Research Papers: Design of Energy, Fluid, and Power Handing Systems

Automatic Generation of Design Space Conversion Maps and Its Application for the Design of Compound Split Hybrid Powertrains

[+] Author and Article Information
Toumadher Barhoumi

Graduate School of Green Transportation,
Korea Advanced Institute of Science and
Technology (KAIST),
291 Daehak-ro,
Daejeon 34141, South Korea
e-mail: toumadher@kaist.ac.kr

Hyunjun Kim

Graduate School of Green Transportation,
Korea Advanced Institute of Science and
Technology (KAIST),
291 Daehak-ro,
Daejeon 34141, South Korea
e-mail: kindhyunjoon@kaist.ac.kr

Dongsuk Kum

Graduate School of Green Transportation,
Korea Advanced Institute of Science and
Technology (KAIST),
291 Daehak-ro,
Daejeon 34141, South Korea
e-mail: dskum@kaist.ac.kr

1Toumadher Barhoumi and Hyunjun Kim are co-first authors, and have equally contributed to this work.

2Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 26, 2017; final manuscript received February 12, 2018; published online March 23, 2018. Assoc. Editor: Hai Xu.

J. Mech. Des 140(6), 063401 (Mar 23, 2018) (13 pages) Paper No: MD-17-1654; doi: 10.1115/1.4039451 History: Received September 26, 2017; Revised February 12, 2018

Most of the prior design studies on compound split hybrids focused on the selection of optimal configurations through evaluating their performance within the physical design space, i.e., powertrain configurations. However, the authors revealed that using the compound lever for the performance analysis dramatically reduces the design space as redundant configurations exist for a single compound lever design, resulting in computational load reduction. Nevertheless, using the compound lever results in the loss of information required to realize the given configurations as these two configurations are represented by two different sets of variables. The powertrain configuration is defined by two physical design variables, i.e., gear ratios of the two planetary gears. However, the compound lever design is defined by two nonphysical design variables, α and β, which are the vertical bar lengths between the output node (vehicle) and the two motor/generators' (MG) nodes. Thus, if the compound lever is used as a design tool, the selected designs should be converted into powertrain configurations. This paper introduces an automatic methodology to generate feasible powertrain configurations for any given compound lever using generic conversion equations that express the relationship between the nonphysical design variables, α and β, and the physical design variables, gear ratios. Conversion maps relating the 252 powertrain configurations to the compound lever design space were generated, and the results confirmed that the compound lever removes the redundancy existing in the physical design space.

Copyright © 2018 by ASME
Topics: Levers , Design
Your Session has timed out. Please sign back in to continue.


Muta, K. , Yamazaki, M. , and Tokieda, J. , 2004, “Development of New-Generation Hybrid System THS II-Drastic Improvement of Power Performance and Fuel Economy,” SAE Trans., 113(3), pp. 182–192.
Ito, M. , Adachi, M. , Endo, H. , Isogai, A. , Omote, K. , and Uchida, T. , 2007, “Hybrid Transmission Development for AWD Luxury Cars,” SAE Paper No. 2007-01-4122.
Kobayashi, K. , Yashiro, T. , Takekawa, H. , and Fujita, K. , 2013, “Development of New Hybrid Transaxle for Front-Wheel Drive (FWD) 2.5-Liter Class Vehicles,” FISITA 2012 World Automotive Congress, Beijing, China, Nov. 27–30, pp. 343–353.
Taniguchi, M. , Yashiro, T. , Takizawa, K. , Baba, S. , Tsuchida, M. , Mizutani, T. , Endo, H. , and Kimura, H. , 2016, “Development of New Hybrid Transmission for Compact-Class Vehicles,” SAE Paper No. 2016-01-1163.
Suzuki, Y. , Nishimine, A. , Baba, S. , Miyasaka, K. , Tsuchida, M. , Endo, H. , Yamamura, N. , and Miyazaki, T. , 2017, “Development of New Plug-In Hybrid Transaxle for Compact-Class Vehicles,” SAE Paper No. 2017-01-1151.
Grewe, T. M. , Conlon, B. M. , and Holmes, A. G. , 2007, “Defining the General Motors 2-Mode Hybrid Transmission,” SAE Paper No. 2007-01-0273.
Hendrickson, J. , Holmes, A. , and Freiman, D. , 2009, “General Motors Front Wheel Drive Two-Mode Hybrid Transmission,” SAE Paper No. 2009-01-0508.
Miller, M. A. , Holmes, A. G. , Conlon, B. M. , and Savagian, P. J. , 2011, “The GM ‘Voltec’ 4ET50 Multi-Mode Electric Transaxle,” SAE Paper No. 2011-01-0887.
Conlon, B. M. , Blohm, T. , Harpster, M. , Holmes, A. , Palardy, M. , Tarnowsky, S. , and Zhou, L. , 2015, “The Next Generation ‘Voltec’ Extended Range EV Propulsion System,” SAE Paper No. 2015-01-1152.
Kim, H. , and Kum, D. , 2016, “Comprehensive Design Methodology of Input- and Output-Split Hybrid Electric Vehicles: In Search of Optimal Configuration,” IEEE/ASME Trans. Mechatronics, 21(6), pp. 2912–2923. [CrossRef]
Bayrak, A. , 2015, “Topology Considerations in Hybrid Electric Vehicle Powertrain Architecture Design,” Ph.D. dissertation, University of Michigan, Ann Arbor, MI. https://deepblue.lib.umich.edu/handle/2027.42/111412
Adam, H. , 2014, “Automated Topology Synthesis and Optimization of Hybrid Electric Vehicle Powertrains,” Master's thesis, University of Waterloo, Waterloo, ON, Canada. https://uwspace.uwaterloo.ca/handle/10012/8810
Zhang, X. , Eben Li, S. , Peng, H. , and Sun, J. , 2015, “Efficient Exhaustive Search of Power-Split Hybrid Powertrains With Multiple Planetary Gears and Clutches,” ASME J. Dyn. Syst., Meas., Control, 137(12), p. 121006. [CrossRef]
Barhoumi, T. , and Kum, D. , 2017, “Automatic Enumeration of Feasible Kinematic Diagrams for Split Hybrid Configurations With a Single Planetary Gear,” ASME J. Mech. Des., 139(8), p. 083301. [CrossRef]
Liu, J. , and Peng, H. , 2010, “A Systematic Design Approach for Two Planetary Gear Split Hybrid Vehicles,” Veh. Syst. Dyn., 48(11), pp. 1395–1412. [CrossRef]
Benford, H. L. , and Leising, M. B. , 1981, “The Lever Analogy: A New Tool in Transmission Analysis,” SAE Paper No. 810102.
Conlon, B. , 2005, “Comparative Analysis of Single and Combined Hybrid Electrically Variable Transmission Operating Modes,” SAE Paper No. 2005-01-1162.
Yang, H. , Cho, S. , Kim, N. , Lim, W. , and Cha, S. , 2007, “Analysis of Planetary Gear Hybrid Powertrain System Part 1: Input Split System,” Int. J. Automot. Technol., 8(6), pp. 771–780.
Yang, H. , Kim, B. , Park, Y. , Lim, W. , and Cha, S. , 2009, “Analysis of Planetary Gear Hybrid Powertrain System Part 2: Output Split System,” Int. J. Automot. Technol., 10(3), pp. 381–390. [CrossRef]
Shi-Hua, Y. , Hong, L. , Zeng, P. , and Xiong, W. B. , 2012, “Analysis of the Compound Split Transmission Based on the Four-Port Power Split Device,” J. Beijing Inst. Technol., 21(1), pp. 50–57.
Wang, W. , Song, R. , Guo, M. , and Liu, S. , 2014, “Analysis on Compound-Split Configuration of Power-Split Hybrid Electric Vehicle,” Mech. Mach. Theory, 78, pp. 272–288. [CrossRef]
Barhoumi, T. , Kim, H. , and Kum, D. , 2017, “Compound Lever Based Optimal Configuration Selection of Compound-Split Hybrid Vehicles,” SAE Paper No. 2017-01-1148.
Kim, N. , Rousseau, A. , and Rask, E. , 2012, “Autonomie Model Validation With Test Data for 2010 Toyota Prius,” SAE Paper No. 2012-01-1040.


Grahic Jump Location
Fig. 1

Several elementary-lever configurations have one single compound lever defined by α and β: (a) four elementary-lever configurations and (b) one unique compound lever

Grahic Jump Location
Fig. 2

Overview of the newly proposed exhaustive design method of compound split hybrids using the compound lever as a design tool

Grahic Jump Location
Fig. 3

Definitions and the logic behind the proposed conversion model using the analogies between the elementary-lever and compound lever design spaces

Grahic Jump Location
Fig. 4

Approach to generate an elementary-lever configuration for a given 2PG arrangement and components arrangement. (a) Approach used to generate a single elementary-lever configuration for given components arrangement and 2PG arrangements and (b) Conversion method used to convert any given 2PG arrangement into a physical compound lever.

Grahic Jump Location
Fig. 5

All existing 21 2PG arrangements. Note that SR2 > SR1 for 2PG arrangements #1, #1r, #7, #7r, #11, and #11r.

Grahic Jump Location
Fig. 6

Flowchart of the automation of the conversion methodology

Grahic Jump Location
Fig. 7

All possible 21 elementary-lever configurations that can be generated for α=−2 and β=3, with only six of them feasible

Grahic Jump Location
Fig. 8

Conversion map of 2PG arrangement #6 when the conversion methodology is applied across the entire design space

Grahic Jump Location
Fig. 9

Conversion map of the entire compound split hybrids design space, i.e., 252 elementary-lever configurations

Grahic Jump Location
Fig. 10

Conversion maps of five configurations including #6r-C1 s (Voltec 2nd) and Prius 3rd configurations plotted on the fuel economy and acceleration time contours for K = 4

Grahic Jump Location
Fig. 11

Conversion maps of the 21 2PG arrangements illustrated in Fig. 5, except for 2PG arrangements #6



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In