CN113032880B - Method for evaluating design rationality of circular curve road section - Google Patents

Method for evaluating design rationality of circular curve road section Download PDF

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CN113032880B
CN113032880B CN202110326064.0A CN202110326064A CN113032880B CN 113032880 B CN113032880 B CN 113032880B CN 202110326064 A CN202110326064 A CN 202110326064A CN 113032880 B CN113032880 B CN 113032880B
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张航
张竞宇
储泽宇
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Wuhan University of Technology WUT
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Abstract

The invention provides an evaluation method for the design rationality of a circular curve road section, which comprises the following steps: establishing a vehicle system model of the lateral driving condition of a vehicle system on a circular curve section by taking a vehicle mass center slip angle and a yaw angular velocity as variables; quantitatively analyzing the quantitative relation between the vehicle mass center slip angle and the yaw angular velocity when the vehicle stably runs on the circular curve section according to the vehicle system model established in the step S1; and (3) building a dynamic simulation system for the vehicle to laterally run on the circular curve section to be evaluated, calculating the mass center slip angle and the yaw velocity of the vehicle when the vehicle runs on the circular curve section to be evaluated according to the vehicle system model in the step S1, and then evaluating the rationality of the design index of the circular curve section by combining the quantitative relation between the mass center slip angle and the yaw velocity of the vehicle in the step S2. The method takes the instability condition of the automobile on the circular curve road section into full consideration from the nonlinear angle, so that the rationality of the circular curve road section is more accurately evaluated and is matched with the actual condition.

Description

Method for evaluating design rationality of circular curve road section
Technical Field
The invention belongs to the technical field of transportation, and particularly relates to an evaluation method for the design rationality of a circular curve road section.
Background
The highway curve segment is the key point and the difficulty of route design, in particular the particularity of the linear condition and the behavior complexity of the driver, and becomes a high-incidence area of traffic accidents. The terrain of China is complex, and a plurality of sharp-curved road sections with small radiuses exist on a highway in a mountainous area, so that the vehicles can slide laterally, the fixed tracks of the vehicles can deviate, even the vehicles can be unstable, and the accident potential is large. According to statistical data, the accident rate on the curve road section is higher than that on the straight road section, and the severity of the accident is obviously higher than that on the straight road section. However, safety evaluation methods such as design specifications only analyze the instability condition of the automobile on a circular curve road section from a linear angle, and the actual road section may have complex geographic factors and vehicle factors, so that the instability of the automobile cannot be simply analyzed from the linear angle.
Disclosure of Invention
The invention aims to provide an evaluation method for the reasonability of the design of a circular curve road section aiming at the defects of the prior art, and the evaluation method takes the instability condition of an automobile on the circular curve road section into full consideration from the nonlinear angle, so that the reasonability of the circular curve road section is evaluated more accurately and is fit for the actual condition.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for evaluating the design rationality of a circular curve road section comprises the following steps:
a method for evaluating the design rationality of a circular curve road section is characterized by comprising the following steps:
s1, establishing a vehicle system model of the lateral driving condition of the vehicle system on the circular curve section by taking the mass center slip angle and the yaw rate of the vehicle as variables;
s2, quantitatively analyzing the quantitative relation between the vehicle mass center and the yaw rate when the vehicle stably runs on the circular curve section according to the vehicle system model established in the step S1;
s3, a dynamic simulation system of the vehicle running laterally on the circular curve section to be evaluated is built, the change conditions of the vehicle mass center side drift angle and the yaw angular velocity when the vehicle runs on the circular curve section to be evaluated are calculated according to the vehicle system model in the step S1, and then the rationality of the design index of the circular curve section to be evaluated is evaluated by combining the quantitative relation between the vehicle mass center side drift angle and the yaw angular velocity in the step S2.
Further, the specific method of step S1 is:
s21, carrying out stress analysis on the lateral motion process of the vehicle on the circular curve road section, and establishing a lateral motion equation and a yaw angle motion equation of the vehicle;
s22, establishing a lateral tire force model of the vehicle based on the Dugoff tire model;
s23, combining the lateral tire force model of the step S22 and the motion equation of the step S21, and establishing a vehicle system model of the vehicle system in a lateral driving state on the circular curve road section, wherein the vehicle system model is as follows:
Figure BDA0002994721500000021
in the formula, beta is a centroid slip angle, and gamma is a yaw angular velocity.
Further, in step S2, a plurality of different initial values of the centroid yaw angle β and the yaw angular velocity γ of the vehicle system model variables are given through the phase plane, each set of different initial values is substituted into the vehicle system model to correspondingly obtain a continuously changing set of solutions (β, γ), each set of solutions (β, γ) obtained is plotted on the coordinate system with the centroid yaw angle β and the yaw angular velocity γ as horizontal and vertical coordinates, so as to obtain a (β - γ) phase plane diagram, and a trajectory of a set of solutions corresponding to each initial value on the phase plane is a phase trajectory.
Further, in step S3, the trajectory holding ability of the vehicle is evaluated by the vehicle centroid slip angle, the vehicle lateral stability is evaluated by the vehicle centroid yaw rate, and if the vehicle centroid slip angle and the yaw rate obtained through simulation change beyond the limit values, that is, the phase trajectory obtained through simulation does not converge on the phase plane, it indicates that the design index of the circular curve section is unreasonable, and vehicle instability is caused; on the contrary, if the mass center slip angle and the yaw velocity change of the vehicle obtained by simulation are always kept within the limit value in the whole-road-section driving process of the vehicle, the phase locus obtained by simulation converges on the phase plane, and the design index of the circular curve road section is reasonable.
Compared with the prior art, the invention has the beneficial effects that: according to the method, from a nonlinear angle, when a vehicle system is in low adhesion steering, the tire works in a nonlinear area, and the lateral stability of the vehicle can be well analyzed by a phase plane method based on a nonlinear theory; the method comprehensively considers the complex condition of the automobile running on the circular curve section, and evaluates the reasonability of the design of the circular curve section by taking the mass center slip angle and the yaw angular velocity of the automobile as the considered indexes, wherein the mass center slip angle of the automobile can well reflect the track holding capacity of the automobile and is used as the evaluation index of the side slip instability; the yaw velocity of the vehicle reflects the steering stability of the vehicle, so that the reasonability evaluation of the design indexes of the circular curve road section is closer to reality, and a method which is more accordant with the actual condition is provided for the selection of the design indexes of the circular curve road section.
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FIG. 1 is a force analysis diagram of a vehicle driving on a circular curve road section according to an embodiment of the present invention, wherein (a) is a side view of the vehicle under force, and (b) is a rear view of the vehicle under force;
FIG. 2 is a graph of lateral tire force versus tire slip angle for a vehicle according to an embodiment of the present invention traveling a round curve;
FIG. 3 is a phase plan view of a multi-set (. beta. -gamma.) solution of an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the following embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The present invention is further illustrated by the following examples, which are not to be construed as limiting the invention.
The invention discloses a method for evaluating the reasonability of a circular curve section based on the driving stability of a vehicle, which comprises the following steps of:
s1, establishing a vehicle system model of the lateral driving state of the vehicle system on the circular curve section by taking the mass center slip angle and the yaw rate of the vehicle as variables;
in this step, first, a 7-degree-of-freedom full vehicle dynamics analysis of the vehicle on a circular curve section is established, and a simplified stress analysis during the lateral movement of the vehicle is shown in fig. 1. In fig. 1: v. ofxThe unit is the longitudinal speed, km/h; v. ofyThe lateral speed is in km/h; beta is the centroid slip angle, in units (°); γ is yaw rate, in units (°/s); δ is the front wheel angle, in units (°); theta is the lateral inclination angle of the road surface in units (DEG); fxiIs the wheel longitudinal force in units of N; fyiIs the lateral force of the wheel in N; a is the distance from the center of mass to the front axis in m; b is the distance from the center of mass to the rear axis in m; d is the track width in m. The analysis results show that the compound can be obtained,
the longitudinal motion equation of the vehicle along the x-axis is:
Figure BDA0002994721500000041
the lateral motion equation of the vehicle along the y-axis is:
Figure BDA0002994721500000042
the yaw motion equation around the z-axis is:
Figure BDA0002994721500000043
in formula (3): i iszFor the moment of inertia of the vehicle about the z-axis, in KN/m2。
Will be provided with
Figure BDA0002994721500000044
tanβ＝vy/vxThe formula (2) and the formula (3) are substituted, and the following can be obtained through simplified calculation:
Figure BDA0002994721500000045
Figure BDA0002994721500000046
the four-wheel motion equation is:
Figure BDA0002994721500000047
in formula (6), JwIs the moment of inertia of the tire, in KN/m2；ωi4 wheel rotational angular speeds in units (°/s); r iswIs the rolling radius of the wheel, in m; t isdiIs the driving torque of 4 wheels, in N · m; t isbiThe braking torque is the braking torque of 4 wheels in the unit of N.m. In this embodiment, the vehicle parameters shown in table 1 are selected for calculation.
TABLE 1 Whole vehicle parameters
Figure BDA0002994721500000048
Then, the force of the four wheels is calculated by using a Dugoff tire model, and the calculation formula of the longitudinal tire force and the lateral tire force of the Dugoff tire model is as follows:
Figure BDA0002994721500000051
Figure BDA0002994721500000052
Figure BDA0002994721500000053
Figure BDA0002994721500000054
Figure BDA0002994721500000055
Figure BDA0002994721500000056
longitudinal stiffness and cornering stiffness of the tire, respectively; lambda [ alpha ]iIs the tire slip ratio; zetaiIs a parameter describing the condition of the tire; zetaiMore than or equal to 1 represents that the tire is in a linear state; zetai< 1 indicates that the tire is in a non-linear state; mu is the road surface adhesion coefficient; alpha is alphaiThe lateral tire force F is calculated from the formula (8) as a tire slip angle in units of °yiAnd alphaiThe relationship of (a) is shown in FIG. 2.
Apply tire force F in Dugoff tire modelyiThe calculation formula (8) is substituted into the formula (4) and the formula (5), so that a first-order differential equation set representing the lateral driving state of the vehicle system on the circular curve road section can be obtained, namely, the vehicle system model established in the embodiment is obtained, and the vehicle system model is as follows:
Figure BDA0002994721500000057
a vehicle system model is established in matlab/simulink according to the formula (12), a mass center side slip angle beta and a yaw angular velocity gamma are taken as system variables, other relevant parameters comprise whole vehicle parameters in a table 1, a road surface lateral inclination angle theta, a vehicle speed v, a front wheel corner delta, a road surface adhesion coefficient mu and the like, and the parameters are selected according to actual conditions. Equation (12) is given by tire State parameter ζiIs a determination index.
S2, quantitatively analyzing the quantitative relation between the vehicle mass center and the yaw rate when the vehicle stably runs on the circular curve section according to the vehicle system model established in the step S1;
in the step, a plurality of groups of different initial values of a variable mass center side offset angle beta and a yaw velocity gamma of a vehicle system model are given through a phase plane, the initial values represent the sizes of the beta and the gamma of the initial state of the vehicle system, each group of different initial values are correspondingly substituted into the vehicle system model to obtain a group of (beta, gamma) solutions which are continuously changed, the group of solutions (beta, gamma) obtained by substituting the initial values represent the change processes of the beta and the gamma of the vehicle system after being restrained by corresponding parameters of a circular curve road section, and the dynamic process is drawn into a phase plane diagram; and respectively taking the centroid side deviation angle beta and the yaw angular velocity gamma as horizontal and vertical coordinates, drawing each group of obtained solutions (beta, gamma) on a coordinate system to obtain a (beta-gamma) phase plane diagram, wherein the track of the group of solutions corresponding to each initial value on the phase plane is a phase track.
In the present embodiment, when μ is 0.4, v is 60km/h, θ is 4%, and δ is 1.56, different initial values (β (0), γ (0)) are substituted into the vehicle system model, and the solution obtained is different, the initial value β (0) is changed between (-0.5,0.5) and γ (0) is changed between (-1,1), all the initial values in a given range are iteratively calculated, the centroid yaw angle β and the yaw angular velocity γ are used as abscissa and ordinate, and the obtained solution (β, γ) is plotted on the coordinate system, and a phase plane diagram (β to γ) can be obtained, and the trajectory of one set of solutions corresponding to each initial value on the phase plane is the phase trajectory, as shown in fig. 3. As can be seen from fig. 3, the balance point in fig. 3 is (0,0), which indicates that the vehicle system does not have any lateral deviation and lateral deviation tendency, and is in an ideal steady state. When the phase trajectory in fig. 3 converges to the equilibrium point, that is, when μ is 0.4, v is 60km/h, θ is 6%, and δ is 1.56, the centroid yaw angle β and the yaw rate γ of the vehicle system gradually approach the steady state, and the system is in the laterally steady state.
S3, building a dynamic simulation system for the lateral driving of the vehicle on the circular curve section to be evaluated, calculating the vehicle mass center side drift angle and the yaw velocity when the vehicle runs on the circular curve section to be evaluated according to the vehicle system model in the step S1, and then evaluating the rationality of the design index of the circular curve section by combining the quantitative relation between the vehicle mass center side drift angle and the yaw velocity in the step S2.
In the step, after a dynamic simulation system for the vehicle to run laterally on the circular curve road section to be evaluated is built in Prescan software, the reasonability of the design index of the circular curve road section can be evaluated. In order to quantitatively evaluate the driving stability of the vehicle on the tested road, the track holding capacity of the vehicle is evaluated according to the vehicle mass center yaw angle, the vehicle lateral stability is evaluated according to the vehicle mass center yaw velocity, and the two parameters can be displayed in matlab/simulink in real time by using a scope display during the simulation operation process.
The method comprises the steps that the track holding capacity of a vehicle is evaluated according to the mass center side slip angle of the vehicle, the lateral stability of the vehicle is evaluated according to the mass center yaw velocity of the vehicle, and if the mass center side slip angle and the yaw velocity change of the vehicle obtained through simulation exceed limit values, namely a phase plane obtained through simulation appears on an unconverged phase track, the design index of a circular curve section is unreasonable, and vehicle instability can be caused; on the contrary, if the mass center slip angle and the yaw velocity change of the vehicle obtained by simulation are always kept within the limit value in the whole-road-section driving process of the vehicle, the phase plane obtained by simulation appears on the convergent phase track, and the design index of the circular curve road section is reasonable.
In order to verify the accuracy of the stability analysis method of the embodiment, a driver-vehicle-road closed loop simulation model is established in Carsim/simulink for simulation verification. A driver model adopts a track preview tracking model, preview time is set to be 2 seconds, and a fuzzy PID controller is used for compensation and correction; the whole car model selects an E-type car, and specific parameters are shown in a table 1; the road model establishes a three-dimensional virtual pavement model according to the second-level asphalt concrete highway in the mountainous area, and the circular loop is selected according to the road line shape.
The speed v is 60km/h of the design speed of a second-level highway, the transverse inclination angles theta of the road surface of a circular loop are selected to be 4%, 6%, 8% and 10% respectively, the road surface adhesion coefficients mu are selected to be 0.24 (ice and snow), 0.4 (wet) and 0.6 (dry) corresponding to different climates respectively to obtain the influences of the transverse inclination angles of the road surface and the road surface adhesion coefficients on the stability of the vehicle, then the radius is initially 200m, the radius value is gradually reduced, the motion state of the vehicle in Carsim is observed, and when the vehicle is in a destabilized state such as wheel turning and the vehicle driving out of a preset lane, the radius of a corresponding circular curve is the destabilized limit radius R obtained by simulation1(ii) a Selecting theta as 4%, 6%, 8%, 10%, mu as 0.24, 0.4, 0.6, v as 60km/h, selecting radius r as 200m, gradually reducing radius value, and substituting into vehicleAnd (3) a vehicle system model, drawing a corresponding phase plane graph, and when the phase track is not converged at the balance point any more, obtaining a corresponding radius value which is the ultimate instability radius R obtained by analyzing the phase plane method2(ii) a The transfer function of the vehicle system model was substituted with values of θ being 4%, 6%, 8%, 10%, μ being 0.24, 0.4, 0.6, and v being 60km/h, with radius r initially being 200m, and with the radius value gradually decreasing, and the specific values are shown in table 2.
TABLE 2 lateral stability analysis accuracy verification
Figure BDA0002994721500000071
As can be seen from the data in table 2, when the lateral gradient of the road surface and the road surface adhesion coefficient are small, the result obtained by the phase plane method analysis is close to the result obtained by the simulation, and the phase plane method stability analysis result based on the nonlinear theory is accurate.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (2)

1. A method for evaluating the design rationality of a circular curve road section is characterized by comprising the following steps:
s1, establishing a vehicle system model of the lateral driving condition of the vehicle system on the circular curve section by taking the mass center slip angle and the yaw rate of the vehicle as variables;
s2, quantitatively analyzing the quantitative relation between the vehicle mass center and the yaw rate when the vehicle stably runs on the circular curve section according to the vehicle system model established in the step S1;
s3, building a dynamic simulation system for the vehicle to laterally run on the circular curve road section to be evaluated, calculating the change conditions of the mass center lateral deviation angle and the yaw angular velocity of the vehicle when the vehicle runs on the circular curve road section to be evaluated according to the vehicle system model in the step S1, and then evaluating the rationality of the design index of the circular curve road section to be evaluated by combining the quantitative relation between the mass center lateral deviation angle and the yaw angular velocity of the vehicle in the step S2;
wherein, in step S2, the centroid slip angle of the vehicle system model variables is given by the phase plane
Figure DEST_PATH_IMAGE001
And yaw rate
Figure 316723DEST_PATH_IMAGE002
Substituting different initial values into vehicle system model to obtain continuously changed group
Figure DEST_PATH_IMAGE003
Solution of value by centroid slip angle
Figure 209724DEST_PATH_IMAGE004
And yaw rate
Figure 235449DEST_PATH_IMAGE002
Respectively as the horizontal and vertical coordinates, and obtaining solutions of each group
Figure 768061DEST_PATH_IMAGE003
Drawing on a coordinate system to obtain
Figure DEST_PATH_IMAGE005
The phase plane diagram, the track of a group of solutions corresponding to each initial value on the phase plane is the phase track;
in step S3, the trajectory holding ability of the vehicle is evaluated by the vehicle centroid slip angle, the vehicle lateral stability is evaluated by the vehicle centroid yaw rate, and if the vehicle centroid slip angle and the yaw rate obtained through simulation exceed the limit values, that is, the phase trajectory obtained through simulation does not converge on the phase plane, it indicates that the design index of the circular curve section is not reasonable, and vehicle instability is caused; on the contrary, if the mass center slip angle and the yaw velocity change of the vehicle obtained by simulation are always kept within the limit value in the whole-road-section driving process of the vehicle, the phase locus obtained by simulation converges on the phase plane, and the design index of the circular curve road section is reasonable.
2. The method for evaluating the design rationality of a circular curve section according to claim 1, wherein the specific method of step S1 is:
s21, carrying out stress analysis on the lateral motion process of the vehicle on the circular curve road section, and establishing a lateral motion equation and a yaw angle motion equation of the vehicle;
s22, establishing a lateral tire force model of the vehicle based on the Dugoff tire model;
s23, combining the lateral tire force model of the step S22 and the motion equation of the step S21, and establishing a vehicle system model of the vehicle system in a lateral driving state on the circular curve road section, wherein the vehicle system model is as follows:
Figure 609372DEST_PATH_IMAGE006
；
in the formula (I), the compound is shown in the specification,
Figure 215934DEST_PATH_IMAGE007
is the side slip angle of the mass center,
Figure 146980DEST_PATH_IMAGE002
is the yaw rate.
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