Assessment of the impact on the railway track of a special purpose passenger car model 61-934

In this work, theoretical studies have been carried out in order to assess the strength of structural elements of the track superstructure from the impact of a special-purpose passenger carriage. The assessment of the impact of the wagon on the railway track was carried out according to the stresses in the edges of the rail base, stresses in the main area of the subgrade and the stability of the track against lateral shear. The calculations showed that the strength and stability of the structural elements of the track superstructure as a result of the impact on it of a special-purpose passenger carriage model 61-934 meets the regulatory requirements.


Introduction
The main priority tasks for the further development of railway transport in the Republic of Uzbekistan, the implementation of which will create the necessary prerequisites for the development of the constantly growing volumes of freight and passenger traffic in the absence of reserves for increasing the carrying and path capacity of cargo-intensive sections of the railway network, are the introduction of modern rolling stock [1][2][3][4].
The possibility of introducing new rolling stock into operation is determined by assessing the stress-strain state of the structural elements of the permanent way and the subgrade, which are indicators of the impact of rolling stock on the railway track [5][6][7][8][9].

Methods
This calculation was carried out to assess the strength of the structural elements of the track superstructure under the impact on it of a new special-purpose passenger carriage model 61-934, manufactured at JSC "Tashkent plant for the construction and repair of passenger cars" [10][11][12][13]. Wherein, the fulfillment of the following regulatory requirements was checked [14,15]: to the edges of the rail foot; to the strains in the main site of the roadbed; -the ratio of the maximum horizontal load acting on the sleeper to the average vertical load on the sleeper.
The calculation was carried out following [14,16]. Following the requirements, a track with the following design was adopted as the design railway track: rail type -R65; reduced rail wear -6 mm; the number of sleepers per 1 km of track -1840; type of sleepers -reinforced concrete; a kind of ballast -crushed stone.
The initial data for the calculation are given in Table 1. Calculated track characteristics with typical rail spacers are shown in Table 2. The assessment of the impact of the car on the track was carried out in accordance with [15] according to the following parameters: stresses in the edges of the rail foot σк; ballast stresses at depth h (σh); the stability of the path against lateral shear, determined by the value of the coefficient α.
In this case, the fulfillment of the following conditions was checked: Calculation of stresses was carried out according to [14], calculation of track stabilityaccording to [16].
The elasticity modulus of rail steel E in the calculations was taken to be 2,1×10 5 MPa.
The calculation was carried out for an equipped carriage taking into account the effective load. Simultaneously, its effect on the track from the side of the most loaded bogie was considered.
The calculation of the edge stresses was carried out for two calculation cases: for a speed of 160 km / h (movement in a straight line, f = 1,35); for a speed of 80 km / h (movement in a curve, f = 1,65).
Here, a speed of 80 km / h corresponds to movement in a curve with a radius of 300 m with a canting of the outer rail of 150 mm and an unbalanced acceleration of 0.7 m / s 2 .
The values of the coefficients f are taken according to [14]; and besides, as in the specified source, the movement with speeds up to 140 km / h is considered, for the case of direct movement, the coefficient is increased by the value of the ratio (160/140).

Results and Discussion
The stresses in the edges of the rail foot were determined by the formula where f is the coefficient of transition from axial stresses to edge stresses; σ 0 is maximum stresses in the rail foot from its bending, determined by the formula where k is the coefficient of the relative stiffness of the rail foot and the rail; W is the resisting moment of the rail relative to its foot; Р I equ is maximum equivalent load for calculating the stresses in rails, determined by the formula Ekv din where  i are the ordinates of the line of influence of the rail bending moments in the track sections located under wheel loads from the vehicle axles adjacent to the design axis.
The value of the ordinate  i is determined by the formula where l i is the distance between the center of the axle of the design wheel and the wheel i is the axle, adjacent to the design one, is taken following [14]; e is base of the natural logarithms; max дин Р is dynamic maximum load from the wheel to the rail, determined by the where Р AV is the average value of the vertical load of the wheel on the rail, determined by the formula СР Р СТ СР P P P   (6) where Р ST is the static load of the wheel on the rail, кг; СР Р P is the average value of the dynamic load of the wheel on the rail from the vertical vibrations of the sprung parts of the car, kg, determined by the formula max 0.75 where max Р P is the maximum dynamic load of the wheel on the rail from vertical vibrations of the sprung parts of the car, determined by the formula where C D is the coefficient of vertical dynamics, determined by the formula: where V is travel speed, km / h; f sт is the static deflection of the spring suspension; q is the weight of the unsprung parts referred to the wheel; λ is normalizing factor that determines the maximum dynamic load occurrence probability, following [14] λ = 2,5; S is the standard deviation of the dynamic load from the wheel on the rail, determined by the formula where S Р is the standard deviation of the dynamic load from vertical vibrations of the sprung parts of the car, determined by the formula max 0.08 where max Р P is maximum dynamic load of the wheel on the rail from vertical vibrations of the sprung parts of the car; S ИП is the standard deviation of the dynamic load from the vertical vibrations of the unsprung parts of the car, determined by the formula where the values of L, l sh , U, k, q see Table 2; V -see Table 1; S NNW is the standard deviation of the dynamic load from the inertia forces of the unsprung parts of the car when the wheel moves with a smooth continuous unevenness on the rolling surface, determined by the formula 2 0.052 0 2 2 3.26 where the values of α 0 , U, k, q, d see Table 2; Vsee Table 1; S INI is the standard deviation of the dynamic load from the inertial forces of the unsprung parts of the car, arising from the presence of isolated irregularities on the rolling surface, determined by the formula where the values of α 0 , U, k see Table 2; е is coefficient taking into account the depth of a smooth isolated unevenness (following [14], it is taken equal to 0.067).
The results of calculating the stresses in the edges of the rail foot are shown in Table 3.
Based on the data given in Table 3, the maximum stresses in the rail feet are 62.3 MPa, which is less than the permissible stresses of 240 MPa.
The calculating formula for determining the normal stresses  h in the ballast (including the top of the subgrade) at a depth h from the foot of the sleeper along the design vertical has the form (15) where σ h1 and σ h3 are stresses on the subgrade under the design sleeper (Sleeper № 2) under the influence of sleepers № 1 and № 3, adjacent to the design one, determined by the formula 0.25 16) where А is design coefficient, determined according [14], where its dependence on h, b and l sh is shown in tabular form (for the accepted design of the path A = 0.255);  (19) where η is the ordinate of the influence of neighboring wheels, determined by [14], where the dependence of η on the product of kx is given in a tabular form. In this case, x = L Тwhen calculated by the formula (18); x = L Тl S -for sleeper №1 when calculated by the formula (19); x = L Т + l S -for sleeper №3 when calculated by the formula (19); η sh is the ordinate of the influence of neighboring sleepers, determined from the dependence of η on the product of kx, given in [14] for x = l sh ; σ h2 are stresses on the subgrade under the impact of sleepers № 2 (design sleepers), determined by the formula where С 1 and С 2 are calculated coefficients, following [14] for the adopted track design  The calculation results are shown in Table 4. As follows from the data given in Table 4, the maximum stresses on the top of the subgrade are 0.047 MPa, which is less than the permissible stress of 0.08 MPa.
The coefficient α (the ratio of the maximum horizontal load to the average vertical load) is determined by the formula where Y is the shear force acting from the wheel on the rail. The Y / P СР ratio is determined by the expression where С 0 is the force of the initial resistance to the pumping of the sleepers in ballast, which is determined by the formula The value of Р СР is given in Table 3 for the case of the movement in a straight line. The calculation results are shown in Table 5. As follows from the data given in Table 5, the value of the coefficient α (the ratio of the maximum horizontal load to the average vertical load) is 1.24, which is less than the maximum allowable value for crushed stone ballast equal to 1.4.

Conclusions
The calculations showed that the strength and stability of the structural elements of the track superstructure as a result of the impact on it of a special-purpose passenger carriage model 61-934 meets the regulatory requirements. In this case, the following results were obtained: the stresses in the edges of the rail foot are 62.9 MPa (permissible stresses are 240 MPa); the stresses on the top of the subgrade are 0.047 MPa (permissible stresses are 0.08 MPa; the ratio of the maximum horizontal load acting on the sleeper to the average vertical load on it is 1.24 (the maximum allowable value is 1.4).
Also, to increase the accuracy of measurements of the force effect of rolling stock on a railway track, it is proposed to apply methods of piecewise continuous recording of vertical and lateral forces from the interaction of a wheel with a rail by measuring stresses in two sections of the rail in tests on the impact on the track [17][18][19][20].