CN113742812A - Road engineering vertical section vertical curve design method based on quartic curve - Google Patents

Road engineering vertical section vertical curve design method based on quartic curve Download PDF

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CN113742812A
CN113742812A CN202110801978.8A CN202110801978A CN113742812A CN 113742812 A CN113742812 A CN 113742812A CN 202110801978 A CN202110801978 A CN 202110801978A CN 113742812 A CN113742812 A CN 113742812A
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连红运
秦连铭
吉炜寰
赵艳艳
马青松
金刚
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Henan Polytechnic Institute
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Abstract

The invention provides a method for designing a vertical curve of a longitudinal section of a road engineering based on a quartic curve, which comprises the following steps: step S1, obtaining ramp parameters of the road engineering needing construction; in step S2, adjacent straight roads are connected using a vertical curve based on a quartic-type curve. The curvatures of the vertical curve line type at the lead-in point and the lead-out point are continuous in the second order, so that the vertical acceleration at the starting point and the terminal point of the vertical curve is continuous, the curvatures are continuous when a train runs at any position of the railway vertical curve, the wheel rail of the train cannot be subjected to sudden impact load, the longitudinal impact on the wheel rail is reduced, the abrasion between the rail and the train is reduced, the maintenance of the railway line type is facilitated, the structural life of the wheel rail is prolonged, and the comfort experienced by high-speed rail passengers is greatly improved.

Description

Road engineering vertical section vertical curve design method based on quartic curve
Technical Field
The invention is suitable for traffic and transportation road engineering, and can be used for line selection of railway lines and highways, in particular to high-speed railways (and pre-developed 600km/h high-speed railways) and design of vertical curves of engineering longitudinal sections.
Background
On the longitudinal section of the railway line, the intersection points between the ramp and between the level and the ramp are called grade changing points. When a train runs on a slope change point of two adjacent slopes, the train can suddenly receive vertical positive pressure due to the change of the slope, vertical additional acceleration is generated, strong impact can be generated on wheel tracks of the train, the train vibrates, passengers feel uncomfortable, and hook breakage accidents can be caused if the vertical impact force is too large. In order to ensure the safety of high-speed running trains and improve the experience comfort of passengers, a vertical curve is used for smooth transition at a railway longitudinal section slope changing point. The vertical curve is a curve connecting two adjacent slope sections on the line vertical section. The main function of the device is to ease the sudden change of two adjacent ramps on the longitudinal section, and properly combine the device with a flat road or a ramp to reduce the impact generated on the wheel rail.
There are many factors that affect the safety of the vehicle and the comfort of passengers, and the design of the longitudinal section of the railway is one of the important factors. In the design of railway vertical curves, circular curves are generally adopted because circular curves are more convenient to measure, set and maintain. At present, the vertical curve line type and the parabolic curve type which are commonly used in China have little difference. From a kinetic point of view analysis, if the curve is only G0 continuous (point continuous) at the point of connection and not G1 continuous or tangential continuous, i.e., the first derivative continuous), the vehicle will theoretically experience an infinite impact force as it passes through that point; if the curve is continuous at the junction G1 but not G2 (or the curvature is continuous, i.e., the second derivative is continuous), the vehicle may experience a sudden change in impact force, causing the vehicle to vibrate. It can be seen that although the circular curves achieve G0 and G1 continuity at the connecting points, the second derivative is discontinuous, which results in discontinuous vertical acceleration when the train is running, and the wheel rail is subjected to a sudden impact force, thereby causing vehicle vibration.
Some scholars conduct other types of vertical curve researches in order to solve the defects of the traditional vertical curve, a design method that a conventional circular curve is replaced by a sectional cubic parabola vertical curve proposed abroad is introduced, for example, a vertical relaxation curve which is fitted by a cubic polynomial is proposed by tsunami of southeast university, and the vertical relaxation curve is arranged in front of and behind the parabola vertical curve, and the mechanical property of driving is improved by adding the relaxation vertical curve.
In addition, scholars such as Wu Yingfeng and the like propose to utilize a cubic interpolation spline curve profile, and the profile can be adjusted according to the number of interpolation points, so that the change requirement of control points can be flexibly adapted. However, the cubic parabola type and cubic interpolation spline type vertical curves are mainly used for the research of highway lines. At present, the research on the vertical curve line type of the high-speed railway is still few, and particularly, the abrasion of the 400km/h high-speed wheel rail and 600km/h magnetic suspension which are currently researched and caused by the impact load of a higher-speed train in a long term and a long term will be more remarkable, so that the problem needs to be solved urgently. At present, the domestic high-speed railway tracks are ballastless tracks, the smoothness of the tracks is greatly improved, and the irregularity of a vertical curve becomes one of the main factors influencing the safety and the comfort of a train. Therefore, the invention improves the linear design of the vertical curve, so that the curvature of the connecting point of the vertical curve and the ramp is continuous, and the problem of vertical impact force is fundamentally solved theoretically.
Disclosure of Invention
The invention aims to provide a railway vertical curve design method based on a quadric curve, which is used for eliminating vertical impact force generated between a track and a vehicle at a connecting point of the vertical curve, is simple in design method, smooth in curve and capable of being applied to linear design of high-speed railways and high-grade highways.
The technical scheme of the invention is as follows.
The invention provides a method for designing a vertical curve of a longitudinal section of a road engineering based on a quartic curve, which is characterized by comprising the following steps of:
step S1, obtaining ramp parameters of the road engineering needing construction;
in step S2, adjacent straight roads are connected using a vertical curve based on a quartic-type curve.
Preferably, the vertical curve is designed according to the following equation:
Figure BDA0003164958830000021
wherein z is a coordinate value of a vertical curve connecting the linear road, and the direction of the z axis is vertical to the horizontal plane; in the formula, the intersection point of a straight line road and a vertical curve introduction point is taken as an original point, and an x axis is the extension line direction of the straight line road; l is the horizontal projection length of the vertical curve, i1、i2The slope of the lead-in end and the slope of the lead-out end of the vertical curve are respectively; and (0, L) represents the value range of the rectangular coordinate x corresponding to z.
Preferably, the ramp parameters in step 1 include: up and down grade, vehicle speed, maximum acceleration.
Preferably, the method for acquiring the vertical curve based on the quartic curve in step 2 includes the following steps:
step S21, taking the vertical curve introduction point as the coordinate origin, the horizontal axis as the x axis, the vertical direction as the z axis, and the second derivative of the vertical curve is as follows:
z″＝ax2-aLx (2)
l is the length of the vertical curve; integrating equation (2) yields:
Figure BDA0003164958830000031
step S22, setting the slope of the ramp at the leading end of the vertical curve as i1The slope of the leading-out end ramp is i2The boundary condition is that z' | x ═ 0 ═ i1，z′|x＝L＝i2In the case of (2), the vertical curve one is solved by substitutingThe first derivative is:
Figure BDA0003164958830000032
step S23, integrating equation (3) and applying boundary condition, zx＝0Get vertical curve equation when being 0:
Figure BDA0003164958830000033
step S24, deriving equation (3) to obtain the second derivative of the vertical curve:
Figure BDA0003164958830000034
preferably, the method further comprises:
in step S3, the acceleration limit is verified.
Preferably, the vertical acceleration a is such that the vehicle passes over the ramp at a constant velocity vs＝v2z ", then the vertical maximum acceleration is:
Figure BDA0003164958830000035
preferably, the method further comprises:
in step S4, the curve length is verified.
Preferably, the vertical curve length limit determined by the maximum vertical acceleration limit is:
Figure BDA0003164958830000036
the second aspect of the invention provides a railway ramp, wherein the vertical curve of the railway ramp is designed by adopting the vertical curve design method of the longitudinal section of the road engineering based on the quartic curve in any one of the first aspects of the invention.
The third aspect of the invention provides a construction method of a railway ramp, which comprises the following steps:
step 1, acquiring parameters of a railway ramp needing to be constructed;
step 2, obtaining a vertical surface vertical curve equation by using the method for designing the vertical curve of the longitudinal section of the road engineering based on the quartic curve in the first aspect of the invention, calculating a numerical coordinate corresponding to each point on the vertical surface vertical curve according to a slope point of a ramp connected during actual application of the ramp, wherein x is an abscissa and z is an ordinate, and the numerical coordinates of a plurality of points form a numerical list;
and 3, designing a roadbed, a ballast bed and a paved rail by using a coordinate method according to the numerical value list of the specific data and the design specification requirement obtained in the step 2, and then paving the rail.
Through the technical scheme, the curvatures of the vertical curve line type at the leading-in point and the leading-out point are continuous in two orders, so that the vertical acceleration at the starting point and the terminal point of the vertical curve is continuous, the curvatures are continuous when a train runs at any position of the railway vertical curve, the wheel rail of the train cannot be subjected to sudden impact load, the longitudinal impact on the wheel rail is reduced, the abrasion between the rail and the train is reduced, the maintenance of the railway line type is facilitated, the structural life of the wheel rail is prolonged, and the comfort experienced by high-speed rail passengers is greatly improved.
Drawings
FIG. 1 is a simulation comparison diagram of vehicle vibration caused by a simplified single-degree-of-freedom vehicle vibration model and a quartic vertical curve and a round vertical curve.
Fig. 2 shows that in example 1, the running speed of the train is set to be v equal to 100m/s (360km/h), and the acceleration limit is set to be amax＝0.4m/s2The ramp elevation combination graph of (a).
Fig. 3 shows that in example 1, the running speed of the train is set to be v equal to 100m/s (360km/h), and the acceleration limit is set to be amax＝0.4m/s2Vertical acceleration diagram of (a).
FIG. 4 shows the vehicle speed v being 167m/s (600km/h) and the acceleration limit still being a in example 1max＝0.4m/s2A vertical combination graph of (a).
FIG. 5 shows that in example 1, the vehicle speed is 167m/s (600km/h) and the acceleration limit is still amax＝0.4m/s2Vertical acceleration diagram of (a).
FIG. 6 is a vertical combination graph of the vehicle speed of 100m/s, the vertical curve length of 1500m, and the slope at both ends of 1000m each in example 2.
FIG. 7 is a vertical acceleration chart of example 2, in which the vehicle speed is 100m/s, the vertical curve length is 1500m, and the slope at each end is 1000 m.
FIG. 8 is a vertical combination graph of the vehicle speed of 100m/s, the vertical curve length of 500m, and the slope of each end of 500m in example 3.
FIG. 9 is a vertical acceleration chart of example 3 in which the vehicle speed is 100m/s, the vertical curve length is 500m, and the slope at each end is 500 m.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention provides a road vertical curve design method based on a quartic curve.
Step S1, obtaining ramp parameters of the road engineering needing construction;
in step S2, adjacent straight roads are connected using a vertical curve based on a quartic-type curve.
In step S2, taking the vertical curve introduction point as the coordinate origin, the horizontal axis as the x-axis, and the vertical direction as the z-axis, the second derivative of the vertical curve is set as:
z″＝ax2-aLx (1)
by integrating the above, the first derivative is obtained:
Figure BDA0003164958830000051
under the boundary condition that z' | x ═ 0 ═ i1，z′|x＝L＝i2When (2) is substituted into the above formula, the following formula is solved:
the first derivative of the vertical curve is:
Figure BDA0003164958830000052
integrating the above equation and applying a boundary condition zx＝0Vertical curve equation is obtained as 0:
Figure BDA0003164958830000053
the second derivative of the vertical curve can be obtained by deriving equation (2):
Figure BDA0003164958830000054
the continuity of the vertical curve of the present invention is discussed on the basis of the vertical curve and the second derivative described above.
1. Geometric continuity:
z'. non-volatile luminous flux as shown in formula (4)x＝0＝0，z″|x＝LIt can be seen that curvature (second derivative) continuity is achieved at both the entry and exit points of the curve when it connects to the linear ramp.
Z'. As shown in formula (2)x＝0＝i1，z′|x＝L＝i2It can be seen that the tangent is continuous at both the entry and exit points of the curve.
Z & lt & gtY & lt & gtx＝0The introduction points are continuous, 0.
Figure BDA0003164958830000061
(5) The formula is the projection height of the vertical curve in the vertical direction, namely the height difference between the end point of the front ramp and the initial point of the rear ramp.
2. Acceleration limit and curve length
According to the formula (4), when
Figure BDA0003164958830000062
Z "has a maximum value. Vertical acceleration a as the vehicle moves through the ramp at a constant velocity vs＝v2z', then the vertical maximum acceleration
Figure BDA0003164958830000063
From this, a limit value of the length of the vertical curve is obtained, which is determined by the maximum vertical acceleration limit value
Figure BDA0003164958830000064
3. And (3) performing simulation comparison on vertical floating and sinking vibration amplitudes of the vehicle running on the quartic vertical curve and the round vertical curve:
let a slope i1Grade of entry ramp i 0220 per mill. Let the vehicle speed be 100m/s and the acceleration limit be amax＝0.4m/s2According to the formula (6), the horizontal length of the quartic vertical curve is 750m (as shown in fig. 2). According to the maintenance experience at home and abroad, the maximum radius of the circular vertical curve of the high-speed railway is not more than 30000m and is the slope i of the secondary ramp 10 into i2The inserted circular vertical curve length is approximately R × Δ i equal to 600 meters, 0.02.
Analysis of passenger car system parameters used: one-half mass M of vehicle bodyc21550kg truck frame Mf2280kg, primary vertical stiffness Kpz1200000N/m, vertical stiffness per air spring Ksz400000N/m, vertical damping coefficient per air spring Csz120000 ns/m, with the axle moving along the vertical curve as the frame of reference. To simplify the model, the bogie frame M can be omitted in comparison to findfAnd (3) establishing a single-degree-of-freedom vertical vibration model of the railway vehicle by taking one half of the vehicle body as an object, as shown in the attached figure 1. The differential equation of the vertical sink-float vibration is as follows:
Mc*z"+Csz*z'+K*z＝Mc*as (7)
wherein K is KpzAnd KszA series value of (d) equal to 300000N/M, Mc*asThe inertia force is the inertia force after walking on the vertical curve.
With time t as a variable, let x be approximately equal to v t, and let vehicle speed be equal to 100m/s, for a quartic vertical curve such as above L750, it can be found from equation (4):
z"＝12t/562500-1.2t2/421875
then a froms＝v2z ", the vertical acceleration of the available axles is approximately:
as1200 t/5625-:
z"+120000z'/21550+300000z/21550＝12t/562500-1.2t2/421875 (8)
initial conditions, t-0, z' -0, z ″ -0, time range: [0, 7.5] second.
Circle vertical curve R30000 m, as＝v 21/3, the differential equation of the vertical sinking and floating vibration on the vertical curve of the circle can be obtained from the formula (7):
z"+120000z'/21550+300000z/21550＝1/3 (9)
initial conditions, t-0, z' -0, z ″ -0, time range: [0, 6] second.
Solving the differential equations (8) and (9) by a numerical method, and simulating to find that: as shown in figure 1, the vehicle consists of a flat road (i)10) into the quartic vertical curve or the circular vertical curve, a low frequency vibration occurs, but the vibration intensity on the quartic vertical curve (right in fig. 1) is much smaller than that on the circular vertical curve (left in fig. 1), reduced by about 4 orders of magnitude, showing the excellent performance of the quartic vertical curve.
Therefore, the curvatures of the vertical curve line type at the leading-in point and the leading-out point are continuous in the second order, so that the vertical acceleration at the starting point and the terminal point of the vertical curve is continuous, and the continuity is known from the analysis of dynamics, the curvatures are continuous when a train runs at any position of the vertical curve of a railway, so that the wheel rail of the vehicle cannot be subjected to sudden impact load, the longitudinal impact on the wheel rail is reduced, the abrasion between the rail and the train is reduced, the maintenance of the railway line type is facilitated, the structural life of the wheel rail is prolonged, and the riding comfort of passengers is greatly improved.
The construction method for constructing the railway ramp by using the vertical curve based on the quartic curve comprises the following steps:
1. and acquiring parameters of the railway ramp to be constructed, wherein the parameters at least comprise an upper gradient, a lower gradient, a train running speed, a maximum acceleration and the like, and the parameters are given by a railway design party.
2. After the parameters of the railway ramp are obtained, the numerical coordinates corresponding to each point on the vertical curve of the vertical surface are calculated by using the vertical surface curve equation given by the formula (3) according to the slope points of the ramp connected in practical application of the ramp, wherein x is the horizontal coordinate and z is the vertical coordinate, and the numerical coordinates of a plurality of points form a numerical list.
3. And (3) according to the numerical value list of the specific data acquired in the step (2) and the design specification requirements, applying a coordinate method to design the roadbed, the ballast bed and the paving track, and then paving the track.
In the step 2, when the coordinates of the control points are calculated, in order to ensure the accuracy, more than 8 effective digits can be kept, so as to reduce the calculation error, and the final reserved digits of the coordinate values can be determined according to the accuracy requirement and the actual situation of the circuit. The calculation method of the numerical value list of the vertical curve and the vertical acceleration can be obtained by calculation of an Excel table or by calculation of other scientific and technical tools.
When the vertical curve is applied to a high-speed railway or a high-grade highway, due to the fact that the length of the curve is relatively large, no matter a theodolite or an intelligent total station is used during work maintenance and survey and set, the relative difference of control points needs to be paid attention to, and errors caused by long distance measurement are prevented from exceeding a line precision value to the greatest extent.
The design, measurement method and construction equipment are the same as the existing traditional vertical curve, and the related calculation can be completed on a personal computer.
Example of engineering design
Example 1: flat-up-flat combination curve
Designing parameters:
the gradient of the uphill slope is set to 0.02. Vertical curve i of the entry ramp1＝0，i20.02; vertical curve off ramp: i.e. i1＝0.02，i 20. Let the vehicle speed v be 100m/s (360Km/h) and the acceleration limit be amax＝0.4m/s2According to the formula (6), the horizontal length of the vertical curve should be 750 m. The length of each of the two horizontal straight roads is 500m, and the length of each of the middle straight roads is 1000 m.
Designing content:
taking the intersection point of the introduction points of the linear track and the vertical curve as an origin, the extension line of the linear track is an x axis, the vertical direction is a z axis, a control point is arranged every 10m, and i1、i2Substituting the values of L into the formulas (3), (4) and as＝v2z ", a vertical combined curve and a vertical acceleration can be obtained, as shown in fig. 2 and 3. Since the number points are many, not all are listed. On a straight ramp section, the vertical coordinate z value and the vertical acceleration asThe variation is very small or zero, so start and end points are enumerated; in the vertical curve segment, a coordinate point is listed every 40m, the number of control points can be arranged according to actual requirements when engineering is implemented, and the following engineering example is similar to the example.
The specific numerical values are listed in tables 1 and 2.
TABLE 1 numerical tabulation units m of elevation combination curves
x(m) z(m) x(m) z(m) x(m) z(m)
500 0 1510 12.7 2510 32.1834
540 0.002215 1550 13.5 2550 32.732
580 0.017234 1590 14.3 2590 33.21929
620 0.056525 1630 15.1 2630 33.64325
660 0.130101 1670 15.9 2670 34.00335
700 0.246519 1710 16.7 2710 34.30049
740 0.412877 1750 17.5 2750 34.53704
780 0.634819 1790 18.3 2790 34.71682
820 0.916533 1830 19.1 2830 34.84511
860 1.260749 1870 19.9 2870 34.92865
900 1.668741 1910 20.7 2910 34.97564
940 2.140327 1950 21.5 2950 34.9957
980 2.673869 1990 22.3 2990 34.99996
1020 3.266272 2030 23.1 3030 35
1060 3.912985 2070 23.9 3070 35
1100 4.608 2110 24.7 3110 35
1140 5.343854 2150 25.5 3150 35
1180 6.111626 2190 26.3 3190 35
1220 6.900941 2230 27.1 3230 35
1260 7.7 2270 27.89972 3270 35
1300 8.5 2310 28.69263 3310 35
1340 9.3 2350 29.46681 3350 35
1380 10.1 2390 30.21154 3390 35
1420 10.9 2430 30.91752 3430 35
1460 11.7 2470 31.57693 3470 35
1470 11.9 2480 31.73373 3480 35
1480 12.1 2490 31.88712 3490 35
1490 12.3 2500 32.03704 3500 35
TABLE 2 vertical acceleration values tabulated units m/s2
x(m) a(m/s2) x(m) a(m/s2) x(m) a(m/s2) x(m) a(m/s2)
500 0 850 0.396468 2260 -0.00353 2650 -0.39931
540 0.061393 890 0.399881 2300 -0.08073 2690 -0.39135
580 0.135348 930 0.394193 2340 -0.15241 2730 -0.37428
620 0.200201 970 0.379401 2380 -0.21499 2770 -0.34811
660 0.255953 1010 0.355508 2420 -0.26847 2810 -0.31284
700 0.302601 1050 0.322513 2460 -0.31284 2850 -0.26847
740 0.340148 1090 0.280415 2500 -0.34811 2890 -0.21499
780 0.368593 1130 0.229215 2540 -0.37428 2930 -0.15241
790 0.374281 1140 0.214993 2550 -0.3794 2940 -0.13535
800 0.379401 1150 0.200201 2560 -0.38395 2950 -0.11771
810 0.383953 1160 0.184841 2570 -0.38793 2960 -0.09951
820 0.387935 1170 0.168913 2580 -0.39135 2970 -0.08073
830 0.391348 1180 0.152415 2590 -0.39419 2980 -0.06139
840 0.394193 1190 0.135348 2600 -0.39647 2990 -0.04148
Considering a higher speed vehicle, let the vehicle speed v be 167m/s (600km/h) and the acceleration limit still be amax＝0.4m/s2According to the formula (6), the horizontal length of the vertical curve is 2091.m, and L is 2100 m. The length of each of the two horizontal straight roads is 500m, and the length of each of the middle straight roads is 1000 m. The vertical combined curve and the vertical acceleration are shown in fig. 4 and 5, and the method of calculating the numerical points is the same as the combined curve.
Example 2: up-down (down-up) ramp combination curve
Designing parameters:
up-down ramp: slope of uphill slope is taken i10.02, the slope of the downhill slope is taken as i2-0.02; down-up ramp: i.e. i1-0.02, slope of downhill i20.02. The vehicle speed is 100m/s, the length of the vertical curve is 1500m, and the slopes at two ends are 1000m respectively.
Designing content:
taking the intersection point of the introduction points of the linear track and the vertical curve as an origin, the extension line of the linear track is an x axis, the vertical direction is a z axis, a control point is arranged every 10m, and i1、i2Substituting the values of L into formulas(3) And (4), a vertical surface combination curve and vertical acceleration can be obtained respectively, as shown in fig. 6 and 7. The specific numerical values are listed in tables 3 and 4, and the value of the z-axis and the vertical acceleration of the up-down ramp combined curve are respectively recorded as z1(m)、a1(m/s2) The combined curves of the down-up ramps are respectively denoted as z2(m)，a2(m/s2)。
Table 3 vertical combination curve value list: unit m
Figure BDA0003164958830000101
Figure BDA0003164958830000111
Table 4 vertical acceleration values list: unit m/s2
x(m) a1(m/s2) a2(m/s2) x(m) a1(m/s2) a2(m/s2)
1010 -1.7718518517E-03 1.7718518517E-03 1760 -3.9998814815E-01 3.9998814815E-01
1050 -4.1517037037E-02 4.1517037037E-02 1800 -3.9885037037E-01 3.9885037037E-01
1090 -8.0770370371E-02 8.0770370371E-02 1840 -3.9543703704E-01 3.9543703704E-01
1130 -1.1774814815E-01 1.1774814815E-01 1880 -3.8974814815E-01 3.8974814815E-01
1170 -1.5245037037E-01 1.5245037037E-01 1920 -3.8178370370E-01 3.8178370370E-01
1210 -1.8487703704E-01 1.8487703704E-01 1960 -3.7154370370E-01 3.7154370370E-01
1250 -2.1502814815E-01 2.1502814815E-01 2000 -3.5902814815E-01 3.5902814815E-01
1290 -2.4290370370E-01 2.4290370370E-01 2040 -3.4423703704E-01 3.4423703704E-01
1330 -2.6850370370E-01 2.6850370370E-01 2080 -3.2717037037E-01 3.2717037037E-01
1370 -2.9182814815E-01 2.9182814815E-01 2120 -3.0782814815E-01 3.0782814815E-01
1410 -3.1287703704E-01 3.1287703704E-01 2160 -2.8621037037E-01 2.8621037037E-01
1450 -3.3165037037E-01 3.3165037037E-01 2200 -2.6231703704E-01 2.6231703704E-01
1490 -3.4814814815E-01 3.4814814815E-01 2240 -2.3614814815E-01 2.3614814815E-01
1530 -3.6237037037E-01 3.6237037037E-01 2280 -2.0770370370E-01 2.0770370370E-01
1570 -3.7431703704E-01 3.7431703704E-01 2320 -1.7698370370E-01 1.7698370370E-01
1610 -3.8398814815E-01 3.8398814815E-01 2360 -1.4398814815E-01 1.4398814815E-01
1650 -3.9138370370E-01 3.9138370370E-01 2400 -1.0871703704E-01 1.0871703704E-01
1690 -3.9650370370E-01 3.9650370370E-01 2440 -7.1170370371E-02 7.1170370371E-02
1730 -3.9934814815E-01 3.9934814815E-01 2480 -3.1348148149E-02 3.1348148149E-02
1740 -3.9970370370E-01 3.9970370370E-01 2490 -2.1037037036E-02 2.1037037036E-02
1750 -3.9991703704E-01 3.9991703704E-01 2500 -1.0583703704E-02 1.0583703704E-02
Example 3: up-up ramp combination curve
Designing parameters:
slope of uphill slope is taken i1Connecting ramp i 0.02 ═ d2＝0.01；
Ascending ramp i1Up slope i of 0.012＝0.02；
Assuming good running conditions of the train, the speed is 100m/s, and the acceleration limit is amax＝0.3m/s2The length of the vertical curve is 500m, and the slopes at two ends are 500m respectively.
Designing content:
taking the intersection point of the introduction points of the linear track and the vertical curve as an origin, the extension line of the linear track is an x axis, the vertical direction is a z axis, one control point is arranged every 5m, and i1、i2And the values of L are respectively substituted into the formulas (3) and (4), so that a vertical surface combination curve and a vertical acceleration can be respectively obtained, as shown in fig. 8 and 9. The numerical values are tabulated in tables 5 and 6, the upward gradient i1Connecting ramp i 0.02 ═ d2The value of the z-axis and the vertical acceleration of the combined curve of 0.01 are respectively denoted as z3(m)、a3(m/s2) Ascending ramp i1Up slope i of 0.012The value of the z-axis and the vertical acceleration of the combined curve, respectively, are denoted as z, 0.024(m)、a4(m/s2)。
Table 5 vertical combination curve value list: unit m
Figure BDA0003164958830000121
Figure BDA0003164958830000131
Table 6 vertical acceleration values list: unit m/s2
x(m) a3(m/s2) a4(m/s2) x(m) a3(m/s2) a4(m/s2)
510 -0.01186 0.01186 760 -0.29986 0.29986
520 -0.0349 0.0349 770 -0.2989 0.2989
530 -0.05698 0.05698 780 -0.29698 0.29698
540 -0.0781 0.0781 790 -0.2941 0.2941
550 -0.09826 0.09826 800 -0.29026 0.29026
560 -0.11746 0.11746 810 -0.28546 0.28546
570 -0.1357 0.1357 820 -0.2797 0.2797
580 -0.15298 0.15298 830 -0.27298 0.27298
590 -0.1693 0.1693 840 -0.2653 0.2653
600 -0.18466 0.18466 850 -0.25666 0.25666
610 -0.19906 0.19906 860 -0.24706 0.24706
620 -0.2125 0.2125 870 -0.2365 0.2365
630 -0.22498 0.22498 880 -0.22498 0.22498
640 -0.2365 0.2365 890 -0.2125 0.2125
650 -0.24706 0.24706 900 -0.19906 0.19906
660 -0.25666 0.25666 910 -0.18466 0.18466
670 -0.2653 0.2653 920 -0.1693 0.1693
680 -0.27298 0.27298 930 -0.15298 0.15298
690 -0.2797 0.2797 940 -0.1357 0.1357
700 -0.28546 0.28546 950 -0.11746 0.11746
710 -0.29026 0.29026 960 -0.09826 0.09826
720 -0.2941 0.2941 970 -0.0781 0.0781
730 -0.29698 0.29698 980 -0.05698 0.05698
740 -0.2989 0.2989 990 -0.0349 0.0349
750 -0.29986 0.29986 1000 -0.01186 0.01186
In view of the precision requirement, the ES100 intelligent total station or the LP400 laser electronic theodolite is preferably used for surveying and setting.
In the description herein, particular features, structures, materials, or characteristics may be combined in any suitable manner in any one or more embodiments or examples.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the present invention should be covered by the present invention.

Claims (10)

1. A road engineering vertical section vertical curve design method based on a quartic curve is characterized by comprising the following steps:
step S1, obtaining ramp parameters of the road engineering needing construction;
in step S2, adjacent straight roads are connected using a vertical curve based on a quartic-type curve.
2. The method for designing the vertical curve of the longitudinal section of the road engineering based on the quartic curve as claimed in claim 1, wherein the vertical curve is designed according to the following equation:
Figure FDA0003164958820000011
wherein z is a coordinate value of a vertical curve connecting the linear road, and the direction of the z axis is vertical to the horizontal plane; in the formula, the intersection point of a straight line road and a vertical curve introduction point is taken as an original point, and an x axis is the extension line direction of the straight line road; l is the horizontal projection length of the vertical curve, i1、i2The slope of the lead-in end and the slope of the lead-out end of the vertical curve are respectively; and (0, L) represents the value range of the rectangular coordinate x corresponding to z.
3. The method for designing a vertical curve of a longitudinal section of a road engineering based on a quartic curve according to claim 1, wherein the ramp parameters in the step S1 include: up and down grade, vehicle speed, maximum acceleration.
4. The method for designing the vertical curve of the longitudinal section of the road engineering based on the quartic curve as claimed in claim 2, wherein the method for acquiring the vertical curve based on the quartic curve in the step S2 comprises the following steps:
step S21, taking the vertical curve introduction point as the coordinate origin, the horizontal axis as the x axis, the vertical direction as the z axis, and the second derivative of the vertical curve is as follows:
z″＝ax2-aLx (2)
l is the length of the vertical curve; integrating equation (2) yields:
Figure FDA0003164958820000012
step S22, setting the slope of the ramp at the leading end of the vertical curve as i1The slope of the leading-out end ramp is i2The boundary condition is that z' | x ═ 0 ═ i1，z′|x＝L＝i2In the case of (2), substituting the formula (2) solves the first derivative of the vertical curve as:
Figure FDA0003164958820000013
step S23, integrating equation (3) and applying boundary condition, zx＝0Get vertical curve equation when being 0:
Figure FDA0003164958820000021
step S24, deriving equation (3) to obtain the second derivative of the vertical curve:
Figure FDA0003164958820000022
5. the method for designing the vertical curve of the longitudinal section of the road engineering based on the quartic curve as claimed in claim 2, further comprising:
in step S3, the acceleration limit is verified.
6. The method for designing the vertical curve of the longitudinal section of the road engineering based on the quartic curve as claimed in claim 5, wherein the vertical acceleration a is obtained when the vehicle passes through the ramp at a constant speed vs＝v2z ", then the vertical maximum acceleration is:
Figure FDA0003164958820000023
7. the method for designing the vertical curve of the longitudinal section of the road engineering based on the quartic curve as claimed in claim 6, further comprising:
in step S4, the curve length is verified.
8. The method for designing the vertical curve of the longitudinal section of the road engineering based on the quartic curve as claimed in claim 7, wherein the vertical curve length limit determined by the maximum vertical acceleration limit is:
Figure FDA0003164958820000024
9. a road ramp, characterized by: the vertical curve of the road ramp is designed by adopting the vertical curve design method of the longitudinal section of the road engineering based on the quartic curve in any one of claims 1 to 8.
10. A construction method of a railway ramp is characterized by comprising the following steps:
step 1, acquiring parameters of a railway ramp needing to be constructed;
step 2, acquiring a vertical surface vertical curve equation by using the vertical curve design method of the longitudinal section of the road engineering based on the quartic curve according to any one of claims 1 to 8, calculating a numerical coordinate corresponding to each point on the vertical surface vertical curve according to slope points of a ramp connected during actual application of the ramp by taking x as a horizontal coordinate and z as a vertical coordinate, and forming a numerical list by the numerical coordinates of a plurality of points;
and 3, designing a roadbed, a ballast bed and a paved rail by using a coordinate method according to the numerical value list of the specific data and the design specification requirement obtained in the step 2, and then paving the rail.
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