CN116910857A - Method for determining longitudinal slope gradient of super-high-speed highway - Google Patents

Method for determining longitudinal slope gradient of super-high-speed highway Download PDF

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CN116910857A
CN116910857A CN202310804631.8A CN202310804631A CN116910857A CN 116910857 A CN116910857 A CN 116910857A CN 202310804631 A CN202310804631 A CN 202310804631A CN 116910857 A CN116910857 A CN 116910857A
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庄稼丰
王丽园
熊文磊
罗丰
马天奕
李正军
杨晶
徐进
侯珊珊
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CCCC Second Highway Consultants Co Ltd
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Abstract

The invention discloses a method for determining the gradient of a longitudinal slope of an ultra-high speed highway, which comprises the steps of constructing a bidirectional ten-lane model and an automobile model; calculating the maximum climbing gradient at different set running speeds; judging whether the maximum climbing gradient at different set running speeds meets the regulation or not; constructing a model of heart rate increase rate under the joint influence of gradient and speed difference; and calculating the heart rate increase rate under the joint influence of the gradient and the speed difference, further obtaining psychological bearing indexes under different gradients, and determining the gradient under the set running speed according to the psychological bearing indexes. According to the invention, based on the speed change of different gradients, the heart rate increase rate of the driver under the common influence of the gradient and the speed difference is calculated by using a calculation model of the heart rate increase rate of the driver, and the psychological bearing index is further calculated to optimally select the gradient.

Description

Method for determining longitudinal slope gradient of super-high-speed highway
Technical Field
The invention belongs to the technical field of highway design, and particularly relates to a method for determining the gradient of a longitudinal slope of an ultra-high speed highway.
Background
At present, the speed limit of the expressway in China is 120km/h, but the design speed of common automobiles sold in the market is mostly 180km/h, and the design speed of partial racing automobiles reaches 400km/h, and the speed limit of the existing expressway influences the exertion of the automobile performance, so that the design speed of the expressway is improved to be necessary. Comfort, safety, and vehicle dynamics of the driver and passengers are one of the main factors of the superhigh road design. Based on the method, the invention provides a method for determining the longitudinal slope gradient of the expressway based on driving comfort.
The automobile and the large-sized truck have obvious difference in dynamic performance, and the capability of overcoming longitudinal slopes of the automobile is obviously superior to that of the large-sized truck. The large-sized truck has remarkable limitation on the speed, can not normally run on a road section with super high speed, has no obvious difference from a flatter road when the automobile runs on a longitudinal slope below 3%, and has no obvious reduction in speed. Thus, the expressway with the speed per hour of 160km/h can only be limited by the gradient and the slope length of the automobile.
In the highway route design rule (JDG D20-2017), it is pointed out that the maximum longitudinal slope of a road section with a speed per hour of 120km/h is 3%, the maximum longitudinal slope length is 900m, the minimum longitudinal slope length is 300m, the recommended value is not suitable for the ultra-high speed running condition of a vehicle, and the unreasonable longitudinal slope length can influence the running safety, so that traffic disorder is caused. Therefore, in order to avoid the reduction of driving comfort and safety caused by improper setting of the longitudinal slope length, the invention provides a method for determining the longitudinal slope gradient of the super highway, and the longitudinal slope gradient is set and verified by using a card simulation software in combination with the vehicle dynamics and the heart rate growth rate of a driver.
Disclosure of Invention
The invention aims to provide a method for determining the longitudinal slope gradient of an expressway, which aims at solving the problem that the existing design standard of the longitudinal slope of the expressway does not consider the running condition of an automobile on the expressway.
The above object of the present invention is achieved by the following technical solutions:
a method for determining the gradient of a longitudinal slope of an ultra-high speed highway comprises the following steps:
step 1: setting up a bidirectional ten-lane model and an automobile model by using Carsim software;
step 2: calculating the maximum climbing gradient i under different set running speeds max
Step 3: if the maximum climbing gradient under different set running speeds meets the specified maximum climbing gradient under different set running speeds, the step 4 is entered; otherwise, changing the bidirectional ten-lane model and the automobile model to return to the step 2;
step 4: constructing a model of heart rate increase rate under the joint influence of gradient and speed difference;
calculating heart rate increase rate N under the joint influence of gradient and speed difference according to gradient obtained by simulation of carsim software and speed difference under set running speed u Further obtaining psychological bearing index K under different gradients 1 N u Selecting 20%<K 1 N u <30% of the corresponding gradient is used as the gradient at the set running speed, wherein K 1 Is a quality influencing factor of a driver.
Maximum climbing gradient i in step 2 as described above max Calculated based on the following formula:
i max =(λD-f)/100
wherein lambda is an altitude load correction coefficient, D is a power factor, and f is a rolling resistance coefficient.
The power factor D is calculated as described above based on the following formula:
wherein F is t For driving the car, F w Air resistance, G is vehicle weight.
Automobile driving force F as described above t And air resistance F w Based on the following formulas, respectively:
wherein T is tq Is torque, i g I is the transmission ratio, i 0 Is the transmission ratio of the main speed reducer, eta T For mechanical efficiency, r is the wheel radius, C D The air resistance coefficient is A, the windward area is A, and the running speed is u.
The model of the driver's heart rate increase rate in step 4 as described above includes:
heart rate increase rate N under gradient influence 1 Is a model of (a):
N 1 =A1*i 2 -B1*i+C1
heart rate increase rate N under the influence of speed differences 2 Is a model of (a):
N 2 =A2*e B2*△V +C2
heart rate increase rate N under the combined influence of gradient and speed difference u Is a model of (a):
N u =A3*N 1 +B3*N 2 +C3
wherein A1, A2, A3, B1, B2, B3, C1, C2 and C3 are fitting parameters, i is gradient, and DeltaV is speed difference.
The step 4 also comprises the following steps:
under the condition that the same vehicle speed is unchanged and the gradient is changed, measuring the heart rate increase rate of a driver, and obtaining A1, B1 and C1 through fitting;
under the condition that the vehicle speed is changed to be delta V and the gradient is unchanged, measuring the heart rate increase rate of a driver, and obtaining A2, B2 and C2 through fitting;
in the case where the vehicle is changed to Δv and the gradient is changed, the heart rate increase rate of the driver is measured, and A3, B3, and C3 are found by fitting.
The method for determining the longitudinal slope gradient of the expressway provided by the invention has the main benefits that:
advantage 1: the vehicle dynamic performance of a driver in an ultra-high speed running state is fully considered, an automobile dynamic formula is applied, when the automobile needs to climb to a maximum gradient, the acceleration resistance is 0, and the vehicle overcomes the rolling resistance and the air resistance and overcomes the gradient resistance by the aid of the total residual force, so that a dynamic factor can be obtained, a linear relation exists between the dynamic factor and the gradient, and when the ground elevation number is higher, the maximum climbing gradient is smaller.
Advantage 2: based on the maximum climbing gradient obtained by vehicle dynamics calculation, the maximum climbing gradient is gradually decreased by 1%, and the driving working condition of the longitudinal slope of the super highway is simulated by using a carsim simulation software, so that a speed change curve of the vehicle at the initial speed of 160km/h and at different gradients can be obtained.
Advantage 3: based on the speed change of different slopes, a calculation model of the heart rate increase rate of the driver is utilized, the heart rate increase rate of the driver under the joint influence of the slopes and the speed difference is calculated, the accidental and uncertainty caused by a single variable is avoided, the heart rate increase rate of the expressway on the longitudinal slope is tested through a real vehicle, a threshold evaluation index of the longitudinal slope travelling comfort, namely a psychological bearing index, is established, and the slopes are optimally selected.
Advantage 4: the simulation software can provide the same road condition, so that errors caused by different experimental conditions for multiple times are avoided, and the gradient value calculated by the model is more accurate. The vehicle is extremely dangerous on the expressway of 160km/h, the simulation experiment avoids the danger and disastrous possibly brought by the superhigh speed running, and the system has the advantages of low cost, easiness in starting the hand, short time and the like.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a graph of speed change for different grades.
Detailed Description
The present invention will be further described in detail below in conjunction with the following examples, for the purpose of facilitating understanding and practicing the present invention by those of ordinary skill in the art, it being understood that the examples described herein are for the purpose of illustration and explanation only and are not intended to limit the invention.
A method for determining the gradient of a longitudinal slope of an ultra-high speed highway comprises the following steps:
step 1: firstly, constructing an ultra-high speed highway scene model by using Carsim software. Including a two-way ten-lane (one-way five-lane) model and an automobile model.
Building an automobile model: through investigation, sedan is the most common vehicle type and is characterized in that: the three-box structure has an independent engine compartment, a passenger cabin and a rear tail cabin, has 4 to 5 seats and is of a 4-door vehicle type. E-classSedan is selected as a model building object, so that the speed per hour of the expressway can be met, and the automobile configuration parameters are specifically shown in table 1.
Table 1 is a table of automobile configuration parameters
Building a road model: in the road surface design, the super highways under different gradient conditions are arranged, and the gradient length is set to 900m.
Step 2: and constructing a calculation formula of the maximum climbing gradient according to the dynamics of the vehicle.
The running equation of the automobile is as follows:
F t =F f +F w +F i +F j (1)
Wherein: f (F) t For driving the car, F f For rolling resistance, F w For air resistance, F i For gradient resistance, F j Is the acceleration resistance.
Wherein each resistance formula is:
F f =gfcosα (2)
Wherein: g is the weight of the car, f is the rolling resistance coefficient, f=0.01, and α is the slope angle, i.e. the angle between the slope and the bottom surface.
Wherein: c (C) D Taking C as the air resistance coefficient D =0.32, a is the windward area, and u is the travel speed.
F i =gsin α (4)
Wherein: delta is the conversion coefficient of the rotating mass of the automobile, m is the mass of the automobile,is the running acceleration.
When α is not large, cos α≡1, sin α≡i, equation 6 can be deduced from the above equation:
wherein: i is gradient, g is gravitational acceleration, g=9.8m/s is taken 2
Automobile driving force F t The expression (7) can be used to obtain:
wherein: t (T) tq Is torque, i g I is the transmission ratio, i 0 Is the transmission ratio of the main speed reducer, eta T For mechanical efficiency, r is the radius of the wheel, and the running speeds are set differentlyDegree corresponds to different automobile driving forces F t
D is a power factor and refers to the capability of overcoming road resistance and inertial resistance per unit vehicle weight when the vehicle is fully loaded on the sea level elevation. Maximum climbing gradient i max To overcome the rolling resistance and the air resistance and to overcome the gradient required by the gradient resistance, the acceleration at this time is thereforeThe calculation can be made using equation 9:
i max = (λd-f)/100 (9)
Wherein: λ is the altitude load correction factor of the power factor D, taking λ=1.
The maximum climbing gradient at different set running speeds obtained according to the above formula is shown in table 2.
Table 2 shows the maximum climbing rate at different speeds
120km/h 140km/h 160km/h
D 0.09 0.08 0.07
i max 8% 7% 6%
Step 3: if the maximum climbing gradient under different set running speeds meets the specified maximum climbing gradient under different set running speeds, the step 4 is entered; otherwise, the two-way ten-lane model and the automobile model are changed, and the step 2 is returned. According to the recommended value of the maximum gradient of the highway in the technical guidelines of the highway engineering special for automobiles (TCHTS 10042-2021) issued by the China Highway society, the maximum gradient value is 8% when the design speed is 120km/h, and 7% when the design speed is 140km/h, the calculated value conforming to the formula is verified, and the rationality of the calculation model is verified. Based on the obtained maximum climbing gradient, gradient values of 2%, 3%, 4%, 5% and 6% are selected, the gradient length is set to 900m, then the car is simulated to run on the expressway with the set running speed of 160km/h through the carsim simulation software, the change of the speed of the car in the climbing process is analyzed, the running speed is set to 160km/h, but the actual simulation and the actual running are both fluctuated around 160km/h, and therefore the speed change can be generated. Firstly, carrying out a simulation real vehicle test on a multi-lane expressway, simulating the same vehicle model to run at a constant speed of 160km/h on roads with different gradients, obtaining speed changes of the vehicles at different moments when running on the expressway with the same gradient, drawing a vehicle speed curve graph of the expressway with each gradient, wherein the abscissa of the vehicle speed curve graph is time, the ordinate of the vehicle speed curve graph is vehicle speed, and the speed difference of the vehicles is obtained based on the vehicle speed curve graphs of the expressways with different gradients due to the fact that the speed changes are different.
Step 4: constructing a model of a driver heart rate increase rate applicable to a highway longitudinal slope section, wherein the model of the driver heart rate increase rate comprises:
heart rate increase rate N under gradient influence 1 Is based on a model of (a)The following formula:
N 1 =A1*i 2 -B1*i+C1
heart rate increase rate N under the influence of speed differences 2 Based on the following formula:
N 2 =A2*e B2*△V +C2
heart rate increase rate N under the combined influence of gradient and speed difference u Based on the following formula:
N u =A3*N 1 +B3*N 2 +C3
wherein A1, A2, A3, B1, B2, B3, C1, C2 and C3 are fitting parameters, i is gradient, and DeltaV is speed difference.
Under the condition that the same vehicle speed is unchanged and the gradient is changed, measuring the heart rate increase rate of a driver, and obtaining A1, B1 and C1 through fitting;
under the condition that the vehicle speed is changed to be delta V and the gradient is unchanged, measuring the heart rate increase rate of a driver, and obtaining A2, B2 and C2 through fitting;
in the case where the vehicle is changed to Δv and the gradient is changed, the heart rate increase rate of the driver is measured, and A3, B3, and C3 are found by fitting.
In this embodiment, the heart rate increase rate under the influence of the gradient is expressed as: n (N) 1 =154.392i 2 -1.737i+0.15, the heart rate increase rate under the influence of the speed difference is given by: n (N) 2 =0.028e 0.087△V +0.101, heart rate increase rate under the combined influence of slope and speed difference is given by: n (N) u =0.464N 1 +0.393N 2 +0.031。
The psychophysiological safety threshold of the person is the physiological and psychological bearing limit of the person, and when the threshold is exceeded, traffic accidents can be caused, and the psychological bearing index threshold is shown in table 3.
Substituting the gradient obtained by the simulation test of the carsim simulation software and the speed difference under the set running speed into a heart rate increase rate calculation model of a driver, calculating the result as shown in table 4, and calculating to obtain psychological bearing indexes K under different gradients 1 N u . Selecting 20%<K 1 N u <30% of the corresponding gradient is used for the preparation of the liquid,as a gradient at the set travel speed.
TABLE 3 psychological stress tolerance index threshold value table for drivers
Psychological bearing index Ideal domain Comfort zone Dangerous area Accident domain
K 1 N u <20% 20%<K 1 N u <30% 30%<K 1 N u <40% >40%
Note that: k1 is a quality influence factor of a driver, and the value range is 1.2-1.5, and in the embodiment, the value is 1.2.
Table 4 heart rate growth rate table for different gradients
Select to satisfy 20%<K 1 N u <30% of the grade of the highway.
According to the calculation result, the speed per hour of the expressway is 160km/h, the longitudinal slope of 900m is set to be 3%, the dynamic property of the vehicle is met, and meanwhile the safety of drivers and passengers is also met.
The technical content described herein is merely illustrative of the spirit of the present invention. Various modifications or additions to the specific embodiments described or similar alternatives may be apparent to those skilled in the art to which the invention pertains. But without departing from the spirit of the invention or exceeding the scope of the invention as defined by the appended claims.

Claims (6)

1. The method for determining the longitudinal slope gradient of the expressway is characterized by comprising the following steps of:
step 1: setting up a bidirectional ten-lane model and an automobile model by using Carsim software;
step 2: calculating the maximum climbing gradient i under different set running speeds max
Step 3: if the maximum climbing gradient under different set running speeds meets the specified maximum climbing gradient under different set running speeds, the step 4 is entered; otherwise, changing the bidirectional ten-lane model and the automobile model to return to the step 2;
step 4: constructing a model of heart rate increase rate under the joint influence of gradient and speed difference;
calculating heart rate increase rate N under the joint influence of gradient and speed difference according to gradient obtained by simulation of carsim software and speed difference under set running speed u Further obtaining psychological bearing index K under different gradients 1 N u Selecting 20%<K 1 N u <30% of the corresponding gradient is used as the gradient at the set running speed, wherein K 1 Is a quality influencing factor of a driver.
2. The method for determining the longitudinal gradient of a highway according to claim 1, wherein the maximum climbing gradient i in the step 2 max Calculated based on the following formula:
i max =(λD-f)/100
wherein lambda is an altitude load correction coefficient, D is a power factor, and f is a rolling resistance coefficient.
3. The method of claim 2, wherein the power factor D is calculated based on the following equation:
wherein F is t For driving the car, F w Air resistance, G is vehicle weight.
4. A method for determining a longitudinal gradient of a highway according to claim 3, wherein said driving force F of said vehicle t And air resistance F w Based on the following formulas, respectively:
wherein T is tq Is torque, i g I is the transmission ratio, i 0 Is the transmission ratio of the main speed reducer, eta T For mechanical efficiency, r is the wheel radius, C D The air resistance coefficient is A, the windward area is A, and the running speed is u.
5. The method for determining the gradient of a longitudinal slope of a highway according to claim 1, wherein the model of the heart rate increase rate of the driver in step 4 comprises:
heart rate increase rate N under gradient influence 1 Is a model of (a):
N 1 =A1*i 2 -B1*i+C1
heart rate increase rate N under the influence of speed differences 2 Is a model of (a):
N 2 =A2*e B2*△V +C2
heart rate increase rate N under the combined influence of gradient and speed difference u Is a model of (a):
N u =A3*N 1 +B3*N 2 +C3
wherein A1, A2, A3, B1, B2, B3, C1, C2 and C3 are fitting parameters, i is gradient, and DeltaV is speed difference.
6. The method for determining the gradient of a longitudinal slope of a highway according to claim 5, wherein said step 4 further comprises the steps of:
under the condition that the same vehicle speed is unchanged and the gradient is changed, measuring the heart rate increase rate of a driver, and obtaining A1, B1 and C1 through fitting;
under the condition that the vehicle speed is changed to be delta V and the gradient is unchanged, measuring the heart rate increase rate of a driver, and obtaining A2, B2 and C2 through fitting;
in the case where the vehicle is changed to Δv and the gradient is changed, the heart rate increase rate of the driver is measured, and A3, B3, and C3 are found by fitting.
CN202310804631.8A 2023-07-03 2023-07-03 Method for determining longitudinal slope gradient of super-high-speed highway Pending CN116910857A (en)

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