# Design Method for Hybrid Electric Vehicle Powertrain Configuration with a Single Motor

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analyses on Basic Scheme

#### 2.1. Analyses of Basic Scheme of Speed Coupling

#### 2.1.1. Speed-Decoupling Capability

_{n}, is defined as the ratio of n

_{e}to n

_{out}. Therefore, determining the engine points distributed in the SER by i

_{n}and n

_{out}along with the constraints of Equations (1) and (2) allows the evaluation of these schemes. The parameters of the power source used in this study are listed in Table 1. The speed-decoupling ability of the six basic schemes was calculated, as shown in Figure 4 and Table 2. The results show that schemes b and d have no speed-decoupling ability, and in the other schemes, the speed-decoupling ability is rapidly weakened with an increase in T

_{out}.

#### 2.1.2. Electric Power Characteristics

#### 2.1.3. Torque Amplification Capability

_{out}, k, and n

_{out}of each scheme were calculated, as shown in Figure 6. Among these schemes, the T

_{out}of schemes a, b, and d decreases with the increase in k; the T

_{out}of schemes e and f increases with the increase in k; however, the T

_{out}of scheme c is less affected by k. For the maximum T

_{out}, schemes b and d have poor torque transmission performance because of their quantities of T

_{out}, whose maximum does not exceed 55 Nm; schemes a and c exhibit the best torque transmission performance; schemes e and f are average. As n

_{out}increases, the MG speed enters the constant-power region, and T

_{mg}decreases. Therefore, the peak of T

_{out}is limited. As shown by a, c, and f, the maximum T

_{out}begins to bend downward and decreases sharply when n

_{out}reaches a certain value.

#### 2.2. Analyses of Basic Scheme of Torque Coupling

_{mg}and i

_{e}, and the second is that i

_{mg}is not related to i

_{e}. Here, the motor transmission ratio and engine transmission ratio are i

_{mg}and i

_{e}, respectively.

#### 2.2.1. Torque-Decoupling Capability

_{mg}is wider, such as in Scheme Ⅱ. Third, for Scheme Ⅰ, with a motor in front of the transmission, a strong torque-decoupling ability can be obtained without a complicated structure.

#### 2.2.2. Torque Amplification Capacity

_{out}of the configurations and n

_{out}should be discussed using the same set of transmission ratios. Accordingly, the k

_{i}of Scheme Ⅰ and the i

_{mg}of Schemes Ⅱ and Ⅲ are optimized, employing an acceleration time of 0–100 km as the objective function. The optimization and simulation results of the maximum T

_{out}are shown in Table 5, and all schemes have similar maximal T

_{out}curve shapes. By comparison, Scheme Ⅰ has a better dynamic performance, with the shortest acceleration time and the highest peak T

_{out}. In the second type of scheme, the dynamic performance of Ⅲ-a is significantly worse than that of the other schemes. For II-a and II-c, they do not require a significant number of motor gears, because the difference in power performance is not guaranteed, and there is no need to increase the motor gears at the expense of the system complexity.

#### 2.3. Selection of Basic Scheme

_{mg}and i

_{e}should be as large as possible, and the gear numbers of i

_{e}and i

_{mg}should not be significantly large. Subsequent works are based on these schemes and the conclusions above.

## 3. Reconstruction of Configuration

_{out}. If transmission can decouple T

_{out}from the wheel, the torque of the PG components can be well adjusted. Therefore, placing a transmission on the output shaft of the PG is the ideal choice. The scheme of torque coupling combined with transmission is analyzed in detail in Section 2.2.

## 4. Optimization and Evaluation

#### 4.1. Multi-Objective Optimization

#### 4.1.1. Parameters and Premise

#### 4.1.2. Objective Function

_{out}, and the calculation processes of peak T

_{out}are shown in Figure 13. The processes were divided into speed coupling and torque coupling.

_{out}is obtained according to Formula (6).

_{i}, corresponding to each working point was calculated using the process shown in Figure 15 under two coupling methods.

_{sys}represents system efficiency at both discharging and charging. The rate of fuel consumption is

_{i}can be obtained by comparing f

_{i_n}and f

_{i_T}to obtain the economy objective function, as follows:

_{1}and w

_{2}are the weights corresponding to the fuel consumption and acceleration time, respectively. In the economic target item, “1000” is a standardization parameter, and the unit is gram. Similarly, “13” is another standardized parameter, and the unit is second.

#### 4.1.3. Constraints and Optimization Results

#### 4.2. Evaluation and Analysis of Configuration

_{k}, corresponding to one driving cycle is defined as:

_{req}(L/100 km), an ideal consumption made by the self-requirement of the working conditions, is not associated with the configuration. Fuel (L/100 km), which is determined by the configuration and working conditions, is a parameter of interest; E is the energy consumption calculated by the integral of P

_{req}; P

_{req}is the power demand at a certain moment; and s is the mileage corresponding to the working conditions.

_{k}are listed in Table 11. The adaptability, f, of the configuration under the four working conditions can be calculated using Formula (18).

_{ij}is the result of standardizing x

_{ij}, $\overline{x}$ is an average from the indicator of a certain row, j, in Table 13, and $\sqrt{\mathit{var}({x}_{j})}$ is the variance of the indicator of a certain row, j.

## 5. Simulation and Verification

#### 5.1. Fuel Economy

#### 5.2. Power Performance

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$HEV$ | Hybrid electric vehicle |

$PG$ | Planetary gear |

$SER$ | Speed economic range |

$TER$ | Torque economic range |

$MG$ | Motor/generator |

$DP$ | Dynamic programming |

${n}_{e}$ | Speed of engine |

${n}_{out}$ | Speed of PG’s output shaft |

${n}_{s}$ | Speed of PG’s sun gear |

${n}_{c}$ | Speed of PG’s carrier gear |

${n}_{R}$ | Speed of PG’s ring gear |

${n}_{mg}$ | Speed of motor/generator |

${T}_{s}$ | Torque of PG’s sun gear |

${T}_{R}$ | Torque of PG’s sun gear |

${T}_{c}$ | Torque of PG’s carrier gear |

${T}_{e}$ | Torque of engine |

${T}_{out}$ | Torque of PG’s output shaft |

${T}_{mg}$ | Speed of motor/generator |

$k$ | Ratio of teeth number of PG ring gear to teeth number of PG sun gear |

${i}_{e}$ | Ratio of engine speed |

${i}_{g}$ | Speed ratio of transmission |

${i}_{mg}$ | Speed ratio of motor |

${k}_{i}$ | Coupling coefficient |

${t}_{100}$ | Acceleration time of 0–100 km/h |

WLTP | World Light Vehicle Test Procedure |

HWFET | Highway Fuel Economy Test |

ARTERIAL | ARTERIAL Cycle |

LA92 | California Unified Cycle |

## References

- Qing, L.; Feng, G. Summary and suggestions on new energy automobile industry development policies. In Proceedings of the 9th China Science and Technology Policy and Management Academic Annual Conference, Jinan, China, 26–27 October 2013; pp. 1–14. [Google Scholar]
- Eshani, M.; Gao, Y.; Gay, S.; Emadi, A. Modern Electric, Hybrid Electric, and Fuel Cell Vehicles; CRC Press: New York, NY, USA, 2009. [Google Scholar]
- Shi, D.; Pisu, P.; Chen, L.; Wang, S.; Wang, R. Control design and fuel economy investigation of power split HEV with energy regeneration of suspension. Appl. Energy
**2016**, 182, 576–589. [Google Scholar] [CrossRef] - Yang, H.; Cho, S.; Kim, N.; Lim, W.; Cha, S. Analysis of planetary gear hybrid powertrain system part 1: Input split system. Int. J. Automot. Technol.
**2007**, 8, 771–780. [Google Scholar] - Yang, H.; Kim, B.; Park, Y.; Lim, W.; Cha, S. Analysis of planetary gear hybrid powertrain system part 2: Output split system. Int. J. Automot. Technol.
**2009**, 10, 381–390. [Google Scholar] [CrossRef] - Lei, Y.; Minghui, H. Parameter optimization and performance analysis of a new power split powertrain. J. Chongqing Univ.
**2020**, 43, 12–20. [Google Scholar] - Shengdun, Z.; Xuesong, Y.; Hongwei, Y.; Yuanyuan, Y. Parameter optimization of a two mode planetary coupled hybrid electric power system. In Proceedings of the China Association for Science and Technology Annual Meeting, Beijing, China, 30 May 2016; pp. 27–31, 52. [Google Scholar]
- Wang, W.; Song, R.; Liu, S.; Zhai, X.; Cao, Y. An analysis on the configuration of dual-mode power-split hybrid powertrain system. Automot. Eng.
**2015**, 724, 648–654. [Google Scholar] - Zhen, W.; Yahui, C.; Baohui, X.; Xiaofeng, X. Analysis and design of dual mode power split continuously variable transmission. J. Mech. Transm.
**2020**, 44, 49–58. [Google Scholar] - Benford, H.; Leising, M. The Lever Analogy: A New Tool in Transmission Analysis; SAE Technical Paper No. 810102; SAE International: Warrendale, PA, USA, 1981. [Google Scholar] [CrossRef]
- Yan, H.-S. A methodology for creative mechanism design. Mech. Mach. Theory
**1992**, 27, 235–242. [Google Scholar] [CrossRef] - West, D.B. Introduction to Graph Theory; Pearson College Div: New York, NY, USA, 2006. [Google Scholar]
- Yan, H.-S.; Chiu, Y.-T. An algorithm for the construction of generalized kinematic chains. Mech. Mach. Theory
**2013**, 62, 75–98. [Google Scholar] [CrossRef] - Yan, H.-S.; Chiu, Y.-T. An improved algorithm for the construction of generalized kinematic chains. Mech. Mach. Theory
**2014**, 78, 229–247. [Google Scholar] [CrossRef] - Hoang, N.-T.; Yan, H.-S. Configuration Synthesis of Novel Series-Parallel Hybrid Transmission Systems with Eight-Bar Mechanisms. Energies
**2017**, 10, 1044. [Google Scholar] [CrossRef] [Green Version] - Ngo, H.-T.; Yan, H.-S. Configuration synthesis of parallel hybrid transmissions. Mech. Mach. Theory
**2016**, 97, 51–71. [Google Scholar] [CrossRef] - Tao, D.; Hao, Z.; Peng, T. Research on structural innovation design of parallel hybrid powertrain. Automot. Eng.
**2018**, 40, 997–1004. [Google Scholar] - Yang, Y.; Mi, J.; Hu, X.; Qin, D. Graph theory modeling and dynamics analysis on the coupled planetary transmission system of HEV. Automot. Eng.
**2015**, 54, 9–15. [Google Scholar] - Yalian, Y.; Qiyuan, D.; Qiangshou, L. A neural network fuel consumption model hybrid of EVT system. J. Chongqing Univ.
**2019**, 42, 1–9. [Google Scholar] - Deng, T.; Tang, P.; Su, Z.; Luo, Y. Systematic Design and Optimization Method of Multimode Hybrid Electric Vehicles Based on Equivalent Tree Graph. IEEE Trans. Power Electron.
**2020**, 35, 13465–13474. [Google Scholar] [CrossRef] - Kang, J.; Kim, H.; Kum, D. Systematic Design of Input- and Output-Split Hybrid Electric Vehicles with a Speed Reduction/Multiplication Gear Using Simplified-Lever Model. IEEE Trans. Intell. Transp. Syst.
**2019**, 21, 3799–3810. [Google Scholar] [CrossRef] - Liu, J.; Peng, H. A systematic design approach for two planetary gear split hybrid vehicles. Veh. Syst. Dyn.
**2010**, 48, 1395–1412. [Google Scholar] [CrossRef] - Jiang, X.; Hu, J.; Peng, H.; Chen, Z. A Design Methodology for Hybrid Electric Vehicle Powertrain Configurations with Planetary Gear Sets. J. Mech. Des.
**2020**, 143, 1–16. [Google Scholar] [CrossRef] - Zhang, X.; Li, S.E.; Peng, H.; Sun, J. Efficient Exhaustive Search of Power-Split Hybrid Powertrains with Multiple Planetary Gears and Clutches. J. Dyn. Syst. Meas. Control
**2015**, 137, 121006. [Google Scholar] [CrossRef] - Peng, H.; Qin, D.; Hu, J.; Fu, C. Synthesis and analysis method for powertrain configuration of single motor hybrid electric vehicle. Mech. Mach. Theory
**2019**, 146, 103731. [Google Scholar] [CrossRef] - Gu, J.; Zhao, Z.; Chen, Y.; He, L.; Zhan, X. Integrated optimal design of configuration and parameter of multimode hybrid powertrain system with two planetary gears. Mech. Mach. Theory
**2019**, 143, 103630. [Google Scholar] [CrossRef] - Silvas, E.; Hofman, T.; Serebrenik, A.; Steinbuch, M. Functional and Cost-Based Automatic Generator for Hybrid Vehicles Topologies. IEEE/ASME Trans. Mechatron.
**2015**, 20, 1561–1572. [Google Scholar] [CrossRef] [Green Version] - Gupta, A.; Ramanarayanan, C. Analysis of circulating power within hybrid electric vehicle transmissions. Mech. Mach. Theory
**2013**, 64, 131–143. [Google Scholar] [CrossRef] - Kim, H.; Kum, D. Comprehensive Design Methodology of Input- and Output-Split Hybrid Electric Vehicles: In Search of Optimal Configuration. IEEE/ASME Trans. Mechatron.
**2016**, 21, 2912–2923. [Google Scholar] [CrossRef] - Wang, W.; Song, R.; Guo, M.; Liu, S. Analysis on compound-split configuration of power-split hybrid electric vehicle. Mech. Mach. Theory
**2014**, 78, 272–288. [Google Scholar] [CrossRef] - Suzuki, Y.; Nishimine, A.; Baba, S.; Miyasaka, K.; Tsuchida, M.; Endo, H.; Yamamura, N.; Miyazaki, T. Development of New Plug-in Hybrid Transaxle for Compact-Class Vehicles; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2017. [Google Scholar]

**Figure 11.**Reconstruction of configuration results. (

**a**) Reconstruction of the S schemes. (

**b**) Reconstruction of T schemes.

**Figure 13.**Calculation process of max T

_{out.}(

**a**) Calculation process of speed-coupling scheme. (

**b**) Calculation process of the torque-coupling scheme.

Power Source | Parameter | Value | Unit |
---|---|---|---|

MG | Rated power | 50 | kw |

Rated/maximum speed | 4000/12,000 | rpm | |

Peak torque | 120 | Nm | |

Engine | Maximum power | 63 | kw |

Peak torque | 138 (@3900 rpm) | Nm | |

Speed range | 800–6000 | rpm |

Scheme | a | b | c | d | e | f |
---|---|---|---|---|---|---|

Percentage of decoupling region | 40.39% | 0 | 46.98% | 0 | 29.44% | 33.25% |

Type | Scheme | MG in Front of Transmission | MG in Transmission | MG behind of Transmission |
---|---|---|---|---|

1 | Ⅰ | i_{mg} = i_{e} | — | — |

2 | Ⅱ-a | — | i_{mg1} = 1, i_{mg2} = 4 | — |

Ⅱ-b | — | i_{mg1} = 1, i_{mg2} = 1.5 | — | |

Ⅱ-c | — | i_{mg1} = 1, i_{mg2} = 2, i_{mg3} = 4 | — | |

Ⅲ-a | — | — | i_{mg} = 1 | |

Ⅲ-b | — | — | i_{mg} = 2 |

Scheme | Ⅰ | Ⅱ-a | Ⅱ-b | Ⅱ-c | Ⅲ-a | Ⅲ-b |
---|---|---|---|---|---|---|

Decoupling region | 50.8% | 51.9% | 45.1% | 56.7% | 39% | 44% |

Scheme | Parameters of Optimization | ${\mathit{t}}_{100}$ | Curve of Speed-T_{out} |
---|---|---|---|

Scheme Ⅰ | k_{i} = 1.38(i _{mg} = k_{i}i_{e}) | 7.05 s | |

Scheme Ⅱ-a | i_{mg1} = 4i _{mg2} = 1.5 | 7.24 s | |

Scheme Ⅱ-c | i_{mg1} = 4i _{mg2} = 2.49i _{mg3} = 1.83 | 7.18 s | |

Scheme Ⅲ-a | i_{mg} = 2 | 8.55 s |

Project | A | B | C | D | E |
---|---|---|---|---|---|

Speed-decoupling ability | c | a | e, f | — | b, d |

Electrical power characteristic | e | a | c, f | — | b, d |

Torque amplification capability | a | c | e, f | — | b, d |

Variable | Scope | Max Quantity |
---|---|---|

Speed ratio of transmission–engine (i_{e}) | 0.5–5 | 4 |

Speed ratio of transmission–motor (i_{mg}) | 0.5–5 | 2 |

Coupling coefficient (k_{i}) | 0.5–2 | 1 |

PG characteristic parameter (k) | 1.5–4 | 1 |

Final drive ratio (i_{0}) | 3–6 | 1 |

Parameter | Value | Unit |
---|---|---|

Curb weight (m) | 1760 | kg |

Frontal area (A) | 2.5 | m^{2} |

Drag coefficient (Cd) | 0.313 | - |

Mass conversion factor (δ) | 1.04 | - |

Tire radius (r) | 0.347 | m |

Adhesion coefficient (μ) | 0.9 | - |

Rolling resistance coefficient (f) | 0.015 | - |

Motor/Generator rated power | 62 | kw |

Motor/Generator rated speed | 4000/9000 | rpm |

Motor/Generator peak torque | 150 | N∙m |

Engine max power | 63 | kw |

Engine peak torque | 138(@3900 rpm) | N∙m |

Engine speed scope | 800–6000 | rpm |

Scheme | Speed Equation | Torque Equation |
---|---|---|

S-1 | ${n}_{o}{i}_{g}=\left(\frac{k{n}_{e}+{n}_{mg}}{(1+k)}\right)$ | $\frac{{T}_{o}}{{i}_{g}}=\left(1+k\right){T}_{mg}=\frac{\left(1+k\right){T}_{e}}{k}$ |

S-2 | ${n}_{o}{i}_{g}=\frac{\left(k{n}_{mg}+{n}_{e}\right)}{\left(1+k\right)}$ | $\frac{{T}_{o}}{{i}_{g}}=\left(1+k\right){T}_{e}=\frac{\left(1+k\right){T}_{mg}}{k}$ |

S-3 | ${n}_{o}{i}_{g}=\frac{\left(\left(1+k\right){n}_{mg}-{n}_{e}\right)}{k}$ | $\frac{{T}_{o}}{{i}_{g}}=k{T}_{e}=\frac{k{T}_{mg}}{(1+k)}$ |

S-4 | ${n}_{o}{i}_{g}=\frac{\left(\left(1+k\right){n}_{e}-{n}_{mg}\right)}{k}$ | $\frac{{T}_{o}}{{i}_{g}}=k{T}_{mg}=\frac{k{T}_{e}}{(1+k)}$ |

T-1 | ${n}_{e}={n}_{o}{i}_{e}$$,{n}_{mg}={n}_{o}{i}_{e}{k}_{i}$ | $\frac{{T}_{o}}{{i}_{e}}={T}_{e}+{T}_{mg}{k}_{i}$ |

T-2 | ${n}_{e}={n}_{o}{i}_{e}$$,{n}_{mg}={n}_{o}{i}_{mg}$ | ${T}_{o}={T}_{e}{i}_{e}+{T}_{mg}{i}_{mg}$ |

Scheme | k | i_{0} | i_{e1} | i_{e2} | i_{e3} | i_{e4} | k_{i} | i_{mg1} | i_{mg2} |
---|---|---|---|---|---|---|---|---|---|

S-1 | 1.98 | 5.69 | 4 | 2.18 | 1.43 | 0.63 | — | — | — |

S-2 | 1.51 | 5.1 | 4 | 2.05 | 1.44 | 0.69 | — | — | — |

S-3 | 3.16 | 4.58 | 4 | 2.28 | 1.6 | 0.78 | — | — | — |

S-4 | 1.5 | 5.97 | 4 | 2.39 | 1.47 | 1.07 | — | — | — |

T-1 | — | 5.51 | 3.9 | 1.83 | 1.21 | 0.65 | 1.5 | — | — |

T-2 | — | 4.75 | 3.93 | 2.3 | 1.54 | 0.76 | — | 3.98 | 1.51 |

f_{k} | HWFET | ARTERIAL | LA92 | WLTC |
---|---|---|---|---|

S-1 | 2.96 | 4.78 | 2.72 | 2.83 |

S-2 | 2.97 | 4.74 | 2.76 | 2.82 |

S-3 | 2.80 | 4.66 | 2.79 | 2.80 |

S-4 | 2.89 | 4.54 | 2.73 | 2.80 |

T-1 | 3.35 | 5.52 | 2.83 | 2.88 |

T-2 | 3.44 | 5.62 | 2.86 | 2.89 |

Indicator | S-1 | S-2 | S-3 | S-4 | T-1 | T-2 |
---|---|---|---|---|---|---|

Fuel consumption (L/100 km) | 4.78 | 4.76 | 4.74 | 4.74 | 4.86 | 4.88 |

Acceleration time 0–100 km(s) | 7.44 | 7.72 | 7.94 | 7.64 | 9.44 | 7.83 |

Adaptability f | 3.32 | 3.32 | 3.26 | 3.24 | 3.64 | 3.70 |

Indicator | S-1 | S-2 | S-3 | S-4 | T-1 | T-2 |
---|---|---|---|---|---|---|

Economy | −0.22 | −0.54 | −0.87 | −0.87 | 1.08 | 1.41 |

Dynamic property | −0.77 | −0.39 | −0.09 | −0.50 | 1.98 | −0.24 |

Adaptability | −0.46 | −0.46 | −0.76 | −0.86 | 1.12 | 1.42 |

Parameter | k | i_{0} | i_{mg} | i_{r} |
---|---|---|---|---|

value | 2.78 | 3.91 | 1.48 | 1 |

Power Loss (kW) | <0.3 | 0.3–0.4 | 0.4–0.5 | 0.5–0.8 | 0.8–1 | 1–1.5 | >1.5 |
---|---|---|---|---|---|---|---|

THS (%) | 17.29 | 3.22 | 5.36 | 19.3 | 16.89 | 29.62 | 8.31 |

S-4 (%) | 68.23 | 6.03 | 5.63 | 11.13 | 5.5 | 3.08 | 0.4 |

Fuel Consumption (g/kWh) | <260 | 260–280 | 280–300 | 300–320 | 320–350 | 350–380 | >380 |
---|---|---|---|---|---|---|---|

THS (%) | 67.69 | 9.79 | 6.84 | 2.41 | 3.49 | 8.71 | 1.07 |

S-4 (%) | 40.21 | 22.65 | 10.32 | 5.76 | 8.18 | 6.84 | 6.03 |

Fuel Consumption/(L/100 km) | Acceleration Time/(s) | Maximum Speed/(km/h) | ||
---|---|---|---|---|

0–50 km | 0–100 km | |||

THS | 4.68 | 5.88 | 13.5 | 205 |

S-4 | 4.74 | 1.79 | 6.69 | 213 |

Difference | −0.06 | 4.09 | 6.81 | 8 |

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## Share and Cite

**MDPI and ACS Style**

Huang, B.; Hu, M.; Zeng, L.; Fu, G.; Jia, Q.
Design Method for Hybrid Electric Vehicle Powertrain Configuration with a Single Motor. *Sustainability* **2022**, *14*, 8225.
https://doi.org/10.3390/su14138225

**AMA Style**

Huang B, Hu M, Zeng L, Fu G, Jia Q.
Design Method for Hybrid Electric Vehicle Powertrain Configuration with a Single Motor. *Sustainability*. 2022; 14(13):8225.
https://doi.org/10.3390/su14138225

**Chicago/Turabian Style**

Huang, Bo, Minghui Hu, Li Zeng, Guangshun Fu, and Qinglong Jia.
2022. "Design Method for Hybrid Electric Vehicle Powertrain Configuration with a Single Motor" *Sustainability* 14, no. 13: 8225.
https://doi.org/10.3390/su14138225