Active differentials are used to improve the overall performance of traction control and vehicle dynamics control systems. This paper presents the development of a unified mathematical model of active differential dynamics using the bond graph modeling technique. The study includes active limited slip differential and various common types of torque vectoring differentials. Different levels of model complexity are considered, starting from a second-order model with lumped input and output inertia toward higher-order models including the gear inertia and half-shaft compliance. The model is used for a theoretical analysis of drivability and time response characteristics of the active differential dynamics. The analysis is illustrated by simulation results.
Issue Section:
Modeling Applications
Keywords:
bond graphs,
differential equations,
gears,
shafts,
torque,
traction,
vectors,
vehicle dynamics
1.
Sawase
, K.
, and Sano
, Y.
, 1999, “Application of Active Yaw Control to Vehicle Dynamics by Utilizing Driving/Braking Force
,” JSAE Rev.
0389-4304, 20
, pp. 289
–295
.2.
Hancock
, M.
, 2006, “Vehicle Handling Control Using Active Differentials
,” Ph.D. thesis, University of Loughborough
, UK.3.
Assadian
, F.
, and Hancock
, M.
, 2005, “A Comparison of Yaw Stability Control Strategies for the Active Differential
,” Proceedings of the 2005 International IEEE Symposium on Industrial Electronics (ISIE 2005)
, Dubrovnik, Croatia, Vol. 1
, pp. 373
–378
.4.
Mimura
, K.
, 2000, “Differential Gear
,” U.S. Patent No. 6,120,407.5.
Mori
, A.
, and Shibahata
, Y.
, 2005, “Drive Force Control Method for Four-Wheel Drive Vehicle
,” EP No. 1582390A2.6.
Honda
, 2005, “Development of SH-AWD (Super-Handling All-Wheel Drive) System
,” Paper presented in Vehicle Dynamics EXPO
, Honda/Tochigi R&D Center, http://www.vehicledynamics-expo.com/05vdx_conf/pres/day2/honda.pdfhttp://www.vehicledynamics-expo.com/05vdx_conf/pres/day2/honda.pdf.7.
Sawase
, K.
, Ushiroda
, Y.
, and Miura
, T.
, 2006, “Left-Right Torque Vectoring Technology as the Core of Super All Wheel Drive Control (S-AWC)
,” Mitsubishi Motors Technical Review
, Vol. 18
, pp. 16
–23
.8.
Asgari
, J.
, and Hrovat
, D.
, 2001, “Limited Slip Differential (LSD) Modeling
,” International Conference on Bond Graph Modeling and Simulation (ICBGM)
, Vol. 33
.9.
Cheli
, F.
, Giaramita
, M.
, Pedrinelli
, M.
, Sandoni
, G.
, and Travaglio
, G. C.
, 2005, “A New Control Strategy for a Semi-Active Differential (Part I)
,” DVD Proceedings of the 16th IFAC Congress
, Prague, Czech Republic.10.
Karnopp
, D. C.
, Margolis
, D. L.
, and Rosenberg
, R.
, 1990, System Dynamics—A Unified Approach
, Wiley
, New York
.11.
Ivanović
, V.
, Herold
, Z.
, Deur
, J.
, Hancock
, M.
, and Assadian
, F.
, 2008, “Modeling and Experimental Validation of Active Limited Slip Differential Clutch Dynamics
,” Proceedings of IMECE2008
, Boston, MA, ASME Paper No. 2008-67411.12.
Hrovat
, D.
, and Tobler
, W. E.
, 1991, “Bond Graph Modeling of Automotive Power Trains
,” J. Franklin Inst.
0016-0032, 328
, pp. 623
–662
.13.
Deur
, J.
, Hancock
, M.
, and Assadian
, F.
, 2008, “Modeling and of Active Differential Dynamics
,” Proceedings of IMECE2008
, Boston, MA, ASME Paper No. 2008-69248.14.
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
0022-0434, 128
, pp. 263
–277
.15.
Deur
, J.
, Asgari
, J.
, and Hrovat
, D.
, 2006, “Modeling and Analysis of Automatic Transmission Engagement Dynamics—Nonlinear Case Including Validation
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 128
, pp. 251
–262
.16.
Pacejka
, H. B.
, 2002, Tyre and Vehicle Dynamics
, Butterworth-Heinemann
, Oxford
.17.
Deur
, J.
, Hancock
, M.
, and Assadian
, F.
, 2008, “Modeling and Analysis of Active Differential Kinematics
,” Proceedings of the 2008 ASME Dynamic Systems and Control Conference
, Ann Arbor, MI.18.
Armstrong-Hélouvry
, B.
, Dupont
, P.
, and Canudas de Wit
, C.
, 1994, “A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction
,” Automatica
0005-1098, 30
, pp. 1083
–1138
.19.
Karnopp
, D. C.
, 1985, “Computer Simulation of Stick-Slip Friction in Mechanical Dynamic Systems
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 107
, pp. 100
–103
.20.
Haessig
, D. A.
, and Friedland
, B.
, 1991, “On the Modeling and Simulation of Friction
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 113
, pp. 354
–362
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
