Improving the capacity of tire normal force via variable stiffness and damping suspension system Yanhai Xu a,b,⇑ , Mehdi Ahmadian b a School of Automobile and Transportation Engineering, Xi Hua University, Chengdu, PR China b Center for Vehicle Systems and Safety, Virginia Polytechnic Institute and State University, VA, USA Received 19 January 2012; received in revised form 3 February 2013; accepted 15 March 2013 Available online 22 April 2013 Abstract Tire normal force of a vehicle equipped with a variable stiffness and damping (VSVD) suspension system is studied via numerical simulation in this paper. The main purpose of the paper is to illustrate the effects of VSVD suspension system on the capacity of tire normal force. Firstly, a modified suspension system and its variable stiffness and damping characteristics are presented based on a con- ventional suspension system. With the application of adjustable suspension system in vehicle, the effects of equivalent stiffness of suspen- sion system on vehicle performance are analyzed by the term of load transfer at tires when cornering. By using a reference model, a simple on/off control strategy is developed to improve normal forces at tires and a fuzzy control strategy to model Direct Yaw moment Control (DYC) based on yaw rate is also developed to show the required longitudinal force. Finally, numerical simulations are carried out to demonstrate the important role of VSVD in improving tire normal force and then ameliorating vehicle lateral stability. It is shown from the results that the normal force at tires can be increased through the application of VSVD suspension system. It also indicates that DYC would be much efficient when implementing this system. Ó 2013 ISTVS. Published by Elsevier Ltd. All rights reserved. Keywords: Tire normal force; Vehicle lateral stability; Variable stiffness and damping 1. Introduction Vehicle stability includes the holding ability between tire and road and anti-rollover ability. Nowadays, more and more vehicles are liable to lose stability because of the increasing running speed or emergency turning. In fact, due to the height of the centre of gravity, SUVs are liable to roll over and many strategies and devices are developed to prevent them from rolling motion. Vehicle lateral stabil- ity means vehicle’s motion cannot keep in the track as the demand of driver’s steering action. This is induced by the change of force generated by contact patch between tire and road. If the amount of resultant force in longitudinal and lateral directions has a margin to its saturation, vehicle can keep its track as intention. In emergency turn, a larger lateral force is needed than during a normal turn. In this case, lateral forces at one or two tires would be saturated. But the other tires have potential and have margins to be saturated. It indicates that vehicle stability can be improved by coordinating the forces acting at different tires. The effective way is to redis- tribute or share the forces at tires rationally. From tire characteristics, longitudinal force usually has a margin to its saturation, even when lateral forces are close to satura- tion. Under such conditions, redistributing or sharing lon- gitudinal tire forces is an effective method to affect vehicle lateral motion. The obvious evidence of vehicle lateral sta- bility is the difference of actual track and demanded one. The phenomenon is depicted by understeer (US) or over- steer (OS). The target of DYC directly controls yaw moment by generating differential longitudinal forces on 0022-4898/$36.00 Ó 2013 ISTVS. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jterra.2013.03.003 ⇑ Corresponding author at: School of Automobile and Transportation Engineering, Xi Hua University, P.R.China. Tel.: +1 862887720534. E-mail addresses: xuyanhai.cn@gmail.com, yanhaixu@vt.edu (Y. Xu). www.elsevier.com/locate/jterra Available online at www.sciencedirect.com Journal of Terramechanics 50 (2013) 121–132 Journal of Terramechanics