CN111994085A - Estimation method for vehicle driving stability area under complex road condition - Google Patents

Estimation method for vehicle driving stability area under complex road condition Download PDF

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CN111994085A
CN111994085A CN202010862189.0A CN202010862189A CN111994085A CN 111994085 A CN111994085 A CN 111994085A CN 202010862189 A CN202010862189 A CN 202010862189A CN 111994085 A CN111994085 A CN 111994085A
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vehicle
wheel
model
tire
slip angle
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王萍
张曦月
李梓涵
陈虹
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Jilin University
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Jilin University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0019—Control system elements or transfer functions
    • B60W2050/0028—Mathematical models, e.g. for simulation
    • B60W2050/0031—Mathematical model of the vehicle
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0019—Control system elements or transfer functions
    • B60W2050/0028—Mathematical models, e.g. for simulation
    • B60W2050/0031—Mathematical model of the vehicle
    • B60W2050/0034—Multiple-track, 2D vehicle model, e.g. four-wheel model
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0043—Signal treatments, identification of variables or parameters, parameter estimation or state estimation

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Abstract

A method for estimating a vehicle driving stability area under a complex road condition belongs to the technical field of vehicle safety. The invention aims to provide a method for estimating a vehicle running stable area under a complex road condition, aiming at the vehicle running on the complex road condition, wherein the method is used for estimating the vehicle running stable area under the complex road condition, and the influence of the parameter changes such as the vehicle state, the road surface condition and the like on the stable area is researched. The method comprises the following steps: building a high-fidelity vehicle model, and identifying and drawing a vehicle driving stability area. The stable region obtained by the estimation method provided by the invention can change along with the vehicle state and the road surface condition in real time, and the stable region is estimated on line, so that more reliable safety evaluation can be carried out on the vehicle. The method considers various factors, namely influences of longitudinal speed, front wheel turning angle, road adhesion coefficient, ramp, curve and the like on stable region estimation, and analyzes the change condition of the stable region under different conditions.

Description

Estimation method for vehicle driving stability area under complex road condition
Technical Field
The invention belongs to the technical field of vehicle safety.
Background
With the continuous development of the automobile industry, the living standard of human beings is increasingly improved, and the quantity of automobiles kept is increased day by day. But the automobile brings convenience to the life of people and brings a series of potential safety hazards. The application of the active safety system is an important means for achieving the aims of improving safety and reducing traffic accidents. In an active safety system of a vehicle, research on the stability of the vehicle is always important, and stability control cannot leave a stable region which is an important method for describing the handling performance of the vehicle. There are many studies on how to determine the stable region and apply the stable region, but the existing studies have the following problems:
1. when a stable region is estimated, most of the stable regions adopt a phase plane formed by a centroid slip angle and a centroid slip angle speed, the traditional phase plane is an off-line stable region, the obtained stable region is often underestimated for a moving vehicle, and the safety evaluation of the vehicle is not very reliable.
2. The existing research on the stable area generally only focuses on the lateral movement of the vehicle, and does not consider the dynamic characteristics in other directions.
3. When the vehicle runs on a curve or a slope, due to the existence of a horizontal included angle and a roll moment, a vertical load can be redistributed to influence the cornering characteristic of the tire, so that the lateral force of the tire is changed, however, the change of the vertical load is not considered in the conventional research on a stable area. Although most of the existing researches consider the influence of longitudinal speed and road adhesion coefficient on a stable area, the researches on the influence of complex roads such as gradient and the like on the stable area are not mature.
Disclosure of Invention
The invention aims to provide a method for estimating a vehicle running stable area under a complex road condition, aiming at the vehicle running on the complex road condition, wherein the method is used for estimating the vehicle running stable area under the complex road condition, and the influence of the parameter changes such as the vehicle state, the road surface condition and the like on the stable area is researched.
The method comprises the following steps:
step one, building a high-fidelity vehicle model;
step two, identifying and drawing a vehicle driving stable area:
1) establishing a non-linear tire model and a tire load model which can describe load transfer:
a. establishing a nonlinear vehicle dynamic model:
Figure BDA0002648519290000011
Figure BDA0002648519290000012
wherein,
Figure BDA0002648519290000013
and
Figure BDA0002648519290000014
respectively representing the derivative of the centroid slip angle of the vehicle and the derivative of the yaw rate of the vehicle, m being the vehicle mass, VxIs the vehicle longitudinal velocity, β is the centroid slip angle, γ is the yaw rate, Fyfl、FyfrAre the lateral forces of the left and right wheels of the front axle, respectively, Fyrl、FyrrAre the lateral forces of the left wheel and the right wheel of the rear axle respectively,fis the corner of the front wheel, IzIs the moment of inertia, L, of the vehicle about the center of massfIs the distance of the center of mass to the front axis, LrIs the distance of the center of mass to the rear axis, LsIs half the distance from the left axle to the right axle of the wheel;
b. establishing a nonlinear tire model:
when the tire slip angle α is small, there is tan (α) ≈ α, and then the nonlinear tire model is:
Figure BDA0002648519290000021
wherein, FyIs the lateral force of the tire, mu is the road adhesion coefficient, FzFor vertical loading, CαIs the tire cornering stiffness, which can be classified as front wheel cornering stiffness CfAnd rear wheel cornering stiffness CrAnd alpha is a tire slip angle;
divided into front wheel side slip angle alphafAnd rear wheel side slip angle alpharCalculated from the following formula:
Figure BDA0002648519290000022
Figure BDA0002648519290000023
wherein,fis the front wheel corner;
c. building a tire load model:
the vertical load model considering the influence of the lateral gradient eta of the curved road surface is as follows:
Figure BDA0002648519290000024
Figure BDA0002648519290000025
Figure BDA0002648519290000026
Figure BDA0002648519290000027
the vertical load model considering the influence of the longitudinal gradient xi of the slope road surface is as follows:
Figure BDA0002648519290000028
Figure BDA0002648519290000031
Figure BDA0002648519290000032
Figure BDA0002648519290000033
wherein, Fzfl、FzfrRespectively, the vertical loads of the left and right wheels of the front axle, Fzrl、FzrrThe vertical load of the left wheel and the right wheel of the rear axle respectively, eta is the lateral gradient of the curve, xi is the longitudinal gradient, axIs the longitudinal acceleration, ayIs the lateral acceleration, h is the distance from the center of mass to the ground, hφIs the side-tipping moment arm of the arm,
Figure BDA0002648519290000034
is the angle of the side rake,
Figure BDA0002648519290000035
respectively, the roll angle stiffness of the front and rear suspensions, d is the wheel track of the automobile, g is the gravity acceleration, and LfIs the distance of the center of mass to the front axis, LrIs the distance of the center of mass to the rear axis;
2) locally linearizing the nonlinear model describing the transverse, longitudinal and vertical motions of the vehicle built in the step 1) through the dynamic model of the formula (1) and the formula (2) and represented by the formula (14):
Figure BDA0002648519290000036
wherein,
Figure BDA0002648519290000037
and
Figure BDA0002648519290000038
representing the linearization points of the centroid yaw angle and yaw rate derivatives respectively,
Figure BDA0002648519290000039
Δβ、Δγ、Δfrespectively, an incremental part, f represents a function consisting of variables of yaw angular velocity, centroid slip angle, front wheel angle, and the like, betao、γo、foRespectively are the linearization points of the centroid slip angle, the yaw angular velocity and the front wheel rotation angle;
linearizing it by Taylor expansion
Figure BDA00026485192900000310
Wherein,
Figure BDA00026485192900000311
Figure BDA00026485192900000312
the following formula is obtained according to the side slip angles of the front wheel and the rear wheel:
Figure BDA00026485192900000313
Figure BDA00026485192900000314
Figure BDA00026485192900000315
from the above formula, the expression a is obtained:
Figure BDA0002648519290000041
expanding each part of A to obtain the following formula:
Figure BDA0002648519290000042
Figure BDA0002648519290000043
Figure BDA0002648519290000044
Figure BDA0002648519290000045
wherein C isαflAnd CαfrLateral deflection stiffness, C, of the left and right tires of the front wheel, respectivelyαrlAnd CαrrThe lateral deflection rigidity of the left and right tires of the rear wheel; similarly, the expression B is obtained by the formula:
Figure BDA0002648519290000046
and expanding each part of the B to obtain the following formula:
Figure BDA0002648519290000047
Figure BDA0002648519290000048
the stable and controlled conditions were as follows:
Figure BDA0002648519290000049
Cαfl+Cαfr≠0 (22)；
3) drawing a vehicle driving stability region
The desired value is obtained by modifying the front and rear wheel side slip angle formula:
Figure BDA0002648519290000051
Figure BDA0002648519290000052
where β is the centroid slip angle and γ is the yaw rate.
The stable region provided by the invention can be updated in real time, and more reliable safety evaluation can be performed on the vehicle. The invention has the beneficial effects that:
1. the stable region obtained by the estimation method provided by the invention can change along with the vehicle state and the road surface condition in real time, and the stable region is estimated on line, so that more reliable safety evaluation can be carried out on the vehicle.
2. The invention establishes a dynamic model comprising transverse, longitudinal and vertical directions, and considers the influence of vertical load redistribution on the tire cornering property and the lateral force when a vehicle is on a slope or a curve.
3. The method considers various factors, namely influences of longitudinal speed, front wheel turning angle, road adhesion coefficient, ramp, curve and the like on stable region estimation, and analyzes the change condition of the stable region under different conditions.
Drawings
FIG. 1 is a block diagram of the general flow of the method of the present invention to map a vehicle driving stability zone;
FIG. 2 is a schematic diagram of a nonlinear vehicle dynamics model involved in the stable region drawn by the method of the present invention;
FIG. 3 is a graph of lateral force versus slip angle for various tire road adhesion coefficients according to the method of the present invention;
FIG. 4 shows the process of the invention at Vx＝25m/s,μ＝0.25,fA simulation graph in the case where η is 0, and ξ is 0;
figure 5 shows the method of the present invention when mu is 0.35,f＝0deg,η＝3％,ξ＝0,Vxsimulation graphs under the conditions of 60km/h,80km/h and 90 km/h;
figure 6 shows the method of the present invention when mu is 0.35,f＝0deg,η＝0,ξ＝5％,Vxsimulation graphs under the conditions of 50km/h,55km/h and 60 km/h;
FIG. 7 is the present inventionThe invented method is characterized by that when mu is 0.35, Vx＝40m/s,η＝0,ξ＝0,fSimulation graphs under the conditions of 0deg,4deg and 8 deg;
FIG. 8 shows the process of the invention at Vx＝25m/s,fSimulation graphs in the case of 0deg, η ═ 0, ξ ═ 0, μ ═ 0.35,0.45, 0.8;
figure 9 shows the method of the present invention when mu is 0.35,f＝0deg,Vxsimulation graph under the condition of 90km/h, 0 and 0, 3% and 6%;
figure 10 shows the method of the present invention when mu is 0.35,f＝0deg,Vx60km/h, 0, 1%, 5%, 6%.
Detailed Description
The invention designs an estimation method capable of reflecting the influence of longitudinal speed, front wheel turning angle, road surface adhesion coefficient, gradient and the like on a vehicle running stability area based on the transverse, longitudinal and vertical dynamic characteristics of the vehicle, and considers various road conditions.
The method comprises the following steps:
step one, building a high-fidelity vehicle model: selecting a vehicle model from CarSim software, reading the motion state parameters of the vehicle into Simulink, and simulating the transverse, longitudinal and vertical motion characteristics of the vehicle which actually runs on the basis of the selected vehicle model and the constructed simulation working conditions of different road conditions;
step two, identifying and drawing the vehicle driving stable area
2.1) considering the influence of vertical load on the tire cornering property in vehicle dynamics, and establishing a dynamic model comprising a transverse direction, a longitudinal direction and a vertical direction;
2.2) carrying out Taylor expansion and local linearization on the nonlinear model established in the step 2.1), and providing a basis for judging the stability of the vehicle, namely a stable condition and a controllable condition;
2.3) according to the obtained stability judgment basis, drawing a stable region obtained by the estimation method of the invention.
For the purpose of illustrating the technical contents, constructional features, objects and the like of the present invention in detail, the present invention will be fully explained with reference to the accompanying drawings.
The overall block diagram of the estimation method based on the method of the invention is shown in fig. 1, wherein the vehicle mass, the gradient, the roll angle and the like are collected from vehicle dynamics simulation software CarSim; the vehicle dynamic model in the invention includes lateral, longitudinal, and vertical dynamics, due to the more complex road conditions to be considered; in order to improve the model precision, a Fiala nonlinear tire model is adopted to describe the lateral force of the tire; and (3) carrying out local linearization on the nonlinear vehicle dynamic model by a Taylor expansion and local linearization method, obtaining a condition for judging the vehicle stability, and finally estimating to obtain a stable region formed by the yaw velocity and the centroid sideslip angle. The influence of complex road conditions on stable area estimation is explored by continuously modifying data in CarSim. In the simulation experiment, the vehicle model and the simulation working condition are both constructed in CarSim, and the others are constructed in Simulink.
The invention aims to realize real-time estimation of a vehicle driving stable area under complex road conditions.
The estimation of the vehicle running stable area and the change of the vehicle state and the road surface condition of the vehicle in the running process are realized by the joint simulation of a software system.
1. Software selection
The simulation model related to the estimation method is built through Matlab/Simulink software and high-fidelity vehicle dynamics simulation software CarSim, the software versions are Matlab R2016a and CarSim2016.1 respectively, and the solver is ODE 1. The simulation step size is 0.001 s. The method mainly comprises the following steps that in a simulation experiment, a model in the CarSim replaces a real vehicle to serve as an implementation object of a designed vehicle driving stability region estimation method; MATLAB/Simulink software is used for building a simulation model related to a stable region, namely, the operation in the method is completed through Simulink programming.
2. Joint simulation setup
To realize the joint simulation of the two, firstly, a path of CarSim needs to be added in the path setting of Matlab; secondly, adding an output interface module in the CarSim interface; then the model information in the CarSim is compiled by the system and then is kept in the Simulink in the form of CarSimS-function, and finally the parameter setting of the CarSim module in the Simulink is carried out. When the Simulink simulation model is run, the CarSim model is also calculated and solved at the same time. And data exchange is continuously carried out between the two in the simulation process. If the model structure or parameter settings in the CarSim are modified, recompilation is required, and then the new CarSim module containing the latest setting information is sent back to Simulink.
The invention relates to a method for estimating a vehicle driving stable region under a complex road condition, which comprises the following steps of firstly, selecting a proper vehicle model from high-fidelity vehicle dynamics simulation software CarSim and acquiring corresponding parameters; secondly, considering the influence of the vertical load redistributed under the conditions of a ramp, a curve and the like on the tire cornering property in the vehicle dynamics, and establishing a dynamic model comprising a transverse direction, a longitudinal direction and a vertical direction; then, carrying out local linearization on the nonlinear vehicle dynamic model by a Taylor expansion and local linearization method, giving a basis for judging the vehicle stability, and estimating a stable region formed by the yaw velocity and the centroid sideslip angle; and finally, analyzing the influence of the parameter changes such as the vehicle state, the road surface condition and the like on the stable point region estimation through a simulation experiment.
The invention specifically comprises the following steps:
step one, building a high-fidelity vehicle model: the high-fidelity vehicle model simulates a real controlled object and has the main function of accurately simulating the transverse, longitudinal and vertical motion characteristics of an actual vehicle.
In the invention, because the joint simulation is used, in CarSim, the vehicle model selection and the construction of the simulation working condition are mainly used.
Firstly, a typical passenger car model is selected, then relevant parameters of the model are modified and obtained, and vehicle model parameters are added into a Simulink simulation model. After selecting the corresponding vehicle model and parameters, corresponding simulation conditions need to be constructed, and the driving route, the driving environment, the driver model and the like of the vehicle can be selected in the simulation conditions. In the invention, only partial parameters of the running motion state of the vehicle are used, so that a driver model carried in CarSim is selected, and the motion state parameters of the vehicle are read into Simulink.
In high-fidelity vehicle dynamics simulation software CarSim, a vehicle mainly comprises a vehicle body, a transmission system, a steering system, a braking system, tires, a suspension, working condition configuration and other systems. The model parameters include vehicle mass m which is 1430kg and distance L from the vehicle mass center to the front axlef1.05m, distance L from the center of mass of the vehicle to the rear axler1.61m, 1.55m for the vehicle wheel track d and the front wheel tire side deflection rigidity Cf＝90700N·m-1Side deflection stiffness C of rear wheelr＝109000N·m-1Moment of inertia of vehicle about center of mass Iz＝2059.2kg·m-2Radius of wheel Re0.325m, and the distance h from the center of mass to the ground is 0.54 m. Longitudinal gradient and lateral gradient are added on the basis of a straight road respectively to simulate the transverse, longitudinal and vertical motion characteristics of an actual vehicle, so that the model is built.
Step two, identifying and drawing a vehicle driving stable area:
1) to meet the requirements of the present invention, a non-linear vehicle dynamics model describing the motion of the vehicle is created, as shown in FIG. 2. Meanwhile, a nonlinear tire model and a tire load model capable of describing load transfer are established for realizing the estimation of the stable region.
a. Establishing a nonlinear vehicle dynamic model:
Figure BDA0002648519290000081
Figure BDA0002648519290000082
wherein，
Figure BDA0002648519290000083
And
Figure BDA0002648519290000084
respectively representing the derivative of the centroid slip angle of the vehicle and the derivative of the yaw rate of the vehicle, m being the vehicle mass, VxIs the vehicle longitudinal velocity, β is the centroid slip angle, γ is the yaw rate, Fyfl、FyfrAre the lateral forces of the left and right wheels of the front axle, respectively, Fyrl、FyrrAre the lateral forces of the left wheel and the right wheel of the rear axle respectively,fis the corner of the front wheel, IzIs the moment of inertia, L, of the vehicle about the center of massfIs the distance of the center of mass to the front axis, LrIs the distance of the center of mass to the rear axis, LsIs half the distance from the left axle to the right axle of the wheel.
b. Establishing a nonlinear tire model:
in the invention, because the vehicle is in a limit state, in order to improve the model accuracy, the lateral force of the tire is described by a nonlinear model, namely, a Fiala tire model is used for calculating the lateral force in the nonlinear vehicle dynamic model. In this model, the tire slip angle is used as an internal variable. When the tire slip angle α is small, there is tan (α) ≈ α, and then the nonlinear tire model can be approximated as:
Figure BDA0002648519290000085
wherein, FyIs the lateral force of the tire, mu is the road adhesion coefficient, FzFor vertical loading, CαIs the tire cornering stiffness, which can be classified as front wheel cornering stiffness CfAnd rear wheel cornering stiffness CrAnd alpha is a tire slip angle.
Can be divided into front wheel side slip angle alphafAnd rear wheel side slip angle alpharThey can be calculated from the following formula:
Figure BDA0002648519290000086
Figure BDA0002648519290000087
wherein,fis the front wheel corner. The relationship between the lateral force and the slip angle for different tire road adhesion coefficients is shown in fig. 3.
c. Building a tire load model:
when the vehicle travels straight on a road surface, the vertical loads of the left and right tires are substantially the same. However, when the vehicle is driving on a curve or a slope road, the vertical load on each tire in the formula (3) is redistributed due to the existence of the horizontal included angle and the roll moment, and the roll characteristic of the tire is affected, so that the steady state response of the vehicle is changed. Therefore, it is particularly important to consider vertical loads.
During cornering, the vertical load on each tire is redistributed. The vertical load model considering the influence of the lateral gradient eta of the curved road surface is as follows:
Figure BDA0002648519290000091
Figure BDA0002648519290000092
Figure BDA0002648519290000093
Figure BDA0002648519290000094
on a slope, the vertical load on each tire is also redistributed. The vertical load model considering the influence of the longitudinal gradient xi of the slope road surface is as follows:
Figure BDA0002648519290000095
Figure BDA0002648519290000096
Figure BDA0002648519290000097
Figure BDA0002648519290000098
wherein, Fzfl、FzfrRespectively, the vertical loads of the left and right wheels of the front axle, Fzrl、FzrrThe vertical load of the left wheel and the right wheel of the rear axle respectively, eta is the lateral gradient of the curve, xi is the longitudinal gradient, axIs the longitudinal acceleration, ayIs the lateral acceleration, h is the distance from the center of mass to the ground, hφIs the side-tipping moment arm of the arm,
Figure BDA0002648519290000099
is the angle of the side rake,
Figure BDA00026485192900000910
respectively, the roll angle stiffness of the front and rear suspensions, d is the wheel track of the automobile, g is the gravity acceleration, and LfIs the distance of the center of mass to the front axis, LrIs the distance of the center of mass to the rear axis.
2) Locally linearizing the nonlinear model describing the lateral, longitudinal and vertical motions of the vehicle established in the step 1) through the dynamic models of the formula (1) and the formula (2) can be represented by the formula (14):
Figure BDA00026485192900000911
wherein,
Figure BDA00026485192900000912
and
Figure BDA00026485192900000913
representing the linearization points of the centroid yaw angle and yaw rate derivatives respectively,
Figure BDA00026485192900000914
Δβ、Δγ、Δfrespectively, an incremental part, f represents a function consisting of variables of yaw angular velocity, centroid slip angle, front wheel angle, and the like, betao、γo、foAre linearization points of the centroid slip angle, yaw rate, and front wheel rotation angle, respectively, and are linearized in the form of taylor expansion.
Figure BDA0002648519290000101
Wherein,
Figure BDA0002648519290000102
Figure BDA0002648519290000103
to further develop the linearization formula, the following formula is obtained according to the front and rear wheel side slip angle:
Figure BDA0002648519290000104
from the above formula, the expression a is obtained:
Figure BDA0002648519290000105
expanding each part of A to obtain the following formula:
Figure BDA0002648519290000106
wherein C isαflAnd CαfrLateral deflection stiffness, C, of the left and right tires of the front wheel, respectivelyαrlAnd CαrrThe rear wheel left and right tire cornering stiffness, respectively.
Similarly, the expression B is obtained by the formula:
Figure BDA0002648519290000107
and expanding each part of the B to obtain the following formula:
Figure BDA0002648519290000111
with the present invention, the nonlinear vehicle dynamics model has been locally linearized by the above steps, and due to the characteristics of the linear system, the stability of the system can be determined from the eigenvalues of a in equation (17). By analytical derivation, stable and controlled conditions were obtained as follows:
Figure BDA0002648519290000112
Cαfl+Cαfr≠0 (22)
3) drawing a vehicle driving stability region
According to the obtained stability condition and controllability condition, the lateral deflection rigidity meeting the condition can be screened out, and then the corresponding lateral deflection angle is obtained. In order to plot a stable region composed of the yaw rate and the centroid slip angle, a desired value is obtained by transforming the front and rear wheel slip angle formula:
Figure BDA0002648519290000113
where β is the centroid slip angle and γ is the yaw rate.
From equation (23), it can be obtained that the stable region mapped by the estimation method of the present invention is shown in fig. 4, wherein the boundary of the dotted line represents the stable boundary and the boundary of the solid line represents the controllable boundary. In the present invention, the stable boundary also represents the oversteer boundary, while the controllable boundary also represents the understeer boundary. A general flow diagram in which a vehicle driving stability region is plotted is shown in fig. 1.
Simulation experiment verification and comparison
The speed, the road surface condition and the like of the vehicle in Carsim are changed, the running stable area of the vehicle under different conditions is contrasted and analyzed, the following simulation verification is carried out, and the influence of different factors on the stable area on a complex road surface is given.
a. Effect of longitudinal velocity on the stability region:
the longitudinal speed of the vehicle affects the lateral force of the tire and thus the estimation of the stability zone. In this case, the invention makes the following parameter settings, discussing the effect of longitudinal speed on the stability region when there is a lateral slope on the turn and a longitudinal slope on the ramp, respectively. Wherein, the mu is 0.35,f＝0deg,η＝3％,ξ＝0,Vx60km/h,80km/h and 90km/h, and a simulation result graph is shown in FIG. 5. Mu is equal to 0.35, and the content of the trace element is less than the content of the trace element,f＝0deg,η＝0,ξ＝5％,Vxthe simulation results are shown in FIG. 6, wherein the values are 50km/h,55km/h and 60 km/h. The three speeds assumed by the invention can be understood as that the vehicle runs under three working conditions of low speed, medium speed and high speed respectively. As can be seen from fig. 5 and 6, the stable region gradually increases with increasing longitudinal speed. Therefore, in both the case of traveling on a slope and the case of turning, the vehicle speed must be strictly controlled, and a speed limit sign must be provided to ensure the driving safety of the driver.
b. Influence of front wheel turning angle on stability area:
since changes in the front wheel angle affect the stability region, the present invention sets the parameters as follows to explore the effect of the front wheel angle. Suppose μ is 0.35, Vx＝40m/s,η＝0,ξ＝0,fFig. 7 shows simulation results when the values of 0deg,4deg and 8deg are satisfied. As can be seen from the simulation diagram, the front wheel rotatesThe change of the angle has no influence on the shape of the estimated stable region, and only when the front wheel rotation angle is changed to increase or decrease the front wheel rotation angle, the position of the stable region is changed according to a certain rule, and the stable region moves to the upper right or the lower left.
c. Influence of road adhesion coefficient on stable area:
whether the road surface condition is smooth or rough affects the tire lateral force, which in turn has a large impact on the estimation of the vehicle stability area. In this case, assume Vx＝25m/s,fFig. 8 shows the simulation result graph, where 0deg, 0 eta, 0 ξ,0 μ 0.35,0.45, 0.8. From the simulation results, it can be seen that the shape of the stable region is similar for different road surface adhesion coefficients, but the stable region decreases as the road surface adhesion coefficient decreases. It is understood that when the road adhesion coefficient is small, the vehicle is difficult to control on a wet road surface.
d. Influence of lateral slope on the stability zone:
during vehicle cornering, the lateral gradient at the cornering has an effect on vehicle stability due to the redistribution of vertical loads. Assuming that the vehicle running condition is μ 0.35,f＝0deg,Vx90km/h, 0, 3%, 6%, the simulation result is shown in fig. 9. When the vehicle speed is constant, as the lateral gradient increases, the yaw rate and the centroid slip angle also increase accordingly, resulting in an increase in the stability zone.
e. Influence of longitudinal gradient on the stability region:
when driving on a sloping road, the influence of the longitudinal gradient at the slope on the stability region is explored for the redistributed vertical load. Assuming that the vehicle operating condition is μ 0.35,f＝0deg,Vx60km/h, eta is 0, xi is 1%, 5%, 6%, the simulation result is shown in fig. 10. It can be seen from the simulation that when the longitudinal gradient changes, the influence on the yaw rate and the centroid slip angle is small, and the stable regions in several different gradient situations almost coincide. However, although the influence of the longitudinal gradient on the stable area cannot be ignored, a gradient board should be arranged on the slope, and the vehicle can pass through the slope boardReminding the driver of driving carefully and ensuring life safety.
According to the simulation example, the estimation method of the vehicle driving stable region under the complex road condition can generate the corresponding stable region in real time according to the external condition, is greatly helpful for future research, and embodies the superiority of the method provided by the invention.

Claims (1)

1. A method for estimating a vehicle driving stability area under a complex road condition comprises the following steps:
step one, building a high-fidelity vehicle model;
the method is characterized in that:
step two, identifying and drawing a vehicle driving stable area:
1) establishing a non-linear tire model and a tire load model which can describe load transfer:
a. establishing a nonlinear vehicle dynamic model:
Figure FDA0002648519280000011
Figure FDA0002648519280000012
wherein,
Figure FDA0002648519280000013
and
Figure FDA0002648519280000014
respectively representing the derivative of the centroid slip angle of the vehicle and the derivative of the yaw rate of the vehicle, m being the vehicle mass, VxIs the vehicle longitudinal velocity, β is the centroid slip angle, γ is the yaw rate, Fyfl、FyfrAre the lateral forces of the left and right wheels of the front axle, respectively, Fyrl、FyrrAre the lateral forces of the left wheel and the right wheel of the rear axle respectively,fis the corner of the front wheel, IzIs wound by vehiclesMoment of inertia of center of mass rotation, LfIs the distance of the center of mass to the front axis, LrIs the distance of the center of mass to the rear axis, LsIs half the distance from the left axle to the right axle of the wheel;
b. establishing a nonlinear tire model:
when the tire slip angle α is small, there is tan (α) ≈ α, and then the nonlinear tire model is:
Figure FDA0002648519280000015
wherein, FyIs the lateral force of the tire, mu is the road adhesion coefficient, FzFor vertical loading, CαIs the tire cornering stiffness, which can be classified as front wheel cornering stiffness CfAnd rear wheel cornering stiffness CrAnd alpha is a tire slip angle;
divided into front wheel side slip angle alphafAnd rear wheel side slip angle alpharCalculated from the following formula:
Figure FDA0002648519280000016
Figure FDA0002648519280000017
wherein,fis the front wheel corner;
c. building a tire load model:
the vertical load model considering the influence of the lateral gradient eta of the curved road surface is as follows:
Figure FDA0002648519280000018
Figure FDA0002648519280000021
Figure FDA0002648519280000022
Figure FDA0002648519280000023
the vertical load model considering the influence of the longitudinal gradient xi of the slope road surface is as follows:
Figure FDA0002648519280000024
Figure FDA0002648519280000025
Figure FDA0002648519280000026
Figure FDA0002648519280000027
wherein, Fzfl、FzfrRespectively, the vertical loads of the left and right wheels of the front axle, Fzrl、FzrrThe vertical load of the left wheel and the right wheel of the rear axle respectively, eta is the lateral gradient of the curve, xi is the longitudinal gradient, axIs the longitudinal acceleration, ayIs the lateral acceleration, h is the distance from the center of mass to the ground, hφIs the side-tipping moment arm of the arm,
Figure FDA0002648519280000028
is the angle of the side rake,
Figure FDA0002648519280000029
respectively, the roll stiffness of the front and rear suspensions, d is the wheel track of the automobile, and g isAcceleration of gravity, LfIs the distance of the center of mass to the front axis, LrIs the distance of the center of mass to the rear axis;
2) locally linearizing the nonlinear model describing the transverse, longitudinal and vertical motions of the vehicle built in the step 1) through the dynamic model of the formula (1) and the formula (2) and represented by the formula (14):
Figure FDA00026485192800000210
wherein,
Figure FDA00026485192800000211
and
Figure FDA00026485192800000212
representing the linearization points of the centroid yaw angle and yaw rate derivatives respectively,
Figure FDA00026485192800000213
Δβ、Δγ、Δfrespectively, an incremental part, f represents a function consisting of variables of yaw angular velocity, centroid slip angle, front wheel angle, and the like, betao、γo、foRespectively are the linearization points of the centroid slip angle, the yaw angular velocity and the front wheel rotation angle;
linearizing it by Taylor expansion
Figure FDA00026485192800000214
Wherein,
Figure FDA0002648519280000031
Figure FDA0002648519280000032
the following formula is obtained according to the side slip angles of the front wheel and the rear wheel:
Figure FDA0002648519280000033
Figure FDA0002648519280000034
Figure FDA0002648519280000035
from the above formula, the expression a is obtained:
Figure FDA0002648519280000036
expanding each part of A to obtain the following formula:
Figure FDA0002648519280000037
Figure FDA0002648519280000038
Figure FDA0002648519280000039
Figure FDA00026485192800000310
wherein C isαflAnd CαfrLateral deflection stiffness, C, of the left and right tires of the front wheel, respectivelyαrlAnd CαrrThe lateral deflection rigidity of the left and right tires of the rear wheel; similarly, the expression B is obtained by the formula:
Figure FDA00026485192800000311
and expanding each part of the B to obtain the following formula:
Figure FDA00026485192800000312
Figure FDA00026485192800000313
the stable and controlled conditions were as follows:
Figure FDA0002648519280000041
Cαfl+Cαfr≠0 (22)；
3) drawing a vehicle driving stability region
The desired value is obtained by modifying the front and rear wheel side slip angle formula:
Figure FDA0002648519280000042
Figure FDA0002648519280000043
where β is the centroid slip angle and γ is the yaw rate.
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