2024年4月10日发(作者：)

3.1.2 Steady-state rolling analysis of a tire

3.1.2轮胎的稳态滚动分析

Product: Abaqus/Standard

This example illustrates the use of steady-state transport in Abaqus (“Steady-state transport

analysis,” Section 6.4.1 of the Abaqus Analysis User's Guide) to model the steady-state dynamic

interaction between a rolling tire and a rigid surface. A steady-state transport analysis uses a moving

reference frame in which rigid body rotation is described in an Eulerian manner and the deformation is

described in a Lagrangian manner. This kinematic description converts the steady moving contact

problem into a pure spatially dependent simulation. Thus, the mesh need be refined only in the contact

region—the steady motion transports the material through the mesh. Frictional effects, inertia effects,

and history effects in the material can all be accounted for in a steady-state transport analysis. 这个例子

说明了在Abaqus中使用稳态传输（“稳态传输分析”，“Abaqus分析用户指南”第6.4.1节）来模拟滚动轮胎和

刚性表面之间的稳态动态相互作用。稳态传输分析使用移动参考系，其中以欧拉方式描述刚体旋转，并且以拉格

朗日方式描述变形。该运动学描述将稳定移动接触问题转换成纯空间依赖性模拟。因此，网格仅需要在接触区域

中精制 - 稳定运动通过网格传送材料。材料中的摩擦效应，惯性效应和历史效应都可以在稳态传输分析中考虑。

The purpose of this analysis is to obtain free rolling equilibrium solutions of a 175 SR14 tire traveling

at a ground velocity of 10.0 km/h (2.7778 m/s) at different slip angles on a flat rigid surface. The slip

angle is the angle between the direction of travel and the plane normal to the axle of the tire. Straight

line rolling occurs at a 0.0° slip angle. For comparison purposes we also consider an analysis of the tire

spinning at a fixed position on a 1.5 m diameter rigid drum. The drum rotates at an angular velocity of

3.7 rad/s, so that a point on the surface of the drum travels with an instantaneous velocity of 10.0 km/h

(2.7778 m/s). Another case presented examines the camber thrust arising from camber applied to a tire

1

at free rolling conditions. This also enables us to calculate a camber thrust stiffness. 该分析的目的是获得

在平坦刚性表面上以不同滑移角以10.0km / h（2.7778m / s）的地面速度行驶的175SR14轮胎的自由滚动平衡

解。滑移角是行进方向和垂直于轮胎轴的平面之间的角度。直线滚动发生在0.0°滑移角。为了比较的目的，我们

还考虑了在1.5m直径的刚性滚筒上的固定位置处轮胎旋转的分析。鼓以3.7rad / s的角速度旋转，使得鼓的表面

上的点以10.0km / h（2.7778m / s）的瞬时速度行进。提出的另一种情况检查在自由滚动条件下施加到轮胎的

外倾引起的外倾推力。这也使我们能够计算外倾推力刚度。

An equilibrium solution for the rolling tire problem that has zero torque,

T

, applied around the axle

is referred to as a free rolling solution. An equilibrium solution with a nonzero torque is referred to as

either a traction or a braking solution depending upon the sense of

T

. Braking occurs when the angular

velocity of the tire is small enough such that some or all of the contact points between the tire and the

road are slipping and the resultant torque on the tire acts in an opposite sense from the angular velocity

of the free rolling solution. Similarly, traction occurs when the angular velocity of the tire is large enough

such that some or all of the contact points between the tire and the road are slipping and the resultant

torque on the tire acts in the same sense as the angular velocity of the free rolling solution. Full braking

or traction occurs when all the contact points between the tire and the road are slipping. 用于滚动轮胎

问题的平衡解被称为自由滚动解决方案，该平衡解决方案具有围绕轴施加的零扭矩T.具有非零扭矩的平衡解被称

为牵引或制动解决方案，取决于T的感觉。当轮胎的角速度足够小时，发生制动，使得轮胎和轮胎之间的接触点

的一些或全部道路正在滑动，并且轮胎上的合成转矩以与自由滚动溶液的角速度相反的方向作用。类似地，当轮

胎的角速度足够大使得轮胎和道路之间的接触点中的一些或全部滑动并且轮胎上的合成转矩以与自由轮胎的角速

度相同的方向作用时，轧制溶液。当轮胎和道路之间的所有接触点都滑动时，发生完全制动或牵引。

A wheel in free rolling, traction, or braking will spin at different angular velocities, , for the same

ground velocity, Usually the combination of and that results in free rolling is not known in

advance. Since the steady-state transport analysis capability requires that both the rotational spinning

velocity, , and the traveling ground velocity, , be prescribed, the free rolling solution must be found

in an indirect manner. One such indirect approach is illustrated in this example. An alternate approach

2