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全面的轮胎模型。Using the Fiala Handling Force Model This section of the help provides detailed technical reference material for defining tires on a mechanical system model using Adams/Tire. It assumes that you know how to run Adams/Car, Adams/Solver, or Adams/Chassis. It also assumes that you have a moderate level of tire-modeling proficiency. The Fiala tire model is the standard tire model that comes with all Adams/Tire modules. This chapter contains information for using the Fiala tire model:
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Tire Models
Adams/Tire
12
Using the Fiala Handling Force Model
This section of the help provides detailed technical reference material for defining tires on a mechanical
system model using Adams/Tire. It assumes that you know how to run Adams/Car, Adams/Solver, or
Adams/Chassis. It also assumes that you have a moderate level of tire-modeling proficiency.
The Fiala tire model is the standard tire model that comes with all Adams/Tire modules. This chapter
contains information for using the Fiala tire model:
• Assumptions
• Inputs
• Tire Slip Quantities and Transient Tire Behavior
• Force Evaluation
• Tire Carcass Shape
• Property File Format Example
• Contact Methods
Fiala Tire Assumptions
The background of the Fiala tire model is a physical tire model, where the carcass is modeled as a beam
on an elastic foundation in the lateral direction. Elastic brush elements provide the contact between
carcass and road. Under these assumptions, analytical expressions for the steady-state slip characteristics
can be derived, which are the basis for the calculation of the longitudinal and lateral forces in Adams.
• Rectangular contact patch or footprint.
• Pressure distribution uniform across contact patch.
• No tire relaxation effects are considered.
• Camber angle has no effect on tire forces.
Fiala Tire Inputs
The inputs to the Fiala tire model come from two sources:
• Input parameters from the tire property file (.tir), such as tire undeflected radius, that the tire
references.
• Tire kinematic states, such as slip angle ( ), which Adams/Tire calculates.
The following table summarizes the input that the Fiala tire model uses to calculate force.
α
13
Tire Models
Input for Calculating Tire Forces
Quantity: Description: Use by Fiala: Source:
M
t
Mass of tire • Damping
• Vertical force (Fz)
Alpha Slip angle Lateral force (Fy) Tire kinematic state from
Adams/Solver
S
s
Longitudinal slip ratio Longitudinal force (F
x
) Tire kinematic state from
Adams/Solver
pen Penetration (tire deflection) Vertical force (F
z
) Tire kinematic state from
Adams/Solver
Vpen d/dt (penetration) Vertical force (Fz) Tire kinematic state from
Adams/Solver
Vertical_damping Vertical damping coefficient • Damping
• Vertical force (Fz)
Tire property file (.tir)
Vertical_stiffness Vertical tire stiffness Vertical force (Fz) Tire property file (.tir)
CSLIP Partial derivative of longitudinal
force (Fx) with respect to
longitudinal slip ratio (S) at zero
longitudinal slip
Longitudinal force (Fx) Tire property file (.tir)
CALPHA Partial derivative of lateral force
(Fy) with respect to slip angle
( ) at zero slip angle
Lateral force (Fy) Tire property file (.tir)
UMIN Coefficient of friction at zero
slip
Fx, Fy, Tz Tire property file (.tir)
UMAX Coefficient of friction when tire
is sliding
Fx, Fy, Tz Tire property file (.tir)
Rolling_resistance Rolling resistance coefficient Rolling resistance moment (Ty) Tire property file (.tir)
α
Adams/Tire
14
Tire Slip Quantities and Transient Tire Behavior
Definition of Tire Slip Quantities
Slip Quantities at combined cornering and braking/traction
The longitudinal slip velocity V
sx
in the SAE-axis system is defined using the longitudinal speed V
x
, the
wheel rotational velocity , and the loaded rolling radius R
l
:
The lateral slip velocity is equal to the lateral speed in the contact point with respect to the road
plane:
The practical slip quantities (longitudinal slip) and (slip angle) are calculated with these slip
velocities in the contact point:
and
Note that for realistic tire forces the slip angle is limited to 90
0
and the longitudinal slip in
between -1 (locked wheel) and 1.
Lagged longitudinal and lateral slip quantities (transient tire behavior)
In general, the tire rotational speed and lateral slip will change continuously because of the changing
interaction forces in between the tire and the road. Often the tire dynamic response will have an important
role on the overall vehicle response. For modeling this so-called transient tire behavior, a first-order
system is used both for the longitudinal slip ? as the side slip angle, ?. Considering the tire belt as a
stretched string, which is supported to the rim with lateral springs, the lateral deflection of the belt can
be estimated (see also reference [1]). The figure below shows a top-view of the string model.
Ω
V
sx
V
x
ΩR
l
–=
V
sy
V
y
=
κ
α
κ
V
sx
V
x
--------
–=
αtan
V
sy
V
x
---------
=
α
κ
15
Tire Models
Stretched String Model for Transient Tire behavior
When rolling, the first point having contact with the road adheres to the road (no sliding assumed).
Therefore, a lateral deflection of the string will arise that depends on the slip angle size and the history
of the lateral deflection of previous points having contact with the road.
For calculating the lateral deflection v
1
of the string in the first point of contact with the road, the
following differential equation is valid during braking slip:
with the relaxation length in the lateral direction. The turnslip can be neglected at radii larger than
10 m. This differential equation cannot be used at zero speed, but when multiplying with V
x
, the equation
can be transformed to:
When the tire is rolling, the lateral deflection depends on the lateral slip speed; at standstill, the deflection
depends on the relaxation length, which is a measure for the lateral stiffness of the tire. Therefore, with
this approach, the tire is responding to a slip speed when rolling and behaving like a spring at standstill.
A similar approach yields the following for the deflection of the string in longitudinal
direction:
1
V
x
------
dv
1
dt
--------
v
1
σ
α
------
+ αtan aφ+=
σ
α
φ
σ
α
dv
1
dt
--------
V
x
v
1
+ σ
α
V
sy
=
σ
κ
du
1
dt
--------
V
x
u
1
+ σ–
κ
V
sx
=
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