The PAC2002 advanced handling tire model

Influence of tyre transience on anti-lock braking

“…Here, the carcass compliance together with the slip model of the contact patch automatically takes care of the vertical load-dependent lag, in addition to a decrease in lag with an increasing slip. This approach was initially employed by Pacejka and Besselink [20], based on an earlier work by van der Jagt et al [8] in their 1997 version of the magic formula transient tyre model, which was later incorporated in the PAC 2002 tyre model [6]. By incorporating the contact patch mass 'm c ', the carcass stiffness 'k cx,y ', and damping ratios 'c cx,y ' (see Fig.…”

“…The first-order relaxation length accounts for the carcass compliance with respect to the wheel rim in both longitudinal and lateral directions Adopted from the work of Pacejka [15], the model follows a simplified form of the string method, originally developed to study the tyre shimmy motion by Pacejka [7]. This approach is also used in the PAC 2002 version of the magic tyre formula [6]. In its simplest form, the string model reduces to a single-contact-point tyre model, whereby the contact patch is connected to the rim by a longitudinal and lateral spring, representing the stiffness of the carcass in the respective directions.…”

“…An alternative and mathematically better approach would be to use the sprung mass m S throughout equations (1) to (6) and provide all unsprung masses with additional lateral and longitudinal DOF. This would bring the model closer to its complex multi-body alternative, increasing unnecessarily the computational cost of simulation.…”

“…Kuiper and Van Oosten [6] extended this approach to semi-empirical tyre models, by applying a stretchedstring model (based on the work of Pacejka [7]) to represent tyre transient behaviour, where the tyre belt is modelled as a stretched string, attached to the wheel rim by longitudinal and lateral springs. The tyre force and moments were then calculated using the standard magic formula coefficients with inclusion of transient slip as an input to the model.…”

Tire Transient Cornering Characteristics on μ-step Road

“…Key words：tire characteristics；transient；cornering；μ-step road；tire modeling 0 前言 * 轮胎作为车辆与路面接触的唯一部件，其力学 特性对车辆动力学性能有非常重要的影响 [3][4] 。AMIR [5] 开发了用于 ABS 的自适应反馈线性化控制器，适用于各种路面 状况以及模型参数不确定工况。KANG [6] 研究了复 杂路面条件下基于发动机转矩和制动压力的车辆驱 动协调控制。王博 [7] 通过 9 自由度车辆模型和轮胎 模型研究了某四轮汽车变路面车辆稳定性控制策 略。然而，由于胎体弹性的影响，对接路面工况下， 轮胎滚动过程中实际上表现出瞬态力学特性。现有 的轮胎模型虽然对滑移率、侧偏角、外倾角以及轮 胎垂直载荷波动造成的瞬态特性都有了比较好的表 达 [8][9][10][11][12][13] ，但是由于对接路面工况的复杂性，针对对 接路面工况下摩擦特性突变造成的轮胎瞬态特性研 究尚不充分。 "Pac2002" [14] 和"TMeasy"…”