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Modified Generalised Maxwell Slip Based Electro-Hydraulic Transfer Case Modeling for All-wheel Drive Vehicle Simulation

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Abstract

This paper describes the modeling of a torque-on-demand transfer case and an all-wheel drive (AWD) vehicle simulation through model integration. To develop the AWD vehicle controller, reliable and robust mathematical modeling of transfer case for AWD vehicle simulation should be proceeded. However, conventional wet clutch model cannot be applied for simulating the AWD vehicle especially when clutch is fully lock up state because of the chattering response of torque followed by the change of external factors. By replacing a slip-regulation equation of lock-up state with a degree of freedom (DOF) reduction equation in the generalized maxwell slip (GMS) model, the chattering and instability issue of original GMS model for AWD vehicle simulation was solved in this study. For parameter verification of the wet clutch, the simulation of the transfer case module and validation with the experimental data were conducted first. Then, the simulation of an AWD vehicle was conducted through the integration of the developed one in CarSim software. Through the comparison of the modified GMS model with the original GMS model, the former is verified to be superior to the latter for stable simulation.

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Abbreviations

T t :

transmission output torque, N·m

T c :

transfer case clutch torque, N·m

T f :

front shaft torque, N·m

T r :

rear shaft torque, N·m

J t :

transmission output shaft inertia, kg·m2

J c :

transfer case clutch inertia, kg·m2

i f :

transfer case gear ratio, -

k f :

front shaft spring constants, N/rad

k r :

rear shaft spring constants, N/rad

b f :

front shaft damping constants, N·s/rad

b r :

rear shaft damping constants, N·s/rad

θ t :

transmission output shaft rotational angle, rad

θ c :

transfer case clutch rotational angle, rad

θ f :

front shaft rotational angle, rad

θ r :

rear shaft rotational angle, rad

F c :

transfer case clutch engagement force, N

M i :

friction torque of ith maxwell element, N·m

M s :

static friction torque, N·m

M c :

coulomb friction torque, N·m

M d :

hydrodynamic drag torque, N·m

k i :

integral gain of wet clutch model in sticking state, -

α i :

normalized maximum friction torque that each maxwell element can sustain, -

C :

attractor gain that the rate of friction torque follows the stribeck effect, -

μ :

road surface friction coefficient, -

μ s :

static friction coefficient, -

μ c :

coulomb friction coefficient, -

μ f :

dynamic viscosity of fluid, kg/(m·s)

r i :

inner radius of clutch friction plate, mm

r o :

outer radius of clutch friction plate, mm

h :

height from ground to vehicle’s center of gravity, m

h d :

clearance length of the clutch pack, m

Reh :

reynolds number, -

ρ :

density of the fluid, kg/m3

L :

wheelbase length, m

L r :

distance from vehicle’s center of gravity to front axle, m

a x :

longitudinal acceleration of vehicle, m/s2

g :

gravitational acceleration, m/s2

References

  • Alizadeh, H. V. and Boulet, B. (2014). Robust control of synchromesh friction in an electric vehicle’s clutchless automated manual transmission. IEEE Conf. Control Applications (CCA), Antibes, France.

  • Bachinger, M., Stolz, M. and Horn, M. (2015). A novel drivetrain modelling approach for real-time simulation. Mechatronics, 32, 67–78.

    Article  Google Scholar 

  • Deur, J., Petric, J., Asgari, J. and Hrovat, D. (2005). Modeling of wet clutch engagement including a thorough experimental validation. SAE Trans., 1013–1028.

  • Duan, S., Ni, J. and Ulsoy, A. G. (2014). Modeling and control of an automotive all-wheel drive clutch as a piecewise affine system. J. Dynamic Systems, Measurement, and Control 136, 1, 011008.

    Article  Google Scholar 

  • Hashimoto, H., Wada, S. and Murayama, Y. (1984). An influence of centrifugal force on the performances of thermo-hydrodynamic turbulent thrust bearings. Bulletin of JSME 27, 228, 1230–1236.

    Article  Google Scholar 

  • Holgerson, M. (1997). Apparatus for measurement of engagement characteristics of a wet clutch. Wear 213, 1–2, 140–147.

    Article  Google Scholar 

  • Jung, H., Jung, D. and Choi, S. B. (2021). LQR control of an all-wheel drive vehicle considering variable input constraint. IEEE Trans. Control Systems Technology 30, 1, 85–96.

    Article  Google Scholar 

  • Kim, H., Lee, S. and Hedrick, J. K. (2015). Active yaw control for handling performance improvement by using traction force. Int. J. Automotive Technology 16, 3, 457–464.

    Article  Google Scholar 

  • Lampaert, V., Al-Bender, F. and Swevers, J. (2003). A generalized Maxwell-slip friction model appropriate for control purposes. IEEE Int. Workshop on Workload Characterization (CAT. No. 03EX775), Saint Petersburg, Russia.

  • Oh, J. J., Choi, S. B. and Kim, J. (2014). Driveline modeling and estimation of individual clutch torque during gear shifts for dual clutch transmission. Mechatronics 24, 5, 449–463.

    Article  Google Scholar 

  • Ompusunggu, A. P., Sas, P. and Van Brussel, H. (2013). Modeling and simulation of the engagement dynamics of a wet friction clutch system subjected to degradation: An application to condition monitoring and prognostics. Mechatronics 23, 6, 700–712.

    Article  Google Scholar 

  • Osborn, R. P. and Shim, T. (2006). Independent control of all-wheel-drive torque distribution. Vehicle System Dynamics 44, 7, 529–546.

    Article  Google Scholar 

  • Piatkowski, T. (2014). Dahl and LuGre dynamic friction models—The analysis of selected properties. Mechanism and Machine Theory, 73, 91–100.

    Article  Google Scholar 

  • Subramanyam, V., Monkaba, V. and Alexander, T. (2000). A unique approach to all-wheel drive vehicle dynamics model simulation and correlation. SAE Paper No. 2000-01-3526.

  • Wheals, J. C., Baker, H., Ramsey, K. and Turner, W. (2004). Torque vectoring AWD driveline: Design, simulation, capabilities and control. SAE Trans., 557–576.

  • Williams, R. C. (2006). 4WD-AWD market trends in vehicles and technology differenwces and similarities, from 1997 to 2004 primarily in the US Market, and also some Global Comparisons. SAE Paper No. 2006-01-0822.

  • Yang, Y., Lam, R. C. and Fujii, T. (1998). Prediction of torque response during the engagement of wet friction clutch. SAE Trans., 1625–1635.

  • Yuan, Y., Liu, E. A., Hill, J. and Zou, Q. (2007). An improved hydrodynamic model for open wet transmission clutches. J. Fluids Engineering 129, 3, 333–337.

    Article  Google Scholar 

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Acknowledgement

The authors would like to thank C. W. Moon of the Korea Automotive Technology Institute for his efforts in providing the results of experiments. This paper has its origin in the project titled “Development of 1,300 Nm Electro-Hydraulic AWD Modularization System and Control Technology to Improve Driving Force and Safety,” without which this paper could not have been completed. This research was partly supported by the BK21+ program through the NRF funded by the Ministry of Education of Korea; and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2020R1A2B 5B01001531).

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Authors and Affiliations

  1. Mechatronics R&D Center, Samsung Electronics, 1-1, Samsungjeonja-ro, Hwaseong, 18448, Korea

    Ho Jin Jung

  2. School of Mechanical, Aerospace & System Engineering, KAIST, Daejeon, 34141, Korea

    Seibum Ben Choi

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  1. Ho Jin Jung
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  2. Seibum Ben Choi
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Correspondence to Seibum Ben Choi.

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Jung, H.J., Choi, S.B. Modified Generalised Maxwell Slip Based Electro-Hydraulic Transfer Case Modeling for All-wheel Drive Vehicle Simulation. Int.J Automot. Technol. 24, 45–54 (2023). https://doi.org/10.1007/s12239-023-0005-x

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  • DOI: https://doi.org/10.1007/s12239-023-0005-x

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