Research Papers

An Automated Model-Order Reduction Method for Automatic Transmissions

[+] Author and Article Information
Vanja Ranogajec

Faculty of Mechanical Engineering and
Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb HR-10002, Croatia
e-mail: vanja.ranogajec@fsb.hr

Joško Deur

Faculty of Mechanical Engineering and
Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb HR-10002, Croatia
e-mail: josko.deur@fsb.hr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 25, 2016; final manuscript received December 14, 2016; published online May 9, 2017. Assoc. Editor: Junmin Wang.

J. Dyn. Sys., Meas., Control 139(7), 071004 (May 09, 2017) Paper No: DS-16-1121; doi: 10.1115/1.4035607 History: Received February 25, 2016; Revised December 14, 2016

New generation of torque converter automatic transmissions (AT) includes a large number of gears for improved fuel economy and vehicle performance, which leads to exponentially increasing number of shift types and shift events. In order to facilitate various numerical/simulation analyses of AT dynamics, shift control optimization, and control strategy design, a full-order AT model is usually reduced by eliminating state variables related to locked clutches in particular gears or shifts. The paper proposes an automated model-order reduction method for an arbitrary, user-specified clutch state, and demonstrates its application on an example of ten-speed AT. The method is based on determining the locked-clutch torque variables and their substitution into the full-order state-space model input vector, as well as finding a linear relation between the reduced-order and full-order model state-space variables.

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Naunheimer, H. , Bertsche, B. , Ryborz, J. , and Novak, W. , 2010, Automotive Transmissions: Fundamentals, Selection, Design and Application, 2nd ed., Springer, Berlin.
Lee, S. , Zhang, Y. , Jung, D. , and Lee, B. , 2014, “ A Systematic Approach for Dynamic Analysis of Vehicles With Eight or More Speed Automatic Transmission,” ASME J. Dyn. Syst. Meas. Control, 136(5), p. 051008. [CrossRef]
Marano, J. , Moorman, S. , Czoykowski, J. , and Ghike, C. , 2011, “ Automatic Transmission Rotational Inertia Effect on Shift Quality,” SAE Technical Paper No. 2011-01-0393.
Marano, J. E. , Moorman, S. P. , Whitton, M. D. , and Williams, R. L. , 2007, “ Clutch-to-Clutch Transmission Control Strategy,” SAE Technical Paper No. 2007-01-1313.
Haj-Fraj, A. , and Pfeiffer, F. , 2001, “ Optimal Control of Gear Shift Operations in Automatic Transmissions,” J. Franklin Inst., 338(2–3), pp. 371–390. [CrossRef]
Nezhadali, V. , and Eriksson, L. , 2015, “ A Framework for Modeling and Optimal Control of Automatic Transmission Systems,” IFAC-PapersOnLine, 48(15), pp. 285–291. [CrossRef]
Čorić, M. , Ranogajec, V. , and Deur, J. , 2016, “ Optimization of Shift Control Trajectories for Step Gear Automatic Transmissions,” ASME J. Dyn. Syst. Meas. Control, 139(6), p. 061005.
Deur, J. , Asgari, J. , Hrovat, D. , and Kovač, P. , 2006, “ Modeling and Analysis of Automatic Transmission Engagement Dynamics-Linear Case,” ASME J. Dyn. Syst. Meas. Control, 128(2), pp. 263–277. [CrossRef]
Liu, Y. , Wang, S. H. , Lu, X. , Song, T. B. , Wei, W. S. , and Xu, X. Y. , 2013, “ Research of Gear Shift Control Technology for a New 8-Step Speed Automatic Transmission,” Appl. Mech. Mater., 455, pp. 376–382. [CrossRef]
Bai, S. , Maguire, J. M. , and Peng, H. , 2013, Dynamic Analysis and Control System Design of Automatic Transmissions, SAE International, Warrendale, PA.
Hrovat, D. , and Tobler, W. E. , 1991, “ Bond Graph Modeling of Automotive Power Trains,” J. Franklin Inst., 328(5–6), pp. 623–662. [CrossRef]
Cho, D. , and Hedrick, J. K. , 1989, “ Automotive Powertrain Modeling for Control,” ASME J. Dyn. Syst. Meas. Control, 111(4), pp. 568–576. [CrossRef]
Phillips, A. W. , Carey, C. E. , Hart, J. M. , and Wittkopp, S. H. , 2011, “ Ten-Speed Transmission,” U.S. Patent No. 8,007,394.
Ranogajec, V. , Deur, J. , and Čorić, M. , 2016, “ Bond Graph Analysis of Automatic Transmission Shifts Including Potential of Extra Clutch Control,” SAE Int. J. Engines, 9(3), pp. 1929–1945. [CrossRef]
Karnopp, D. C. , Margolis, D. L. , and Rosenberg, R. C. , 1990, System Dynamics: A Unified Approach, Wiley, New York.
Armstrong-Hélouvry, B. , Dupont, P. , and De Wit, C. C. , 1994, “ A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction,” Automatica, 30(7), pp. 1083–1138. [CrossRef]
Karnopp, D. , 1985, “ Computer Simulation of Stick-Slip Friction in Mechanical Dynamic Systems,” ASME J. Dyn. Syst. Meas. Control, 107(1), pp. 100–103. [CrossRef]
Jacobson, B. , 2001, “ Outline of a New Control Concept for Power Shifting of Fixed Step Ratio Automotive Transmissions,” Proc. Inst. Mech. Eng. Part D, 215(5), pp. 613–624. [CrossRef]
Meyer, C. D. , 2000, Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Carpinteri, A. , 2002, Structural Mechanics: A Unified Approach, Taylor & Francis, Abington, UK.
Kleijn, C. , Groothuis, M. A. , and Differ, H. G. , 2015, 20-Sim 4.5 Reference Manual, Controllab Products B.V., Enschede, The Netherlands.


Grahic Jump Location
Fig. 1

Power train model schematic

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Fig. 2

Schematic of AT gearbox [13]

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Fig. 3

Bond graph model of AT gearbox

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Fig. 4

Static clutch friction model based on the Coulomb friction description (a), and its realization through the classical (b) and Karnopp static model (c)

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Fig. 5

Principal block diagram of overall gearbox model based on the Karnopp clutch friction model [8]

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Fig. 6

Clutch torque capacity profiles, engine speed, clutch torques, and transmission output torque for 3–4 upshift (a) and 5–4 downshift (b)

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Fig. 7

Comparison of simulation execution time values for full- and reduced-order AT models and various shifts: (a) classical clutch friction model and (b) Karnopp clutch friction model



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