ADAMS路面模型和轮胎UA模型中各全参数含义

2D Road Types
The available road types are:
•
DRUM - Tire test drum (requires a zero-speed-capable tire model). •
FLAT - Flat road.
•
PLANK - Single plank perpendicular, or in oblique direction relative to x-axis, with or without bevel edges. • POLY_LINE - Piece-wise linear description of the road profile. The profiles for the left and right track are independent. •
POT_HOLE - Single pothole of rectangular shape. •
RAMP - Single ramp, either rising or falling. •
ROOF - Single roof-shaped, triangular obstacle. •
SINE - Sine waves with constant wave length. •
SINE_SWEEP - Sine waves with decreasing wave lengths.
•
STOCHASTIC_UNEVEN - Synthetically generated irregular road profiles that match measured stochastic properties of typical roads. The profiles for left and right track are independent, or may have a certain correlation. Examples of 2D Roads
Sample files for all the road types for Adams/Car are in the standard Adams/Car database:
install_dir /shared_car_database.cdb/roads.tbl/
Sample files for all the road types for Adams/Tire are in: install_dir /solver/atire/
Sample files for all the road types for Adams/Chassis are in: install_dir /achassis/examples/rdf/
Note that you must select a specific contact method, such as point-follower or equivalent plane, to define how the roads will interact with the tires. Not all
combinations of road, tire, and contact methods are permitted. Allowable combinations are explained in Tire Models help under the description of the specific tire model.
2D Road Model Parameters
The [PARAMETERS] block must contain the following data, some of which are independent of the type of road. Learn about parameters:
•
Independent of Road Type •
Drum •
Flat •
Plank •
Polyline
•
Pothole
•
Ramp
•
Roof
•
Sine
•
Sweep
•
Stochastic Uneven
Parameters Independent of Road Type
The following parameters are required regardless of the road type.
If ROAD_TYPE = drum, then define the following parameters:
If ROAD_TYPE = flat, then no further parameters are required.
Parameters for Road Type of Plank
If ROAD_TYPE = plank, then define the following parameters:
If ROAD_TYPE = poly_line, then the [PARAMETERS] block must have a (XZ_DATA) subblock. The subblock consists of three columns of numerical data:
•
Column one is a set of x-values in ascending order.
•
Columns two and three are sets of respective z-values for left and right track.
The following is an example of the full [PARAMETERS] Body for a road type of polyline: $---------------------------PARAMETERS
[PARAMETERS]
OFFSET = 0
ROTATION_ANGLE_XY_PLANE = 180
$
(XZ_DATA)
0 0 0
1000 100 50
2000 -1000 100
3000 -100 100
3001 50 0
4000 -100 100
The XZ_DATA subblock can be extremely large. In this case, only the portion that is needed at the moment is loaded. To facilitate efficient reloading while simulation is running, do not use any comment lines in a subblock that contains more than 2000 lines. Parameters for Road Type of Pothole
If ROAD_TYPE = pot_hole, then the parameters are:
If ROAD_TYPE = ramp, then the parameters are:
If ROAD_TYPE = roof, then the parameters are:
If ROAD_TYPE = sine, then the parameters are:
amplitude Amplitude of sine wave (a).
wave_length
Wave length of sine wave ().
start Start of sine waves (travel
distance) (s s).
The road height, z, is given by:
Parameters for Road Type of Stochastic Uneven
A stochastic uneven road profile both for left and right wheels is generated, with properties very close to measured road profiles.
In a first step, discrete white noise signals are formed on the basis of nearly uniformly distributed random numbers. Two of these numbers are assigned to every 10 mm of travel path. The distribution of these random numbers is approximated by summing several equally distributed random numbers, taking advantage of the ‘law of large numbers’ of mathematical statistics.
Next, these values are integrated with respect to travel distance, using a simple
first order time-discrete integration filter. The independent variable of that filter is not time, but travel path. That is why the filter cutoff frequency is controlled by a path constant instead of a time constant. The filter process results in two approximate realizations of white velocity noise; that is, two signals, the
derivatives of which are close to white noise. Signals with that property are known as road profiles with waviness 2. Several investigations in the past showed that the waviness derived from measured road spectral densities ranges from about 1.8 to 2.2. The last step is to linearly combine the two realizations of the above
process:,, resulting in the left and right profile,. This is done such that the two signals are completely independent if , and identical if:
If ROAD_TYPE = stochastic_uneven, then the parameters are:
The parameter: Indicates:
intensity Variable to control intensity of white velocity noise, which
approximates measured spectra of road profiles fairly well.
path_constant Variable to control high-pass integration filter.
correlation_rl Variable to control correlation between left and right track:
•If 0, no correlation.
•
If 1, complete correlation (that is, left track = right track). Can be any value between 0 and 1.
start
Start of unevenness (travel distance).
Parameters for Road Type of Sweep
If ROAD_TYPE = sine_sweep, then the parameters are:
[PARAMETERS] Data for Road Type of Sine Sweep The parameter: Indicates:
start Start of swept sine wave (travel distance) (). end
End of swept sine wave (travel distance) (
).
amplitude_at_sta rt
Amplitude of swept sine wave at start travel distance (). amplitude_at_end Amplitude of swept sine wave at end travel distance (
).
wave_length_at_s tart
Wave length of swept sine wave a start travel distance (
).
wave_length_at_e nd
Wave length of swept sine wave at end travel distance. Must be less than or equal to wave_length_at_start (
).
sweep_type
•
sweep_type = 0: frequency increases linearly with respect to travel distance. •
sweep_type = 1: wave length decreases by a constant factor per cycle. Depending on the value of sweep_type, the road height is given by the following functions, where:
• Linear sweep: (sweep_type = 0) The frequency increases linearly with respect to travel distance. The road height value z (s) as function of travel distance s is alculated as follows:
Note the factor 2 in the denominator is not an error. The actual frequency (= derivative of the sine function argument with respect to travel path, divided by ; this is not equal to that factor that is multiplied by in the sine function) is given by the
following:
•
Logarithmic sweep: (sweep_type = 1) with every cycle, the wave length decreases by a constant factor. The road height value is calculated as follows:
where:
is the travel path where theoretically an infinitely high frequency was reached, measured relative to sweep start . The
actual frequency is given by:
Using the UA-Tire Model
Learn about using the University of Arizona (UA) tire model:
•
Background Information •
Tire Model Parameters •
Force Evaluation •
Operating Mode: USE_MODE •
Tire Carcass Shape •
Property File Format Example
Background Information for UA-Tire
The University of Arizona tire model was originally developed by Drs. P.E. Nikravesh and G. Gim. Reference documentation: G. Gim, Vehicle Dynamic Simulation with a
Comprehensive Model for Pneumatic Tires, PhD Thesis, University of Arizona, 1988. The UA-Tire model also includes relaxation effects, both in the longitudinal and lateral direction.
The UA-Tire model calculates the forces at the ground contact point as a function of the tire kinematic states, see Inputs and Output of the UA-Tire Model. A description of the inputs longitudinal slip k, side slip a and camber angle can be found in About Tire Kinematic and Force Outputs. The tire deflection and deflection velocity are determined using either a point follower or durability contact model. For more information, see Road Models in Adams/Tire . A description of outputs, longitudinal force Fx, lateral force Fy, normal force Fz, rolling resistance moment My and self aligning
moment Mz is given in About Tire Kinematic and Force Outputs. The required tire model parameters are described in Tire Model Parameters.
Inputs and Output of the UA-Tire Model
Definition of Tire Slip Quantities
Slip Quantities at Combined Cornering and Braking/Traction
The longitudinal slip velocity Vsx in the SAE-axis system is defined using the
longitudinal speed Vx, the wheel rotational velocity , and the effective rolling radius Re:
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:
When the UA Tire is used for the force calculation the slip quantities during positive Vsx (driving) are defined as:
The rolling speed Vr is determined using the effective rolling radius Re:
Note that for realistic tire forces the slip angle is limited to 45 degrees and the
longitudinal slip Ss (= ) 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 spring, the lateral deflection of the belt can be estimated (see also reference [1]). The figure below shows a top-view of the string model.
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 v1 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 Vx, 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. When the UA Tire is used for the force calculations, at positive Vsx (traction) the Vx should be replaced by Vr in these differential equations.
A similar approach yields the following for the deflection of the string in longitudinal direction:
Now the practical slip quantities, ’ and ’, are defined based on the tire deformation:
These practical slip quantities and are used instead of the usual and definitions for steady-state tire behavior. kVlow_x and kVlow_y are the damping rates at low speed applied below the LOW_SPEED_THRESHOLD speed. For the LOW_SPEED_DAMPING parameter in the tire property file yields:
kVlow_x= 100 · kVlow_y= LOW_SPEED_DAMPING
Note: If the tire property file's REL_LEN_LON or REL_LEN_LAT = 0, then steady-state tire behavior is calculated as tire response on change of the slip and .
Tire Model Parameters
Symbol: Name in tire property
file: Units*: Description:
r1 UNLOADED_RADIUS L Tire unloaded radius
kz VERTICAL_STIFFNESS F/L Vertical stiffness
cz VERTICAL_DAMPING FT/L Vertical damping
Cr ROLLING_RESISTANCE L Rolling resistance parameter Cs CSLIP F Longitudinal slip stiffness,
C CALPHA F/A Cornering stiffness,
C CGAMMA F/A
Camber stiffness,
UMIN UMIN - Minimum friction coefficient
(Sg=1)
UMAX UMAX - Maximum friction coefficient
(Ssg=0)
x REL_LEN_LON L Relaxation length in
longitudinal direction
y REL_LEN_LAT L Relaxation length in lateral
direction
* L=length, F=force, A=angle, T=time
Force Evaluation in UA-Tire
•
Normal Force
•
Slip Ratios
•
Friction Coefficient
Normal Force
The normal force F z is calculated assuming a linear spring (stiffness: k z ) and damper (damping constant c z ), so the next equation holds:
If the tire loses contact with the road, the tire deflection and deflection velocity become zero so the resulting normal force F z will also be zero. For very small positive tire deflections the value of the damping constant is reduced and care is taken to ensure that the normal force Fz will not become negative.
In stead of the linear vertical tire stiffness cz , also an arbitrary tire deflection - load curve can be defined in the tire property file in the section
[DEFLECTION_LOAD_CURVE], see also the Property File Format Example. If a section called [DEFLECTION_LOAD_CURVE] exists, the load deflection datapoints with a cubic spline for inter- and extrapolation are used for the calculation of the vertical force of the tire. Note that you must specify VERTICAL_STIFFNESS in the tire property file but it does not play any role.
Slip Ratios
For the calculation of the slip forces and moments a number of slip ratios will be introduced:
Longitudinal Slip Ratio: Ss
The absolute value of longitudinal slip ratio, Ss, is defined as:
Where k is limited to be within the range -1 to 1.
Lateral Slip Ratios: Sa , Sg , Sag
The lateral slip ratio due to slip angle, S, is defined as:
The lateral slip ratio due to inclination angle, S, is defined as:
A combined lateral slip ratio due to slip and inclination angles, S, is defined as:
where is the length of the contact patch.
Comprehensive Slip Ratio: Ssag
A comprehensive slip ratio due to longitudinal slip, slip angle, and inclination angle may be defined as:
Friction Coefficient
The resultant friction coefficient between the tire tread base and the terrain surface
is determined as a function of the resultant slip ratio (Ss) and friction parameters (UMAX and UMIN ). The friction parameters are experimentally obtained data representing the kinematic property between the surfaces of tire tread and the terrain.
A linear relationship between Ss and , the corresponding road-tire friction coefficient, is assumed. The figure below depicts this relationship.
Linear Tire-Terrain Friction Model
This can be analytically described as:
m = UMAX - (UMAX - UMIN) * Ssag
The friction circle concept allows for different values of longitudinal and lateral
friction coefficients (x and y) but limits the maximum value for both coefficients
to . See the figure below.
Friction Circle Concept
The relationship that defines the friction circle follows:
or and
where:
Slip Forces and Moments
To compute longitudinal force, lateral force, and self-aligning torque in the SAE coordinate system, you must perform a test to determine the precise operating conditions. The conditions of interest are:
•
Case 1: 0
•
Case 2: 0 and C S C S
•
Case 3: 0 and C S C S
•
Forces and moments at the contact point
The lateral force Fh can be decomposed into two components: Fha and Fhg. The two
components are in the same direction if a· g < 0 and in opposite direction if 0. Case 1. ag < 0
Before computing the longitudinal force, the lateral force, and the self-aligning torque, some slip parameters and a modified lateral friction coefficient should be
determined. If a slip ratio due to the critical inclination angle is denoted by S c, then it can be evaluated as:
If Ssc represents a slip ratio due to the critical (longitudinal) slip ratio, then it can be evaluated as:
If a slip ratio due to the critical slip angle is denoted by S c, then it can be determined as:
when Ss Ssc.
The term critical stands for the maximum value which allows an elastic deformation of a tire during pure slip due to pure slip ratio, slip angle, or inclination angle. Whenever any slip ratio becomes greater than its corresponding critical value, an elastic deformation no longer exists, but instead complete sliding state represents
the contact condition between the tire tread base and the terrain surface.
A nondimensional slip ratio Sn is determined as:
where:
A nondimensional contact patch length is determined as:
A modified lateral friction coefficient is evaluated as:
where is the available friction as determined by the friction circle.
To determine the longitudinal force, the lateral force, and the self-aligning torque, consider two subcases separately. The first case is for the elastic deformation state, while the other is for the complete sliding state without any elastic deformation of a tire. These two subcases are distinguished by slip ratios caused by the critical values of the slip ratio, the slip angle, and the inclination angle. Specifically, if all of slip ratios are smaller than those of their corresponding critical values, then there exists an elastic deformation state, otherwise there exists only complete
sliding state between the tire tread base and the terrain surface.
(i) Elastic Deformation State: S S c, Ss Ssc, and S S c
In the elastic deformation state, the longitudinal force F, the lateral force F, and three components of the self-aligning torque are written as functions of the elastic stiffness and the slip ratio as well as the normal force and the friction coefficients, such as:
where:
•
is the offset between the wheel plane center and the tire tread
base.
•
is set to zero if it is negative.
•
the length of the contact patch.
Mz is the portion of the self-aligning torque generated by the slip angle . Mzs
and Mzs are other components of the self-aligning torque produced by the
longitudinal force, which has an offset between the wheel center plane and the tire tread base, due to the slip angle and the inclination angle , respectively. The self-aligning torque Mz is determined as combinations of Mz, Mzs and Mzs.
(ii) Complete Sliding State: S S c, Ss Ssc, and S S c
In the complete sliding state, the longitudinal force, the lateral force, and three components of the self-aligning torque are determined as functions of the normal force and the friction coefficients without any elastic stiffness and slip ratio as:
Case 2:0 and C S C S
As in Case 1, a slip ratio due to the critical value of the slip ratio can be obtained as:
A slip ratio due to the critical value of the slip angle can be found as:
when Ss Ssc.
The nondimensional slip ratio Sn, is determined as:
where:
The nondimensional contact patch length ln is found from the equation ln = 1 - Sn, and the modified lateral friction coefficient is expressed as:
For the longitudinal force, the lateral force and the self-aligning torque two subcases should also be considered separately. A slip ratio due to the critical value of the inclination angle is not needed here since the required condition for Case 2,
C S C S, replaces the critical condition of the inclination angle.
(i) Elastic Deformation State: Ss Ssc and S Sac
In the elastic deformation state:
(ii) Complete Sliding State: Ss Ssc and S Sac
Case 3:0 and C S C S
Similar to Cases 1 and 2, slip ratios due to the critical values of the inclination angle and the slip ratio are obtained as:
The nondimensional slip ratio Sn, is expressed as:
where:
For the longitudinal force, the lateral force, and the self-aligning torque, two subcases should also be considered similar to Cases 1 and 2. A slip ratio due to the critical value of the slip angle is not needed here since the required condition for
Case 3, C S C S, replaces the critical condition of the slip angle. (i) Elastic Deformation State: S S c and Ss Ssc
In the elastic deformation state, F and Mz can be written:
(ii) Complete Sliding State: S S c and Ss Ssc
In the complete sliding state, F, F, Mz, Mzs, and Mzs can be determined by using:
respectively. The longitudinal force F , the lateral force F
, and three components
of the self-aligning torques, Mz , Mzs , and Mzs , always have positive values, but they can be transformed to have positive or negative values depending on the slip ratio s, the slip angle , and the inclination angle in the SAE coordinate system. Tire Forces and Moments in the SAE Coordinate System
For the general formulations of the longitudinal force Fx, lateral force Fy, and self-aligning torque Mz, in the SAE coordinate system, the three possible combinations of the slip ratio, the slip angle, and the inclination angle are also considered. Longitudinal Force:
Fx = sin(k) F , for all cases Lateral Force: F y = -sin(
) F
, for cases 1 and 2
F y = sin() F , for case 3 Self-aligning Torque:
M z = sin() M z - sin() [-sin() M zs + sin()M zs ]
Rolling Resistance Moment:
My = -Cr Fz, for a forward rolling tire. My = Cr Fz , for a backward rolling tire.
Operating Mode: USE_MODE
You can change the behavior of the tire model through the switch USE_MODE in the [MODEL] section of the tire property file.
•
USE_MODE = 0: Steady-state forces and moments • The tire forces and moments react instantaneously to changes in the tire kinematic states. •
USE_MODE = 1: Transient tire behavior • The tire will have a lagged response because of the so-called relaxation length in both longitudinal and lateral direction. See Lagged Longitudinal and Lateral Slip Quantities (transient tire behavior).
•The effect of the relaxation lengths will be most pronounced at low forward velocity
and/or high excitation frequencies. •
USE_MODE = 2: Smoothing of forces and moments on startup of the simulation •
When you indicate smoothing by setting the value of use mode in the tire property file, Adams/Tire smooths initial transients in the tire force over the first 0.1
seconds of simulation. The longitudinal force, lateral force, and aligning torque are multiplied by a cubic step function of time. (See STEP in the Adams/Solver online help.) Longitudinal Force FLon = S*FLon Lateral Force FLat = S*FLat Aligning Torque Mz = S*Mz
Tire Carcass Shape
You can optionally supply a tire carcass cross-sectional shape in the tire property file in the [SHAPE] block. The 3D-durability, tire-to-road contact algorithm uses this information when calculating the tire-to-road volume of interference. If you omit the [SHAPE] block from a tire property file, the tire carcass cross-section defaults to the rectangle that the tire radius and width define.
You specify the tire carcass shape by entering points in fractions of the tire radius and width. Because Adams/Tire assumes that the tire cross-section is symmetrical about the wheel plane, you only specify points for half the width of the tire. The following apply:
•
For width, a value of zero (0) lies in the wheel center plane. •
For width, a value of one (1) lies in the plane of the side wall. •
For radius, a value of one (1) lies on the tread. For example, suppose your tire has a radius of 300 mm and a width of 185 mm and that the tread is joined to the side wall with a fillet of 12.5 mm radius. The tread then begins to curve to meet the side wall at >+/- 80 mm from the wheel center plane. If you define the shape table using six points with four points along the fillet, the resulting table might look like the shape block that is at the end of the property format example (see SHAPE ).
Property File Format Example
$--------------------------------------------------------MDI_HEADER [MDI_HEADER]
FILE_TYPE = 'tir' FILE_VERSION = 2.0 FILE_FORMAT = 'ASCII'
(COMMENTS) {comment_string} 'Tire - XXXXXX'
'Pressure - XXXXXX' 'TestDate - XXXXXX' 'Test tire'
'New File Format v2.1'
$-------------------------------------------------------------units [UNITS] LENGTH
= 'meter' FORCE
= 'newton'
ANGLE
= 'rad'
MASS
= 'kg'
TIME
= 'sec'
$-------------------------------------------------------------model [MODEL]
! use mode
1
2
3
! ------------------------------------------
! relaxation lengths
X
! smoothing
X !
PROPERTY_FILE_FORMAT
= 'UATIRE'
USE_MODE
= 2
$---------------------------------------------------------dimension [DIMENSION]
UNLOADED_RADIUS
= 0.295
WIDTH
= 0.195
ASPECT_RATIO
= 0.55
$---------------------------------------------------------parameter [PARAMETER]
VERTICAL_STIFFNESS
= 190000
VERTICAL_DAMPING
= 50
ROLLING_RESISTANCE
= 0.003
CSLIP
= 80000
CALPHA
= 60000
CGAMMA
= 3000
UMIN
= 0.8
UMAX
= 1.1
REL_LEN_LON
= 0.6
REL_LEN_LAT
= 0.5
$-------------------------------------------------------------shape
[SHAPE]
{radial width}
1.0 0.0
1.0 0.2
1.0 0.4
1.0 0.6
1.0 0.8
0.9 1.0
$---------------------------------------------------------------------load_curve $ For a non-linear tire vertical stiffness (optional)
$ Maximum of 100 points
[DEFLECTION_LOAD_CURVE]
{pen
fz}
0.000
0.0
0.001
212.0
0.002
428.0
0.003
648.0
0.005
1100.0
0.010
2300.0
0.020
5000.0
0.030
8100.0。