Mathematical model of the moment distribution algorithm along the axes of an electric vehicle with a two-motor type

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Abstract

BACKGROUND: The development of electric and hybrid vehicles is impossible without the creation of schemes in which torque is generated by electric motors independently on the front and rear axles or on each wheel and the best dynamics is achieved. The development of a function for distributing torque between the axles or wheels of a car is a relevant technical task.

AIMS: Creation of a mathematical model for the torque distribution requested by the driver to the front and rear electric motors in order to assist the course stability system and counteract wheel slip when driving in a turn close to drifting/skidding or driving on surfaces with a low or variable grip coefficient.

METHODS: The algorithm model was built in the MATLAB/Simulink environment, was tested in the model-in-the-loop mode on a simulation model developed in the Simcenter Amesim environment, was tested in the hardware-in-the-loop mode on the LabCar real-time machine (ETAS GmbH) and was tested in a vehicle.

RESULTS: The function based on the abovementioned methods was built in MATLAB/Simulink. Testing in simulation mode on the simulation model developed in Simcenter Amesim was performed and the initial values of calibration parameters were determined. Implementation of the function into the software structure of the prototype and compilation of the executable C-code for the master file loaded into the control unit were completed. Testing of the function implemented into the control unit on the LabCar real-time test rig was carried out. After eliminating the shortcomings identified at the previous stages of testing, calibrations and tests of the function integrated into the vehicle were carried out, which showed the effectiveness of the described torque distribution model.

CONCLUSIONS: The practical value of the study lies in the possibility of using the proposed control laws to develop systems for torque distribution between the axles or wheels of modern vehicles.

About the authors

Alexander M. Zavatsky

Central Scientific Research Automobile and Automotive Engines Institute NAMI

Author for correspondence.
Email: Alex7061@yandex.ru
ORCID iD: 0000-0003-0616-1350
SPIN-code: 9509-1069

Design Engineer of the Hybrid Vehicle Calibrations Department

Russian Federation, 2 Avtomotornaya street, 125438 Moscow

Vladimir V. Debelov

Central Scientific Research Automobile and Automotive Engines Institute NAMI

Email: vladimir.debelov@nami.ru
ORCID iD: 0000-0001-6050-0419
SPIN-code: 8701-7410
Scopus Author ID: 57209468691

Cand. Sci. (Tech.), Head of the Software Technologies Department

Russian Federation, 2 Avtomotornaya street, 125438 Moscow

Andrey N. Malyshev

Central Scientific Research Automobile and Automotive Engines Institute NAMI

Email: andrey.malyshev@nami.ru
ORCID iD: 0000-0003-0233-0348
SPIN-code: 6196-3162

Head of the Hybrid Vehicle Calibrations Department

Russian Federation, 2 Avtomotornaya street, 125438 Moscow

Andrey V. Keller

Central Scientific Research Automobile and Automotive Engines Institute NAMI

Email: andrey.keller@nami.ru
ORCID iD: 0000-0003-4183-9489
SPIN-code: 4622-5727

Professor, Dr. Sci. (Tech.), Acting Deputy Director

Russian Federation, 2 Avtomotornaya street, 125438 Moscow

References

  1. World statistics 2021: electric vehicles and plug-in hybrids. Autoreview.ru [internet] Accessed: 15.12.2022. Available from: https://autoreview.ru/news/mirovaya-statistika-2021-elektromobili-i-podzaryazhaemye-gibridy
  2. Larin VV. Theory of movement of all-wheel drive wheeled vehicles: a textbook. Moscow: MGTU im NE Baumana, 2010.
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  4. Patent US № 6598721 / 21.05.2019. Michelis A, Ravier C, Moulaire P. Understeer and oversteer detector for a motor vehicle.
  5. Agliullin T, Ivanov V, Ricciardi V, et al. Torque Vectoring Control on Ice for Electric Vehicleswith Individually Actuated Wheels. In: Conference: The 26th IAVSD Symposium on Dynamics of Vehicles on Roads and Tracks. Gothenburg; 2019.
  6. Grachev EV, Debelov VV, Endachev DV, et al. Development of a concept for controlling the distribution of torque of the driving wheels of electric vehicles with an individual drive of the driving wheels. Intellektualnye transportnye sistemy. Sbornik trudov Mezhdunarodnogo avtomo-bilnogo nauchnogo foruma MANF-2017. Moscow: Izd-vo FGUP «NAMI»; 2017:257-267.
  7. Debelov VV. Vehicle motion control systems. textbook. Moscow: Izd-vo FGUP «NAMI»; 2021.

Supplementary files

Supplementary Files
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1. JATS XML
2. Fig. 1. The all-wheel drive electric vehicle layout.

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3. Fig. 2. The main structure of the torque distribution function.

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4. Fig. 3. Analytical scheme of longitudinal motion.

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5. Fig. 4. Dependence of the part of torque transmitted to the rear axle on lateral acceleration.

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6. Fig. 5. Analytical scheme of curvilinear motion of a vehicle.

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7. Fig. 6. Comparison of expected and measured yaw rate: a) at driving without side slip and with front axle skidding; b) at rear axle drifting and countersteering.

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8. Fig. 7. Adjustment of torque distribution according to the yaw rate error: a) at the front axle skidding; b) at the rear axle drifting; c) at countersteering.

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9. Fig. 8. Obtaining the two-variable polynomial function.

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10. Fig. 9. Defining the state of slipping.

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