WO2022178612A1 - Transition section of a railway track curve - Google Patents

Abstract

The present invention relates to the configuration and use of a transition section of a curve in a railway track, the novel relationships of the harmonizable shape of which provide for high quality cornering movement of a railway vehicle through said section at a set speed V , where, with respect to a length I, the curvature of the axis of the track k(l) in said section and the transverse inclination i(/) of the track are variable. The shape of the track axis in the transition section is determined by the position N of equidistant points having the coordinates х[n] and у[n], which are determined using formulas (1) and (2), the variables of which are determined in turn using formulas (3)-(5). The transverse inclination i[n] of the track at these points is determined using formula (6), the variables of which are determined in turn using formulas (7)-(9). Alongside the traditional controlled parameter L (length of the transition section), the present invention envisages the additional possibility of variation of the values of the controlled parameters Z and U, which have an effect on the overall geometric properties of the non-identity functions of an angle, the curvature and the transverse inclination of the track in the transition section.

Description

Transition section of railroad gauge rounding

This invention relates to the device and operation of the transition section (hereinafter referred to as PU) of the rounding of the railroad, the high quality of the turning movement of the crew along which at a given speed V with variable along the length I curvature of the axis of its track £ (/) and its transverse slope / (/ ) provide new patterns of its harmonized form.

. При этом НПУ а ^ вычисляется как результат векторного сложения действующих в горизонтальной плоскости гравитационных G и центробежных С ускорений а_тях = С - G · tan (or) , где а - это угол поперечного наклона колеи, вычисляемый как a = arcsin(/) . The plan of the track track of the railroad (rail track) consists of an alternating sequence of straight sections and roundings inscribed in the angles of their rotation. Each rounding consists of a circular and two transition sections of length L. The axis of the track of the circular section is described by an arc of a circle with a given constant curvature К = !/ R , and its outer rail is raised above the inner one also by a constant height D. This allows to partially reduce the lateral acceleration acting on the circular part of the curvature at the calculated speed V. This reduction is achieved due to the cross slope directed to the center of its curvature / = D / S . Within the circular part of the rounding, this slope is also constant, because along its length, it depends only on the constant value of the elevation D and the track width S. The constancy of the values of the parameters V, R, D and S within the circular part of the rounding of the track determines the constancy of the theoretically maximum value of the outstanding lateral acceleration throughout the entire length (hereinafter referred to as the TSL) and ₁ . The consistency of the values of the parameters V, R, D and S provides that between the value determined by them and its allowable value i _{g l} the balance is observed, which is specified by the condition

. In this case, the NPU a ^ is calculated as the result of vector addition of the gravitational G and centrifugal accelerations C acting in the horizontal plane a m _ax = C - G tan (or) , where a is the angle of the transverse inclination of the track, calculated as a = arcsin (/) .

в зависимости от относительной доли текущей длины колеи x = l / L , непрерывно изменяющейся в диапазоне 0 < c < 1 . Функции большинства известных форм ПУ предшествующего уровня техники описаны в публикациях [ 1-4]. В каждой из них закономерность её кривизны к(%) и поперечного уклона ί(c) задана единообразно по принципу к (х) = К - f (c) и ί(c) = I · /(c) с соблюдением требования 0 < /(^) < 1 . Этот принцип обусловил тождественность свойств графиков кривизны и поперечного уклона у подавляющего большинства известных форм ПУ предшествующего уровня техники. При этом основное различие между ними состоит в G" порядке геометрической гладкости строго монотонных единичных функций /(%) - Он определяет максимальный порядок отличной от нуля /7-ой производной, которая в точках X = 0 и X = ! имеет нулевые значения. У широко распространённой формы ПУ G° -ro порядка гладкости функция / ( c ) = c Поэтому графики закономерности её кривизны к(%) и поперечного уклона ΐ(c) представлены прямыми линиями к

c·I . Закономерности относительных прямоугольных координат x(z) ^и у{%) горизонтальной проекции оси колеи такой формы ПУ соответствуют только одной плоской кривой определяемой в уровне техники как клотоида, clothoid или spiral· In contrast to the circular track rounding section, its transitional section has a more complex shape. It is determined by the form of the curvature functions k x) and the transverse slope ΐ(c) , varying in the range

depending on the relative share of the current track length x = l / L , continuously changing in the range 0 < c < 1 . The functions of most known prior art forms of PU are described in publications [1-4]. In each of them, the regularity of its curvature k(%) and transverse slope t(c) is set uniformly according to the principle k(x) = K - f(c) and t(c) = I /(c) subject to the requirement 0 < /(^) < 1 . This principle led to the identity of the properties of the curves of curvature and transverse slope in the vast majority of known forms of PU of the prior art. Moreover, the main difference between them is in the G "order of geometric smoothness of strictly monotone unit functions / (%) - It determines the maximum order of the non-zero / 7th derivative, which has zero values at the points X \u003d 0 and X \u003d! widespread form of PU G° -ro order of smoothness function / ( c ) \u003d c Therefore, the graphs of the regularity of its curvature k (%) and the transverse slope ΐ (c) are represented by straight lines k

c I . The patterns of relative rectangular coordinates x(z) ^and y{%) of the horizontal projection of the axis of the track of this form of PU correspond to only one flat curve defined in the prior art as a clothoid, clothoid or spiral

For all other forms of PU of the G "th order of smoothness with n > 0, the smooth outlines of the graphs of the regularities of their curvature k (x) and the transverse slope ϊ (c) are similar to the first half of the sinusoid graph. This determined the common name for their forms half-sine, t (i.e., sub-sinusoidal. With the same order of smoothness, semi-sinusoidal forms of PU have different regularities of the function f(x). They differ in smoothness, which is estimated by the maximum of their first derivative d f(x)/ x , calculated at the point c = 0.5.

The device of half-sine forms of PU reduced the severity of the problem of the so-called lateral jerk (lateral jerk), observed at the beginning and at the end of PU of the clothoid form. However, in the process of their operation, problems of the quality of movement were revealed, due to low-frequency oscillations of the crews. This is indicated by the results of studies conducted at the end of the last century in Japan on straight and curved sections of the gauge of high-speed rail lines of PU [5]. With the increase in speeds and the development of high-speed highways (hereinafter referred to as HSR), the urgency of the problems of the rotary movement of the crew with a variable curvature of the axis of the launcher and with a variable transverse slope of its track increased. This is indicated by modern trends towards the complication of regularities. half-sine of PU forms in such a way as to reduce the value of the maxima of the first derivatives of their functions df(x)jd x in their central part [3]. In addition to this, so-called methods are also used. “elevated tracing” [2,3], in which the curvature pattern k x ') = K - f (c) determines not the axis of the PU track, but the trajectory of the calculated point of the vehicle, which is “raised” above the level of the top of the rail heads (hereinafter referred to as the VGR ) to height I.

As a rule, the whole set of these measures is aimed at solving the main problem of the functioning of the “Track + Crew” system (hereinafter referred to as PE), which, on the PU of railroad roundings, manifests itself in the unfavorable dynamics of the force interaction of its elements and in reducing the level of passenger convenience. Because of this, the rate of breakdown of the track geometry of the launcher and adjacent sections increases, and the rails and wheels of the vehicles wear out prematurely. The degree of destructiveness of these processes largely depends on the geometric properties of the PU shapes. The results of the analysis of the kinematic indicators of the PE system on launchers with traditional and most progressive forms [6] indicate that each of them has certain disadvantages that do not provide the required quality of the curvilinear movement of crews. However, even in the standard of the EU countries there are no theoretically substantiated priorities for the selection and application of any one of the 5 forms of PP recommended in it, which would provide the highest level of quality for the functioning of the PE system.

The existing problems of substantiation and practical application of the overwhelming number of forms of PU of the prior art are due to insufficiently adequate and extremely simplified models of the PE system and methods for assessing the quality of its functioning. As a rule, they are based on the indicators of the kinematics of an abstract point located at the level of the VGR. In contrast, the provisions of the present invention are based on the indicators of the kinematics of points located at functionally significant levels of the vehicle. Depending on the nature of transportation and priority aspects of quality, the calculated levels at which they can be located take into account the position of the center of mass of the crew (hereinafter referred to as CM) and / or the position of the vestibular apparatus of its passenger.

This approach is consistent with the goal of ensuring the quality of the curvilinear movement of the crew, which traditionally means an acceptable level of passenger comfort and a smooth change in the forces of interaction between the wheels of the crew and the track rails. However, to ensure it using any of the forms of PU of the previous of the prior art, the only possibility was provided to vary the values of only their lengths L. In addition, a simplified model of the PE system did not allow an objective assessment of the influence of this factor on the quality of its functioning in these areas.

Studies conducted on Japanese railways have shown that discomfort and adverse health effects for passengers are caused by low-frequency oscillations of lateral accelerations with a frequency below 1 Hz [5]. As shown by the results of calculations obtained using the multi-factor deterministic kinematic model (hereinafter referred to as MDKM) described in the article [6], such a character of the oscillations of transverse accelerations acting at the calculated level of the crew R > 0 is inherent in varying degrees in all half-sine forms of the launcher of the previous level technology. This is indicated by the significant amplitudes of oscillations of the values of the NCL o(/) functions inherent to them and the rates of its change y = dajdl , variable along the length I and time t of movement along the CL. The same vibrations lead to an uneven change in the reaction forces of the rails, as a result of which the dynamic component of the load acting on them increases.

The values and patterns of these indicators are due to the complex interaction of the geometric and physical factors that affect them, the most important result of which is manifested and evaluated at the calculated level of the crew I. This is due to the integrative nature of these indicators, which differs significantly from the local indicators of the kinematics of an abstract point, traditionally calculated and estimated earlier at the level of GVR = 0. The complex interaction of the properties of the PE system is taken into account in its multifactorial deterministic kinematic model (hereinafter MDKM), described in the article [6]. The integrative indicators of the quality of its functioning calculated in the MDCM depend on the values of the following parameters:

- crew speed V; radius of the circular part of the rounding R

- estimated elevation of the outer rail above the inner rail £>; the distance between the axes of the rail gauge S; elevation I of the calculated point above the level of the WGR;

- lengths of PU L of the regularity of the angle /?(/) of the tangent to the axis of the track and its curvature k(1) ;

- patterns of removal of the transverse slope of the track /(/) ; - patterns of curvature of the projection of the trajectory of the calculated point to _n (/) on the horizontal plane;

- the value of a boolean variable, set depending on the symmetrical ( true ) or asymmetric {false ) withdrawal of the outer rail elevation above the inner one; patterns of curvature of the projection of the axis of the track on the vertical plane

*, (/) :

- patterns of curvature of the projection of the longitudinal axis of the outer (left) rail on the vertical plane k , (/);

- patterns of curvature of the projection of the longitudinal axis of the inner (right) rail on the vertical plane k _R (/) ;

As the analysis of the results obtained with the use of MDCM [6] showed, varying within an acceptable range only the lengths L of PUs of the prior art does not make it possible to coordinate the interaction of all the above properties of their half-sine forms in such a way as to eliminate or reduce the amplitudes of oscillations of their inherent functions. NLE a(ί) and rates of their change y = dajdt . As a result, it is also not possible to ensure a uniform and smooth increase in the difference in the reaction forces of the outer and inner rails of the gauge AF = F _L - F _R .

The nature of these hard-to-remove shortcomings, which are inherent in half-sine forms of PU of the prior art, is illustrated by an example of assessing the integral quality indicators of one of the best forms of PU [3], described by the Order (3, 7) function. From the list of all alternatives proposed in [3], it has the highest G ^4th order of smoothness. There is a characteristic “plateau” on the graph of the 1st derivative of the cross-slope removal function and the curvature of its axis (see Fig. 9). This clearly indicated the desire of the author of this solution to eliminate the amplitudes of the NPL oscillations a(1) and to reduce the maximum of its constant rate of change y/ _max over a considerable length of the central part of the PL.

её эпюры от абсолютного, но практически недостижимого минимума

However, as shown by a kinematic analysis of the functioning of the PE system on a launcher of this form, the achievement of this goal leads to a significant dispersion of these indicators and other integrative indicators of the quality of movement at its beginning and end (see Fig. 10 - Fig. 13). Thus, the main ones for evaluating the SP obtained by one method or another are the plots of the NPL a(1) diagrams and the rate of its change y(1)=άa/ώ operating at the calculated level I. a sign of a high level of quality of the launcher design, provided under the condition of a smooth and smooth plot of its rate of change y(1)=άa/ώ on the approaches to its central, plateau-like section. From this it follows that the comfort of the movement of passengers and the positive dynamics of the force interaction of the elements of the SPE should be ensured by a smooth and smooth change in the diagrams a(1) and y(1), acting at those calculated levels of the crew, which are critical for indicators of all aspects of the quality of its movement. The priority of passenger comfort necessitates the linearization of the diagram y(1) over a greater length of the central section of the launcher with a minimum deviation of the constant maximum values

its plots from an absolute, but practically unattainable minimum

In terms of the totality of general technical features, the closest to the claimed shape of the PU for rounding the rail track is the PU form described in the invention “Railroad curve transition spiral design method based on control of vehicle banking motion” by the Order (3, 7) pattern [3]. Within the framework of the method proposed there for designing the transition curve of a railway track, one of 18 mathematical expressions is selected that determines the acceleration value (i.e., the second derivative) of the angle of the transverse slope (roll) of the track, depending on the variable distance, which varies from zero to a given length transition curve. Depending on the selected mathematical expression, the geometric properties of the shape of the PU track axis with length I and its transverse slope are determined. Due to the lack of a methodology and functionally justified criteria for choosing the necessary mathematical expression, assigning the length X of the PU, as well as the values of additional parameters required in some cases, the shape of the transition section obtained within the framework of this invention does not eliminate the disadvantages known from the prior art.

To identify these shortcomings and find ways to eliminate them due to the new form of the PU with the geometric properties corresponding to this purpose, a more advanced kinematic model of the curvilinear movement of the vehicle with a variable curvature of the track axis and its transverse slope was used [6]. The results of the analysis of the PU shapes known from the prior art [6] made it possible to formulate the task of the present invention in establishing such regularities in the shape of the gauge and the length L of the PU of the rounding of the railroad, the observance of which during its design and construction will ensure the achievement of the highest level of quality of the functioning of the PE system for given values of the following e parameters: speed V, radius of curvature R, elevation of the outer rail above the inner D, height H of the location of the crew reference point above the VG level and the distance between the axes of the rail S. Thus, the technical result of the claimed invention should be to ensure the highest level of quality of the system PE on the PU for rounding the track of the railroad, subject to the calculated values of its parameters.

The problem is solved, and the indicated technical results are achieved by the claimed transitional section of the rounding of the rail track, mating on the length L the straight section adjacent to it and the circular part of the rounding with a constant radius R, containing the base and forming the track rail and sleeper grid laid on it in accordance with the coordinates projections of the points of the axis of the transition section onto a horizontal plane with a variable along the length L value of the transverse slope i normal to the axis of the line tangent to the surface of the top of the rails, while the shape of the axis of the track of the transition section is determined by the location of N equidistant points with coordinates x[u] and [i] , and the transverse slope /[«] of the track at these points varies along the axis of the transition section in the range 0 < /[«] < D / S, where D is the calculated elevation of the outer rail of the track above the inner one within the circular part of the rounding axis railroad, a S is the distance between the vertical axes of the cross section ii rail gauge, as it grows evenly by a constant value D, = L/ N - 1) distances /[i] to each of its n-th points from / [O] = 0.0 m, at the beginning of the axis of the transition section, and to / [/V - l] = L , at its end. The problem is solved, and these technical results are achieved due to the fact that the relative rectangular coordinates of the projection points of the track axis [u] and

_y[n] are defined by the formulas:

(2) где: h - порядковый номер точки оси переходного участка, изменяющийся в диапазоне \ < h < (N- \) , х[л] - координата, характеризующая расстояние от начала переходного участка до места проекции л-ой точки оси на линию, касательную к ней в точке х[0] и [О] , у [л] - координата, характеризующая смещение в сторону центра кривизны оси её п- ой точки, измеряемое по нормали от линии, касательной к ней в точке c[q] и v[0]-0)

(2) where: h is the serial number of the point of the axis of the transition section, changing in the range \ < h < (N- \) , x[l] is the coordinate characterizing the distance from the beginning of the transition section to the place where the l-th point of the axis is projected onto the line tangent to it at the point x[0] and [O], y[l] is the coordinate characterizing the displacement towards the center of curvature of the axis of its nth point, measured along the normal from the line tangent to it at the point c[q] and v[ 0]-

fi_h{S) - значение функции основного угла касательной к оси колеи переходного участка, вычисляемого в зависимости от относительной доли d текущей длины 1 + А,/ 2 до точки касания по формуле:

D, - constant value of the increment of the current length I of the track axis of the transitional section, measured along its arc from its beginning to each l-th point, d - relative share of the current length Z + D,/2 of the axis of the track of the transitional section, measured from its beginning to the midpoint of the segment of the axis enclosed between its adjacent points l - 1 and , calculated by the formula:

fi _h {S) - the value of the function of the main angle of the tangent to the axis of the track of the transition section, calculated depending on the relative share d of the current length 1 + A, / 2 to the touch point according to the formula:

D _r (d) - the value of the complement function to the main angle of the tangent to the axis of the transition section, calculated depending on the relative share d of the current length Z + D,/2 to the point of contact according to the formula:

где U - параметр, определяющий величину дополнений к основным значениям угла касательной к оси колеи переходного участка в каждой её точке с относительной долей d текущей длины Z + D,/2. , (5)

where U - a parameter that determines the amount of additions to the main values of the angle of the tangent to the axis of the track of the transitional section at each of its points with a relative share d of the current length Z + D,/2.

The transverse slope / ^' [«] of the gauge of the transitional section at each «-th point of its axis, changing in the interval 0 < n < (N - 1) , is determined by the formula

'[«] = '* + z) ( ⁶ ) where

i_h ( c ) - значение функции основного поперечного уклона колеи переходного участка в точке п, вычисляемое в зависимости от относительной доли X по формуле:

D, (c) - значение функции дополнения к основному поперечному уклону колеи в точке п, вычисляемое в зависимости от относительной доли X по формуле:

где: Z - параметр, определяющий величину дополнений к основным значениям поперечного уклона колеи в каждой её точке с относительной долей c . X - the relative share of the current length I of the track axis to the point ", calculated as:

i _h ( c ) - the value of the function of the main transverse slope of the track of the transition section at point p, calculated depending on the relative share of X according to the formula:

D, (c) - the value of the addition function to the main transverse slope of the track at point n, calculated depending on the relative share of X according to the formula:

where: Z is a parameter that determines the amount of additions to the main values of the transverse slope of the track at each of its points with a relative share c .

There can be a lot of options for combining the predefined values of the parameters V, R, D, S and R of the PE system that are in demand by practice. This significantly complicates the task of ensuring a consistently high level of quality in the functioning of the PE system with a significant difference in the options for combining their values. As shown by the results of studies [7], the achievement of the best consistency in the interaction of the elements of the PE system is facilitated by adjusting the final values of the geometric properties of the form ί I \ ' Г\ and 1 due to the additions taken into account in them and D, . The value of these , , additions depends on the difference between the current combination of the design values of the parameters V, R, D, S and H and the variant that was taken into account when substantiating the functions of the main (basic) values of the PU shape properties

Therefore, along with the traditionally controlled parameter L, this invention includes an additional possibility of varying the values of the controlled parameters Z and U, which affect the final geometric properties of non-identical functions of the angle, curvature and cross-slope of the PU track. At each point of its axis, remote from its origin at a distance /, this influence is realized due to the dependence of its coordinates x(1)

1 l and y(1) on the function of the angle of the tangent to it b\ - - consisting of calculated by the formula (4)

которое вычисляется по формуле (5), а также за счёт зависимости соответствующего этой точке текущего значения превышения d{l) наружного рельса колеи над внутренним от функции поперечного уклона колеи / Г , состоящего из вычисляемого по формуле (8) основного его значения ^и зависящего от параметра Z дополнения к нему А

которое вычисляется по формуле (9). \ L ) its main meaning and its complement depending on the parameter U ,

which is calculated by formula (5), as well as due to the dependence of the current value corresponding to this point of the excess d(l) of the outer rail of the track over the inner one on the function of the transverse slope of the track / Г, consisting of its main value calculated by formula (8) ^and depending on parameter Z addition to it A

which is calculated by formula (9).

уклона колеи 'ίg| · При x = l/L функция значений кривизны оси колеи ^к (х) каждой текущей координате длины / ПУ определена как

MZ) = ^ Z⁵ (315 - ^20 3 - ^6720- Z(M085 - _Z(I 9795 - (1857 - /(1 M 78 - 2 (3 00- 600_Z)))))))^ ( 1 1 )

The minimum and maximum degrees of the terms of the polynomial functions (4), (5), (8) and (9), their coefficients, as well as the ranges of variation of the values of the controlled parameters Z and U are justified taking into account the provision of strict monotonicity of the G ⁴ -smooth curvature function of the track axis , described by the first derivative of the function of the angle tangent to it with respect to the length PU - jdl , and non-identical to it C ³ -smooth function of the transverse

gauge slope 'ίg| At x = l/L, the function of the curvature values of the track axis ^to (x) for each current coordinate of the length / PU is defined as

MZ) = ^ Z ⁵ (315 - ^20 3 - ^6720- Z(M085 - _Z (I 9795 - (1857 - /(1 M 78 - 2 (3 00- 600 _Z )))))))^ ( eleven )

U - a parameter that determines the maximum value of the addition to the main value of the curvature of the axis of the track of the transitional section.

Such a mathematical description of functions (4), (5), (8), (9), (1 1 ), (12) significantly expands the possibilities of coordinating the interaction of all properties of the PE system in order to ensure a consistently high level of quality of its functioning in any expedient variant combinations of values of its predetermined V, R, D, I. S and controlled L, Z, U parameters. Further in the text, the process of achieving such consistency will be called harmonization, the resulting form of PP will be called harmonized, and the corresponding values of the controlled parameters L, Z and U will be called optimal.

Quasilinear G ^! a smooth and smooth diagram of the FPU a(/) associated with the desired level of quality of the functioning of the PE system on the PU of a harmonized form, should correspond to G ⁰ smooth and smooth diagram of the rate of its change y(ΐ) = da/dt.

Compliance with this requirement eliminates the risk of the so-called lateral jerk (English: lateral jerk), observed at the beginning and end of the PU. In this case, the maximum value of this speed over a significant length of the central section of the launcher should be constant. With ideal observance of these requirements, the outlines of the diagram of the function ^(/) will be similar to the outlines of an isosceles trapezoid with smoothed corners and with a fairly extended "plateau" in its central part. Such outlines contribute to the greatest extent to the closest approximation of the “plateau” line with constant values of y/ _tzh to the absolute, but practically unattainable minimum of y/ _f! . This is in line with the generally accepted view of achieving the highest level of motion quality.

к y _IN в пределах «плато» эпюры y (1) необходимо оценивать по дисперсии W скоростей изменения значений dy jdt от соответствующей постоянству y/_maii нулевой скорости. Из этого следует, что синергический эффект, достигаемый при разных вариантах сочетания значений предопределённых V, R , D, Н, S, и управляемых L , Z, U параметров системы ПЭ, обратно пропорционален дисперсии W. С учётом этого цель поиска оптимальных значений параметров L, Z и U формализована как

где The half-sine forms of PU known from the prior art are characterized by low-frequency oscillations of the integrative indicators of kinematics at the calculated level of crews I. This is indicated by the results of their evaluation using MDCM [6] The magnitude and frequency of the amplitudes of these oscillations are due to inconsistent interaction identical properties of non-linear patterns of removal of the transverse slope of the track and the curvature of its axis. The PU device with the form claimed in this invention makes it possible to significantly reduce the amplitudes of these oscillations to an almost insignificant level. At the same time, “constancy” and the degree of approximation

to y _IN within the “plateau” of the diagram y (1) must be estimated from the dispersion W of the rates of change in the values of dy jdt from the zero rate corresponding to the constancy of y/ _maii . From this it follows that the synergistic effect achieved with different options for combining the values of predetermined V, R, D, H, S, and controlled L, Z, U parameters of the PE system is inversely proportional to the variance W. With this in mind, the goal of finding the optimal values of the parameters L , Z and U is formalized as

where

3 _h - the relative proportion of the beginning of the "plateau" of the diagram of the functional y(ΐ) ; - the relative share of the end of the "plateau" of the functional diagram

M - the number of points uniformly distributed over the interval from d to 5 _e with relative fractions of length 3, in which the amplitude of oscillations of the values of the functional _dyr /df is numerically estimated,

For objective reasons, the solution of this problem cannot compensate for the negative impact that the vertical curvature of the launcher axis and/or the asymmetric (see Fig. 16, 17) retraction of elevation D can have. Therefore, the goal function (13) should be minimized without taking into account these factors , i.e. with a hypothetically zero vertical curvature of the PU axis and a symmetrical retraction method (see Fig. 14, 15) of the elevation D. As analytical dependences of the MDCM [6] show, with a symmetrical retraction of the elevation D, the vertical curvature of the height diagrams along the outer and inner rails is halved , and its opposite signs exclude the influence of this curvature on _the accelerations acting along the vertical axis of the vehicle. Taking into account these conditions, the values of the functional dy _/ jdt in each relative coordinate 3 _n < 3 < 5 of the length of the PS can be calculated using the simplified formula where k _n is the function of the curvature of the trajectory of the calculated point of the crew at the calculated level AND

Variable values of the parameters Z, U and predefined values of the parameters V, R, D H and S are included in the equations of functions that are members of the functional (!4). This ensures the purposefulness of the search for the optimal variant of the combination of the values of the parameters L, Z, and U, at which the variances W of the oscillation amplitudes calculated by formula (13) will tend to a minimum. In accordance with the justifications outlined above, this will ensure the highest quality of the curvilinear motion of the crew, evaluated at the level of the CM or at any other functionally significant level of the crew.

In the course of checking the reliability and quality of such harmonization of the PR forms, it was found that for the calculated values ^of CL _amax > 0.4 m/s relative fractions of the length of the boundary 6 _h = 1/4 and 5 _e = 3/4 With the values of the boundary in the range O.1 < a _rm < 0.4 m/s ² , these relative fractions of the boundary should be calculated by empirical formulas

< 0.1 м/с², требуется существенное увеличение длин ПУ [7]. Ввиду этого целесообразность практической реализации таких конструкций закруглений является крайне сомнительной и далеко не всегда осуществимой В основном - из-за ограничений по углу поворота или по другим причинам. Поэтому минимальное расчётное значение НПУ а_тах , при котором целесообразно гармонизировать форму ПУ, не должно быть меньше 0.1 м/с². During this test, it was also found that for roundings that provide the so-called balanced mode of movement of crews with

< 0.1 m/s ² , a significant increase in the length of the launcher is required [7]. In view of this, the feasibility of the practical implementation of such rounding designs is extremely doubtful and far from always feasible. Basically, due to restrictions on the angle of rotation or for other reasons. Therefore, the minimum calculated value of FCL _amax , at which it is expedient to harmonize the shape of the launcher, should not be less than 0.1 m/s ² .

Harmonization of the form of PU can be carried out by "manual" selection of a combination of L, Z, and U values close to the optimum. the minimum of functional (13) varied in the range I .OE-7 <W< 1.0Е-4 m/s ⁴ . These values of W are relevant for the design speed of the vehicle, which varies in the range of 100 <К< 400 km/h, the curvature radii R, which provide the calculated values of NPU a _max in the range 0.1 < a _pix < 1.0 m/s ² with the calculated elevation of the outer rail above internal, varying in the range 25 < D < 150 mm, as well as with the design level of the crew H - 2200 mm and track width S = 1520 mm. Under other conditions, the range of variation of the minimum of the functional ( 13) may be different.

However, even for the "manual" harmonization of PU forms, it is highly desirable to automate routine calculations and plotting, which make it possible to control the efficiency of this process and the quality of its results. Ideally, each step of refining the values of the parameters L , 2, or U should lead to the minimization of the numerical values of the objective function (13), and also make the NPL diagram <з(/) and the plot

"plateau" of the plot y (1) · In the course of working on this invention, the implementation of this process in the Microsoft Excel program turned out to be quite convenient and effective. Along with a numerical assessment of the degree of harmonization of the PU form, its quality was confirmed by diagrams of all geometric and functional properties of the PE system. Also in this program, the coordinates and other parameters necessary for the breakdown of roundings with harmonized forms of PU, corresponding to the provisions of this invention, were calculated.

\ L на всём протяжении длины L переходного участка строго монотонно и непрерывно изменяется от 0 до L/2R, значение её первой производной по длине /, определяющей закономерность кривизны оси переходного участка также строго монотонно

и непрерывно изменяется от 0 до ///?, а для суммы всех последующих 2-ых, 3-их, 4-ых и 5-ых производных этих функций по этой же длине I обеспечивается непрерывность изменения их значений, а также равенство их нулю на обеих концах интервала 0 < 1 < L . При этом функция кривизны оси колеи

определяется по приведённым выше формулам (10) - (12). Также предпочтительными являются формы реализации заявляемого переходного участка, в которых при заданной величине параметра Z, варьируемой в диапазоне от -88 до +33, значение суммы функций основного поперечного уклона колеи ^и Дополнений к нему

Thus, in the preferred forms of implementation of the proposed transitional section, with a given value of the parameter U, varying in the range from -45 to +55, the value from 1_ is the sum of the functions of the main angle of the tangent to the axis of the track and additions to it

\ L throughout the length L of the transition section is strictly monotonous and continuously changes from 0 to L / 2R, the value of its first derivative with respect to the length /, which determines the regularity of the curvature of the axis of the transition section is also strictly monotonous

and continuously changes from 0 to ///?, and for the sum of all subsequent 2nd, 3rd, 4th and 5th derivatives of these functions along the same length I, the continuity of their values is ensured, as well as their equality to zero at both ends of the interval 0 < 1 < L . In this case, the curvature function of the track axis

is determined by the above formulas (10) - (12). Also preferred are the forms of implementation of the proposed transition section, in which, for a given value of the parameter Z, which varies in the range from -88 to +33, the value of the sum of the functions of the main cross-slope of the track ^and Additions to it

D, throughout the length L of the transition section strictly monotonously and continuously change from 0 to D / S, and the values of its 1st, 2nd and 3rd derivatives with respect to the length / continuously change while maintaining their equality to zero at both ends of the interval 0 < 1 < L .

It should be noted that for the application of the claimed invention in modern technologies for computer-aided design of railroads, software harmonization of PU shapes using the numerical Newton method is more effective. The main provisions of the algorithm required for this and the results of its work, illustrating the advantages of the proposed transition section of the railroad gauge rounding, will be discussed further in more detail using examples of some preferred, but not limiting forms of implementation with reference to the positions of the figures of the drawings, which are schematically presented:

Fig. 1 - plan for rounding the track gauge of the railroad;

Fig. 2 - schemes for calculating the action of gravitational accelerations (G) at the level of the VGR of the curved section of the rounding of the rail track gauge;

Fig 3 - schemes for calculating the action of centrifugal accelerations (C) at the level of the VGR of the curved section of the rounding of the track gauge of the railroad;

Fig. 4 - gravitational components of accelerations and forces of interaction of elements of the PE system;

Fig. 5 - centrifugal components of accelerations and interaction forces of the elements of the PE system;

Fig. 6, Fig 7 - the total vectors of the reaction forces of the rails FL and FR, determined taking into account the direction of the NPU vector a ^ and the force Fc\

Fig. 8 - coordinate method for describing the kinematics of the calculated point of the vehicle M, taking into account the geometric properties of the shape of the launcher;

Fig. 9 - normalized graphs of the function Order (3, 7) and its derivatives;

Fig. 10 - graphs of curvature £(/) of the track axis and curvature k _n (/) of the trajectories of the calculated points; Fig. 1 1 - graphs of outstanding transverse accelerations "(/) acting at different levels R of the calculated crew;

Fig. 12 - graphs of the rates of change of outstanding transverse accelerations a(/) y - da/di ;

5 Fig. 13 - graphs of the reaction forces of the rail and their differences;

Fig. 14 - cross-section of the track PU with a symmetrical removal of elevation D;

Fig. 15 - diagrams of rail excesses over the longitudinal profile of the PU axis with a symmetrical removal of the elevation Z ⁾ ;

Fig. 16 - cross-section of the track PU with asymmetric removal of the elevation D;

10 FIG. 17 - diagrams of excesses of the outer rail and the resulting excesses of the PU axis over the design profile of the inner rail with asymmetric removal of elevation D;

Fig. 18 - calculation scheme of the unified method for calculating the rectangular coordinates of the n-th point of the PU track axis in the local tangent system

15 rounding;

Fig. 19 is a graphical representation of the goal function minimization process of a harmonized form of PU in accordance with the invention;

Fig. 20 - Fig. 24 is an example of the geometric and functional properties of the PE system provided by the harmonized shape of the PU according to the invention;

20 Fig, 25 - an example of the dependence of the optimal lengths L of harmonized forms of PU on the NCL u _max , the calculated speed V and elevations D, as well as the dependence of the minimum lengths L of clothoid and recommended [4] half-sine forms of PU on a similar speed K at D = 150 mm and allowable speed of lifting the wheel along the elevation of the outer rail R = ₀ km/h.

25 FIG. 26 - an example of the velocity-invariant dependence of the maximum values Y MAX of the harmonized forms of the launcher on the NPL o and elevations D

Fig. 27 - an example of a velocity-invariant dependence of the shifts p of the circular sections of the axes of curvature of the harmonized forms of the launcher from the FCL amax and _the elevations D

IN The track plan of the rail track consists of an alternating sequence of straight sections 1 and roundings inscribed in the angles of their rotation. Each rounding (schematically shown in Fig. 1) consists of two transition sections (PU) 2 and located between them a circular section 3 of the rail track of a given curvature K = J/R. With a known track width S, the radius of its axis R is consistent with the calculated values: the speed of the vehicles V, the elevation of the outer rail above the inner rail D, and the value of the NPU a _max operating at the level of the VGR. Axis PU 2 is marked with the number 4.

On FIG. 2 and FIG. Figure 3 shows the schemes for calculating the action of gravitational accelerations (G) and centrifugal accelerations (C) acting on the crew at the level of the VGR of the curved section of the railroad gauge curvature. These schemes correspond to the traditionally used formulas that evaluate the action of the vectors of gravitational G = 9.81 m/s ² (Fig. 2) and centrifugal acceleration C = kv ² m/s ² (Fig. 3) on sections of track rounding with constant or variable curvature without taking into account the elevation of the CM of the crew or the vestibular apparatus of the passenger above the level of the VGR. On FIG. 3 are denoted by reference 5, also referred to as "left" outer rail, and reference 6, also referred to as "right" inner rail.

On FIG. Figure 4 schematically shows the acceleration vectors G _L and G _lt , acting along the normal to the axis of the wheelset of the vehicle 7, the values of which depend on the acceleration of the force of gravity g = 9.81 m/s ² , the angle a of the transverse slope of the track / and the ratio of the value of the parameter And to S , as well as from vertical accelerations due to the speed of movement V , the vertical curvature of the axis k _v , as well as the curvature k, and k ₁₍ diagrams of the removal of the elevation D along the left and right track rails (gravitational components).

On FIG. 5 schematically shows a graphical representation of the vectors acting along the normal to the axis of the wheel pair of accelerations C _: and C _d , the values of which depend on the curvature of the trajectory of the reference point of the vehicle 7 and the speed V, as well as on the angle a of the transverse slope of the track / and the ratio of the value of the parameter H to S (centrifugal components).

Fig. 6, FIG. 7 schematically shows the total reaction force vectors Fi of the left 5 (outer) and the reaction forces FR of the right b (inner) rails, determined taking into account the direction of the vector NPU a _max , as well as the centripetal or centrifugal direction of the transverse reaction force vector Fc of the left (outer ) or right (inner) rails. On FIG. Figure 8 shows the calculation scheme for taking into account the geometric properties of the PU track shape, as well as the elevation of the H point M above the level of the VGR in the coordinate method for describing its kinematics.

On FIG. 9 - Fig. Figure 13 schematically shows graphs of normalized geometric properties of the function Order (3, 7) [3] closest to the declared form of the PU, as well as its inherent amplitudes of oscillations of the integrative quality indicators of the functioning of the PE system. which are represented by graphs: the curvature of the axis of its track and the trajectories of the calculated points at different levels of the vehicle (Fig. 10), NPU a (1) (Fig.

рельсов и их разности (Фиг. 13). Все показатели, положенные в основу этих графиков, рассчитаны по зависимостям МДКМ [6] при V = 400 км/ч, /?=8000 м, D= 150 мм, S = 1520 мм и L = 420 м на расчётном уровне #=2200 мм. 1 !) and the rate of their change da/di (Fig. 12) acting at the same levels of the crew, as well as the reaction forces of the left FL AND the right

rails and their differences (Fig. 13). All indicators underlying these graphs are calculated from the dependences of MDKM [6] at V = 400 km/h, /? = 8000 m, D = 150 mm, S = 1520 mm and L = 420 m at the calculated level #=2200 mm.

On FIG. Fig. 14 schematically shows the cross section of the track of the launcher and the corresponding half-sine patterns of diagrams of excesses of the rail heads above the line of the longitudinal profile of the axis of the launcher when they are symmetrically retracted by ±D/2 (see Fig. 15).

On FIG. 16 schematically shows the cross-section of the track of the launcher and the corresponding half-sine pattern of the diagram of the excess of the head of the outer (left) rail above the line of the longitudinal top of the head of the inner (right) rail with its asymmetric retraction by the value D, as well as the pattern of the diagram of additional excesses of the axis of the track over its design position (see position 8) due to this retraction method (see Fig. 17).

On FIG. 18 shows the calculation scheme of the unified method for calculating the local rectangular coordinates of the l-th point of the axis of the PU track of any shape with a known function of the angle of the tangent to it b (d) . In the drawing, the positions indicate the axis 9 of the straight section of the gauge, the axis 4 of the transition section of the rounding of the gauge and the axis 10 of the circular section of the rounding of the gauge of radius R.

On FIG. 19 shows a graphical and analytical representation of the goal function of harmonizing the form of PU, the geometric properties of which are described by regularities (formulas) (I) - (12). The dotted lines show the nature of the regularities of the diagrams of the values _άy ( ί of the functional (14) and their oscillations, the amplitude dispersion of which successively decreases in the course of harmonization. On FIG. 20 - Fig. 24 graphically shows an example of the geometric and functional properties of the LE system provided by the harmonized form of the PU according to the invention (in one of the possible, but not limiting forms of implementation) at the optimal values of L ~ 420 m, Z = 0.64, U ^~ -0.38 and given values parameters V = 400 km/h, R = 8000 m, D ^~ 150 mm, S = 1520 mm and H = 2200 mm.

, варьируемой в диапазоне 0. 1 < а ^ < 1.0 м/с². On FIG. Fig. 25 shows the dependences of the optimal lengths L of the rounding of the track S = 1520 mm on the NCL y _ax , obtained as a result of their harmonization at fixed values of H-2200 mm for 240 options for combining a sample of values of predetermined parameters V, R and D. This sample included 4 discrete values speed, varied with a step of 100 km/h in the range of 100 < V < 400 km/h, for each of which 6 discrete values of the elevation of the outer rail over the inner one were set, varied with a step of 25 mm in the range of 25 < D < 150 mm. For each of the 24 combinations of different values of the pairs of parameters V and D formed in this way, 10 values of the radii R were calculated, providing the corresponding number of discrete values of FCL, varied with a step of 0.1 m/s ² in the range 0.1 < _amax < 1.0 m/s ² . When displaying points with coordinates a^ , L, the scale of the abscissa axis and the range of optimal lengths L displayed on it for each of the 3 speed values V = 300 km/h, V = 200 km/h and V = 100 km/h were consistent with the abscissas of the optimal lengths L calculated at an estimated speed V = 400 km/h. As a result, the position of all 180 points with the same ordinates _amax and different abscissas t, calculated at design speeds V - 300 km/h, V = 200 km/h and V = 100 km/h, coincided with the position of 60 points with the same ordinates a ^ and abscissas L, calculated at an estimated speed V - 400 km / h. This made it possible to present the results of the harmonization of the forms of SP, obtained over the entire sample volume, with only 6 lines of one graph of hypothetically power-law dependences of the optimal lengths L of SP on a subset of options for combining the values of the parameters V, R, D, I and S, in each of which the radius R coordinated with the parameter and V, D and S according to the calculated value of the FCL of the rounding

, varying in the range 0. 1 < a ^ < 1.0 m/s ² .

[4, 8, 9, 10] не устранит принципиальные отличия в представленных на Фиг. 25 зависимостях. Поэтому положения практической реализации данного изобретения предусматривают устройство гармонизированных форм ПУ исключительно только с соответствующими их параметрам оптимальными длинами L. Similarly, in FIG. 25 shows the vertical line of the graph, which traditionally limits the minimum lengths L of clothoid forms of PU according to the maximum allowable wheel lifting speed R = c _o km / h. Also in FIG. 25 shows lines of graphs that limit the minimum lengths of some types of half-sine forms of PU with the same values of parameters V, R and D = 150 mm. These lengths are determined taking into account the coefficients recommended in [4]. With these parameters, the optimal lengths of the harmonized PU forms coincide with the minimum lengths of the clothoid and half-sine PU forms only at one of the NPU values a ^ , which in this case varies in the range 0.1 < a _mto < 0.3 m/s ² . For other calculated values of the FSL, these lengths differ significantly. It is quite obvious that the variation in acceptable wheel lift speed allowed in different countries in the range

[4, 8, 9, 10] will not eliminate the fundamental differences in the presented in Fig. 25 addictions. Therefore, the provisions of the practical implementation of this invention provide for the device of harmonized forms of PU only with the optimal lengths L corresponding to their parameters.

On FIG. Figures 26 - 27 show examples of the dependences of the maximum values (Fig. 26) and shifts p of the circular sections of the rounding axes (Fig. 27) on the calculated values of the FCL a _max and elevations D corresponding to the optimal values of the parameters L, Z, and V of the same 240 harmonized forms PU according to the invention (in one of the possible, but not limiting forms of implementation), taken into account when plotting FIG. 25. In contrast to those shown in FIG. 25 graphs of dependencies of optimal lengths L, dependencies of the maximum values y _MAC (Fig. 26) and shifts p of the circular sections of the rounding axes

(Fig. 27), in this form of representation are invariant to the design speed V.

The geometry of the inventive PU of the rounding of the track gauge of the railroad is determined, and the inventive PU functions as follows.

Each rail track rounding consists of a circular 3 and two transition sections (PU) 2 connecting it with the corresponding straight sections 1. The axis 4 of the circular track section is described by an arc of a given curvature K = 1/R. With a known track width S, its radius R is assigned depending on the calculated values: the speed of the vehicles V, the elevation D of the outer rail 5 over the inner 6 and the value of the NPU a^ acting at the functionally significant level of the calculated crew

максимальное значение НПУ о_тах на круговом участке колеи вычисляют с достаточной для практических целей точностью по формуле 2 D H. As shown in FIG. 8 by the calculation scheme of the kinematic model [6], the radius of curvature of the horizontal projection of the trajectory of the point A/, elevated above the level of the WGR by the value H, in a circular section of the trajectory with a constant radius of curvature of the axis gauge R differs from it by a very small, in comparison with it, value H - . That's why

the maximum value of FCL o _max on the circular section of the track is calculated with sufficient accuracy for practical purposes according to the formula 2 D

'max ^{K' V} - g ^' (17)

With a fixed value of the design speed V, the required balance of constant values < a _add in this section of curvature is ensured by selecting the necessary combination of the values of the parameters R and D that are acceptable according to the design conditions.

In contrast, the shape of the inventive PU of the rounding of the rail track gauge, preceding the circular section, is determined taking into account two geometric and one functional requirements:

- observance of a strictly monotonous and smooth change in the transverse slope of the track /(/) and the curvature L(/) of its axis throughout the area of change in the values of these parameters from zero values in the straight section of the track to maximum values in the circular section of the rounding;

- conformity of the geometrical properties of the PU form to the theory of beam bending on an elastic foundation;

- harmonization of the length and regularities of the bending properties of the PU gauge rails in the horizontal and vertical projection planes in order to achieve the highest quality level of the TS system functioning.

Compliance with geometric requirements is ensured by the claimed properties of the functions of changing the angle of the arc of the track axis, its curvature and its transverse slope. The bending of the rail described by them provides the G^-th order of geometric smoothness in the vertical projection plane and G ⁶ - th - in the horizontal projection plane.

Compliance with the functional requirement is ensured due to the variability of the claimed properties of non-identical functions of changing the curvature of the track axis and its transverse slope. Variation of the launcher length and properties of its shape affects the kinematics of the calculated point at the functionally significant level of the crew, elevated above the level of the VGR by the value H> 0. The integrative quality indicators of this process are included in the formalized goal of the procedure for matching the values of the controlled and predetermined parameters of the PE system, providing the greatest efficiency of their interaction. This goal is achieved with the optimal values of the controlled parameters LZ and I ⁷ calculated for the given values of the parameters V, R, D, H and S in the following sequence.

1. Taking into account the calculated according to the formula (17) NPU o _max according to the formulas (15) and (16), the corresponding relative shares <5 _l and <5 of the length of the plot of the functional diagram (14) are calculated, within which it is necessary to estimate and, in accordance with the goal function (13), to minimize the dispersion of the amplitudes of the oscillations W of its values.

2. Set the initial values of the desired parameters L = 20 m, Z - 0 and U = 0.

3. The optimal values of these parameters are approached in the course of 5 cycles, within each of which, during 20 iterations, the Newton method sequentially approximates first the value of L at fixed current values of Z and U, then the value of Z at fixed current values of L and U, and, finally, the value of U at fixed current values of L and Z. In this case:

- the new value of each of the parameters, set at the end of each 20th iteration cycle of its approximation, which will then be taken into account in the process of approximating the values of subsequent parameters, is selected from the list of their correct values, providing, according to condition (13), the smallest dispersion W

при М > 1000 ; - the values of the functional (14) dy/jdt and its partial derivatives necessary for calculation should be calculated with a step

at M >1000;

- the results are incorrect:

- with a negative or with a length L exceeding the allowable for a given rounding

- with values of the Z parameter that go beyond the allowable values -88 < Z < 33 during the calculation:

Z_n, _/ и ϋ _Ί вычисляют по формулам

- соблюдение этих рекомендаций позволяет минимизировать функцию цели (13) при W < 1.0Е-03 или с гораздо лучшим результатом. - with the values of the parameter U, which go beyond the limits of its admissible values during the calculation -45 < U <55; the curvature k _H of the trajectory of the calculated point of the vehicle at the level R, as well as its derivatives necessary for calculating the current values of the functional (14), should be calculated taking into account the deterministic dependences of the MDCM described in [6]; each of those claiming a new approximate value of the parameter

Z _n , _/ and ϋ _Ί are calculated by the formulas

- compliance with these recommendations allows minimizing the goal function (13) with W < 1.0E-03 or with a much better result.

4. The optimal length L of the launcher calculated in this way is rounded up to the nearest larger integer multiple of 1 m. Rougher rounding, for example, a multiple of 5, 10 or up to 20 or more meters is highly undesirable. Especially in a smaller direction, because. leads to a significant increase in the dispersion of the amplitudes of the oscillations of the function

₍ Iy jdt . Ultimately, this can lead to vibration, shocks or rocking of the crew body during the operation of the gas turbine at the design values of the parameters V. R , D N and S.

5. The values of the parameters Z and U can be rounded off with an accuracy of ±0.01. The values of the parameters L, Z and U that meet these requirements are harmonized with the values of other predetermined parameters for the rounding of the track and the calculated vehicle V, 1?, O, I and S. They will be relevant and can be repeatedly used in the device of the launcher of the claimed form in other roundings of the rail track with the same or with a different angle of rotation ±q, subject to the condition \q\ > Lj R and the constancy of the calculated values of the predetermined parameters V, R, D, H and S. In the case changes in at least one of them calculations according to p.p. 1-5 of the procedure described above for harmonizing the values of the parameters !, Z and U should be repeated. With the actual values of the parameters L, ZHU, the relative rectangular coordinates of the axis of the claimed GTP x[i] and [u] should be calculated using formulas (1) and (2) with N = L* 10 + 1. Subject to this condition, the difference between the arc length D ,= 0.1 m and the length of the chord tightening it from the point n-1 to the point and will be very insignificant. This will provide sufficient for practical purposes the detail and accuracy of the calculation of both the absolute coordinates of the rounding axis in the system installed on the object, and its other geometric characteristics. At the same time, the values of the tangents, the bisector, the center of the circular curve and its shift, necessary for the device of the rounding of the track with the PU of the claimed shape, are calculated according to the standard method and according to the well-known formulas applicable to the rounding with any other form of the PU at known local coordinates X[JV - 1 ] and U [ L ^; - 1 ] points at the end of the track axis of each of the PU and the angle b of the entire arc of its axis.

With the traditional technology of point-by-point breakdown of the PU axis of the claimed shape on the ground with a step greater than D, , you can use the coordinates of only those points whose multiplicity of numbers meets these requirements. When arranging a launcher gauge of the claimed shape using automated control systems for straightening and tamping machines, as well as when forming their 3D models in modern information technologies, it is advisable to determine the location of the launcher gauge axis with a fairly detailed, decimeter step. To do this, it suffices to take into account the coordinates of the entire number N of points calculated by formulas (1) and (2).

The design and functional advantages of track roundings with PU of the claimed shape are confirmed by the results of harmonization of 240 options for combining the values of predetermined parameters of track roundings with a width S = 1520 mm, formed at 4 discrete values of speed V, varied with a step of 100 km/h in the range 100 < V < 400 km/h, for each of which 6 discrete values of the elevation of the outer rail above the inner rail were set, varying with a step of 25 mm in the range 25 < D < 150 mm. For each of the 24 combinations of different values of the pairs of parameters V and D, 10 values of the radii R were calculated, providing the corresponding number of discrete values of the FCL _max , varied with a step of 0.1 m/s ² in the range 0.1 < o _max < 1.0 m/s ² .

от абсолютного, но практически недостижимого минимума

были существенно меньше, чем у известных форм ПУ предшествующего уровня техники с аналогичными значениями параметров V, R, D и L. Наряду со значениями параметра ^_тах результаты гармонизации форм ПУ дополнялись значениями так называемой сдвижки круговой кривой р. по значению которой в комплексе со значениями R и L можно судить о конструктивных преимуществах заявляемой формы ПУ, имеющих важное для трассирования рельсовых дорог значение. Часть результатов, полученных при гармонизации форм ПУ с расчётным возвышением D = 150 мм для расчётных скоростей V - 400 км/ч и V = 100 км/ч, приведена в Таблице 1 . Они указывают на наличие устойчивой их зависимости от расчётных значений НПУ ^а _та* · Более наглядно характер и особенности этой зависимости иллюстрируют графики, представленные на Фиг. 25, Фиг. 26 и Фиг. 27. The optimal values of L, Z and U of all 240 combinations of V, R and D values with a fixed elevation of the functionally significant level of the design crew H= 2200 mm were calculated at I .0E-07 <W< 4.0E-04. Such a degree of minimization of the goal function (13) ensured a high level of quality of the functioning of the PE system, confirmed by G'-smooth quasi-linear NPU plots i(/) (see Fig. 22) and G°-smooth trapezoidal plots of its rate of change y - da/dt (see Fig. 23). In this case, the deviations of the maximum values of this speed

from an absolute but practically unattainable minimum

were significantly less than those of the known forms of PU of the prior art with similar values of the parameters V, R, D, and L. Along with the values of the parameter ^ _max , the results of harmonization of the PU forms were supplemented by the values of the so-called shift of the circular curve p. by the value of which, in combination with the values of R and L, one can judge the design advantages of the proposed form of PU, which are important for tracing railroads. Some of the results obtained by harmonizing the forms of launchers with a design elevation D = 150 mm for design speeds V - 400 km/h and V = 100 km/h are shown in Table 1. They indicate the presence of their stable dependence on the calculated values of FCL ^a _{ta *} · The nature and features of this dependence are more clearly illustrated by the graphs shown in Fig. 25, Fig. 26 and FIG. 27.

Из анализа графиков, представленных на Фиг. 25, следует, что степенные зависимости оптимальных длин L_opt гармонизированных ПУ заявляемой формы существенно отличаются от вертикальной линии графика зависимости минимальных длин Л_т,„ клотоидных форм ПУ, традиционно нормируемых по так называемой допустимой скорости подъёма наружного колеса по возвышению Я = V · DjL . В данном примере она ограничивает минимальные длины Lmm клотоидных форм ПУ закруглений с расчётным возвышением D = 1500 мм при рекомендованной в [8, 9, 10] допустимой скорости подъёма наружного колеса Я = 1/10 км/ч { ~ 28 мм/с). В случае применения рекомендованных в [4] half-sine форм ПУ их минимальные длины будут ещё больше отличаться от оптимальных длин гармонизованных ПУ заявляемой формы. Исходя из явной тенденции к увеличению коэффициентов пропорциональности, коррелирующих с порядком геометрической гладкости соответствующих им типов half-sine форм ПУ, минимальные длины более совершенных и более гладких half-sine форм ПУ могут быть ещё больше. Это указывает на явные проблемы эмпирических методов нормирования длин ПУ по любому из допустимых значений параметра Я или отношения DjL , не опосредованная причинно-следственная связь которых с интегративными показателями качества движения не обоснована. Table 1 . An example of the optimal values of the parameters L, Z and U of the claimed forms of PU with L = 150 mm, harmonized for the calculated values of the PU, varying in the range 0.1 < d _max < 1.0 m/s ² at V = 400 km/h (see numerator) and V = 100 km/h (see denominator) for I = 2200 mm and S = 1520 mm

From the analysis of the graphs presented in Fig. 25, it follows that the power-law dependences of the optimal lengths L _opt of the harmonized PU of the claimed form differ significantly from the vertical line of the graph of the minimum lengths L _t , „ of the clothoid forms of the PU, traditionally normalized by the so-called permissible speed of lifting the outer wheel along the elevation R = V DjL . In this example, it limits the minimum lengths Lmm of clothoid forms of PU roundings with a calculated elevation D = 1500 mm at the recommended in [8, 9, 10] admissible lifting speed of the outer wheel R = 1/10 km/h { ~ 28 mm/s). In the case of using the half-sine forms of PU recommended in [4], their minimum lengths will differ even more from the optimal lengths of the harmonized PU of the claimed form. Proceeding from a clear tendency towards an increase in proportionality coefficients that correlate with the order of geometric smoothness of the corresponding types of PU half-sine forms, the minimum lengths of more perfect and smoother PU half-sine forms can be even greater. This points to the obvious problems of empirical methods for normalizing the lengths of the PU for any of the allowable values of the parameter R or the ratio DjL , the non-mediated causal relationship of which with the integrative indicators of the quality of movement is not justified.

проектный уровень комфорта движения на гармонизированном ПУ заявляемой формы будет тем выше, чем больше будет расчётное возвышение D. Как следует из графика функции y_itac при D = 150 мм, её значения во всём диапазоне варьирования НПУ 0· ' - О м/с² не превышают даже нижней границы диапазона традиционно рекомендуемых норм 0.4 <

< 0.6 м/с³. From the analysis of the graphs presented in Fig. 26 it follows that the harmonized PU of the claimed form is characterized by polynomial dependences of the maximum rate of change _Yhac on the calculated values of the NPU and _max , which, in contrast to the optimal values of the lengths, are invariant with respect to the calculated speed V. At the same time, corresponding to the indicator

the design level of driving comfort on a harmonized launcher ^of the claimed shape will be the higher, the greater the design _elevation D. exceed even the lower limit of the range of traditionally recommended norms 0.4 <

< 0.6 m/s ³ .

From the analysis of the graphs presented in Fig. 27 it follows that the shifts p of circular rounding curves with harmonized PU of the claimed form also have polynomial dependences invariant with respect to the design speed V on the calculated values of the CL o _mas . At the same time, the values of shifts p of circular rounding curves with harmonized PUs of the claimed shape are several times less than the shifts p of circular curves of very common and problematic roundings with clothoid forms of PUs. How calculations show that the multiple difference of these shifts contributes to the conversion of roundings with clothoid forms of PU to roundings with harmonized PUs of the claimed shape in order to increase the speed and ease of movement with the lowest straightening parameters of the existing track.

Taking into account the above regularities can contribute to the adoption of optimal decisions when constructing new or reconstructing existing railroad curves. Due to the large number of possible combinations of predetermined values of the parameters V, R, D, H and S, varying over a fairly wide range, the traditional presentation of pre-calculated optimal values of Z, Z and (/ harmonized forms of PP in the form of tables or graphs does not seem appropriate For modern automated technologies for the design, construction and operation of railroads, a software implementation of algorithms for harmonizing the forms of PU and calculating the coordinates necessary for their device in accordance with the provisions of this invention is more acceptable.

In contrast to the solutions of the prior art, the objective laws of physics and mathematically and substantiated methods of harmonization, which are the basis of this invention, provide the search for the optimal values of all the necessary parameters for the design of transition sections of roundings, the geometric properties of the shape of which are described by regularities (1) - (12). They directly and directly, and not indirectly and indirectly, ensure the integrative quality of the Path + Crew system functioning. At the same time, the level of this quality depends on the consistency and commensurability of its parameters such as the elevation of the crew reference point R, its speed V, the radius of curvature R, the elevation of the outer rail D and the method of its retraction. Therefore, the provisions and distinctive features of this invention should also be taken into account at the stage of making decisions about the main values of the parameters of the curves of the designed rail routes.

Sources of information.

1. Bjorn Kufver, VT1 rapport 420A, “Mathematical description of railway alignments and some preliminary comparative studies”, Swedish National Road and Transport Research Institute, 1997. Digitala Vetenskapliga Arkivet (digital scientific archive). [Electronic resource] - July 17, 2020. - Access mode: hup: vv _\ v and diva-po rial. >gcd mas 1 rcco rd . I t pi dd

2. Patent F.P. Ks 1523597B1. publ. July 16, 2008

3. Clauder, Louis. T., Jr. Railroad curve transition spiral design method based on control of vehicle banking motion. Available from: https://patentscope.wipo.int/search/en/detail.jsf?docId=W02001098938&recNum=1 &maxRec= &ofFice=&prevFiIter=&sortOption=&queryString=&tab=PCTDescription

4, EN 13803-1;2010: Railway applications -Track-Track alignment design parameters - Track gauges 1435 m and wider - Part 1 :Plain line [Required by Directive 2008/57/EC] 5. M. Ueno et al.: Motion Sickness Caused by High Curve Speed Railway Vehicles. Jpn J Ind Health

1986; 28:266-274.

6. Velichko, G. 2020. Quality analysis and evaluation technique of railway track + vehicle system performance at railway transition sections with various shape curves, In Transport Means 2020: Proceedings of the 24th International Scientific Conference, Part II: 573-578. Available from: inifis _{: :} :ra(is _] wrlinc;in .k!u.cdi _: r_\' _L p-.:qn!cnj uplii,:i(Js i rev 3b 7 20 I ST >2 f rnnspori- mcans-

\ 4-11-daiK.pdf

7. Velichko, G. 2020. Shape Harmonization of the Railway Track Transition Section & the

Kinematics of Vehicle Body Design Point, In Transport Means 2020: Proceedings of the 24th International Scientific Conference, Part H: 910-915. Available from:

8. Shakhunyants G. M. Railway way / G. M. Shakhunyants. - Moscow: Transport, 1987. - 479 p.

9. Theoretical! Foundations for the implementation of a high speed train in Ukrapp: monograph / M.B. Kurgan, D.M. Mound; Dnshropetr. nat. un-t hall1zn. transp. hm. acad. AT,

Lazaryan. - Dntro, 2016, - 283 p.

10. S. V. Shkurnikov et al. Community requirements for the design of the Moscow-Kazan high-speed line "Transport of the Russian Federation" ^ 2 (57) 2015 26-29 p.

Claims

Claim 1. The transition section of the rounding of the rail track, mating on the length L the straight section adjacent to it and the circular part of the rounding with a constant radius R, containing the base and the rail-sleeper grid forming the track, laid on it in accordance with the coordinates of the projection of the points of the axis of the transition section on the horizontal plane with a variable along the length L value of the transverse slope i normal to the axis of the line tangent to the surface of the top of the rail heads, while the shape of the axis of the gauge of the transition section is determined by the location of N equidistant points with coordinates x[u] and y[l], and the transverse the slope /[i] of the track at these points varies along the axis of the transition section in the range 0 < /[u] < D/S, where D is the calculated elevation of the outer rail of the track over the inner one within the circular part of the railroad curvature axis, and S is the distance between the vertical axes of the cross-section of the gauge rail, as it grows uniformly by a constant value D, \u003d L / (N- 1) the distance /[u] to each of its l-th point from /[O] = 0.0 m, at the beginning of the axis of the transition section, and to /[ Vl] = L , at its end, differs in that the relative rectangular coordinates of the points of the projection of the axis gauges x[l] and y [l] are determined by the formulas: x[0] = 0.0; x[n] = x[n - 1] + D, cosf^ (D) + D^ (D)) (1) [0] = 0.0;

where: n is the ordinal number of the point of the axis of the transition section, changing in the range 1 < l < (L ^g -1) , x[l] is the coordinate characterizing the distance from the beginning of the transition section to the point of projection of the l~th point of the axis onto the line, tangent to it at the point ^c [q] and y [O] , y [l] - the coordinate characterizing the displacement towards the center of curvature of the axis of its lth point, measured along the normal from the line tangent to it at the point x[0] and y[°] , A, is a constant value of the increment of the current length / axis of the track of the transitional section, measured along its arc from its beginning to each l-th point, d - the relative share of the current length Z + D,/2 of the axis of the gauge of the transition section, measured from its beginning to the middle of the segment of the axis enclosed between its adjacent points l-1 and and, calculated by the formula: 2/7-1 d = (3) 2(WI) b _H (d is the value of the function of the main angle of the transition section tangent to the track axis, calculated depending on the relative share d of the current length 1 + A _/ /2 up to the touch point according to the formula: / { _, ( / 315 2043 6720 14085 19795 18579 / 1 1 178 3900 600 \ W=^ ⁶ -d -d -d -d -d -dd 6 7 8 9 7G 1 1 1 VVV n \ \ n 2 I 13 14 J

b(d) - the value of the complement function to the main angle of the tangent to the axis of the transition section, calculated depending on the relative share d of the current length 1 + A, / 2 to the point of contact according to the formula: /f/ 340 885 1425 1452 914 / 325 50 <0 = "7^‘ 1-d /1-g -S -d -d -<5 - d 6 7 8 9 \ 10 1 1 I 12 13 14 VVV\

(5) where U - a parameter that determines the amount of additions to the main values of the angle of the tangent to the axis of the track of the transitional section at each of its points with a relative share d of the current length 1 + A _; / 2, and the transverse slope r [i] of the track of the transition section at each n-th point of its axis, changing in the interval 0 < H < (JV -1) , is determined by the formula

where is the relative share of the current track length/axle up to point n, calculated as: P x ^: (7) N - 1 i _h (x) - the value of the function of the main transverse slope of the track of the transitional section at the point and, calculated depending on the relative share of X according to the formula; ,(c) - the value of the addition function to the main cross-slope of the track at point n, calculated depending on the relative share of X according to the formula:

where: Z is a parameter that determines the amount of additions to the main values of the transverse slope of the track at each point p with its relative share c. 2. The transition section according to p. K, characterized in that for a given value of the parameter U, which varies in the range from -45 to +55, the value of the sum of the functions of the main angle (1\ (Il tangent to the axis of the track

- and additions to it DJ - throughout the length L V L at LJ of the transition section is strictly monotonous and continuously changes from 0 to L / 2R, the value of its first derivative with respect to the length /, which determines the regularity of the curvature of the axis of the transition section to dl, is also strictly monotonous and continuously changes from -U + SH) 0 to 1/R, and for the sum of all subsequent 2nd, 3rd, 4th and 5th derivatives of these functions over the same length I, the continuity of their values is ensured, as well as their equality to zero at both ends of the interval 0 <1 < L , while the curvature function of the track axis k ( c) , where x=ljL , in each current coordinate of the length I PU is defined as x) = ^k Ax) + {x) (10) where ^( ) = ⁵ 315- (2043- _Z (6720- (l4085- _Z (l9795- (l8579- {lll78- (3900-600 _Z )))))))j, (И) U - a parameter that determines the maximum value of the addition to the main value of the curvature of the axis of the track of the transitional section. 3. The transition section according to claim 1, characterized in that for a given value of the parameter Z, which varies in the range from -88 to +33, the value of the sum of the functions of the main cross-slope of the track and additions to it throughout the length L

of the transitional section strictly monotonously and continuously change from 0 to D/S, and the values of its 1st, 2nd and 3rd derivatives with respect to the length I change continuously if they are equal to zero at both ends of the interval 0 < / < L .