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Int. J. Vehicle Design, Vol. x, No. x, xxxx 1

Copyright © 200x Inderscience Enterprises Ltd.

Optimal design of power-split hybrid tracked vehicles using two planetary gears

Zhaobo Qin, Yugong Luo and Keqiang Li* Department of Automobile Engineering, State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China Email: [email protected] Email: [email protected] Email: [email protected] *Corresponding author

Ziheng Pan and Huei Peng Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA Email: [email protected] Email: [email protected]

Abstract: Power-split hybrid powertrains have been thus far successfully used for production passenger cars and SUVs but not for tracked vehicles. For example, track-type dozer (TTD) models available on the market tend to use series hybrid powertrains, which frequently require a separate steering mechanism, resulting in lower operating efficiency and the need for large space arrangements. Looking to the future, power-split hybrid technologies have high potential for tracked vehicles to circumvent the limitation. This paper proposes a design process for multi-mode power-split powertrains for TTDs. The powertrain consists of one engine, two motors, and two outputs connected independently to the left and right tracks. This powertrain is designed to achieve separate control of the two sides of the tracks to enable skid steering. In addition, multi-mode ensures that the powertrain can realise central steering and driving backwards using the engine power. To systematically search for all possible designs with two planetary gears, an optimal methodology is proposed. By establishing two characteristic matrices, an automated modelling process is proposed to obtain the dynamic equations quickly and efficiently. A near-optimal energy management strategy call PEARs+ is used to achieve near-optimal fuel economy. The approach successfully identifies two designs that achieve better overall performance compared with the benchmark.

Keywords: hybrid tracked vehicles; power-split hybrid vehicles; optimal design.

Reference to this paper should be made as follows: Qin, Z., Luo, Y., Li, K., Pan, Z. and Peng, H. (xxxx) ‘Optimal design of power-split hybrid tracked vehicles using two planetary gears’, Int. J. Vehicle Design, Vol. x, No. x, pp.xxx–xxx.

AQ1: Please reduce abstract of no more than 150 words.

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Biographical notes: Zhaobo Qin received his BS degree from Tsinghua University in Beijing, China in 2013. He is currently working toward a PhD degree at Tsinghua University of Beijing, China and University of Michigan, Ann Arbor. His research interests include the powertrain design and control of HEV.

Yugong Luo received his BS and MS degrees from Chongqing University in Chongqing, China in 1996 and 1999, respectively, and a PhD degree from Tsinghua University in Beijing, China in 2003. He is currently an Associate Professor with the Department of Automotive Engineering at Tsinghua University. He has authored more than 100 journal papers and holds 48 patent applications. His research interests include electric vehicle dynamics and control and vehicle noise control.

Keqiang Li received his BTech degree from Tsinghua University in Beijing, China in 1985 and a MS and PhD degrees from Chongqing University in Chongqing, China in 1988 and 1995, respectively. He is currently a Professor with the Department of Automotive Engineering at Tsinghua University. He has authored more than 100 papers and holds 32 patents in China and Japan. His research interests include vehicle dynamics and control for driver-assistance systems and hybrid electric vehicles.

Ziheng Pan is currently working toward a Ph.D. degree at University of Michigan, Ann Arbor. His research interests includes the powertrain design and control theory.

Huei Peng received his PhD in Mechanical Engineering from the University of California, Berkeley, CA, USA, in 1992. He is currently a Professor with the Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA. He currently serves as the Director of the University of Michigan Mobility Transformation Center, which is a centre that oversees the Mcity Test Facility and studies connected and autonomous vehicle technologies and promotes their deployment. His research interests include adaptive control and optimal control, with emphasis on their applications to vehicular and transportation systems. His current research focuses include the design and control of electrified vehicles and connected/automated vehicles. He is an Active Member of the Society of Automotive Engineers (SAE) and the American Society of Mechanical Engineers. He is both an SAE fellow and an ASME Fell.

This paper is a revised and expanded version of a paper entitled [title] presented at [name, location and date of conference].

1 Introduction

The depletion of oil resources and environmental concerns have signalled the need for both cars and off-highway vehicles to reduce fuel consumption. Hybrid vehicles can improve fuel economy while enhancing dynamic performance. Hybrid tracked vehicles can be used in the areas of construction, agriculture and the military. This paper aims to design power-split hybrid tracked vehicles, i.e., track-type dozers (TTDs).

Hybrid powertrains for tracked vehicles can be classified into three basic types: series, parallel, and power-split (series-parallel) (Salmasi, 2007). The series hybrid has

AQ2: If a previous version of your paper has originally been presented at a conference, please complete the statement to this effect or delete if not applicable.

Optimal design of power-split hybrid tracked vehicles using two planetary gears 3

been widely researched and become quite popular. Zou et al. (2012) proposed a dual-motor series hybrid powertrain for heavy-duty tracked vehicles, which also considered engine and motor power size. However, as the track-type vehicle consumes significantly more power during steering, the motor size in series hybrids can restrict steering ability and limit their practical use. To solve the steering problem, some research has proposed a separate gear unit for transferring steering power (Chen and Zhao, 2012; Shanmuganathan et al., 2006), while other may use an additional turning horizontal axis for more power (Zhang and Xie, 2005; Wong and Chiang, 2001). The steering mechanism is sizeable, however, and becomes a design challenge. Gai et al. (2015) devised an improved series hybrid powertrain by adding planetary gears between the two motors and the tracks, thus reducing motor power on one side when steering. The structure also became more complex, however, and there was also a disadvantage of lower overall efficiency. The parallel hybrid has also been tested, but the engine performs inefficiently at low speeds (Lin et al., 2003). Some research has studied power-split hybrid tracked vehicles using multi-modes to achieve higher efficiency. However, an additional steering mechanism is also used to effectuate steering which occupies a great deal of space and is not very practical (Schmidt, 2002). In summary, series hybrids have been widely used on tracked vehicles and are cost effective but have a lower efficiency. One well-known series hybrid design is the Caterpillar D7E, which is available as a production TTD (Jo and Kwak, 2011).

Power-split powertrains combine the benefits from both series and parallel hybrid (Taghavipour et al., 2006; Zhang et al., 2015). Since first being released, the Prius, a power-split hybrid vehicle, has drawn people’s attention with its strong performance and superior fuel economy. Two other famous power-split hybrids with different designs are Chevy Volt and Ford Fusion (Grewe et al., 2007; Miller, 2006). A major benefit of these power-split vehicles is that continuously variable transmission can be achieved (Cho et al., 2006). To improve the performance of power-split hybrids, researchers have focused on their control and design (Silvas et al., 2017). Some researchers have worked on developing and verifying control algorithms to achieve better efficiency and performance (Serrao and Rizzoni, 2008; Van Berkel et al., 2012); some others have concentrated on choosing the appropriate design for a power-split powertrain, given a particular type of vehicle. For example, Liu (2007) developed a design approach to exhaustively search all possible designs using two planetary gears. An automated modelling method was proposed as the core technology which made the exhaustive search possible. Yang et al. (2009) compared different types of power-split hybrid powertrains and analysed their behaviours under varying conditions. Zhang et al. (2015) thoroughly searched all power-split designs using two planetary gears and three clutches to determine the optimal multi-mode designs. Bayrak et al. (2013) and Silvas et al. (2015) modelled a topology design as a bond graph and used constraints to automatically generate the feasible near-optimal designs. Zhuang et al. (2016) and Dagci and Peng (2016) took the similar approach. They first identified modes with good driving or fuel economy, and then tried to find clutches to realise the selected modes in a powertrain. While all of the research cited studied different aspects of hybrid powertrain designs, for example, topology, multi-mode, automated modelling, fast near-real-time controls, they all focused on powertrains with one output shaft, meaning the results are applicable to 2WD vehicles. The first to use two outputs in planetary gears to control the front and rear shafts together was Yoshimura (2013) from Toyota. Their design, however, requires an automatic transmission, which adds to the cost and complexity. Pan et al. (2015) first

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conducted an exhaustive search of power-split powertrains with two output shafts which can be applied to 4WD vehicles.

Inspired by the major breakthrough in two-output designs, we will apply the design technology, but for tracked vehicles. A major difference between a hybrid 4WD vehicle and a tracked vehicle is that while the two driven axles achieve largely the same speed, the torques may differ greatly. In contrast, the two tracks on a tracked vehicle can rotate at a very similar speed with the same torque when driving straight, or they can also have very different speed, and very different torques. Especially when turning at a small radius, the torque of the inside track may even be negative. Thus, this paper aims to conduct an exhaustive search for a power-split hybrid TTD for two-planetary gear (PG) designs with up to three clutches. The new type of device will have two output shafts driving the left and right tracks independently. In addition, parameter sizing is also searched to identify the most cost-effective designs. The main contributions of this paper are summarised as follows.

1 We propose a new type of drive system for hybrid TTDs with two planetary gears and three clutches. The power-split configuration enables compact and efficient powertrain designs. In addition, parameter optimisation is included to ‘right-size’ the power components.

2 To enable automatic screening, rules to automatically screen the designs for required attributes are presented. The attributes are verified based on the newly proposed characteristic matrix of the powertrain, which can reflect the speeds and torques relationship of the powertrain components.

3 To check unique driving of the track-type vehicles, for example, skid-steering, central steer, and drive backwards using the engine power, conditions for these attributes to be satisfied are developed. The maximum traction torque is then checked to ensure optimal driving performance. The traction torque and turning radius over all speeds are calculated and used to filter out poorly performing designs. Finally, fuel economy is checked to identify the final optimal designs.

The remainder of this paper is organised as follow. In Section 2, we briefly introduce the design approach for a power-split hybrid TTD. Section 3 describes the dynamics of planetary gears and automated modelling with the generation of two characteristic matrices. In Section 4, the rapid screening process is discussed by progressive conditions. The results of the design process are also presented, compared with the benchmark results. Finally, conclusions are drawn in Section 5.

2 Design approach

The proposed powertrain design consists of one engine, two motors and two outputs connected to the left and right track shafts, respectively, with two planetary gears, similar to the framework in Yoshimura (2013). The initial lever diagram framework for the structure is shown in Figure 1(a) (Benford and Leising, 1981).

Based on Figure 1(a), the components can be assigned to different nodes and clutches are added, so that various powertrain designs for tracked vehicles can be listed. In this paper, a configuration shows how the connections are made between components and nodes as in Figure 1(b). A design means the clutch assignment is determined,


as in Figure 1(c). A mode means the state of clutches for a design is certain, whether engaged or disengaged, as in Figure 1(d). Before explaining the design process, all the design candidates should be generated. The number of PGs in this paper is two, and the total number of PG nodes is six. According to Figure 1(b), configuration represents the location of four components which are the engine, MG1, left output, and right output together with MG2. Each of the four components can connect with any of the six nodes in two PGs. Thus, the total number of configurations is 4

6 360P = . A design represents a configuration with determined number of clutch connections and locations as shown in Figure 1(c). To control the two sides of tracks, respectively, a tracked vehicle requires as least two degrees of freedom (DOF). Few clutches may lead to few modes and low flexibility; too many clutches result in impractical. We use three clutches, which has six modes (three modes with 3-DOF and three modes with 2-DOF). In terms of (Zhang et al., 2015), there are 16 nonredundant clutch positions for two planetary gears with a single output. For a design with two outputs, the number decreases to 15, as both outputs cannot be connected to the brake. Choose three different clutch positions to form a design. Thus, the total design candidate number comes to 4 3

6 15 163,800P C = . Many of them may not be feasible, as they cannot satisfy the requirements of powertrain for TTDs. To arrive at the optimal design rapidly, an optimal design approach is proposed which can be applied to all kinds of power-split hybrid tracked vehicles, as can be seen in Figure 2.

Figure 1 (a) Powertrain components of the design framework; (b) example of a configuration; (c) example of a design and (d) example of a mode (see online version for colours)

First, all designs are mathematised through automated modelling to reflect the speed and torque relations of components. Rapid screening is done taking into consideration the special features of TTDs. In addition, parameter sizing is also included. Finally, the survived optimal designs are compared with the existing series hybrid TTD.

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Figure 2 Diagram of the overall design process (see online version for colours)

3 Dynamics of planetary gears and automated modelling

An analysis of the dynamics of all six nodes in Figure 1(b) of two planetary gears, yields equation (1).

1 1 1 1

_ 2 2 _ 2 2 2

1 1 1 1 1 1

_ 2 _ 2 2 2

1 1 1 1 1

2 2 1 2 2

1 1 1 1 1 1

2 2 _ 2 2 2 2

( ) ( )( )

( )

( ) ( )

( )

( )

e c e e

V r s mg R V r mg

mg s mg mg

V l c F V l

r r cl

r r cl

e r mg

V l r mg

I I T F R SI I I T T F S

I I T F S

I I T F R S

I T F RI T F RR S R S

R S R S

ωω

ωω

ωω

ω ω ωω ω ω

+ = − ++ + = − + +

+ = +

+ = − +

= += − +

+ = +

+ = +

(1)


In equation (1), iR and iS are the radii of the ring gear and sun gear for the ith PG set. eI , _v lI , _v rI , 1mgI , 2mgI represent the rotational inertia of the engine, left output, right

output and motors. T and ω are the torque and angular acceleration of all components. 1F , 2F and 3F represent the internal force of three PGs.

Equation (1) can be matriculated and decomposed into four parts, as in equations (2) and (3).

1 1 1

_ 2 2 2 _

1 1 1 1

2 _ 2 2 _

1 1 1

2 2 2

1 1 1 1 1

2 2 2 2 2

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

0 0 0 0 00 0 0 0 0

e c e

V r s mg V r

mg s mg

c V l V l

r r

r r

I I R SI I I S

I I SI I R S

I RI R

R S S R FS R S R F

ωωωωωω

+ + + + − + − + + −

− + − −

− + −

_ 2

1

_

0000

e

V r mg

mg

V l

TT T

TT

− + − =

(2)

0 0T

J D TD F

Ω =

(3)

J matrix represents the inertias. As the inertias of planetary gears are much smaller compared with those of the components, they will not be considered in this paper. Ω and T matrices are the speeds and torques of the components. F is the internal force of the planetary gears. D matrix is the most important, as it can correspond to a unique design. The details and rules of forming D matrix can be found in Liu (2007).

When clutches are engaged, the D matrix will change with various connections. A new modelling approach is proposed which can improve computation efficiency significantly compared with previous studies by Liu (2007) and Zhang et al. (2015). Transition matrix N is defined according to the clutch engagement. N is initialised as a unit matrix 3 3n nI × , where n represents the number of planetary gears. Then change the initial N matrix as follows:

• If the ath PG node is connected to bth PG node by an engaged clutch, add the elements of ath row of N to bth row, then remove the ath row (ath row is eliminated), which means that th row th row th row and th row []b a b a= + = .

• If the ath PG node is grounded by an engaged clutch, then remove the ath row directly, which means that th row []a = .

After these steps, N becomes a new matrix with the size (3 ) 3n c n− × , where c represents the number of engaged clutches. N is used to obtain the dynamics characteristics of the system after clutch engagement, and the new characteristics matrix is shown in equation (4) together with the new inertia matrix.

* * * *, , ,TD N D J NJN N T N T= ⋅ = Ω = ⋅Ω = ⋅ (4)

While calculating, however, we need to know the exact relationship of speeds and torques among all components, as in equation (5).

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1 2 1 1*

1 1

2 2

=A

eng eng

out mg out mg

mg mg

out out

TT T

TT

ωω

ωω

−

+

(5)

Zhang et al. (2015) has given a kind of transforming method to get A*. When two components are connected directly, however, the method will be complicated by judging the inertia matrix J*, which needs ‘manual’ calculation. To cover all circumstances, the whole process is improved in this paper.

Assuming that: 1* *

* 0 TT

A BJ DB CD

−

=

(6)

Then we can know from equation (2) that:

=ATΩ (7)

From the equation below:

* *

* =0 TT

A BJ DI

B CD

⋅

(8)

We can derive the A, B and C matrices. * *T TB J D C−= − (9)

* * 1 * * * * 1 *( ) ( )T T T T TC D D D J D D D− −= − (10)

* * * * 1 * * * 1=[ ( ) ]T T T TA I J D D J D D J− − − −− (11)

The problem, however, is that the size of A is (3 ) (3 )n c n c− × − , but we need to guarantee that the size of A* is 4 4× , as in equation (5). If the size is A is not 4 4× :

Define another Q matrix with the size of 3 4n×

4 43 4 0n

IQ ×

×

=

(12)

Then matrix A* can be derived as below.

( ) ( )* TA NQ A NQ= (13)

( ) * * * * * 1 * * * 1[ ( ) ] ( )T T T T TA NQ I J D D J D D J NQ′ − − − −= − (14)

It should also be noted that the modelling method above can be applied to all kinds of powertrain with PGs, regardless whether wheeled or tracked.


4 Rapid screening process

Once the state-space model for a mode is obtained, we need to examine whether the mode is feasible. The mode is infeasible if the two outputs are connected to each other in one mode, as it cannot realise skid steering. After screening out the infeasible modes, the remaining can be used for further screening.

4.1 Attribute screening

TTDs require the specification of four attributes. The two outputs can be controlled independently with the engine on, which can also ensure different torques on both sides during skid steering. The powertrain must also take into account driving backwards and central steering. From the A* matrix in equation (15), the attribute screening conditions can be easily written as in Table 1.

* * * *11 12 13 14

* * * ** 21 22 23 24

* * * *31 32 33 34

* * * *41 42 43 44

a a a aa a a a

Aa a a aa a a a

=

(15)

The explanation of Table 1 appears below. From equation (5), we know that: ** *

1 2321 241 1 2 2* * * *

22 22 22 22** *

2 4341 421 1 2 2* * * *

44 44 44 44

( )

outeng out mg mg out

outeng out mg mg out

aa aT T T T T

a a a a

aa aT T T T T

a a a a

ω

ω

= + + + +

= + + + + (16)

If positive output torque at both output shafts can be controlled independently, the engine torque should have the same direction with the output torque, namely

* ** 21 41

* *22 44

rank( ) 2, 0, 0.a a

Aa a

≥ > >

In terms of steering, the powertrain must realise both left and right turning by providing a different and sometimes opposite torque for each side, which means that one of the motors must provide a different direction of torque to outputs. The same applies to central steering. For backwards driving with engine-on, the engine must provide an opposite direction of torque compared with the output torque.

For each design candidate, the four attributes must be checked together. When all attributes can be realised by any of the modes in the design, the design is considered feasible. The parameter sizes will not influence this step, as the relative sign relationship never changes for a specific mode. An exhaustive check of the designs reveals 16 designs that survive without changing parameter sizes.

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Table 1 Attribute screening conditions

Performance Screening conditions

Two outputs controlled independently with engine-on

* ** 21 41

* *22 44

rank( ) 2, 0, 0a aAa a

≥ > >

Steering while driving forwards *rank( ) 2A ≥ , * *

23 43* *

22 44

0A AA A

⋅ <

Driving backwards * * * *

21 41 23 43* * * *

22 44 22 44

0, 0 >0A A A AorA A A A

< < ⋅

Central steering * * * *

* 21 41 23 43* * * *

22 44 22 44

rank( ) 2, 0 or 0A A A AAA A A A

≥ ⋅ < ⋅ <

4.2 Performance screening

After attribute screening, the straight driving and turning performance should be further checked to see whether the powertrain can satisfy the specific requirements. In this study, we adopt the component sizes of a series hybrid TTD in Zou et al. (2014) as reference. The structure of this TTD can be found in Figure 3. The detailed parameters are shown in Table 2.

Figure 3 Schematic diagram of the series hybrid TTD

The series hybrid TTD has two motors and a generator, we adopt only two motors here. The initial component sizes are the same as those of the engine and the two motors of the series benchmark. The battery adopted is a small-sized one, with maximum power of about 130 kW. In this study, parameter sizes, including component sizes, are considered as follows in Table 3. In the table, 0.6, 0.8, 0.9, or 1.0 means the power size of the component is 0.6, 0.8 0.9 or 1.0 times of its initial size, and R/S is the gear ratio.

Every surviving design type after attribute screening can generate 73 =2187 designs with different parameter sizes in Table 3.

The straight and turning performance indexes are first chosen to be loosely restricted to ensure that the design can realise all speeds operating without exceeding the


components’ speed and torque limits. For example, we choose an output torque of 100 Nm at all speeds as the straight driving index and a turning radius of 80 m at all speeds as the steering index. If the design can satisfy both, it will be selected for further validation.

Table 2 Parameters for the series hybrid TTD

Parameter Value Vehicle Vehicle mass (kg) 28,000 Track length (m) 2.73 Track gauge(m) 1.786 Engine Engine displacement (L) 9.3 Rated speed (rom) 1700 Rated power (kW) 200 Generator Max. power(kW) 180 Max. working speed (rpm) 2400 Two Motors Rated power (kW) 85 Max. working speed (rpm) 6200 Battery Capacity (Ah) 45 Rated power (kW) 130

Table 3 Parameter sizing variables

Parameter 1st value 2nd value 3rd value PG1 R/S ratio 1.5 2 2.5 PG2 R/S ratio 1.5 2 2.5 Final drive ratio of output 1 70:1 75:1 80:1 Final drive ratio of output 2 70:1 75:1 80:1 Motor 1 scaling factor 0.8 0.9 1.0 Motor 2 scaling factor 0.8 0.9 1.0 Engine scaling factor 0.6 0.8 1.0

A total of 6848 design candidates with different parameter combinations from six unique design types survive, which means that they can realise basic straight and turning performance at all speeds. The lever diagrams for all kinds of feasible designs are listed as follows in Figure 4. All 6848 designs survived are from these six design types with different variable sizes.

Further screening is conducted in order to compare with the series hybrid benchmark. According to ISO 53.100, the maximum traction torque for dozers while operating is an important index. Thus, the maximum traction torque of all 6848 surviving feasible design candidates are identified and compared with that of series hybrid TTD. The results are shown in Figure 5, where the blue circles are the result of design candidates and the red line represents the maximum traction torque of series hybrid benchmark. A total of 3025 design candidates survive.

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Figure 4 Six feasible design types after preliminary screening (see online version for colours)

Figure 5 Maximum traction torque of all design candidates (see online version for colours)

Following that, the maximum straight driving traction torque and the minimum turning radius should be calculated to attain competitive designs against the benchmark. While straight driving, the speed and torque of both sides of tracks can be regarded as the same. For a determined design, the output torque of both sides of tracks can be calculated using equation (16). Under each determined speed v , the maximum traction torque can be calculated by searching the torque and speed combinations of all components in equation (17).


max

1 2 1 1*

1 1

2 2

_ max

_ max

_ max

1_ max 1 1 1_ max 1

1_ max 1 1_ max

Maximum: ( )Subject to :

=A

00

( ) ( )

eng eng

out mg out mg

mg mg

out out

Batt Batt

e e

e e

mg mg mg mg mg

mg mg mg

m

T v

TT T

TT

P PT T

T T T

T

ωω

ωω

ω ωω ω

ω ω ω

−

+

≤≤ ≤≤ ≤

− ≤ ≤− ≤ ≤

− 2 _ max 2 2 2 _ max 2

2 _ max 2 2 _ max

( ) ( )g mg mg mg mg

mg mg mg

T Tω ωω ω ω

≤ ≤

− ≤ ≤

(17)

While skid steering, the speed and torque of both sides of tracks can be different. The paper adopts differential steering. While the TTD is operating under the speed v , it means that the central speed of the geometric centre cv equals v . The speed of both sides of tracks can be calculated using equation (18).

1

2

12

1+2

Bv vR

Bv vR

= ⋅ −

= ⋅

(18)

where 1v is the speed of the inside track, 2v is the speed of the outside track, R is the turning radius and B is the track gauge. When it comes to the traction torque on both sides of tracks, equation (19) can be obtained with the assumption of zero angular acceleration. Details can be found in Bekker (1956).

1

2

1

2

max

2 2 12

2 2

2 2 12

2 2

0.925 0.15

G LT f rB

R BG LT f r

B

G LT f rB

R BG LT f r

B

RB

µ

µ

µ

µ

µµ

= − ⋅ + ≤ = − ⋅ +

= − ⋅ − > = − ⋅ +

= +

(19)

where G is the gravity of the TTD, r is the rolling radius of the driving wheel, f is the rolling friction coefficient, L is the track length, maxµ is the maximum steering resistance

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coefficient related to the ground type. Equation (19) shows that the torque on both sides of tracks will vary with different values of turning radius. Given the determined central speed of TTD, the minimum turning radius can be calculated using equation (20)

min

1 2 1 1*

1 1

2 2

_ max

_ max

_ max

1_ max 1 1 1_ max 1

1_ max 1 1_ max

Minimum : ( )Subject to :

=A

00

( ) ( )

eng eng

out mg out mg

mg mg

out out

Batt Batt

e e

e e

mg mg mg mg mg

mg mg mg

m

R v

TT T

TT

P PT T

T T T

T

ωω

ωω

ω ωω ω

ω ω ω

−

+

≤≤ ≤≤ ≤

− ≤ ≤− ≤ ≤

− 2 _ max 2 2 2 _ max 2

2 _ max 2 2 _ max

( ) ( )g mg mg mg mg

mg mg mg

T Tω ωω ω ω

≤ ≤

− ≤ ≤

(20)

To evaluate the overall performance, we have chosen the indexes as in equation (21). max max

max min0 1

max max

( ) ( );

1

v v

v vT v R v

T Rv v

= == =+

∑ ∑ (21)

where max ( )T v is the maximum traction torque for the design at the speed vs. min ( )R v is the average minimum left and right turning radius for the design at the central speed v. T and R represent the mean values of the traction torque and turning radius of all speeds, which will be used to judge the overall performance. Calculate all the 3025 design candidates surviving; results are shown in Figure 6. The x-axis is the expectation of maximum traction torque, while the y-axis represents the expectation of minimum turning radius. For all design candidates, larger traction torque with smaller turning radius is preferred.

The red large circle point in Figure 6 is the performance of the series hybrid benchmark. Design candidates which have larger traction toque and smaller turning radius are regarded as better designs compared with the benchmark. All designs in the better design area in Figure 6 are reserved. 212 surviving design candidates are all from design types (3), (5) and (6) in Figure 4. Other candidates of design types (1), (2) and (4), with either weaker straight driving performance or turning performance, cannot satisfy the requirements. These 212 surviving design candidates will be further verified.

4.3 Fuel economy screening

For TTDs, fuel economy is also considered. Dynamic programming (DP) is a typical method used for global optimisation. However, using DP in our complicated design with different modes will greatly increase the computation time. For each design, the


computation time would be about 4 hours using an Intel i-5 16G computer. To minimise the overall losses and improve the computation load, an algorithm proposed by Zhang et al. (2015) named power-weighted efficiency analysis for rapid sizing (PEARS+) is used and improved to give near-optimal control of all the remaining designs. The procedure is shown in Figure 7. The typical cycle is first discretised into vehicle speed-torque cells. All EV and HEV modes are analysed to determine the maximum overall efficiency with optimal operating states. The EV and HEV modes here refer to those with and without the engine running. Then DP is used only to identify the optimal mode shift control strategy. Details can be found in Zhang et al. (2015). It should also be noted that the mechanical path efficiency in PGs is negligible as the power loss can be relatively low. The power loss in the hydraulic system of TTDs is not considered.

Figure 6 Straight driving and turning average performance at all speeds (see online version for colours)

Figure 7 Procedures of PEARs+

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Figure 8 The Simulink diagram of the hybrid powertrain for TTD: (a) electric system; (b) engine system and (c) transmission system


The Simulink diagram of the hybrid powertrain is presented in Figure 8, which consists of the transmission system, engine system and electric system. The transmission system is modelled by the procedure proposed in Section 3, namely the automated modelling approach. The engine system is modelled by the look-up table formed by the experimental data. The electric system consists of two motors and the battery. The motors are also identified by the static look-up tables, while the battery model is an equivalent circuit with an open circuit voltage plus internal resistance. The rotational inertias of the engine, motors and the vehicle are all included in order to simulate the dynamic response of all components. Since the inertias of the gear nodes in PGs are much smaller than the components, they are negligible. The power losses of the electric path are included by using the operating efficiency of the motors and the battery. The power loss of the engine can be calculated using the power and fuel rate. The efficiency of the mechanical path in PGs is negligible as the power loss can be relatively low. The Simulink model will be used together with the control strategy generated by the Matlab codes to conduct the forward simulation. The process can be summarised: the demand output speed and torque are used as the input of the control strategy, PEARs+, to calculate the control executions of engine and motor torque under each speed and torque segment in the determined driving cycle; then the dynamic trajectories and states of the TTD can be simulated using the Simulink model with the input of engine and motor torque which is generated by PEARs+.

This paper adopts a typical driving cycle of a real TTD’s working velocities shown in Figure 9 (Zou et al., 2014; Song et al., 2016; Wang et al., 2017). The working stages in the cycle can be described as follows: 1~4 s travelling; 4~16 s soil-cutting; 16~31 s soil-transportation; 31~33 s unloading soil stage; and 33~50 s no-load travelling.

Figure 9 Typical driving cycle with demand speeds and torques (see online version for colours)

The operating torque can be calculated through the speed and the soil-cutting depth. It is assumed here that the depth is confirmed and that the ground condition does not change. The torque can be calculated from Bekker (1956).

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The fuel economy of the series hybrid benchmark is calculated first through PEARs+, which is approximately 0.902 mpg. The fuel economy results for all 212 design candidates which have survived the previous performance screening are shown in Figure 10. The figure has shown that three of the design candidates have better fuel economy than the series hybrid TTD. Two of these final surviving design candidates fall into design type (5), while the other one falls into design type (6). Since the control of the series hybrid benchmark and our design candidates are both conducted by PEARs+, the results are fair. Moreover, the fuel economy of the best design is about 2.6% better than that of the series benchmark.

The three better designs that survived can be used as optimal designs, with better overall performance than the series hybrid TTD in Figure 3. The detailed parameters can also be found in Table 4. The specific modes of the three better designs are shown in Figure 11.

Figure 10 Fuel economy of all 212 surviving designs under certain cycle (see online version for colours)

Table 4 Parameters of three optimal designs

Design type in Figure 4 (5) (5) (6) Design number 1 2 3 PG1 R/S ratio 2 2.5 1.5 PG2 R/S ratio 2.5 2.5 2.5 Final drive ratio of output 1 80:1 80:1 70:1 Final drive ratio of output 2 70:1 70:1 70:1 Motor 1 scaling factor 1.0 1.0 1.0 Motor 2 scaling factor 0.9 0.9 1.0 Engine scaling factor 0.6 0.6 0.6 Fuel economy (mpg) 0.916 0.925 0.907 Improvement (compared with series hybrid TTD) 1.6% 2.6% 0.7%

AQ3: Please check if the highlighted design types are ok.


Figure 11 Modes of design type (5) and (6) (see online version for colours)

For the three optimal designs, the best performance of straight driving and turning are calculated at all speeds, compared with those of the series benchmark in Figure 12. In Figure 12(b), despite the fact that at certain speeds design No. 2 performs a little worse, it has better average performance than the series benchmark.

The results show that the designs have much better driving performance than the series benchmark. In addition, the number of motors has decreased to two, compared with three in the series hybrid TTD. Moreover, the selected optimal designs have adopted motors and the engine with a smaller power size to realise even better overall performance.

The optimal control using PEARs+ for design No. 1 and series hybrid TTD are shown in Figure 13. The figure indicates how the outputs and power components operate under a typical cycle. Figure 13(a) shows the working state of the series hybrid TTD, where MG2 means the generator in Figure 3 and MG1 means one of the two driving motors, with a fuel economy of 0.902 mpg. Figure 13(b) shows that the design No. 1 achieves near-optimal fuel economy of 0.916 mpg.

The engine operating points during the cycle for design No. 1 are given in Figure 14. It shows that the engine does not always work in the high efficiency area. That is also why the design did not show much improvement in fuel economy, which is one of the disadvantages of using two motors. For the 3DOF mode in the design, the engine speed can be controllable while the engine torque is well-determined without flexibility; for the 2DOF mode in the design, the engine torque can be controllable while the engine speed is unchangeable (Pan et al., 2015). Thus the fuel economy may not be guaranteed under all conditions. If another motor or another PG is used, the engine can be ‘fully’ controllable, which is also illustrated in Liu (2007). It is one of our future tasks to overcome the disadvantage.

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Figure 12 Overall performance comparison: (a) performance of design No. 1 (design type (5)); (b) performance of design No. 2 (design type (5)) and (c) performance of design No. 3 (design type (6)) (see online version for colours)


Figure 13 (a) PEARs+ result for the series hybrid TTD and (b) PEARs+ result for design No. 1 (see online version for colours)

To conclude, the new kind of powertrain using 2 PGs presents many advantages and great potential for the design of hybrid tracked vehicles with improved overall performance. For future work, another motor will be added to improve overall performance even further.

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Figure 14 Engine operating points of design No. 1 under certain cycle (see online version for colours)

5 Conclusions

In this paper, an optimal design approach is proposed for conducting an exhaustive search of all designs for power-split hybrid tracked vehicles using two planetary gears and three clutches. The approach consists of three steps: automated dynamics modelling, rapid feasible screening, and fuel consumption optimisation. The dynamic characteristic matrices have been established to indicate one unique configuration in a new method. To reduce computational load, PEARs+ is used to evaluate fuel economy performance. The series hybrid TTD is used as the benchmark. In the end, the three designs that survived have shown better straight driving and turning performance with improved fuel consumption. The principal conclusions can be drawn as follows:

• A new kind of powertrain with two planetary gears using one engine, two motors, two outputs and three clutches for tracked vehicles is proposed, having advantages over the current series hybrid powertrain and potential in the future for tracked vehicles.

• A design approach for the powertrain of power-split hybrid tracked vehicles is proposed. This paper takes TTD as an example, though the design approach is comprehensive and can also be used for other types of tracked vehicle powertrain designs.

• Straight driving, steering, central steering and driving backwards are used to reduce the design pool to a manageable size. In addition, maximum traction torque, traction torque and turning radius expectations are also used to screen the design candidates.


• Parameter sizing is also done in this work. The results show that while using two motors and reducing the size of both the engine and the motor, the overall performance can be better than the benchmark. In future work, the design will adopt three motors in order to achieve much better designs.

Acknowledgements

This paper was sponsored by National Science Foundation of China (Grant No. 51575295), and National Key R&D Program (Grant No. 2016YFB0100905).

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