CN103048144A - Geometric algorithm for high-speed circuit transition curve - Google Patents

Abstract

The invention discloses a geometric algorithm for a high-speed circuit transition curve, which adopts a McConnell transition curve calculation formula and is characterized in that a Simpson integration algorithm is introduced into the McConnell transition curve calculation formula; an angle of declination of a random point on the transition curve is calculated; and each coordinate of the transition curve is calculated by the angle of declination. According to the invention, the Simpson integration algorithm is introduced into the McConnell transition curve calculation formula and curve integral adopts a Simpson iteration method; a calculation error is not influenced by the length of a calculation route or an account step; the defects that in a conventional offset method, an accumulated error is increased along with increase of the calculated length and the error is increased along with increase of the iteration step size are overcome; and the geometric algorithm is beneficial for controlling calculation accuracy. The McConnell curve integration algorithm adopted by the geometric algorithm overcomes the defects of a conventional McConnell curve offset iteration method and creates beneficial conditions for accuracy control of automatic paving of a newly constructed high-speed circuit curved surface machinery.

Description

A kind of geometric algorithm of high speed circuit adjustment curve

Technical field:

The present invention relates to the geometry designs technical field of proving ground high speed circuit, specifically a kind of geometric algorithm that is mainly used in high speed circuit adjustment curve.

Background technology:

The high speed circuit is as the main body facility of proving ground, and General Requirements adopts special geometric design method to provide effective, safe and pleasant service condition for automobile carries out the continuous high speed running test in the place of limited.The technical requirements such as its plane surface radius, horizontal superelevation have all been broken through the restriction of freeway geometry designing technique standard far away.On the other hand, the bend of high speed circuit part is different from Ordinary Rd fully, and security, the comfortableness of the geometrical property of its space three-dimensional curved surface during to high vehicle speeds all has considerable influence.These characteristics of high speed circuit have determined that high speed circuit geometry designs technology is goed deep into systematic research has special important meaning.

The high speed circuit adjustment curve that the countries in the world proving ground is commonly used at present is Mike Connell curve and Bloss curve.Mike Connell curve mainly by setting up mathematical model on the Research foundation to the human motion index, has obtained successful Application in its unique advantage is in the design of proving ground high speed circuit.Its advantage is: considered the kinematics characteristic of Vehicle Driving Cycle, and with human body to the motion susceptibility as design objective, vehicle transition when sailing into and roll adjustment curve away from is comparatively mild.Bloss curve carries out high speed circuit geometry designs take mathematical model as the basis, the geometric design method of namely deriving with whole characteristic parameters such as the centre of gravity of vehicle track are continuous and smooth, curvature is continuous, curvature variation is continuous, but lack the parameter evaluation index of considering driving comfort and sports safety with kniesiological angle.Therefore, in the design of various countries' proving ground high speed circuit, more extensive with the application of Mike Connell curve.

But existing Mike Connell curve exists limitation and weak point in computing method, and be mainly reflected in: Mike Connell Curve Design is planimetric coordinates and the drift angle that obtains each pile No. point by offset method.This is actually the method for manual approximate integration, produces inevitably error in computation process.Need to error be controlled on the level basis that is starkly lower than construction error, to satisfy the design accuracy requirement by adjusting step pitch Δ L.The coordinate that can't calculate arbitrfary point on the adjustment curve is a defective all the time, and the data input that pave for adjustment curve section asphalt curved surface brings very big inconvenience, is unfavorable for quality control on construction and monitoring.In recent years, improving constantly of responsive motor power performance, newly-built and to plan to build the design speed increase rate of proving ground high speed circuit very large, the surface layer type is all tended to the bituminous concrete pavement that adopts usability good, and adopts quality controllable curve paver to realize laying.Therefore, the weak point of existing Mike Connell curve design method is more obvious, and its application is restricted.

Summary of the invention

The object of the invention is to propose a kind of geometric algorithm of high speed circuit adjustment curve, derive the coordinate Calculation formula of arbitrfary point on the adjustment curve by infinitesimal analysis, be used for data input and quality monitoring that proving ground high speed circuit curved surface machinery paves, improve the computational accuracy of adjustment curve construction lofting, realized the controllability that machine automatization paves.

To achieve these goals, technical scheme of the present invention is as follows: a kind of geometric algorithm of high speed circuit adjustment curve, adopt Mike Connell adjustment curve computing formula, it is characterized in that described Mike Connell adjustment curve computing formula is introduced Simpson's integral algorithm, calculate arbitrfary point angle of deviation on the adjustment curve, and utilize this angle of deviation to calculate each coordinate of adjustment curve.

According to a particular embodiment of the invention, calculate the skew angle of arbitrfary point on the adjustment curve:

(1)0～S/4

(2)S/4～3S/4

(3)3S/4～S

In the formula, r-calculates arbitrarily the radius of horizontal curve at website place; K-calculates arbitrarily the curvature at website place; G-acceleration of gravity; The v-design speed;

-side-sway angle formula;

θ ₀The road surface cross dip at-origin of transition curve place; L-calculates website to the distance of point of tangent to spiral or point of spiral to tangent; The S-length of transition curve; The C-calculating parameter, Wherein

Side-sway angle on the-circular curve,

R is circular curve radius.

Mike Connell (McConnell) easement curve design method with human body to the susceptibility of motion as the geometry designs criterion of road, and from the maximum side-sway rate of acceleration change of the permission of vehicle when adjustment curve is run at high speed, derived because the Formula Series of easement curve design.The present invention introduces Simpson's integral algorithm curvilinear integral to described Mike Connell adjustment curve computing formula and adopts Simpson's process of iteration, the error of calculation is not subjected to the impact of calculated route length or calculation step, overcome that traditional offset method causes along with the increase of computational length that cumulative errors increase and error with the defective that the increase of iteration step length increases, be conducive to control computational accuracy.Mike Connell curvilinear integral algorithm so can calculate Point Coordinates and position angle on the adjustment curve, is not subjected to the impact of iteration step length because need to not carry out iteration with integer step.Computational data can be used for the computer data input that bituminous concrete curved surface machinery paves, and realizes the full-automation of Construction control and quality monitoring.Mike of the present invention Connell curvilinear integral algorithm has overcome the defective of traditional Mike Connell curve offset distance process of iteration, for advantage has been created in the precision control that newly-built high speed circuit curved surface machine automatization paves.

Description of drawings:

Fig. 1 is the freedom of motion schematic diagram.

Fig. 2 is Mike Connell curve plane coordinate Calculation schematic diagram.

Angle of deviation and the coordinate figure comparing result of Fig. 3 for adopting Limit Step Length Iteration Method and Simpson's Integral computation method to obtain, wherein Fig. 3 a calculates angle of deviation difference variation diagram in the length of transition curve scope, Fig. 3 b calculates △ X difference variation diagram in the length of transition curve scope, Fig. 3 c calculates △ Y difference variation diagram in the length of transition curve scope.

Embodiment

Mike Connell (McConnell) easement curve design method with human body to the susceptibility of motion as the geometry designs criterion of road, and from the maximum side-sway rate of acceleration change of the permission of vehicle when adjustment curve is run at high speed, derived because the Formula Series of easement curve design.

Mike Kang Naer curve is with the characteristic value of the side-sway motion control index as high speed circuit geometry designs, and with the rate of change J (side-sway angle accelerating sections rate of change) of the side-sway acceleration of motion controlled design parameter as high speed circuit adjustment curve.

Side-sway characteristic value computing formula summary sheet table 1

Mike Connell adjustment curve coordinate Calculation table table 2

In the table:

(8) α ₁=β ₁+ β ₂+ ... + β _I-1+ β _i/ 2

(11)Δa ₁＝ΔS·cosα ₁(12)Δb ₁＝ΔS·sinα ₁ $\left(13\right),a_1=\underset{i=1}{\overset{1}{\mathrm{\Σ}}}\mathrm{\Δ}{a}_1$ $b_1=\underset{i=1}{\overset{1}{\mathrm{\Σ}}}\mathrm{\Δ}{b}_1$

Mike Connell (MC) adjustment curve coordinate Calculation need to be carried out projected coordinate according to the website step delta S that sets.The website coordinate is derived and need to be controlled the step-length precision, easily cause the accumulation of error in computation process, and computational accuracy is subjected to website step delta S to affect larger.

The improvement Mike Connell adjustment curve computing method that the present invention proposes are to introduce Simpson's integral algorithm, by calculating the pointwise position angle adopting the position angle improving computational accuracy, and realize data arbitrarily and random desirable property.The specific algorithm formula is:

Dl=rd τ (formula 1)

The both sides integration is asked angle of deviation τ:

$\mathrm{\τ}=\∫\frac{1}{r}\mathrm{dl}$ (formula 2)

By

(formula 3)

Obtain

(formula 4)

In the formula, r-calculates arbitrarily the radius of horizontal curve (m) at website place;

K-calculates arbitrarily the curvature (1/m) at website place;

G-acceleration of gravity (m/s ²);

V-design speed (m/s);

The cubic polynomial of l (radian) among-table 1;

θ ₀The road surface cross dip at-origin of transition curve place;

L-calculates website to the distance (m) of point of tangent to spiral or point of spiral to tangent;

The S-length of transition curve;

The C-calculating parameter,

Wherein Side-sway angle on the-circular curve,

R is circular curve radius.

In table 1 Cubic polynomial introduce following formula, obtain that the computing formula of τ is respectively in Three regions:

(1)0～S/4

$\mathrm{\τ}=\∫\frac{g\·\tan [{\mathrm{\θ}}_0+{\mathrm{Cl}}^3/6]}{v^2}\mathrm{dl}$ (formula 5)

(2)S/4～3S/4

$\mathrm{\τ}=\∫\frac{g\·\tan [{\mathrm{\θ}}_0+C\·(-l^3/6+S\·l^2/4-S^2/16)]}{v^2}\mathrm{dl}$ (formula 6)

(3)3S/4～S

$\mathrm{\τ}=\∫\frac{g\·\tan [{\mathrm{\θ}}_0+C\·(l^3/6-S\·l^2/2+S^2\·l/2-13S^3/96)]}{v^2}\mathrm{dl}$ (formula 7)

If following formula is adopted analytic solution, then need following formula expansion in Taylor series or Maclaurin series, its expression formula is difficult calculating, and adopts Simpson's integration to address this problem.τ in the Three regions is carried out respectively Simpson's integral and calculating, can draw the skew angle of (x represents the length of transition curve between point of tangent to spiral and calculation level) of arbitrfary point x on the adjustment curve:

(1)0～S/4

(formula 8)

(2)S/4～3S/4

(formula 9)

(3)3S/4～S

(formula 10)

For guaranteeing computational accuracy, the error of calculation that Simpson formula adopts should be less than 10 ^-6, and for the constant term in S/4～S highway section, its error of calculation should be less than 10 ^-8According to measuring and calculating, above error amount can be taken into account precision and computing time.

After trying to achieve skew angle, can calculate according to following formula the relative coordinate of arbitrfary point x on the adjustment curve:

$\left\{\begin{array}{c}\mathrm{dx}=\cos \mathrm{\τ}\·\mathrm{dl}\\ \mathrm{dy}=\sin \mathrm{\τ}\·\mathrm{dl}\end{array}\right.$ (formula 11)

$\left\{\begin{array}{c}X={\∫}_0^l\cos \mathrm{\τ}\·\mathrm{dl}\\ Y={\∫}_0^l\sin \mathrm{\τ}\·\mathrm{dl}\end{array}\right.$ (formula 12)

Because dl approximately equal on skew angle and τ numerical value when very little, the τ in the following formula should adopt piecemeal that the interior accumulative total skew angle of scope replaces respectively, namely obtains

$\left\{\begin{array}{c}X={\∫}_0^l\cos \mathrm{\α}\·\mathrm{dl}\\ Y={\∫}_0^l\sin \mathrm{\α}\·\mathrm{dl}\end{array}\right.$ (formula 13)

In the formula, the result of calculation in α-(formula 8)～(formula 10).

L-calculates website to the distance (m) of point of tangent to spiral or point of spiral to tangent.

This equation still needs to find the solution by Simpson's integral formula, and its error of calculation should be slightly larger than the error of calculating angle of deviation, through the actual computation checking, adopts 10 ^-5Can take into account computational accuracy and computing time.

Mike Connell (MC) curvilinear integral algorithm examples:

Design one is passed through point of spiral to curve radius 500m, length of transition curve is 380m, angle of deviation and coordinate that the adjustment curve of design speed 180km/h adopts respectively Limit Step Length Iteration Method and Simpson's Integral computation method to calculate gained compare, and can draw the following conclusions:

1) calculate angle of deviation accumulative total difference and change the trend that is first quick and back slow with length of transition curve, in length of transition curve was in (1/4～3/4) S interval range, accumulative total difference rate of change was the fastest.

2) the coordinate difference that is caused by accumulative total deflection angle difference is not obvious at (0～1/4) S highway section graticule, but along with the growth of calculating distance, coordinate difference changes very fast, when arriving point of spiral to curve, coordinate deviation value between the different calculation methods is near 0.2m, and offset error is larger.

Angle of deviation and coordinate comparison result that two kinds of computing method obtain are seen accompanying drawing 3.

The Mike Connell curvilinear integral method that the present invention proposes is compared with traditional offset method, has following features:

1) traditional offset method is along with the increase of computational length, and its cumulative errors can increase gradually, and error can increase because of the increase of iteration step length, so affects the many factors of error in the computation process; And Simpson's process of iteration has been owing to having adopted unified error control accuracy, so the error of calculation is not subjected to the impact of calculated route length or calculation step, and precision control is comparatively favourable.

2) owing to not needing to carry out iteration with integer step, therefore can calculate times point coordinate and position angle on the adjustment curve, and not be subjected to the impact of iteration step length.

3) total arithmetic speed is limited by Computing speed in the Simpson formula computation process, the thereupon fast development of computer core arithmetic speed, and it is 10 that present all kinds of computing machines can reach computational accuracy ^-6, be enough to satisfy requirement of engineering.

Claims (3)

1. the geometric algorithm of a high speed circuit adjustment curve, adopt Mike Connell adjustment curve computing formula, it is characterized in that described Mike Connell adjustment curve computing formula is introduced Simpson's integral algorithm, calculate arbitrfary point angle of deviation on the adjustment curve, and utilize this angle of deviation to calculate each coordinate of adjustment curve.

2. by the geometric algorithm of high speed circuit adjustment curve claimed in claim 1, it is characterized in that: the skew angle that calculates arbitrfary point on the adjustment curve is:

(1)0～S/4

(2)S/4～3S/4

(3)3S/4～S

$\mathrm{\α}={\∫}_0^{S/4}\frac{g\·\tan [{\mathrm{\θ}}_0+{\mathrm{Cl}}^3/6]}{v^2}\mathrm{dl}+{\∫}_{S/4}^{3S/4}\frac{g\·\tan [{\mathrm{\θ}}_0+C\·(-l^3/6+S\·l^2/4-S^2/16)]}{v^2}\mathrm{dl}$

$+{\∫}_{3S/4}^{l-3S/4}\frac{g\·\tan [{\mathrm{\θ}}_0+C\·(l^3/6-S\·l^2/2+S^2\·l/2-13S^3/96)]}{v^2}\mathrm{dl}$

In the formula, r-calculates arbitrarily the radius of horizontal curve at website place; K-calculates arbitrarily the curvature at website place; G-acceleration of gravity; The v-design speed;

-side-sway angle formula;

θ ₀The road surface cross dip at-origin of transition curve place; L-calculates website to the distance of point of tangent to spiral or point of spiral to tangent; The S-length of transition curve; The C-calculating parameter,

Wherein Side-sway angle on the-circular curve,

R is circular curve radius.

3. by the geometric algorithm of high speed circuit adjustment curve claimed in claim 1, it is characterized in that: the relative coordinate of calculating arbitrfary point on the adjustment curve is: $\left\{\begin{array}{c}X={\∫}_0^l\cos \mathrm{\α}\·\mathrm{dl}\\ Y={\∫}_0^l\sin \mathrm{\α}\·\mathrm{dl}\end{array}\right..$

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