10.2

Comparison between Input Coupled and Output Coupled Power-split Configurations in Hybrid Vehicles

Kai Loon Cheong, Perry Y. Li, Stephen Sedler, and Thomas R. Chase Department of Mechanical Engineering, University of Minnesota

ABSTRACT

Hybridizing powertrains of vehicles has been a popular solution to reduce fuel consumption. The power-split architecture offers advantages from both the series and parallel architectures. The two simplest power-split configurations are input coupled and output coupled transmissions. This paper presents a comparison between these two power-split configurations on a light weight hydraulic hybrid vehicle. The size of the pump/motors and gear ratios in the transmission are optimally selected to minimize the total loss for a standard federal driving cycle on each configuration. In the optimization process, in addition to the normal power-split operation, individual pump/motors were allowed to be locked up to reduce losses in the components. This results in each configuration being able to operate in four distinct modes. The optimization process then chooses the operation mode at each time instant to minimize the overall fuel consumption. Results show that mileage is similar for both architectures but the optimal pump/motor sizes of input coupled is slightly smaller and their operational characteristics are different. However, the two architectures present different challenges to controlling the vehicle dynamics, depending on whether control of the wheel speed or torque is desired. Applying the same optimization method, electric hybrid is briefly compared with hydraulic hybrid vehicle, and result shows they are comparable in fuel economy.

INTRODUCTION

Hybrid drivetrain systems has been studied intensively and developed in recent years, in pursuit of more fuel efficient propulsion systems due to concerns about energy availability and environmental impacts. Hybrid powertrain systems involve two or more power sources for propulsion. Generally, the primary power source is supplied by an internal combustion engine, and the secondary power source can be hydraulic, pneumatic or electric machines. Excess power and braking power is stored into batteries, ultra-capacitors, accumulators or flywheels and then used in vehicle launch or engine load leveling.

When the secondary power source is small, it is not used to propel the vehicle, only to achieve engine start-stop. Such methods are generally referred to as mild

hybrids. When the secondary power source is substantial, both power sources drive the vehicle simultaneously. Such vehicles are referred to as full hybrids [5]. Several hybrid architectures are commonly available in the market and they offer different advantages due to different operational characteristics. Three major types of hybrids exist, i.e. series, parallel and power-split hybrids. A series hybrid has no direct mechanical linkage that connects the engine to the wheels. Therefore, it is capable of decoupling the engine operation from the vehicle power requirement at one instant, allowing the engine to operate at any desired point. Nevertheless, the series architecture suffers a double energy conversion loss all the time. In contrast, parallel architectures transfer the majority of the power through an efficient and reliable mechanical shaft. However, it lacks the freedom to manage the engine operation optimally. The power-split architecture offers the advantages of both the series and parallel architectures, yielding an attractive configuration.

The basic idea of a power-split transmission is to transmit a portion of the power though a continuously variable unit (CVU) and to send the remaining power through a mechanical path that is generally higher in efficiency. Equipping the transmission with a secondary power source provides an extra degree-of-freedom, enabling the powertrain to perform full engine management. This can have significant impact on fuel economy. Unlike a pure power-split transmission, or a continuous variable transmission (CVT), the engine operation can be limited to a instantaneous power curve. In this paper, analysis will focus on hybrid operation instead of operation as a CVT.

A methodology to design a hydraulic hybrid delivery truck is presented in [2]. It involves permutation of the input/output relationship and screens the possibilities through a mechanical feasibility check. Using two planetary gearsets and two clutches to construct the transmission, this method yields 1,152 potential candidate configurations. This three-step-methodology requires exhaustive search through all possibilities. The approach taken in this study consider generalized instead of discrete choice configurations, which results in simpler optimization procedure.

Two basic configurations of power-split architecture are analyzed in this paper: input and output coupled. They

are defined by the location of the power-split device in the transmission. As a stand-alone transmission, each configuration has distinct efficiency characteristics which have been analyzed in [1]. However, hybrid operation could potentially change the operation of the transmission entirely, thus transforming the operational characteristics and efficiency of different configurations. Fuel economy over the prescribed drive cycle is used as the performance index to be optimized for comparison. For the energy management strategy, the Lagrange multiplier method [10] is utilized for rapid simulation and optimization. It has been found that the fuel economy approximates the case when the energy storage capacity is limited but moderately large. To ensure each configuration is evaluated equally, the component sizes, including the gear ratios and continuously variable units, are optimized to assess the maximum possible performance achievable by each architecture.

In this paper, analysis and simulation is mainly focusing on light weight hydraulic hybrid vehicles (HHV). However, the optimization methodology presented in this paper can be used on electric hybrids and a brief comparison between hydraulic and electric hybrid vehicle is discussed.

TRANSMISSION CONFIGURATIONS

The Hydro-Mechanical Transmission (HMT), a form of hydraulic power-split transmission, is the focus of this paper. HMT combines a hydrostatic transmission and at least one power-split device, for example a planetary gearset (PG), to achieve the power-split feature. The two simplest power-split configurations are input coupled and output coupled transmissions. This paper presents a comparison between these two power-split configurations.

Figure 1: Input coupled power-split Hydraulic Hybrid Passenger Vehicle at University of Minnesota

One example of the output coupled power-split vehicle is the Toyota Prius hybrid electric vehicle. One example of the input coupled power-split vehicle is the Hydraulic Hybrid Passenger Vehicle (HHPV) testbed at the Center for Compact and Efficient Fluid Power (see Fig.1) [3]. This light-weight hybrid vehicle design, approximately 900kg, consists of a downsized 1.1L diesel engine with

peak power of 19.5kW. This light vehicle is modified with 28cc swash-plate variable displacement pump/motors, together with two hydraulic composite accumulators. The hydraulic units are connected to a high pressure and a low pressure accumulator.

The motivation of this paper is to study the differences between an input coupled and an output coupled hybrid vehicle. The current design of the HHPV is investigated and the potential improvements that can be achieved by optimizing the pump/motor sizes and gear ratios are explored. More importantly, we explore whether one architecture is clearly superior to the other.

INPUT COUPLED ARCHITECTURE

11, PMPM Tω

engeng T,ω vehveh T,ω

22, PMPM Tω

Figure 2: Input coupled transmission architecture

An input coupled transmission splits the power from the engine with a fixed gear and returns it to the output shaft with a power-split device [7], as shown in Fig. 2. The speed of pump/motor 1, ʻUnit 1ʼ, is in fixed ratio of the input speed, hence the name Input Coupled (IC) configuration. This configuration is also called Output Split as the planetary gear is connected to the output shaft.

Since speed of Unit 1 is coupled to the engine speed, its torque serves as a torque control variable, meaning that the engine torque operation can be manipulated by Unit 1 torque. Therefore, Unit 1 is described as the ʻtorquerʼ. Using the same analogy, pump/motor 2, or ʻUnit 2ʼ, is denoted as ʻspeederʼ because one can change the engine speed by changing the speed of Unit 2 [3]. Thus, full engine management can be achieved.

OUTPUT COUPLED ARCHITECTURE

An output coupled transmission reverses the arrangement of the input coupled configuration. Engine power is split using a power-split device and returned to the output shaft using a fixed gear (Fig.3). Unit 2 has a fixed speed ratio with the output shaft speed, hence this architecture is named the output coupled (OC) configuration or input split configuration [6]. Analogous to the terminology used for input coupled, Unit 1 is the ʻspeederʼ and Unit 2 is the ʻtorquerʼ for output coupled

power-split, the control torque is however, applied to the output shaft.

The transmissions mentioned above use only one planetary gearset to realize the power-split feature. Additional planetary gearsets and clutches can be used to achieve discrete gear shifts that are similar to a conventional automatic transmission. Two or more planetary gearsets can potentially improve performance and reduce hydrostatic unit size at the price of increasing complexity and cost. Other power-split configurations are described in [1], such as compound coupled and dual stage input coupled transmissions. They are, however, not discussed or simulated in this paper.

11, PMPM Tω 22, PMPM Tω

engeng T,ω vehveh T,ω

Figure 3: Output coupled architecture

Unlike pure power-split transmissions in which the hydraulic power produced by one pump/motor is totally consumed by the other, a hydraulic hybrid power-split transmission incorporates accumulators that can absorb or supplement power. This allows the engine to operate at a different, potentially more efficient, power curve than that indicated by the instantaneous demand from the vehicle.

GENERALIZED TRANSMISSION MODELING

Despite the differences in the architectures, power-split transmissions can always be interpreted as a four-port device that transfers power from one port to another [4]. On a hydraulic hybrid vehicle, these four ports link to the engine, the two pump/motor units and the wheels.

Therefore, any power-split transmission can be represented using the following generalized notation:

!!"!!!"! =

!!! !!"!!" !!!

!!"!!"# (1)

and G is defined as

! =!!! !!"!!" !!!

where ωpm1 and ωpm2 are the pump/motorsʼ speed, ωin is the input shaft speed, normally equal to the engine speed, and ωout is the output shaft speed or the wheel speed. The matrix G is the geometrical matrix that describes the connections and the kinematic relationships of the power-split transmission.

Since the speed relationships are defined by G, the steady-state torque relationship can be derived from power conservation within the transmission, by ignoring the inertias and losses of the planetary components,

!!"!!!"!

= −!!! !!"!!"#

Thus, with the torque relationship directly obtained from the kinematic matrix, static analysis can be done with ease.

Physically, the kinematic relationship of the transmission in Eq. (1) can generally be realized with gears that are commonly present in a hydro-mechanical transmission, shown as

!!"!!!"! =

−!!!!"!! !!!!"#!(1 + !!)−!!!!"(1 + !!) !!!!"#!!

!!"!!"# (2)

where R1, R2 are fixed gear ratios on the two pump/motors, Rin is the fixed gear ratio from the engine, and Rout is the ratio of the output shaft, which is equivalent to the final drive ratio. ρ1 and ρ2 represent the ratios between sun gear and ring gear of the planetary gearsets. These ratios correspond to the components shown in Fig. 4. From Eq. (2), it can be determined that the combinations of the gear ratios are not unique. Theoretically, one can select different gear ratios to generate the identical matrix G.

R1

K

R2

11 , PMPM Tω

vehveh T,ωengeng T,ω

22, PMPM Tω

Rin Routρ1 ρ2

Figure 4: Generalized representation of a power-split configuration

The input coupled configuration is realized by simply select ρ1 = -1. The kinematic relationship then becomes

!!"!!!"! !"

=!!!!" 0

−!!!!"(1 + !!) !!!!"#!!!!"!!"# (3)

where the speed coupling between the engine and Unit 1 becomes evident. The Unit 2 speed can be determined if the desired engine and wheel speed are known. Speed limitations are easily checked during the optimization of the design.

Similarly, to represents the output coupled architecture, simply select ρ2 = -1. Equation (2) then takes the form:

!!"!!!"! !"

= −!!!!"!! !!!!"#(1 + !!)0 −!!!!"#

!!"!!"#  (4)

Setting either ρ1 or ρ2 = -1 physically reduces either the input or output planetary gearset to a fixed gear ratio.

From a different perspective, Eq. (1) can be interpreted as a multiplication of Eq. (3) and Eq. (4), i.e. a combination of input and output coupled into one compound power-split. Mathematically, this can be shown by decomposing Eq. (1) with LU factorization.

!!"!!!"! !"

= !!! !!"0 !!!

!!! 0!!" !!!

!!"!!"# (5)

As a consequence to the non-uniqueness of this factorization, it allows the optimization of the power-split transmission to be unconstrained. This generalized representation allows input or output coupled configurations as well as compound power-split configurations to be considered.

OPTIMIZATION OF TRANSMISSION DESIGN AND HYBRID OPERATION

For equal comparison between the two power-split architectures, two aspects must be addressed: the optimal sizing of the components and the optimal operation of the hybrid powertrain. These aspects are discussed in the following two sections.

COMPONENT SIZING

Component sizing plays a significant role in a hydraulic hybrid vehicle as it is required to fulfill certain performance requirements but also determines the overall efficiency of the split power flow. In this study, vehicle weight and engine size are picked apriori and not optimized in the process. For consistent comparison, the same engine, reference vehicle weight (1000kg) and drag characteristics (drag coefficient = 0.5, frontal area = 1.784 m2) as taken from the HHPV testbed in Fig. 1 are

utilized throughout the study. A combined drive cycle, shown in Fig. 6, consisting of the EPAʼs Urban Dynamometer Driving Schedule (UDDS) and the Highway Schedule is used as the standard drive cycle. It is assumed a clutch is available between the transmission and the engine so that the engine can be disengaged from the vehicle speed when deemed advantageous.

The selected reference engine map is as shown in Fig. 5. The engine used in this study is the 1.1L 3 cylinder diesel engine used in the HHPV testbed. Fuel consumptions at only a few operating points are available from the manufacturer. For comparison purpose, a Willansʼ line method [12] is used to extrapolate the data to form a complete engine efficiency map (Fig. 5). The maximum possible fuel economy of the drivetrain can be determined by assuming ideal transmission efficiency and that the engine is running at its most efficient operating point. In this case, 29.3% peak efficiency is achieved at 2600 rpm, 70Nm. Table 1 shows the upper bound fuel economy for this particular engine. These values serve as an ultimate target for designing the transmission and managing energy within it. An important point to be noted is that the more efficient the engine is, the higher the fuel economy that the hybrid vehicle can ideally achieve.

Figure 5: Willansʼ line approximated engine efficiency map

The hydraulic pump/motor sizes are to be optimized in this study. To do so, a set of scalable baseline torque and flow characteristic maps are used. As the displacement varies, the torque and flow are assumed to scale linearly with displacements for a given pressure and speed. Thus, it is assumed that the efficiency maps of the pump/motor are invariant when plotted with respect to the normalized torque or flow. The maximum overall efficiency of this map is 95.6% but the efficiency drops off quite rapidly at lower displacements. While these maps are representative of legacy pump/motors, more efficient pump/motors are available.

2.9289e-008 2.9289e-0080.01 0.010.02 0.020.03 0.030.04 0.04

0.05

0.050.05

0.06

0.060.06

0.07

0.070.07

0.080.08

0.080.08

0.090.09

0.090.09

0.10.1

0.10.1

0.110.11

0.110.11

0.120.12

0.120.12

0.130.13

0.130.13

0.140.14

0.14 0.14

0.150.15

0.15 0.15

0.160.16

0.160.1

6

0.17

0.17

0.17

0.17

0.18

0.18

0.18

0.19

0.19

0.19

0.2

0.2

0.2

0.21

0.21

0.21

0.22

0.22

0.22

0.23

0.23

0.23

0.24

0.24

0.25

0.25

0.26

0.26

0.26

0.27

0.27

0.28 0.29

Engine speed [rpm]

Engi

ne to

rque

[Nm

]

1000 1500 2000 2500 3000 35000

10

20

30

40

50

60

70

Output Coupled Input Coupled

Table 1: Maximum possible mileage performance for the specific engine

Drive cycle Mileage [mpg] City 104.9

Highway 63.9 Combined 76.5

Optimization of the gear ratios is achieved by optimizing the elements in the Matrix G in Eq. (1) instead of optimizing individual gears (i.e. R1, R2, ρ1, ρ2, etc). For input coupled architecture, the G12 element is set to 0 whereas for output coupled architecture, G21 is set to 0. Once an optimal G matrix has been obtained, it can be realized by choosing individual gear designs according to the relationships in Eq. (3) and (4). Notice that this realization is not unique but each realization provides the same performance. Additional criteria such as compactness can be used in determining the choice. By avoiding the evaluation of multiple realizations with ultimately the same kinematic relation, the approach of optimizing the matrix G should be computationally more efficient than direct enumeration approach in [2].

HYBRID OPERATION OPTIMIZATION

Optimal control is used to evaluate the performance of each configuration of the two power-split architectures.

The control of the hydraulic hybrid vehicle can be explicitly decomposed into a three level hierarchical structure [3]. Low level control is dedicated to regulate and track the transmissionʼs desired speed and torque in real time. In this particular analysis, it is assumed to achieve ideal regulation and tracking. The mid level control specifies, for the given vehicle speed, demand wheel torque and the desired hydraulic accumulator power, the optimal operating speed and torque of the engine and hydrostatic unit that minimizes losses. This control level interfaces with both the high level and low level controllers. High level control manages the accumulator state-of-charge by determining the optimal accumulator power usage over the drive cycle.

Figure 6: Combined Federal Drive Cycle for transmission optimization

Instead of minimizing the fuel consumption, the definition of optimality is minimizing the total losses. Minimization of total loss over the powertrain system is equivalent to reducing the fuel consumption [3]. Thus for a given vehicle operating condition, a static optimization problem for a specific powertrain design can be formulated as follows:

!"##∗ !!"! ,!!"#$% ,!,!!""=

!"#!!"#,!!"#

!"##!"! !!"! ,!!"#$% ,!!"#,!!"#,! (6)

where ωveh is the vehicle wheel speed, Tdrive is the required torque on the wheel, Qacc is the net flow to the accumulator, ωeng is the engine speed, Teng is the engine torque, and P is the system pressure.

High level optimal control can be expressed as:

!"#!!""(∙)

!"##∗ !!"! ! ,!!"#$% ! ,!,!!"" ! !"!"#$%  !"!#$

(7)

subjected to the terminal condition constraint on the SOC. The hydraulic accumulator charge is required to stay within this capacity at all time and to return to its initial charge state at the end of the specified drive cycle, i.e. SOC(t0) = SOC(tfinal).

Generally, to solve the constrained optimization problem of the hybrid vehicle operating over a prescribed drive cycle, deterministic dynamic programming is required for obtaining the global optimum. However, the computation can be greatly simplified if the accumulator size is unrestricted and the operating pressure is assumed to be constant. This method of analysis can offer rapid optimal solution and yet provide insight into the drivetrain design apart from sizing the accumulator [3].

200 400 600 800 1000 1200 1400 1600 1800 20000

5

10

15

20

25

Vehi

cle

spee

d [m

/s]

Time [s]

Urban-Highway Combined Cycle

City

Highway

With these assumptions made, a Lagrange multiplier method can be utilized for solving the vehicle operation optimal control design over the drive cycle. The problem in Eq. (7) is then re-formulated into Eq. (8). This method significantly reduces the computational burden.

!"#!

!"#!!""(∙)

(!"##∗ !!"! ! ,!!"#$% ! ,!,!!"" !!"#$%  !"!#$

+ ! ⋅ !!!""(!))!"

(8)

Another operation that can further improve the efficiency of the powertrain is to provide the option to shut off the hydraulic units individually from the hydraulic line. Volumetric and/or friction losses can be reduced considerably by doing so. Moreover, adding the ability to lock up the pump/motors offers the flexibility to operate in different modes.

Table 2: Definitions of the operating modes

Archit. Modes Input coupled Output coupled

HMT Power-split operation

Power-split operation

S-only Engine disengaged ʻTʼ unit locked up

Engine disengaged ʻTʼ unit free-spin

T-only Engine disengaged ʻSʼ unit locked up

Engine disengaged ʻSʼ unit locked up

Parallel ʻSʼ unit locked up ʻSʼ unit locked up Four distinct operating modes are defined for both power-split configurations. For the input coupled case, the first mode is the HMT mode, which is the normal power-split operation. Second mode is the S-only mode, meaning the propulsion of the vehicle relies only on the ʻspeederʼ unit, with the ʻtorqueʼ unit being locked up and the engine declutched. Similarly, the third mode is the T-only mode, where only the ʻtorqueʼ unit is driving the vehicle, and the ʻspeederʼ unit is locked up and the engine is disengaged. Lastly, the fourth mode is Parallel mode, which is essentially the parallel hybrid architecture with the ʻspeederʼ unit locked up. Modes for the output coupled configuration are then defined in a similar manner. In principle, one other mode is possible by disengaging the engine and drive with both pump/motors cooperatively. However, this mode does not offer much efficiency benefits, hence excluded in the simulation. Mode switching smoothness is not considered in this preliminary analysis for simplicity. The modes of operations are summarized in Table 2.

With the modes defined, simulation through the drive cycle can be further simplified by allowing only specific operating points of the engine. From results from dynamic programming, it was shown that energy management control tends to operate the engine only at the most efficient ʻsweetʼ spot and turn it off (or subject it

to zero load) when itʼs not needed and drive with the hydraulics only. This translates to the reduction of HMT mode to operating the engine only at its most efficient point, and parallel mode to operating engine at the highest efficiency for the instantaneous engine speed. With this simplification and the inclusion of operating modes, the high level drive cycle optimization in Eq. (8) reduces to

!"#!

!"#!"#$% (!"##!"#$ !!"! ! ,!!"#$% ! ,!

!"#$%  !"!#$

+      ! ⋅ !!!""(!"#$%, !))!"

(9)

where Lossmode is defined as the losses of all modes at that instant. Meanwhile, this optimization requires that the drive cycle is at least drivable in HMT mode when Twheel > 0, or else the particular transmission design is rejected. This restriction ensures the vehicle is drivable regardless of the accumulator charge

The overall optimization process can be summarized as follows:

1. Initialize the matrix G in Eq. (1) (with G12 = 0 for input coupled and G21 = 0 for output coupled architecture) and pump/motor sizes.

2. Calculate system losses for each operating mode at each time point throughout the drive cycle.

3. Check HMT mode drivability requirements. If fails,

iterate design parameters.

4. Optimize the drive cycle by determining the mode to apply at each time point throughout the drive cycle according to Eq. (9).

5. Evaluate the achieved fuel economy for the combined drive cycle.

6. Iterate the design parameters step 2, 3 and repeat step 3 to minimize fuel consumption for the combined drive cycle.

7. Evaluate the optimized designʼs fuel economies for the individual urban and highway cycles.

RESULTS AND DISCUSSIONS

Preliminary results show that fuel economies achieved by both architectures throughout the combined drive cycle are similar, with input coupled architecture performed about 5% slightly more efficient, as shown in Table 3. In terms of hydraulic units sizing, total pump

displacement for output coupled architecture is 14% larger, which could result in projected 15kg heavier. The results shown are optimized at a constant pressure of 13 MPa (1950 psi), the lowest pressure possible, as set by the pre-charge pressure of the high pressure accumulator.

Table 3: Comparison of design and mileage

Architecture Input coupled

Matrix G 1.0175 02.0660 −8.3570

P/Msʼ size P/M-1 = 26.6 cc P/M-2 = 28.8 cc

City 78.6 [mpg]

Highway 56.1 [mpg]

Combined 64.2 [mpg]

Architecture Output coupled

Matrix G 1.2768 −4.04240 4.7239

P/Msʼ size P/M-1 = 23.9 cc P/M-2 = 39.1 cc

City 72.7 [mpg]

Highway 54.9 [mpg]

Combined 61.2 [mpg]

Comparing results to the upper bound fuel economy in Table 1, both architectures achieves near ideal fuel economy for highway cycle. While they are generally efficient on combined cycle, there is still a substantial room for improvement in the City cycle. A discrete gear shift could potentially ameliorate the need for optimizing City and Highway drive cycles simultaneously.

In reality, system pressure varies from the pre-charge pressure to the maximum pressure of the accumulator (assumed to be 34.5 MPa (5000 psi) in this study) throughout the entire drive cycle. Therefore, with the optimized transmission design parameters, the fuel economy performance is evaluated again using a higher system pressure. Since the hydraulic pump/motor units assumed are inherently inefficient at low displacement, fuel economy of the transmission tends to be lower, setting the lower bound for the specific design. Thus, in actual driving conditions, the fuel mileage should lie between the bounds depicted in Fig. 7.

Figure 7: Fuel economy bounds for varying system pressure (red line: input coupled, light green line: output coupled architecture expected fuel consumption band)

Figures 8 and 9 show the distribution of the operating modes throughout the prescribed drive cycle. The operating modes are plotted according to the wheel speed and torque. Notice that the engine is on only during HMT and parallel modes. These account for approximately 33% of the time when the engine is at full power generating the excess energy efficiently to be stored for use at other times.

As seen in both cases, parallel mode operation is preferred at conditions of high speed and low torque, as experienced mainly in highway situations. As for regenerative braking scenarios (wheel torque < 0), the ʻtorquerʼ unit is frequently used at lower braking torque level while the ʻspeederʼ unit is used for heavy braking in the input coupled configuration. Output coupled transmissions brake using the ʻtorquerʼ unit only.

For the input coupled configurations (Fig. 10), the ʻspeederʼ unit operates generally in efficient regions with a very small amount of power recirculation. The ʻtorquerʼ unit operates in a widespread fashion but only in positive speed.

1500 2000 2500 3000 3500 4000 4500 500020

25

30

35

40

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60

65

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75

Fuel

Eco

nom

y [m

pg]

Operating pressure [psi]

Input coupledOutput coupled

0 10 20 30 40 50 60 70 80 90-600

-400

-200

0

200

400

600

wheel speed (rad/s)

whee

l tor

que

(Nm

)

HMTSonlyTonlyParallel

Figure 8: Input coupled configuration modes distribution

Figure 9: Output coupled configuration modes distribution

Figure 10: Hydraulic Units operation for input coupled configuration (blue: 'speeder', red: 'torquer')

For the output coupled configuration, the ʻspeederʼ unit operates throughout the entire ranges of displacement, while the ʻtorquerʼ mainly operates in pumping mode. Both units are aligned to drive in positive speed only (Fig. 11).

Operating points of the pump/motors are plotted in Fig. 10 and Fig. 11. The contour lines are the stylized efficiency map. These results indicate that the pump/motors are not operating in very high efficient regions in order to optimize the engine performance. Thus, improving pump/motor efficiencies over a broad range of operating conditions is expected to benefit the fuel economy greatly.

Figure 11: Hydraulic Units operation for output coupled configuration (blue: 'speeder', red: 'torquer')1

CONTROLS ASPECT

Even though the low level control that enables the transmission to track the desired trajectories is ignored in the analysis and performance evaluation, a few distinctions between the two configurations are evident in terms of drivability of the vehicle.

Torque control: the input coupled architecture has a simpler control strategy since the torque applied by the ʻspeederʼ directly influences the wheel torque, as shown in Eq. (10). For output coupled architecture, wheel torque is a summation from the planetary gear output and the ʻtorquerʼ unit, as seen in Eq. (11); thus, a good coordination of torque is necessary.

!!"!!!"! !"

=

!!!!!!"

!(!!!!)!!!!"#!!

0 !!!!!!"#!!

!!"!!"#

(10)

!!"!!!"! !"

=

!!!!!"!!

0(!!!!)!!!!"!!

!!!!!"#

!!"!!"#

(11)

Neutral position: While a clutch is assumed to be available between the engine and the transmission to achieve neutral in this study. A hydro-mechanical transmission can, in principle, achieve neutral without a clutch. For the input coupled architecture, this is achieved by setting the ʻspeederʼ unit to zero displacement. For the output coupled architecture, precise control of the ʻspeederʼ unit is needed to oppose the engine torque on the planetary gearset to achieve zero wheel torque.

Hill-hold mode: Here zero wheel speed is desired. Output coupled architecture needs only to set the 1 The actual efficiency map is not shown to protect confidential data.

0 10 20 30 40 50 60 70 80 90-600

-400

-200

0

200

400

600

wheel speed (rad/s)

whee

l tor

que

(Nm

)

HMTTonlySonlyParallel

ʻspeederʼ unit to zero displacement. For input coupled architecture the ʻspeederʼ unit needs to be controlled to achieve braking torque, i.e. opposite sign to the vehicle speed.

HYBRID ELECTRIC TRANSMISSION OPTIMIZATION

The optimization procedures presented in the previous section are also applicable to designing and analyzing hybrid electric (HEV) power-split vehicles. The main difference between the hydraulic and electric optimization is the power-split components and the energy storage units. Electric hybrids replace the hydrostatic unit with a set of permanent magnet motor/generators. Figure 12 shows the baseline efficiency characteristic map provided by ADVISOR [11], rated to 49 kW. The average efficiency is higher than the hydraulic units, with a wide range of high 90% efficiency operating points. For energy storage, the accumulator from the previous simulation is replaced with a NiMH battery pack (30kW and 300V nominal voltage). The rest of the parameters and components remain the same as in the HHV case.

Figure 12: Motor/Generator efficiency map from ADVISOR

The component sizing optimization results are summarized in Table 4. The major difference is that the units on electric machines differ in size by a factor of two or more. Interestingly, this analysis has produced a set of optimal component sizes that is comparable to the Toyota Prius (output coupled). Similar to HHV, the optimized HEV drivetrain is highly fuel efficient in the highway cycle. Unlike the hydraulic hybrid, electric hybrid output coupled performed better in City cycle while input coupled architecture is slightly more efficient in Highway cycle. Both of them, however, yield the same fuel economy in combined cycle.

Table 4: HEV configurations comparison

Fuel Economy Input Coupled Output Coupled City 82.4 mpg 83.5 mpg

Highway 58.5 mpg 57.9 mpg Combined 66.8 mpg 66.8 mpg

M/G sizes M/G 1: 29.4 kW M/G 2: 65.0 kW

M/G 1: 14.2 kW M/G 2: 64.2 kW

The chart in Fig. 13 summarizes the overall comparison of the fuel economy between input/output coupled configurations and HHV/HEV type hybrids.

Figure 13: Fuel economy comparison for input and output coupled configurations on HHV and HEV

In general, HEVs and HHVs have comparable fuel economies being 8% more fuel efficient on the combined cycle. This result is reasonable given the electric motor/generator being more efficient than the hydraulic pump/motors over a broad operating range, and the assumption of a light-weight vehicle (approx. 1000kg), where regenerative braking does not significantly impact the fuel economy.

For the HEV to achieve the fuel economy in Fig. 13, the batteries need to be sufficiently large to absorb and provide the power needed (~30kW). This would require a battery pack that is 50% larger than the one in Toyota Prius (which is capable of 21kW). This translates to higher cost and weight. The power requirement on the battery would be more severe if the vehicle weight or a more stringent acceleration requirement is imposed. The weight of the battery is projected to increase from 40kg to 60kg. This issue, however, does not arise with a hydraulic accumulator. Especially on heavy duty vehicles, high power density leads to accumulators being favored over batteries.

This analysis also shows that an optimized drivetrain design and a well-designed energy management strategy is crucial, as it allows the engine to operate mainly in the most efficient region, substantially increasing the mean engine efficiency throughout the drive cycle.

Further studies are required to compare not only different architectures, but also the effects of various vehicle sizes, weights and the imposition of additional

9.6231e-008

9.6231e-008

9.6231e-008

9.6231e-0089.6231e-0089.6231e-0089.6231e-008

9.6231e-008

0.05

0.05

0.05 0.05

0.05

0.05 0.050.05

0.05

0.05

0.1 0.10.1 0.1

0.1

0.1

0.1 0.1

0.1

0.1

0.15

0.15

0.15 0.15

0.15

0.15 0.150.15

0.15

0.15

0.2

0.2

0.2 0.2

0.2

0.2 0.20.2

0.2

0.2

0.25

0.25

0.25 0.25

0.25

0.25 0.250.250.25

0.25

0.3

0.3

0.3 0.3

0.3

0.3 0.30.3

0.3

0.3

0.35

0.35

0.35 0.35

0.35

0.35 0.350.350.35

0.35

0.4

0.4

0.4 0.4

0.4

0.4 0.40.4

0.4

0.4

0.45

0.45

0.45 0.45

0.45

0.45 0.450.45

0.45

0.45

0.5

0.5

0.5 0.5

0.5

0.5 0.50.5

0.5

0.5

0.55

0.55

0.55 0.55

0.55

0.55 0.550.55

0.55

0.55

0.6

0.6

0.6 0.6

0.6

0.6 0.60.6

0.6

0.6

0.65

0.65

0.65 0.65

0.65

0.65 0.650.650.65

0.65

0.7

0.7

0.7 0.7

0.7

0.7 0.70.70.7

0.7

0.75

0.75

0.75 0.75

0.75

0.75 0.750.75

0.75

0.75

0.8

0.8

0.8 0.8

0.8

0.8 0.8

0.80.8

0.8

0.85

0.85

0.85 0.85

0.85

0.85 0.85

0.850.85

0.85

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.90.9

0.9

0.95

0.95

0.95

0.95

Speed [rpm]

Torq

ue [N

m]

49kW motor efficiency map

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

-250

-200

-150

-100

-50

0

50

100

150

200

250

0  

20  

40  

60  

80  

100  

120  

City   Highway   Combined  

Ideal  

HHV  (IC)  

HHV  (OC)  

HEV  (IC)  

HEV  (OC)  

acceleration requirements. Drive cycle or duty cycle will also affect the optimal sizing of the powertrain, which in turn could potentially change the operational characteristics of different configurations.

CONCLUSION

This paper has presented a generalized power-split transmission model and the methodology to optimize the hybrid drivetrain. The Lagrange Multiplier method is applied to greatly reduce the computational burden as compared to dynamic programming, allowing rapid simulation for different optimized power-split designs.

Preliminary results show that the fuel economy for both transmissions is similar, with input coupled architecture yields slightly better fuel economy and smaller pump/motor sizes. However, each transmission type exhibits distinct operating behavior.

A major distinction between the two configurations occurs in the controls aspect. Depending on which control scenario on the wheel is desired, input coupled configuration is advantageous to wheel torque control, while output coupled benefits wheel speed control.

The same optimization method is also applied to hybrid electric vehicles, and the component sizing trend is considerably different than the hydraulic case. Further study is planned to investigate the effect of overall vehicle weight and duty cycle on the optimal design for both configurations and on both HHV and HEV.

ACKNOWLEDGMENTS

This material is based upon work supported by the National Science Foundation under grant number EEC-0540834.

REFERENCES

1. Blake Carl, Monika Ivantysynova and Kyle Williams, “Comparison of Operational Characteristics in Power Split Continuously Variable Transmissions,” SAE International, 2006-01-3468.

2. C-T, Li and H. Peng, “Optimal Configuration Design for Hydraulic Split Hybrid Vehicles,” American Control Conference, Baltimore, MD, 2010.

3. P.Y. Li and F. Mensing, “Optimization and Control of a Hydro-Mechanical Transmission based Hybrid Hydraulic Passenger Vehicle,” 7th International Fluid Power Conference, Aachen 2010.

4. Sciarretta, A., Dabadie, J-C. and Albrecht, A., “Control-Oriented Modeling of Power Split Devices in Combined Hybrid-Electric Vehicles,” SAE International, 2008-01-131.

5. Jinming Liu, Huei Peng and Zoran Filipi, “Modeling and Analysis of the Toyota Hybrid System,” Proceedings of the 2005 IEEE/ASME, International Conference on Advanced Intelligent Mechatronics, Monterey, California, USA, 2005.

6. John M. Miller, “Hybrid Electric Vehicle Propulsion System Architectures of the e-CVT Type,” IEEE Transactions on Power Electronics, vol. 21, no. 3, May 2006.

7. T. Kohmascher and H. Murrenhoff, “Advanced Modeling of Hydro-Mechanical Power Split Transmission,” Proceedings of 6th FPNI-PhD Symposium, West Lafayette 2010.

8. Doug Fussner, Glenn Wendel and Chris Wray, “Analysis of a Hybrid Multi-Mode Hydromechanical Transmission,” SAE International, 2007-01-1455.

9. M. Duoba, H. Lohse-Busch, R.Carlson, T. Bohn and S. Gurski, “Analysis of Power-Split HEV Control Strategies Using Data from Several Vehicles,” SAE 2007-01-0291.

10. A. Bryson and Y.-C. Ho, “Applied Optimal Control,” Taylor and Francis Group, 1975.

11. Advanced Vehicle Simulator (ADVISOR), NREL. 12. Richard Stone, “Introduction to Internal Combustion

Engines”, SAE International; 3rd Edition, 1999. DEFINITIONS, ACRONYMS, ABBREVIATIONS

IC: Input Coupled configuration

OC: Output Coupled configuration

HMT: Hydro-Mechanical Transmission

CVU: Continuous Variable Unit

CVT: Continuous Variable Transmission

HHV: Hydraulic Hybrid Vehicle

HEV: Hybrid Electric Vehicle

SOC: State-Of-Charge

P/M: Hydraulic Pump/Motor

M/G: Electric Motor/Generator

NiMH: Nickel-Metal Hydride