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