness
Original Paper

Abstract

The paper explains the influence of the transmission on the energy consumption of a vehicle. In addition to the efficiency of the transmission, the conversion quality has been introduced, which quantifies how efficiently the transmission can operate the connected drive machine. Conversion quality and transmission efficiency influence the energy consumption in different ways. Therefore, the transmission effectiveness is developed to be able to compare different transmissions directly with one another using just one parameter. The higher the transmission effectiveness, the more efficient the transmission operates in the overall context of the drive concept. Furthermore, the transmission effectiveness quantifies the consumption potential of the considered transmission concept. It is described that in the case of conventional drives, an increase in the conversion quality due to an increased ratio spread has led to reductions in energy consumption, although additional mechanical components tend to result in higher mechanical transmission losses. In the case of electrified drives, however, these correlations are reversed. As the recuperation becomes more efficient, especially through an increase in the transmission efficiency, the transmission efficiency will become increasingly important. At the same time, the electrification allows a significant improvement in the conversion quality with the same transmission concept. Due to these fundamentals, dedicated hybrid transmissions will be a key technology to further reduce the energy consumption of hybrid vehicles.

Keywords

Conversion quality Transmission Efficiency Effectiveness Benchmark 

Abbreviations

AMT

Automated manual transmission

AT

Automatic transmission

BEV

Battery electric vehicle

CVT

Continuously variable transmission

DCT

Dual clutch transmission

DHT

Dedicated hybrid transmission

DM

Drive machine

EV

Electric vehicle

GE

Transmission effectiveness (German: Getriebeeffektivität)

HEV

Hybrid electric vehicle

ICE

Internal combustion engine

ICV

Internal combustion engine vehicle

MM

Multi mode

MT

Manual transmission

TM

Transmission

PS

Power split

WLTP

Worldwide harmonized light vehicles test procedure

1 Introduction

The basic task of a transmission is the conversion of torque and speed. This is done according to the number of gears and the selected gear ratios.

Transmission concepts have become much more diverse by integrating one or more electric machines (EM). In addition to the known “classic concepts” such as MT (manual transmission), AMT (automated manual transmission), DCT (dual clutch transmission), AT (automatic transmission) and CVT (continuously variable transmission) new hybrid transmissions are developed. These are either hybridizations based on conventional transmissions in terms of add-on concepts [P0, P1, P2, P3 and P4 (e-axis)] or dedicated hybrid transmissions (DHT), where the EM is indispensable for basic functions of the transmission. Figure 1 shows a possible classification of propulsion systems [1].

Fig. 1

Classification of conventional, hybrid and electric drives

Figure 2 shows the variety of requirements which are related to powertrains. In general, these have to be fulfilled by all transmission concepts. Since CO2 and pollutant requirements have become particularly important, the criterion of “environmental compatibility” is essential. Nevertheless, further improvements regarding all criteria will be achieved through the use of electrification [1].

Fig. 2

Requirements of the powertrain [1]

With regard to more stringent requirements for fuel and energy consumption, CO2 emissions as well as pollutants, such as NOx or soot particles, the cycle-related characteristics of the transmission are particularly important. In this paper, the following characteristic parameters are introduced and defined to quantify the transmission characteristics:

  • Conversion quality.

  • Transmission efficiency.

  • Effectiveness.

With these parameters, it is possible to compare different transmission concepts in different drive concepts such as ICV, HEV or EV. Furthermore, benchmarking of various transmissions can be carried out.

2 Conversion quality and transmission efficiency

The conversion quality \(W\) is introduced as one of the essential transmission parameters (in conjunction with a given energy converter).

Conversion quality: It represents a measure of how well the gear ratios allow the energy converter to operate at its optimal operating points. Accordingly, the conversion quality of an ideal CVT with an unlimited ratio spread is 100%. However, transmissions with a limited number of gears, and therefore, a limited ratio spread always have conversion qualities of less than 100%.

The conversion quality \(W\) is defined as the efficiency of the drive machine (DM) operating in the actual operating point (OP) \({\eta _{{\text{DM,OP}}}}\) related to the optimal efficiency of the drive machine \({\eta _{{\text{DM,opt}}}}\) for a given power demand:
$${\text{Conversion~quality~}}W:=~\frac{{{\eta _{{\text{DM,OP}}}}~}}{{{\eta _{{\text{DM,opt}}}}}}.$$
(1)

The efficiency of the drive machine in the actual operating point \({\eta _{{\text{DM,OP}}}}\) is dependent both on the current power demand and the present transmission ratio.

The optimal efficiency of the drive machine \({\eta _{{\text{DM,opt}}}}\) is only dependent on the power demand on the drive machine since a transmission with optimal gear ratios is used here. The definition of the conversion quality \(W\) in Eq. (1) can be applied for both the traction and thrust phase. As a consequence, the conversion quality \(W\) can be used to evaluate the recuperation efficiency of a drive system.

Figure 3a shows an exemplary efficiency map of an ICE. The curve of optimal efficiency is shown, which represents the optimal efficiency operating points for all mechanical power outputs of the ICE \({P_{{\text{ICE}}}}\). The curve of the optimal ICE efficiency \({\eta _{{\text{ICE,opt}}}}\) can be illustrated as a function of the ICE power \({P_{{\text{ICE}}}}\) in Fig. 3b.

Fig. 3

Exemplary ICE efficiency map and derivation of the operating curve for optimal efficiency (\({\eta _{{\text{ICE,opt}}}}\) curve) in a and representation of the optimal ICE efficiency as a function of the ICE power \({P_{{\text{ICE}}}}\) in b. Representation of an operating point with optimum efficiency \({\eta _{{\text{ICE,opt}}}}\) (circle) as well as an operating point with actual efficiency \({\eta _{{\text{ICE,OP}}}}\) (star) as a function of the ICE power \({P_{{\text{ICE}}}}\)

If ideal gear ratios are available, the operating points of the ICE are set on the \({\eta _{{\text{ICE,opt}}}}\) curve. This is illustrated by an example of a specific ICE power \({P_{{\text{ICE}}}}\) (circle). In case of a real transmission with non-ideal transmission ratios, operating points are usually not located on the \({\eta _{{\text{ICE,opt}}}}\) curve. This is shown in Fig. 3b using the operating point with the efficiency \({\eta _{{\text{ICE,OP}}}}\) (star).

The conversion quality \(W\) according to Eq. (1) is defined for a current driving state. For the evaluation of vehicle transmissions, it is necessary to use average values for a certain driving cycle. Therefore, the vehicle and cycle-related average conversion quality \(\overline {W}\) is introduced as a ratio of the average actual efficiency of the drive machine \({\bar {\eta }_{{\text{DM,OP}}}}\) and the average optimal efficiency of the drive machine \({\bar {\eta }_{{\text{DM,opt}}}}\) and defined as follows:
$$\bar {W}:=~\frac{{{{\bar {\eta }}_{{\text{DM,OP}}}}~}}{{{{\bar {\eta }}_{{\text{DM,opt}}}}}}.$$
(2)

The average conversion quality \(\overline {W}\) is vehicle and cycle-dependent since the required drive power depend both on the cycle and the vehicle parameters. Moreover, the implemented drive machine has a considerable influence on the conversion quality.

The average efficiency of the drive machine \({\bar {\eta }_{{\text{DM}}}}\) results from the weighting of the time-resolved efficiencies \({\eta _{{\text{DM}}}}\) with the associated energy conversion. To be able to assess which operating ranges of the drive machine are most important for the overall efficiency, the time share of the wheel-related drive power \({P_{{\text{Wheel}}}}\) is used. Figure 4 shows the time share TS of the wheel power \({P_{{\text{Wheel}}}}\) for a C-segment ICV (internal combustion engine vehicle) in the WLTP. It can be seen that in the traction phase, in which the wheel-related drive power \({P_{{\text{Wheel}}}}\) is positive (\({P_{{\text{Wheel}}}}>0\)), the time share of low wheel power ranges is relatively high.

Fig. 4

Time share of the wheel power of a C-segment vehicle in the WLTP

Figure 5a shows the corresponding operating points in the WLTP using a 6-speed transmission with a progressive ratio design, a ratio spread of 6.0 and a total ratio in the highest gear of 2.5. Despite an efficiency-optimized shifting strategy, which is generated by means of a global-optimal operation strategy from [2], there are noticeable deviations from the efficiency-optimized operation. The average conversion quality is \({\overline {W} _{6{\text{G}}}}=95.9~\%\). Figure 5b shows the ICE operating points using a CVT with the same ratio spread as the 6-speed transmission. The continuously variable operation results in a better average conversion quality of \({\overline {W} _{{\text{CVT}}}}=97.0~\%\). Nevertheless, the CVT in the WLTP does not achieve an optimal conversion quality either. The reason for this is the limited ratio spread of 6.0. Above the lowest gear ratio (i > 2.5), the CVT can operate the ICE along the \({\eta _{{\text{ICE,opt}}}}\) curve. At higher speeds, however, lower gear ratios are necessary. This shows that in addition to small gear steps, the ratio spread in particular has a significant influence on the conversion quality. The correlations are always vehicle and cycle-dependent.

Fig. 5

ICE operating points in the WLTP for a C-segment vehicle in combination with a 6-speed transmission in a and with a CVT in b with an identical transmission range

The cycle-related average transmission efficiency \({\bar {\eta }_{\text{G}}}\) is introduced as a second characteristic parameter of the transmission. Figure 6 shows an example of two efficiency maps for the 1st and the 6th gear of a 6-speed transmission. It can be seen that the shapes of the efficiency maps differ from one another, which is due to the transmission kinematics. In the case of a DHT, they are considerably more complex since, in addition to various gears (modes), further speed or torque degrees of freedom can be present. In this case, the dimension of the efficiency maps increases.

Fig. 6

Exemplary efficiency characteristics of a 6-speed transmission for 1st and 6th gear, with M TM,in = transmission input torque, n TM,in = transmission input speed, P TM,in = transmission input power and η TM = transmission efficiency

While the conversion quality directly influences the energy consumption, changes in the transmission efficiency only have a proportionate effect on the energy consumption. The reason for this is the efficiency behavior of the ICE. Since the ICE efficiency is a function of the ICE power and the transmission efficiency directly influences the ICE power, the ICE efficiency depends on the transmission efficiency as well. Ultimately, the transmission efficiency also affects the conversion quality. For example, a higher average efficiency of the transmission \({\bar {\eta }_{\text{G}}}\) results in a lower load requirement for the ICE. At lower loads, the average ICE efficiency \({\bar {\eta }_{{\text{ICE}}}}\) is also lower.

Figure 7 shows the average conversion quality \(\overline {W}\) and the average transmission efficiency \({\bar {\eta }_{\text{G}}}\) for C-segment vehicles in the WLTP for various drive concepts. The values for hybrid vehicles (P2-HEV and DHT) are related only to ICE operation. Since the ICE is operated with higher loads in the hybrid vehicle due to the battery operation during partial load and load point shift during hybrid operation, this also results in higher transmission efficiency compared to the ICV. However, this does not mean that the transmission efficiency with an HEV is generally better than in case of an ICV, since the transmission also causes losses during battery operation, but those are not taken into account in this illustration. Both the ICV and the HEV show that the number of gears and the resulting ratio spread of the transmission have a great influence on the conversion quality. Transmissions with a high number of gears generally have a higher ratio spread than transmissions with fewer gears. With 8-speed transmissions almost perfect conversion qualities can be achieved with the P2 HEV. This is partly due to the load decrease as a result of the load increase (LPA). The load can either be increased beforehand or afterwards. The combination of load decrease and load increase further enhances the conversion quality, producing additional LPA losses. The ICV, on the other hand, still has a potential of about 1.5% due to optimum transmission ratios. In addition to the P2 HEV, three DHT concepts are also presented. The Power Split DHT (PS DHT) and the Multi Mode DHT (MM DHT), similar to concepts in [1], have two EM. The electrical losses from the power split are included in the transmission losses. The operation strategy chooses the optimal compromise between electrical losses of the power split and the conversion quality, which is particularly important for the PS DHT. The 4G DHT is a DHT with one EM, 4 fixed gears and 4 eCVT modes, comparable to the 4G DHT concept in [3] with a modular DCT approach as in [4]. It also represents an MM DHT but only with one EM. Compared to the P2 concepts, the DHT concepts achieve significantly better transmission efficiencies without compromising the conversion quality.

Fig. 7

Average transmission efficiencies and average conversion quality for C segment vehicles in the WLTP for various drive and transmission concepts. ICV, DCT: conventional vehicle with DCT, P2 HEV: hybrid drive with P2 topology and DCT, 4G DHT: multi Mode DHT with one EM and 4 fixed gears, PS DHT: power split DHT with 2 EM. The parameters for HEV are solely related to ICE operation

In addition, results for a BEV are shown. Here the conversion quality is already relatively high with a 1-speed transmission. This can be increased by a second and a third gear, but with a higher transmission loss, in particular, when the transmission allows for power shifts. If transmission concepts with 2 or 3 speeds with slight additional losses are used, the efficiency gains can also be achieved with the BEV.

The average conversion quality and the average transmission efficiency are significant for the energy consumption of the vehicle. However, it is important to understand, which parameter has a greater influence on the energy consumption. To be able to quantify this, a new characteristic parameter for the evaluation of transmissions is introduced: the transmission effectiveness GE. This is explained in the following.

3 Transmission effectiveness GE

The transmission effectiveness GE describes the potential with regard to the energy consumption of a considered transmission compared to an ideal transmission. For this purpose, the GE can be represented as the ratio of the (specific) fuel consumption \({B_{{\text{S,ideal}}}}\) with an ideal transmission in relation to the fuel consumption \({B_{\text{S}}}\) of the considered transmission. Parameters in combination with an ideal transmission are in the following referred to as “ideal” in the index.
$${\text{GE}}=\frac{{{B_{{\text{S,ideal}}}}}}{{{B_{\text{S}}}}}.$$
(3)
The (specific) fuel consumption \({B_{\text{S}}}\) is proportional to the ratio of the average ICE power \({\bar {P}_{{\text{ICE}}}}\) in relation to the average ICE efficiency \({\bar {\eta }_{{\text{ICE}}}}\):
$${\text{GE}}=\frac{{{B_{{\text{S,ideal}}}}}}{{{B_{\text{S}}}}}=\frac{{\frac{{{{\bar {P}}_{{\text{ICE,ideal}}}}}}{{{{\bar {\eta }}_{{\text{ICE,ideal}}}}}}}}{{\frac{{{{\bar {P}}_{{\text{ICE}}}}}}{{{{\bar {\eta }}_{{\text{ICE}}}}}}}}.$$
(4)
For a vehicle with a conventional powertrain (ICV) and without taking the auxiliary consumers (AUX) into account, the mean ICE power \({\bar {P}_{{\text{ICE}}}}\) can be expressed by the mean wheel power during the traction phase \({\bar {P}_{{\text{Wheel,traction}}}}\) in relation to the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\). At the same time, the average ICE efficiency \({\bar {\eta }_{{\text{ICE}}}}\) can be described as the product of the average conversion quality \(\overline {W}\) and the optimal average ICE efficiency \({\bar {\eta }_{{\text{ICE,opt}}}}\) in terms of an efficiency-optimized operation:
$$\begin{aligned} {\text{GE}} & =\frac{{{B_{{\text{S,ideal}}}}}}{{{B_{\text{S}}}}}=\frac{{\frac{{{{\bar {P}}_{{\text{ICE,ideal}}}}}}{{{{\bar {\eta }}_{{\text{ICE,ideal}}}}}}}}{{\frac{{{{\bar {P}}_{{\text{ICE}}}}}}{{{{\bar {\eta }}_{{\text{ICE}}}}}}}} \\ & =\frac{{\frac{{{{\bar {P}}_{{\text{Wheel,traction}}}}}}{{{{\bar {\eta }}_{{\text{ICE,opt,ideal}}}}\cdot{{\bar {W}}_{{\text{ideal}}}}\cdot{{\bar {\eta }}_{{\text{TM,ideal}}}}}}}}{{\frac{{{{\bar {P}}_{{\text{Wheel,traction}}}}}}{{{{\bar {\eta }}_{{\text{ICE,opt}}}}\cdot\bar {W}\cdot{{\bar {\eta }}_{{\text{TM}}}}}}}}. \\ \end{aligned}$$
(5)
For an ideal transmission, both the conversion quality \({\overline {W} _{{\text{ideal}}}}=1\) and the transmission efficiency \({\bar {\eta }_{{\text{G,ideal}}}}=1\). Thus,
$$\begin{aligned} {\text{GE}} & =\frac{{\frac{1}{{{{\bar {\eta }}_{{\text{ICE,opt,ideal}}}}\cdot1\cdot1}}}}{{\frac{1}{{{{\bar {\eta }}_{{\text{ICE,opt}}}}\cdot\overline {W} \cdot{{\bar {\eta }}_{{\text{TM}}}}}}}} \\ & =\frac{{{{\bar {\eta }}_{{\text{ICE,opt}}}}}}{{{{\bar {\eta }}_{{\text{ICE,opt,ideal}}}}}}\cdot\overline {W} \cdot{{\bar {\eta }}_{{\text{TM}}}}. \\ \end{aligned}$$
(6)
Since, as already mentioned above, the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\) influences the average power \({\bar {P}_{{\text{ICE}}}}\) delivered by the ICE, \({\bar {\eta }_{{\text{TM}}}}\) also influences the ICE efficiency \({\bar {\eta }_{{\text{ICE}}}}\). The sensitivity \({S_{{\text{TM}}}}\) of the mean optimum ICE efficiency \({\bar {\eta }_{{\text{ICE,opt}}}}\) with respect to the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\) is introduced. The sensitivity \({S_{{\text{TM}}}}\) quantifies the change in the optimal ICE efficiency \({\bar {\eta }_{{\text{ICE,opt}}}}\) as a function of the change in the transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\):
$${S_{{\text{TM}}}}~=~\frac{{\frac{{{{\bar {\eta }}_{{\text{ICE,opt,ideal}}}}}}{{{{\bar {\eta }}_{{\text{ICE,opt}}}}}} - 1}}{{\frac{{{{\bar {\eta }}_{{\text{TM,ideal}}}}}}{{{{\bar {\eta }}_{{\text{TM}}}}}} - 1}}.$$
(7)
With regard to the transmission effectiveness (Eq. 6), Eq. 7 can be rewritten as follows:
$$\frac{{{{\bar {\eta }}_{{\text{ICE,opt}}}}}}{{{{\bar {\eta }}_{{\text{ICE,opt,ideal}}}}}}=\frac{1}{{{S_{\text{G}}} \cdot \left( {\frac{1}{{{{\bar {\eta }}_{{\text{TM}}}}}} - 1} \right)+1}}.$$
(8)
The sensitivity \({S_{\text{G}}}\) is dependent on both the vehicle and the cycle, but can be calculated relatively accurately on the basis of approximations. The efficiency-optimized operation curve of an ICE can be approximated by a linear function until reaching its best efficiency according to [5]. \({P_{{\text{0,ICE}}}}\) represents a constant power loss, which basically occurs when the ICE is activated and not dragged. The reciprocal value of the ICE differential efficiency \(1/\Delta {\eta _{{\text{VKM}}}}~\)indicates how the power loss of the ICE increases with an increase of the mechanical power output \({P_{{\text{ICE}}}}\). This results in the power of the fuel tank \({P_{{\text{Tank}}}}\):
$${P_{{\text{Tank}}}}={P_{{\text{0,ICE}}}}+\frac{1}{{\Delta {\eta _{{\text{ICE}}}}}} \cdot {P_{{\text{VKM}}}}.$$
(9)
The ICE efficiency \({\eta _{{\text{ICE}}}}\) is described using the approximation as follows:
$${\eta _{{\text{ICE}}}}=~\frac{{{P_{{\text{ICE}}}}}}{{{P_{{\text{Tank}}}}}}=\frac{{{P_{{\text{ICE}}}}}}{{{P_{{\text{0,ICE}}}}+\frac{1}{{\Delta {\eta _{{\text{ICE}}}}}} \cdot {P_{{\text{ICE}}}}}}.$$
(10)
The ICE power \({P_{{\text{ICE}}}}\) can be expressed by the ratio of the wheel power \({P_{{\text{Wheel}}}}\) and the transmission efficiency \({\eta _{{\text{TM}}}}\) when the influence of the AUX is neglected. This results in the ICE efficiency,
$$\begin{aligned} {\eta _{{\text{ICE}}}} & =~\frac{{{P_{{\text{ICE}}}}}}{{{P_{{\text{Tank}}}}}}=\frac{{\frac{{{P_{{\text{Wheel}}}}}}{{{\eta _{{\text{TM}}}}}}}}{{{P_{{\text{0,ICE}}}}+\frac{1}{{\Delta {\eta _{{\text{ICE}}}}}} \cdot \frac{{{P_{{\text{Wheel}}}}}}{{{\eta _{{\text{TM}}}}}}}} \\ & =\frac{{{P_{{\text{Rad}}}}}}{{{\eta _{{\text{MT}}}} \cdot {P_{{\text{0,ICE}}}}+\frac{1}{{\Delta {\eta _{{\text{ICE}}}}}} \cdot {P_{{\text{Wheel}}}}}}. \\ \end{aligned}$$
(11)
The approximated sensitivity \({S_{{\text{TM}}}}\) results as follows:
$$\begin{aligned} {S_{{\text{TM}}}}~ & =~\frac{{\frac{{{{\bar {\eta }}_{{\text{ICE,opt,ideal}}}}}}{{{{\bar {\eta }}_{{\text{ICE,opt}}}}}} - 1}}{{\frac{{{{\bar {\eta }}_{{\text{TM,ideal}}}}}}{{{{\bar {\eta }}_{{\text{TM}}}}}} - 1}} \\ & =\frac{{\frac{{{{\bar {\eta }}_{{\text{TM}}}} \cdot {P_{{\text{0,ICE}}}}+\frac{1}{{\Delta {\eta _{{\text{ICE}}}}}} \cdot {{\bar {P}}_{{\text{Wheel,traction}}}}}}{{1 \cdot {P_{{\text{0,ICE}}}}+\frac{1}{{\Delta {\eta _{{\text{ICE}}}}}} \cdot {{\bar {P}}_{{\text{Wheel,traction}}}}}} - 1}}{{\frac{1}{{{{\bar {\eta }}_{{\text{TM}}}}}} - 1}}. \\ \end{aligned}$$
(12)

For example, the parameters \({P_{{\text{0,ICE}}}}=5~\;{\text{kW}}\) and \(\Delta {\eta _{{\text{ICE}}}}=0.38\) can be selected for a turbo-charged gasoline engine with stoichiometric direct injection and a peak power of 100 kW. For this case, the sensitivity \({S_{{\text{TM}}}}\) for a particular cycle can be calculated solely depending on the transmission efficiency. NEDC (low loads), WLTP (medium loads) and US06 (high loads) are considered below. The correlations can be represented by the approximation of the \({\bar {\eta }_{{\text{ICE,opt}}}}\) curve. Figure 8 shows the average ICE power and mean optimal ICE efficiency with an ideal transmission (triangle: NEDC, star: WLTP and square: US06). If the transmission efficiency drops, the average ICE power has to increase, since the ICE has to cover the transmission losses. This leads to an increase in the ICE efficiency. Figure 8 shows that the efficiency increases at low loads are higher than at high loads where the average efficiency is already relatively high. In the best efficiency range, the sensitivity \({S_{{\text{TM}}}}~\) is close to zero.

Fig. 8

Approximation of the efficiency-optimal operation curve (\({\eta _{{\text{ICE,opt}}}}\) curve) of a gasoline engine with 100 kW peak power as well as mean ICE efficiencies in the NEDC (triangle), WLTP (star) and US06 (square) with ideal transmissions and the influence of decrease in transmission efficiency. Various ranges of differing sensitivity \({S_{{\text{TM}}}}\) of the average ICE efficiency with respect to the average transmission efficiency. I: high sensitivity, II: average sensitivity, III: low sensitivity, IV: nearly no sensitivity

The relationship shown above can be quantified by calculating the sensitivity \({S_{{\text{TM}}}}\) for the three cycles US06, WLTP and NEDC. As already mentioned, the magnitude of the sensitivity of the optimal average ICE efficiency \({\bar {\eta }_{{\text{ICE,opt}}}}\) with respect to the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\) is relatively high, especially at low loads. This is shown in Fig. 9.

Fig. 9

Sensitivity \({S_{{\text{TM}}}}\) according to Eq. (12) of the optimal average ICE efficiency \({\bar {\eta }_{{\text{ICE,opt}}}}\) with respect to the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\) for mean transmission efficiencies between 90 and 100% for a C segment vehicle in US06, WLTP and NEDC

It can also be seen from Fig. 9 that the sensitivities are negative since, with decreasing transmission efficiency, the ICE can generally be operated in operation ranges with higher efficiencies. However, in case of a hybrid drive, a higher transmission efficiency leads to a higher ICE efficiency in most cycles since more energy can be recuperated due to lower transmission losses. In this case, the sensitivity \({S_{{\text{TM}}}}\) is positive. Furthermore, the sensitivity \({S_{{\text{TM}}}}\) can be positive if the average driving resistance power is within the peak power range of the ICE and thus beyond the maximum ICE efficiency. This can be the case, for example, during a sporty highway drive according to the 3D method, which is introduced in [6].

By substituting Eq. (8) into Eq. (6), the following relation is obtained for the transmission effectiveness GE for conventional drives:
$${\text{GE}}=~\frac{{\overline {W} ~ \cdot {{\bar {\eta }}_{{\text{TM}}}}}}{{{S_{{\text{TM}}}} \cdot \left( {\frac{1}{{{{\bar {\eta }}_{{\text{TM}}}}}} - 1} \right)+1}}$$
(13)
Thus, Eq. (13) defines the transmission effectiveness GE as a function of the average conversion quality \(\overline {W}\), the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\) and the sensitivity \({S_{{\text{TM}}}}\) of the optimal average ICE efficiency with respect to the average transmission efficiency. Since, as already described, the sensitivity \({S_{{\text{TM}}}}\) is usually negative, the following holds for the denominator of Eq. (13):
$${S_{{\text{TM}}}}<0~ \Rightarrow ~{S_{{\text{TM}}}} \cdot \left( {\frac{1}{{{{\bar {\eta }}_{{\text{TM}}}}}} - 1} \right)+1<1.$$
(14)
This means that the energy consumption potential of the transmission is less than the product of transmission efficiency and conversion quality suggests, since improvements in the transmission efficiency are partly compensated by efficiency reductions of the ICE. Considering the efficiency approximation in Eq. 12, the following results for the transmission effectiveness GE:
$${\text{GE}}=~\frac{{\overline {W} ~ \cdot {{\bar {\eta }}_{{\text{TM}}}}}}{{\frac{{{{\bar {\eta }}_{{\text{TM}}}} \cdot {P_{{\text{0,ICE}}}}+\frac{1}{{\Delta {\eta _{{\text{ICE}}}}}} \cdot {{\bar {P}}_{{\text{ICE}}}}}}{{1 \cdot {P_{{\text{0,ICE}}}}+\frac{1}{{\Delta {\eta _{{\text{ICE}}}}}} \cdot {{\bar {P}}_{{\text{ICE}}}}}}}}.$$
(15)

In the diagram of the mean conversion quality \(\overline {W}\) as a function of the mean transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\), curves of the same transmission effectiveness GE can now be illustrated. For two transmission concepts with the same transmission effectiveness, the energy consumption potential is the same, although the combinations of the conversion quality and the transmission efficiency can be different. Depending on how the transmission efficiency affects the ICE efficiency, the curves in Fig. 10 are either steeper (as in the US06) or flatter (as in the NEDC). The steeper the lines are, the more important the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\) is for a high transmission effectiveness GE. The flatter the lines, the more important is the conversion quality \(\overline {W}\) to achieve a high transmission effectiveness GE.

Fig. 10

Curves of equal transmission effectiveness GE with variation of driving cycles [US06 (dashed line), WLTP (solid line) and NEDC (dash-dotted line)] as a function of the average conversion quality \(\overline {W}\) and the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\) for a C-segment ICV with a gasoline engine with a peak power of 100 kW

In the idealized case of a transmission with no losses (\({\bar {\eta }_{{\text{TM}}}}\)= 1), the transmission efficiency GE is equal to the average conversion quality \(\overline {W}\). For this case, however, according to Eq. (7), no sensitivity \({S_{{\text{TM}}}}\) can be calculated.

If the mean conversion quality \(\overline {W}\) and the average transmission efficiency \({\bar {\eta }_{{\text{TM}}}}\) are increased to the same extent, the conversion quality leads to higher savings in fuel consumption due to the described sensitivity \({S_{{\text{TM}}}}\) in conventional drives. In addition, the transmission losses tend to increase moderately with an increase in the number of gears. This is the reason why transmissions with many gears and high ratio spread have been developed.

However, for electrified powertrains, different constraints have to be considered due to the recuperation and battery operation. Both conversion quality and transmission efficiency are influenced by the efficiency of the recuperation. Due to the efficiency behavior of an EM, the influence of transmission efficiency and conversion quality on the energy consumption is almost identical. At the same time, as shown in Fig. 7 on the basis of the BEV, a high conversion quality for an electric drive is already achieved with a fixed transmission ratio. Hence, the conversion quality cannot be improved significantly using a transmission with many gears. As a consequence, a reduction of mechanical components to increase the transmission efficiency is more beneficial for the recuperation. Furthermore, the recuperated energy has an increasing effect on the ICE efficiency during the traction phase since lower partial load operation of the ICE is replaced by the battery operation. As can be seen in Fig. 7, the conversion quality increases without modifying the transmission. Applying the concept of load decrease as a consequence of load increase, the conversion quality (but with additional losses) can be further increased.

These effects explain why, in case of electrified drives, an increase in transmission efficiency will lead to further reductions in energy consumption. As shown in [3], an improvement in transmission efficiency of 2% leads to an improvement in fuel consumption of 3%. This will be particularly achieved with dedicated hybrid transmissions (DHT) [1, 2, 7].

The following central aspects can be derived from the transmission effectiveness:

  • Transmission effectiveness is the key benchmark parameter for transmissions.

  • For ICV, the influence of the conversion quality dominates.

  • For HEV, the influence of the transmission efficiency dominates.

  • The transmission efficiency will become more important in all drive concepts.

4 Summary and outlook

The paper explains the influence of the transmission on the energy consumption of a vehicle. In addition to the efficiency of the transmission, the conversion quality has been introduced, which quantifies how efficiently the transmission can operate the connected drive machine. Conversion quality and transmission efficiency influence the energy consumption in different ways. Therefore, the transmission effectiveness is developed to be able to compare different transmissions directly with one another using just one parameter. The higher the transmission effectiveness, the more efficient the transmission operates in the overall context of the drive concept. Furthermore, the transmission effectiveness quantifies the consumption potential of the considered transmission concept.

It is described that in the case of conventional drives, an increase in the conversion quality due to an increased ratio spread has led to reductions in energy consumption, although additional mechanical components tend to result in higher mechanical transmission losses. In the case of electrified drives, however, these correlations are reversed. As the recuperation becomes more efficient, especially through an increase in the transmission efficiency, the transmission efficiency will become increasingly important. At the same time, the electrification allows a significant improvement in the conversion quality with the same transmission concept. Due to these fundamentals, dedicated hybrid transmissions (DHT) will be a key technology to further reduce the energy consumption of hybrid vehicles.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institute of Automotive EngineeringTU BraunschweigBrunswickGermany

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