Citation: Kobayashi, I.; Kuroda, J.;
Uchino, D.; Ogawa, K.; Ikeda, K.;
Kato, T.; Endo, A.; Peeie, M.H.B.;
Narita, T.; Kato, H. Research on Yaw
Moment Control System for Race
Cars Using Drive and Brake Torques.
Vehicles 2023, 5, 515–534. https://
doi.org/10.3390/vehicles5020029
Academic Editors: Mohammed
Chadli, Peter Gaspar and Junnian
Wang
Received: 13 January 2023
Revised: 18 April 2023
Accepted: 24 April 2023
Published: 30 April 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Research on Yaw Moment Control System for Race Cars Using
Drive and Brake Torques
Ikkei Kobayashi
1
, Jumpei Kuroda
2,3
, Daigo Uchino
2,3
, Kazuki Ogawa
4
, Keigo Ikeda
5
, Taro Kato
6
,
Ayato Endo
7
, Mohamad Heerwan Bin Peeie
8
, Takayoshi Narita
9,
* and Hideaki Kato
9
1
Course of Mechanical Engineering, Tokai University, Kitakaname 4-4-1, Hiratsuka 259-1292, Japan
2
Course of Science and Technology, Tokai University, Kitakaname 4-4-1, Hiratsuka 259-1292, Japan
3
Research Institute of Science and Technology, Tokai University, Kitakaname 4-4-1, Hiratsuka 259-1292, Japan
4
Department of Electronic Robot Engineering, Aichi University of Technology, 50-2 Manori, Nishihasama-cho,
Gamagori 443-0047, Japan
5
Department of Mechanical Engineering, Hokkaido University of Science, 7-Jo 15-4-1 Maeda,
Sapporo 006-8585, Japan
6
Department of Mechanical Engineering, Tokyo University of Technology, 1404-1 Katakuramachi,
Hachioji 192-0982, Japan
7
Department of Electrical Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-Higashi,
Fukuoka 811-0295, Japan
8
Faculty of Mechanical and Automotive Engineering Technology, University Malaysia Pahang,
Pekan 26600, Malaysia
9
Department of Mechanical Systems Engineering, Tokai University, Kitakaname 4-4-1,
Hiratsuka 259-1292, Japan
* Correspondence: narita@tsc.u-tokai.ac.jp; Tel.: +81-463-58-1211
Abstract: The yaw acceleration required for circuit driving is determined by the time variation of
the yaw rate due to two factors: corner radius and velocity at the center of gravity. Torque vectoring
systems have the advantage where the yaw moment can be changed only by the longitudinal force
without changing the lateral force of the tires, which greatly affects lateral acceleration. This is
expected to improve the both the spinning performance and the orbital performance, which are
usually in a trade-off relationship. In this study, we proposed a yaw moment control technology that
actively utilized a power unit with a brake system, which was easy to implement in a system, and
compared the performance of vehicles equipped with and without the proposed system using the
Milliken Research Associates moment method for quasi-steady-state analysis. The performances of
lateral acceleration and yaw moment were verified using the same method, and a variable corner
radius simulation for circuit driving was used to compare time and performance. The results showed
the effectiveness of the proposed system.
Keywords: torque vectoring; vehicle dynamics control; race car; brake torque; drive torque
1. Introduction
To improve the vehicle performance of race cars on circuits, we must consider not only
the maximization of the friction ellipse, which is indicated by the longitudinal acceleration
during braking/acceleration and the lateral acceleration during steady circle turns, but
also the yaw rotational motion of the vehicle body itself. This is because in circuit driving
with a series of various corner radii, the vehicle needs not only the orbital motion of the
turning center, based on the lateral acceleration, owing to the generation of a cornering
force balanced by centrifugal force, but also the spinning motion of the center of gravity
position of the vehicle body to change its orientation in accordance with the track. For
these spinning motions, yaw acceleration must be acquired, and a yaw moment must be
generated in the vehicle. The yaw moment in a vehicle is mainly determined by three
factors: longitudinal force, lateral force, and self-aligning torque of each of the four tires, as
Vehicles 2023, 5, 515–534. https://doi.org/10.3390/vehicles5020029 https://www.mdpi.com/journal/vehicles