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UDC 629.4.017:625.1.032.84
A. O. SHVETS1*, K. I. ZHELIEZNOV2*, A. S. AKULOV3*, O. M. ZABOLOTNYI4*, YE. V. CHABANIUK5*
1 EDSD MBCSS, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (050) 214 14 19, e-mail angela_shvets@ua.fm, ORCID 0000-0002-8469-3902
2*EDSD MBCSS, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (095) 545 38 87, e-mail constantinz@i.ua, (ORCID 0000-0003-3648-1769
3*EDSD MBCSS, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (067) 178 16 90, e-mail asakulov@gmail.com, ORCID 0000-0002-6123-5431
4*EDSD MBCSS, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (067) 282 13 41, e-mail zabolotnyi@i.ua, ORCID 0000-0003-1651-7082
5*EDSD MBCSS, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (066) 633 55 95, e-mail 457m@ukr.net, ORCID 0000-0001-5695-5955
DETERMINATION OF THE ISSUE CONCERNING
THE LIFT RESISTANCE FACTOR OF LIGHTWEIGHT CAR
Purpose. The analytical study of the connection between the longitudinal force, acting on the light-weight car, lateral and vertical forces of interaction in the contact zone «wheel - rail» with the lift resistance factor value is to provide a simple relationships between them. Methodology. Research was conducted by the method of mathematical modeling of loading the freight car when driving at different speeds on straight and curved sections of a track. Findings. Even in the absence of «lift» accordingly the classical train stability theory, as the hinge-rod system, the presence of the longitudinal compressive forces may become a factor provoking cars derailment. The main reason of wheel climbing on rails is the combination of processes of dynamic interaction between the hunting vehicle and the track with simultaneous action of longitudinal compressive forces, and not the destabilization of train as a hinged-rod system. To assess the impact of the longitudinal forces value on the lift resistance factor there are presented the calculation results for the empty gondola car motion, model No. 12-532, on 250 m radius curve with 150 mm rise and cross starting of car underframe relating to the track axis in 50 mm guiding section. The calculations were made in such a curve excluding the inertial forces from outstanding acceleration and taking into account the unbalanced acceleration with the permissible speed of 65 km/h. Originality. This study provides the technique of determining the lift resistance factor by longitudinal forces, which is somewhat different from the standard one, as well as evaluates impact of rolling stock speed on this factor. Practical value. The authors clarify the current method of determining the lift resistance factor by longitudinal forces and assess the impact of rolling stock speed on the value of this factor. From these studies one can conclude that because of cars hunting their lift is possible even when the train as hinge-rod system does not lose stability. The developed proposals allow reducing the number of car derailment by taking into account important parameters and characteristics during the process of calculation and design that increase their stability in the rail track especially in case of increased speed of freight trains.
Keywords: traffic safety; rules for the calculation; car lift resistance factor; movement speed; lift resistance factor
Introduction
Traffic safety is a basic condition for normal operation of the railways. Problems of traffic safety of trains and shunting operations are the main ones for the rail transport since it is hard to completely avoid crashes and accidents occurring due to car derailment [9].
The main causes of accidents in locomotive economy of railways of Ukraine are a combination of car malfunctions and track condition, as well as foot-plate staff s actions leading to violations of train driving modes.
The traffic accident analysis of the locomotive facilities of Ukrainian railways for the period of
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2015, № 6 (60)
2008 - 2010 (Fig. 1) shows that most of accidents are caused by the actions of foot-plate staff (Fig. 1a) and freight traffic - freight electric locomotives and diesel locomotives (Fig. 1 b) [1, 16, 20].
Since the driving of freight trains results in quite large longitudinal forces acting on cars, it becomes important to conduct the research aimed at identifying the causes of the situations in which the cars might be lifted.
technical liicUiry roundhouse actions of other
iasues repair servicing locomoltve
craws
О200Я «Î009 «Mid
Fig. 1. The histogram of traffic accidents caused by locomotive facilities of Ukrainian railways:
a - causes of transport accidents; b - transport accidents by type of rolling stock and traction
Increased safety of freight car traffic is one of the priorities of the Ukrainian railways and it represents a set of measures aimed at reducing the likelihood of threat to life and health of passengers, transported goods, as well as at the safety of infrastructure and rolling stock of the railway transport, environmental safety.
For effective training of specialists in such a complex area as railway transport currently the simulator complexes are widely used [10]. The simulator is usually used for developing practical skills, bringing them to automatism, especially for modelling abnormal and emergency situations It is important for a simulator to have a high-quality mathematical model describing the longitudinal
dynamic processes in train and able to assess the lift resistance of each car, since any discrepancy in the actual situation involves inadequate response of a locomotive driver when emergency situations occur in real life [15, 21].
Purpose
To ensure the stability the limit values for certain indicators are set. These indicators determine the conditions of rail top wheeling-in. One of such conditions is the ratio of lateral and vertical forces acting on the wheel. However, if the above indicators exceed the permissible limits, it does not mean that derailment will take place; it is the necessary but not sufficient condition for the wheel running off the rails [12].
When designing the new and upgrading the existing freight cars one of the mandatory conditions, which determines their suitability for use, is the fulfilment of conditions for ensuring the car resistance factor against the lift caused by longitudinal forces in the train.
The purpose of the analytical study of the relationship between the longitudinal force acting on the lightweight car, lateral and vertical forces acting in the contact area of the wheel flange and the rail with the lift resistance factor value is to provide simple functional connections between them.
Methodology
Wheel stability against re-railing is determined by two main factors: the ratio of the lateral interaction force to the vertical load on a wheel and by the angle of rail top side edge wheeling-in, which depend on dynamic processes of vehicle movement in the rail track and the longitudinal forces acting on the car in train.
As a result of the use of certain driving modes the train can evoke large longitudinal dynamic forces both tensile and compressive ones. The effect of the action of the longitudinal forces is defined by their direction and car position relative to the neighbouring vehicles in coupling [2, 3, 7, 8]. When placing the cars at an angle to each other in the plan, the transverse horizontal components of the longitudinal forces appear; and in case of difference in height of their automatic couplings -vertical components, which create additional loading or off-loading of the respective wheels of the
a
b
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vehicle [3, 6, 13]. This has an effect on the value of the lateral and vertical interaction forces, defining the conditions necessary for rail top wheeling-in [23, 24, 25].
Since the set of the cars with central automatic couplings of shock-traction action is a multilink hinge-rod circuit, the instability of equilibrium of this mechanism depends on the location and characteristics of the horizontal and vertical components of the longitudinal forces [3]. The force, by analogy with Euler static problem, corresponding to hinge-rod circuit buckling moment, is called buckling (Fig. 2). The calculated buckling forces for freight cars occur the least ones when skewing according to the diagram (a). Consequently, the cars coaxially arranged on a straight track section would not be out of alignment under the action of compressive forces lower than the buckling one [2, 3]. In fact, due to the meandering motion of vehicles, track gaps, spring, axle and centre plate arrangements, and for other reasons the cars almost always have some oblique settings relating to each other [2, 3, 6, 13].
Despite the fact that the theoretical studies found that, when the compressive force value is lower than the buckling value, the car lift should not occur due to the stability loss of the train as a hinged-rod system, the practice shows that the train derailments occur even at lower values of the longitudinal forces. This is particularly evident for the trains with empty cars, which are characterized
by intense hunting in the operational speed range. Therefore, apart from the train longitudinal stability as a hinged-rod system, for the speeds above the critical speed of hunting, in the presence of the longitudinal compressive forces one must consider longitudinal and transverse stability of the motion of the train cars [18, 19].
It should be noted that the presence of longitudinal forces not only leads to an increased hunting, but also helps to reduce the vertical loads in the wheel-rail system, that is to reduce the forces that prevent rail top wheeling-in, as well as to a greater turn of carriages with increased angle of rail wheeling-in. In such situations, the rail top wheel-ing-in resistance is seen not as a direct result of the high value of the longitudinal force, but as a result of intense vibrations of the hunting vehicle. This is particularly evident in the area of transition curves, characterized by additional perturbations of impact nature [2, 3, 6-8].
Let's consider the car motion in a curve, where there are different on both sides of the car cant angles of rigid rods (bodies) to the track plane ^ and
the angles of coupling rotation with respect to the track axis ^1and and the car rotation within the gap in the track at an angle y. Herewith the car is set in the track under the diagram (a) - «herringbone» and is subjected to the action of longitudinal compressive forces. We introduce a number of assumptions, simplifying the problem [6].
Fig. 2. Design diagram of the train and oblique settings of its elements in the plan under the action of longitudinal compressive forces
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Fig. 3. The forces acting on the car
Fig. 3, all the forces acting on the car are designed on the track plane, as well as the planes perpendicular to it - the longitudinal, relative to the track, and the cross axis. Where G0 -weight of the car body, kN; Pcf - centrifugal force, kN;
m; A2 - axe level difference of automatic couplings behind the car, m;
7! = N -V!, 72 = N -V2;
(5)
G ■V
Pcf
g ■ R
Pcp -centripetal force, kN;
Pcp = G0
(1)
(2)
Y1 and Y2 - horizontal lateral components of the longitudinal force, kN;
Since the angles ^ and ^ and y2 are rather small, then:
X = X 2 = N.
(6)
a - track inclination angle towards the horizontal, rad; N1 and N2 -longitudinal forces acting in a car coupler, kN; Z1 and Z2 - vertical components of the longitudinal force, kN;
X1 and X2 - horizontal longitudinal components of the longitudinal force, kN.
Assuming that the turning angles of all cars in a curve are equal, we find:
S0
A.
Z1 = N ■Фl, Ф1 = —;
2a
(3)
v=-
80 ■ L Lc
2a ■
R
(7)
(8)
Z2 = N ■ Ф2, Ф2 = T2;
2a
(4)
80■L Lc
v 2 =--C
2a ■
R
(9)
2a - the distance between the centres of the cotter hole of automatic coupling, m; A1 - axe level difference of automatic couplings in front of the car,
In view of the elastic transverse deformation of the bogie spring sets the formulas (7, 8, 9) take the following form:
2
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у =
So
N
2 • i M • C
So • L _f1 + L^ 2Lc
a ) R
(10)
S0 • L N
w = —-+-x
1 2a • i 4C
assumption is made about the equality of the horizontal lateral stiffness of spring group on one bogie) and denoted H and H2.
Having formed the equations of equilibrium and compatibility of vertical displacements (vertical stiffness of all the spring sets are equal, and the car frame is absolutely rigid), we determine the reactions of the supports:
So • L f_ L \ 2Lc
a ) R
— + Ll ai R
(11)
фэ =Ф: -I — +11 + Ф2 •! L -1
(13)
W 2 =
S0 • L N
—-+-x
2a • i 4Cr
S0 •L i1+L
D G0 N N
Rj = —---фэ + — x
1 4 4 4
G0
R
—-(12) ai R
x b Kf • g; • a«n, (14)
where 2Lc - car coupled length, m; 21 - truck-centre spacing, m; R - curve radius, m; 2S0 - total cross-run play of the car body frame relative to the track axis in the run section, m; L - horizontal distance from the car axis to the cotter hole centre of automatic coupling, m; a - coupler casting length (from the axis of coupling to the end of the shank), m; Ch - horizontal stiffness of the spring suspension of a bogie, kN/m.
The vertical components of support reactions are indicated in Fig. 3 as R1, R2, R3, R4, the horizontal components of the reactions belonging to the same bogie are taken equal to each other (the
R G0 N N
R2 =---Фэ--x
2 4 4 4
c
G0
x7--(( -V2 )--T ™T aun , (15) b 4 gb
H = N/ 4 ;
L
L
L
Ф1 •! T+11+Ф2 •! T-11+2ф~
G0
+—• a .
/л un
2 g
(16)
Fig. 4. Car layout on a curved track section under the action of longitudinal compressive forces
x
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Where 2b - distance between the points of application of the vertical forces acting on the journal box of the wheel pair on the climbing and non-climbing wheel respectively, kN; h - height of the car body centre of gravity over the bolster supporting plane, m; c - vertical distance from the top plane of the central spring set to the coupling axis level, m; aun - unbalanced acceleration, m/s2; g - gravity acceleration, m/s2.
Having considered the balance of non-sprig part of the bogie, we can find vertical P1t P2 and the horizontal force Hf acting on the wheel pair:
Л = Gl+RL,
1 4 2
P2 =
G. + R2
(17)
(18)
Having considered the balance conditions of a single wheel pair, we get [6, 22]:
X Z = P. + P2 + Gwp - N2 - Pcar = 0 XM = N2 ■ 2S - Gwp ■ S + P ■ bi -
-P2 ■ b2
■Hf ■ hs = 0
(20)
X7 = Pf -HfN2 = 0
Where hhs - height from the rail level to the top plane of the central spring set, m; Gwp - weight of the wheel pair, kN; Hf - frame force acting on the wheel pair, kN; p - coefficient of flange friction against the rail top fillet.
Solving the system of linear equations we determine the vertical and lateral cross reactions of rail to the climbing wheel:
Hf = Hi
Gl 2 g
(19)
Pcar = G + G
N
(Vi - V2)■ S-(Ф1 Ф2)■ J^-(i Ф2Уb + ( + V2 + 2V>
hs
(21)
Fig. 5. Calculation diagram of forces acting on the bogie as a result of longitudinal compression
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Pb = 1
Г G Gbg } N
(1 -V2)| 2y]-!^ +Ф2)• J^b + Иф Ф2)• b +
L
+(1 + V2 + 2v) — •f 2-^S
(22)
кув =
tgß-i 1+ |tgß
Pcar + N • av ^ - b S S (ф +Ф2 + АФ Lh +(V1 + v2 + 2v) • Ss
1 Pcar + N • M2-i-f ]+i S (ф +Ф2 ) +АФ + (V1 +V 2 +2V)) •( 2-|- h h
(23)
Where Pcar = Go + 2Gb - car weight, kN; forces in the curve, the vertical (21) and the lateral
Ay = ^ - y2 - difference between the swivel an- (22) reactions of the rail on the climbing wheel are
. ,, .. . . . . ,, ,, added to the inertia forces caused by unbalanced
gles of couplings against the track axis in front of ,
H1-11 i acceleration: and behind the car, rad.
If it is necessary to take into account inertia
кув = tgß-il 1 + !• tgß^PB + Рин • h^lРб + Рин • (2-!• KlS), Рт =(G0 + 2• Gbg)• ^ = Pcar • ^ .
(24)
(25)
Using analytical expressions for determining ences for the vertical (21) and the lateral (22) reac-angles (10, 11, 12), we write the obtained depend- tions of the rail on the climbing wheel as follows:
Pb = P
N С
Va ■ hhs , Vcur ■ L Г К + ^ ^ К
S i S
250 • S
■N •
2Vc
—+Va •—
S a S
(26)
t N
Pb = +С-
_VL• f 2hh^ 1. ^L
250
S
a • j
2. fi+a U, f к + a. hhL ^
I I ] f S I S
Where P<Scjr - static weight of car in view of unloading by longitudinal force, kN;
PsI = P - N • ф
car car Тэ'
ya - rotation angle, rad;
V a =50-L/•(l + J a ), Wcur - rotation angle from the curve, rad;
V cur = Lc/R.
+N-
2Vcur-| 2-l
S
■V a ' | 2S
. (27)
Substituting the expressions (26) and (27) into the formula (24) we can obtain the dependence similar to that described in [6], excluding (31) and taking into (28) account the inertial forces in a curve (32). In addition, we recall dependence for determining the longitudinal forces lift resistance factor excluding (33) and (2Q) taking into account the inertial forces in a curve (34) which has been studied in [11].
(30)
X
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к! =
pst car N2 v a •
tgß-Ц Ch 250
1+ ^tgß ц. Pst csr N2 +-- Ch "v a 250
-N •
2Vcur + Va
S
S
+N-
Vcur • L
hs
S
2Vcur 'I 2-Ц.S l + Va-I 2-Ц-^
f2.fl + ^h- + « .hs^ v I 11 IS t S „
(31)
К1 =-
t N2 Pst + — • car tgß-Ц Ch va . hhs + Vcur . L f ha + a hhs 1 250. S a. 1 V S 1 S | + N. 2Vcur . S + Va . S + P A m S
1+ Ц • tgß t N2 ц. par+f- • Ch "V 2 .f 2 -Ц. hhs 1+Vcur . L 250 V S | a. 1 2 C1+1MI+&и +
, (32)
+N •
Ki,u =. tgß
2Vcur .| 2-Ц
S
Va .| 2-Ц"^
Pn .| 2-Ц-
S
Рт +yN.
50 • L
i+L^ ±a.L,
R
S
1 + Ц • tgß
KI,II = _ tgß^
ц.Рт + 2yN •
50 • L
1 + L
a
f
\
2S
Lc
1 -Ц^ ±a—.| 1 — Ц• ——
R
(33)
2 S
1 + Ц • tgß
Pbs + YN'
50 •L .f1+L
cp
a l h
±a.
cpl
4
R
hcpl_ ± I p mhCL
S
S
(34)
ц.Рт + 2yN •
50 • L
L
2S
Lc
R
1 + -M 1 -Ц.-^ |±a^ • 1 -Ц.^ ± -| 1 -Ц.-C
2S
2S
Where Pcar - car weight, kN; Pin - car inertial force, kN; Pb - vertical load by bogie, which takes into account off-loading under the longitudinal force, kN; N - longitudinal force on automatic coupling during the car compression, kN; 2Lc -coupled length, m; 2L - car length over head stock, m; 21 - truck-centre spacing, m; hcp - height of the centre plate working plane above the rail top, m; hhs - height of the spring set top above the rail top, m; hcpi _ height of the coupling axis above the rail top, m; hc - height of the car gravity centre above the rail top, m. 2b - distance between the points of application of the vertical forces acting on the journal box of the wheel pair on the climbing and non-climbing wheel respectively, kN; 2S - distance between the taping lines, m; R - curve radius, m; 2S0 - total cross-run play of the car body frame relative to the track axis in the run section,
m; a - coupler casting length (from the axis of coupling to the end of the shank), m; ^ - coefficient of flange friction against the rail top fillet; / -angle formed by the straight part of the wheel flange profile contour to the track plane; aun - unbalanced acceleration, m/s2; a and y - coefficients taking into account the effect of longitudinal buckling forces, leading to a relative imbalance of cars and the coupling axes in the plan.
Findings
To assess the impact of the longitudinal forces value on the lift resistance factor Fig. 6 presents the calculation results for the empty gondola car motion, model No. 12-532, on 250 m radius curve with 150 mm rise and cross starting of car under-frame relating to the track axis in 50 mm guiding section [12]. The calculations were made in such
X
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a curve excluding the inertial forces from outstanding acceleration and taking into account the unbalanced acceleration with the permissible speed of 65 km/h [14, 17].
Fig. 6 shows the calculation results for lift resistance factor of the empty car depending on the value of longitudinal forces caused by the neighbouring cars with the difference in coupling heights of 100 mm. The horizontal lines show the allowable value of the lift resistance factor (1.2 [12]) and the value of this factor (1.0), which provides the necessary condition for instability.
The diagrams in Fig. 6 show that the car speed has some significant impact on the lift resistance factor value only at small values of the longitudinal
forces, in case of which the lift is impossible. Therefore, as noted previously [3] and as follows from Fig. 6, the impact of the car speed on the longitudinal force lift resistance factor can be neglected.
Fig. 7 shows the dependence of the lift resistance factor obtained using 2 different design diagrams. The dotted line corresponds to the design diagram, which takes into account the loss of stability of the train, as the hinge-rod system [6]. The solid line - to calculation diagram, shown in Fig. 3.
This figure proves that, according to the results obtained from the formula (33), the lift resistance is not provided at the force 605 kN and by the formula (31) - even at the force 530 kN.
Fig. 6. Dependence diagram of lift resistance factor from longitudinal force:
1 - (33) without inertia force; 2 - (34) taking into account the inertia force by unbalanced acceleration; 3 - (31) without inertia force; 4 - (32) taking into account the inertia force by unbalanced acceleration
V
ta bi lit У ione uck Hi « ZOIl
■■ J:
Stability zc n t Ir stability
E uck ing zone
In St ability — zone
200 300 400 500 600 700 800 900 1000 1100 1ИЮ
N[kH]
Fig. 7. Dependence diagram of lift resistance factor for different design schemes: solid line - (31), dotted line - (33)
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A necessary condition for the loss of stability is fulfilled, in the first case, when the value of the longitudinal force is 800 kN, in the second case -695 kN. Thus the results obtained by the formula (31) impose more stringent requirements to ensure the car lift resistance.
As it is known, the lowest values of the lift resistance factor are peculiar to the cars with small coupled length, truck-centre spacing and unladen weight. In future, the comparative analysis is made only for this category of freight cars [4, 5]. The calculations were performed according to the dependencies (31) and (33) - excluding the inertial forces by unbalanced acceleration, and according to the dependencies (32) and (34) - taking into account the inertial forces by unbalanced acceleration when driving with permitted speed [17]. The results are summarized in Table 1-5.
Table 1
The lift resistance factors for gondolas
Formula No Covered car types
12-1505 12-5326 12-2122-01
Standards [10] 1.367 1.399 1.360
Formula (31) 1.223 1.264 1.223
Table 2
The lift resistance factors for tank cars
Formula No Tank-car types
15-145 15-869 15-1548
Standards 1.597 1.647 1.423
[10]
Formula (31) 1.459 1.524 1.277
Table 3
The lift resistance factors for covered cars
Formula No Covered car types
11-N002 11-066 10-475
Standards 1.315 1,492 1.642
[10]
Formula (31) 1.17 1.357 1.513
Table 4
The lift resistance factors for hopper cars
Formula No Hopper car types
11-715 19-1217 20-4078
Standards 1.349 1.564 1.455
[10]
Formula (31) 1.198 1.289 1.305
Table 5
The lift resistance factors for platforms
Formula No Platform types
131796 13-1798 13-3103-01
Standards [10] 1.472 1.410 1.415
Formula (31) 1.342 1.279 1.273
The results of calculations in Tables 1-5 show that for all the above cars the values of the lift resistance factor obtained by the proposed formula (31) are smaller than the standards [12]. And for some cars the value Kres is lower than the permissible value.
It follows that, even in the absence of «lift» according to the classical train stability theory, as the hinge-rod system, the presence of the longitudinal compressive forces may become a factor provoking cars derailment. Thus the main reason of wheel climbing on rails is the combination of processes of dynamic interaction between the hunting vehicle and the track with simultaneous action of longitudinal compressive forces, and not the destabiliza-tion of train as a hinged-rod system.
Originality and practical value
This study provides the technique of determining the lift resistance factor by longitudinal forces, which is somewhat different from the above mentioned one [3, 6], as well as evaluates impact of rolling stock speed on this factor. The developed proposals for the refinement of existing methods for determining the resistance factor of the car lift by longitudinal force will increase the stability margin.
The research results have found their scientific use in a number of publications in the special and
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scientific journals, presentations at scientific meetings.
Conclusions
As a result of analytical research there are obtained the dependencies of longitudinal forced lift resistance factor in the train with and without consideration of the speed of its movement. It is shown that as the value of this factor gets closer to the buckling area the influence of speed decreases.
From these studies one can conclude that because of cars hunting their lift is possible even when the train as hinge-rod system does not lose stability.
Thus, the calculation results allow an objective assessment of the effect of the longitudinal force and the freight car speed on the lift resistance factor value.
LIST OF REFERENCE LINKS:
1. Аналiз стану безпеки руху поiздiв у локомотивному господарст затзниць Украши за 2010 piK // Локомотив-информ. - 2010. - № 5. -С. 14-18.
2. Вершинский, С. В. Динамика вагонов / С. В. Вер-шинский, В. И. Данилов, И. И. Челноков. - Москва : Транспорт, 1991. - 360 с.
3. Вершинский, С. В. Динамика, прочность и устойчивость вагонов в тяжеловесных и скоростных поездах / С. В. Вершинский // Сб. тр. / ВНИИЖТ. - Москва : Транспорт, 1970. - Вып. 425. - 208 с.
4. Грузовые вагоны колеи 1520 мм железных дорог СССР : альбом. - Москва : Транспорт. -1982. - 111 с.
5. Грузовые вагоны колеи 1520 мм железных дорог СССР : альбом-справочник / М-во путей сообщ. СССР, Гл. упр. вагон. хоз-ва. - Москва : Транспорт. - 1989. - 175 с.
6. Лазарян, В. А. Движение легковесных вагонов в составах тяжеловесных поездов / В. А. Лаза-рян, Е. П. Блохин, Е. Л. Стамблер / Тр. ДИИТа. - Москва : Транспорт, 1968. - Вып. 76 : Вопросы динамики подвижного состава и применения математических машин. - С. 34-46.
7. Лазарян, В. А. Динамика вагонов / В. А. Лаза-рян. - Москва : Транспорт, 1964. - 256 с.
8. Лазарян, В. А. Динамика транспортных средств / В. А. Лазарян. - Кив : Наукова думка, 1985. - 528 с.
9. Мямлин, С. В. Прогресс транспорта - залог развития национальной экономики / С. В. Мям-
лин // Наука та прогрес трансп. Вюн. Дншро-петр. нац. ун-ту залiзн. трансп. - 2013. - № 1 (43). - С. 7-12. 10.15802^2013/9786.
10. Навчальш тренажери машишспв локомотивiв / А. С. Акулов, К. I. Железнов, О. М. Заболотний [та ш.] // Проблеми та перспективи розвитку залiзн. трансп. : тези 74 Мiжнар. науково-практ. конф. (15.05-16.05.2014) / Мш-во шфраструктуры Украши, Дншропетр. нац. ун-т залiзн. трансп. iм. акад. В. Лазаряна. -Дншропетровськ, 2014. - С. 102-103.
11. Некоторые аспекты определения устойчивости порожних вагонов от выжимания их продольными силами в грузовых поездах / А. А. Швец, К. И. Железнов, А. С. Акулов [и др.] // Наука та прогрес трансп. Вюн. Дншропетр. нац. ун-ту залiзн. трансп. - 2015. - № 4 (58). - С. 175-189. аог 10.15802^р2015/49281.
12. Нормы для расчета и проектирования новых и модернизируемых вагонов железных дорог МПС колеи 1520 мм (несамоходных). - Москва : ВНИИВ : ВНИИЖТ, 1983. - 260 с.
13. О движении легковесных вагонов в составах тяжеловесных поездов : отчет о НИР : 80 / Днепропетр. ин-т инж. ж.-д. трансп. ; рук. Лазарян В. А. / Днепропетровск, 1966. - 38 с. -Исполн.: Блохин Е. П., Стамблер Е. Л. - Биб-лиогр.: с. 38. - Инв. № 80.
14. Определение допускаемых скоростей движения грузовых вагонов по ж.-д. путям колеи 1 520 мм / В. Д. Данович, В. В. Рыбкин, С. В. Мямлин [и др.] // Вюн. Дншропет. нац. ун-ту залiзн. трансп. iм. акад. В. Лазаряна. -Дншропетровськ, 2003. - Вип. 2. - С. 77-86.
15. Пат. 87837 Украша. МПК в 09 В 9/04 (20.06.01/). Тренажер для навчання машишста мапстрального локомотива / Железнов К. I., Акулов А. С., Свдомаха Г. В., Заболотний О. М., Чабанюк £. В., Швець А. О. (Украша) ; заявник та патентовласник Дшпропетр. нац. ун-т залiзн. трансп. iм. акад. В. Лазаряна. - № и 2013 09075 ; заявл. 19.07.2013 ; опубл. 25.02.14. Бюл. № 4. - 2 с.
16. Посмиюха, А. А. Аналiз стану безпеки руху поiздiв у локомотивному господарствi залiз-ниць Украши за 2008 р1к / А. А. Посмтюха // Локомотив - информ. - 2009. - № 3/4. - С. 27-30.
17. Правила визначення шдвищення зовнiшньоi' рейки i встановлення допустимих швидкостей в кривих донках коли : ЦП 02336. - Кшв : Укрзалiзниця, 2013. - 44 с.
18. Продольная и поперечная динамика 2-осных автосцепных вагонов в тяжеловесных поездах и при повышенных скоростях : отчет о НИР / Всесоюз. науч.-исслед. ин-т ж.-д. трансп.,
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2015, № 6 (60)
Днепропетр. ин-т инженеров трансп. ; рук. Вершинский С. В. - Москва, 1954. - 312 с. - Исполн.: Лазарян В. А., Львов А. А., Блохин Е. П. - № И - 05 - 54 р. 2. - Инв. № 2.
19. Продольная и поперечная динамика 2-осных вагонов в тяжеловесных поездах и при повышенных скоростях : отчет о НИР / Всесоюз. науч.-исслед. ин-т ж.-д. трансп., Днепропетр. инт инженеров трансп. ; рук. Вершинский С. В. -Москва, 1953. - 351 с. - Исполн.: Лазарян В. А., Львов А. А., Конашенко С. И., Коротенко М. Л. -№ И - 05 - 54 р. 1. - Инв. № 1.
20. Пустовгар, В. О. Аналiз стану безпеки руху поiздiв у локомотивному господарствi залiз-ниць Украши за 2009 рш / В. О. Пустовгар // Локомотив-информ. - 2010. - № 3. - С. 14-17.
21. Сввдоцтво про реестрацш авторського права на твiр № 54184 Украша. Комп'ютерна про-грама «Обучение вождению поездов машинистов магистральных локомотивов» / Железнов К. I., Акулов А. С., Свдомаха Г. В., Заболотний О. М., Чабанюк е. В., Швець А. О. (Укра1на) ; заявник та патентовласник Дшпропетр. нац.
ун-т залiзн. трансп. iM. акад. В. Лазаряна. - за-явл. 20.03.2014.
22. Шадур, Л. А. Вагоны. Конструкция, теория и расчет / Л. А. Шадур. - Москва : Транспорт, 1980. - 440 с.
23. Anyakwo, A. A New Method for Modelling and Simulation of the Dynamic Behaviour of the Wheel-rail Contact / A. Anyakwo, C. Pislaru, A. Ball // Intern. J. of Automation and Computing. - 2012. - Vol. 9. - Iss. 3. - P. 237-247. doi: 10.1007/s11633-012-0640-6.
24. Kurhan, D. M. Features of perception of loading elements of the railway track at high speeds of the movement / D. M. Kurhan // Наука та прогр. трансп. Вюн. Дншропетр. нац. ун-ту залiзн. трансп. - 2015. - № 2 (56). - С. 136-145. doi: 10.15802/stp2015/42172.
25. Marquis, B. Application of Nadal limit in the prediction of wheel climb derailment (JRC2011-56064) / B. Marquis, R. Greif // Proc. of the ASME/ASCE/IEEE. 2011 Joint Rail Conf. (16.03.-18.03.2011). - Pueblo, Colorado, USA, 2011. - P. 1-8. doi: 10.1115/jrc2011-56064.
А. О. ШВЕЦЬ1*, К. I. ЖЕЛеЗНОВ2*, А. С. АКУЛОВ3*, О. М. ЗАБОЛОТНИЙ4*, е. В. ЧАБАНЮК5*
1 СКТБ МСУБ, Дтпропетровський нацюнальний ушверситет з^зничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Укра1на, 49010, тел. +38 (050) 214 14 19, ел. пошта angela_shvets@ua.fm, ШСГО 0000-0002-8469-3902
2*СКТБ МСУБ, Дтпропетровський нацюнальний ушверситет залiзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Укра1на, 49010, тел. +38 (095) 545 38 87, ел. пошта constantinz@i.ua, ШСГО 0000-0003-3648-1769
3*СКТБ МСУБ, Дтпропетровський нацюнальний ушверситет залiзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Укра1на, 49010, тел. +38 (067) 178 16 90, ел. пошта asakulov@gmail.com, ШСГО 0000-0002-6123-5431
4*СКТБ МСУБ, Дтпропетровський нацюнальний ушверситет залiзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Укра1на, 49010, тел. +38 (067) 282 13 41, ел. пошта zabolotnyi@i.ua, ШСГО 0000-0003-1651-7082
5*СКТБ МСУБ, Дтпропетровський нацюнальний ушверситет залiзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Укра1на, 49010, тел. +38 (066) 633 55 95, ел. пошта 457m@ukr.net, ОЯСГО 0000-0001-5695-5955
ДО ПИТАННЯ ВИЗНАЧЕННЯ КОЕФЩ1СНТА ЗАПАСУ СТ1ЙКОСТ1 В1Д ВИЧАВЛЮВАННЯ ЛЕГКОВАГОВИХ ВАГОН1В
Мета. Аналггичне дослщження зв'язку мiж поздовжньою силою, що дie на легковаговий вагон, бiчними й вертикальними силами взаемодп в зон контакту колеса та рейки з величиною коефщента запасу стткосп ввд вичавлювання, передбачае отримання простих залежностей мiж ними. Методика. Дослвдження проводилося методом математичного моделювання навантаженостi вантажного вагона при рус з рiзними швидкостями по прямих та кривих донках шляху. Результати. Навпь за вiдсутностi «вичавлювання» за класичною теорii стiйкостi по1зда, як шаршрно-стрижнево! системи, наявнiсть поздовжнiх стискаючих сил може стати фактором, провокуючим схiд вагонiв. Основною причиною вповзання колеса на рейку
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2015, № 6 (60)
е поеднання процесiв динамiчноi взаeмодii виляння ек1пажа та коли з одночасною дieю поздовжнiх стискаючих сил, а не порушення стiйкостi по1зда як шаршрно-стрижнево! системи. Для оцiнки впливу величини поздовжнiх сил на коефщент запасу стiйкостi ввд вичавлювання наведеш результати розрахунк1в руху порожнього шввагона моделi № 12-532 по кривш радiусом 250 м з пвднесенням 150 мм й поперечним розгоном рами кузова вагона щодо ос колii в направляючому перетинi в 50 мм. Розрахунки проводилися в такш кривiй без урахування сил шерцп ввд непогашеного прискорення та з урахуванням непогашеного прискорення при допустимш швидкостi руху, рiвнiй 65 км/год. Наукова новизна. У даному дослiдженнi наведено методику визначення коефщента запасу стiйкостi ввд вичавлювання поздовжшми силами, яка дещо вiдрiзняеться вщ загальноприйнято!, а також оцiнюеться вплив на цей коефщент швидкостi руху рухомого складу. Практична значимкть. Авторами уточнюеться iснуюча методика визначення коефщента запасу стiйкостi ввд вичавлювання поздовжшми силами, а також оцшюеться вплив на величину цього коефщента швидкосл руху рухомого складу. З проведених дослвджень випливае, що через виляння вагошв 1х вижимання можливо навпъ тодi, коли по1зд, як шаршрно-стрижнева система, не втрачае стiйкостi. Розроблеш пропозицп дозволяють знизити кiлькiсть сходiв вагонiв iз рейок за рахунок облiку при розрахунках та проектуванш важливих параметрiв й характеристик, що пвдвищують 1х стiйкiсть в рейковш колii (особливо при збiльшеннi швидкостей руху вантажних поiздiв).
Ключовi слова: безпека руху; норми для розрахунку; стшшсть вагонiв ввд вичавлювання; швидшсть руху; коефiцiент стiйкостi
A. А. ШВЕЦ1*, К. И. ЖЕЛЕЗНОВ2*, А. С. АКУЛОВ3*, А. Н. ЗАБОЛОТНЫЙ4*, Е. В. ЧАБАНЮК5*
1 СКТБ МСУБ, Днепропетровский национальный университет железнодорожного транспорта имени академика
B. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (050) 214 14 19, эл. почта angela_shvets@ua.fm, (ЖСГО 0000-0002-8469-3902
2*СКТБ МСУБ, Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (095) 545 38 87, эл. почта сош1ж1Йш@1.иа, (ЖСГО 0000-0003-3648-1769
3*СКТБ МСУБ, Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (067) 178 16 90, эл. почта asakulov@gmail.com, (ЖСГО 0000-0002-6123-5431
4*СКТБ МСУБ, Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (067) 282 13 41, эл. почта zabolotnyi@i.ua, (ЖСГО 0000-0003-1651-7082
5*СКТБ МСУБ, Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (066) 633 55 95, эл. почта 457m@ukr.net, ОЯСГО 0000-0001-5695-5955
К ВОПРОСУ ОПРЕДЕЛЕНИЯ КОЭФФИЦИЕНТА ЗАПАСА УСТОЙЧИВОСТИ ОТ ВЫЖИМАНИЯ ЛЕГКОВЕСНЫХ ВАГОНОВ
Цель. Аналитическое исследование связи между продольной силой, действующей на легковесный вагон, боковыми и вертикальными силами взаимодействия в зоне контакта колеса и рельса с величиной коэффициента запаса устойчивости от выжимания, предполагает получение простых зависимостей между ними. Методика. Исследование проводилось методом математического моделирования нагруженности грузового вагона при движении с различными скоростями по прямым и кривым участкам пути. Результаты. Даже при отсутствии «выжимания» по классической теории устойчивости поезда, как шарнирно-стержневой системы, наличие продольных сжимающих сил может стать фактором, провоцирующим сход вагонов. Основной причиной всползания колеса на рельс является сочетание процессов динамического взаимодействия виляющего экипажа и пути с одновременным действием продольных сжимающих сил, а не нарушение устойчивости поезда как шарнирно-стержневой системы. Для оценки влияния величины продольных сил на коэффициент запаса устойчивости от выжимания приведены результаты расчетов движения порожнего полувагона модели № 12-532 по кривой радиусом 250 м с возвышением 150 мм и поперечным разбегом рамы кузова вагона относительно оси пути в направляющем сечении в 50 мм. Расчеты производились в такой кривой без учета сил инерции от непогашенного ускорения и с учетом
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2015, № 6 (60)
непогашенного ускорения при допустимой скорости движения равной 65 км/ч. Научная новизна. В данном исследовании приведена методика определения коэффициента запаса устойчивости от выжимания продольными силами, несколько отличающаяся от общепринятой, а также оценивается влияние на этот коэффициент скорости движения подвижного состава. Практическая значимость. Авторами уточняется существующая методика определения коэффициента запаса устойчивости от выжимания продольными силами, а также оценивается влияние на величину этого коэффициента скорости движения подвижного состава. Из проведенных исследований следует, что из-за виляния вагонов их выжимание возможно даже тогда, когда поезд как шарнирно-стержневая система не теряет устойчивости. Разработанные предложения позволяют снизить количество сходов вагонов с рельсов за счет учета при расчетах и проектировании важных параметров и характеристик, повышающих их устойчивость в рельсовой колее (особенно при увеличении скоростей движения грузовых поездов).
Ключевые слова: безопасность движения; нормы для расчета; устойчивость вагонов от выжимания; скорость движения; коэффициент устойчивости
REFERENCES
1. Analiz stanu bezpeky rukhu poizdiv u lokomotyvnomu hospodarstvi zaliznyts Ukrainy za 2010 rik [Analysis of traffic safety in railway locomotive economy of Ukraine in 2010 year]. Lokomotyv-Inform - Locomotive-Inform, 2010, no. 5, pp. 14-18.
2. Vershinskiy S.V., Danilov V.I., Chelnokov I.I. Dinamika vagonov [Dynamics of cars]. Moscow, Transport Publ., 1991. 360 p.
3. Vershinskiy S.V. Dinamika, prochnost i ustoychivost vagonov v tyazhelovesnykh i skorostnykh poyezdakh. [Dynamics, durability and the stability of cars in heavy and high-speed trains]. Sbornik trudov VNIIZhTa [Proc. Of All-Russian Research Railway Institute]. Moscow, Transport Publ., 1970, issue 425, 208 p.
4. Gruzovyye vagony kolei 1520 mm zheleznykh dorog SSSR: albom [Freight cars, a track of 1520 mm at railways of the USSR: The Album]. Moscow, Transport Publ., 1982. 111 p.
5. Gruzovyye vagony kolei 1520 mm zheleznykh dorog SSSR: albom-spravochnik [Freight cars 1520 mm track railways of the USSR: Album Directory]. Moscow, Transport Publ., 1989. 175 p.
6. Lazaryan V.A., Blokhin Ye.P., Stambler Ye.L. Dvizheniye legkovesnykh vagonov v sostavakh tyazhelovesnykh poyezdov. Voprosy dinamiki podvizhnogo sostava i primeneniya matematicheskikh mashin [Movement of lightweight cars in heavy trains. The dynamics of the rolling stock and the application of mathematical machines]. Trudy Dnepropetrovskogo instituta inzhenerov zheleznodorozhnogo transporta imeni akademika V. Lazariana [Studies of Dnepropetrovsk Institute of Railway Engineers named after Academician V. Lazaryan], 1966, issue 59, pp. 34-47.
7. Lazaryan V.A. Dinamica vagonov [Dynamics of cars]. Moscow, Transport Publ., 1964. 256 p.
8. Lazaryan V.A. Diynamica transportnykh sredstv [Dynamics of transportation facilities]. Kyiv, Naukova Dumka Publ., 1985. 528 p.
9. Myamlin S.V. Progress transporta - zalog razvitiya natsionalnoy ekonomiki [Transport progress as a pledge of national economy development]. Nauka ta prohres transportu. Visnyk Dnipropetrovskoho natsionalnoho uni-versytetu zaliznychnoho transportu - Science and Transport Progress. Bulletin of Dnipropetrovsk National University of Railway Transport, 2013, issue 1 (43), pp. 7-12. doi: 10.15802/stp2013/9786.
10. Akulov A.S., Zhelieznov K.I., Zabolotnyi A.N., Povstenko J.L., Chabanyuk E.V., Shvets A.O. Navchalni trenazhery mashynistiv lokomotyviv [Training simulators of locomotive drivers]. Tezy 74 Mizhnarodnoi naukovo-praktychnoi konferentsii «Problemy ta perspektyvy rozvytku zaliznychnoho transportu» (15.0516.05.2014). [Proc. of the 74rd Int. Sci. and Practical Conf. «Problems and Prospects of Railway Transport»]. Dnipropetrovsk, 2014, pp. 102-103.
11. Shvets А.А., Zhelieznov K.I., Akulov A.S., Zabolotnyi A.N., Chabaniuk E.V. Nekotoryye aspekty opredeleniya ustoychivosti porozhnikh vagonov ot vyzhimaniya ikh prodolnymi silami v gruzovykh poyezdakh [Some aspects of the definition of empty cars stability from lift their longitudinal forces in the freight train]. Nauka ta prohres transportu. Visnyk Dnipropetrovskoho natsionalnoho universytetu zal-iznychnoho transportu - Science and Transport Progress. Bulletin of Dnipropetrovsk National University of Railway Transport, 2015, issue № 4 (58), pp. 175-189. doi: 10.15802/stp2015/49281.
12. Normy dlya rascheta i proyektirovaniya novykh i moderniziruyemykh vagonov zheleznykh dorog MPS kolei 1520 mm (nesamokhodnykh) [Standards for strength calculations and design of the mechanical part of the new
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2015, № 6 (60)
and modernized railway cars MPS, track of 1520 mm (unpowered)]. Moscow, VNIIIV-VNIIZhT Publ., 1983. 260 p.
13. Lazaryan V.A., Blokhin Ye.P., Stambler Ye.L. O dvizhenii legkovesnykh vagonov v sostavakh tyazhelovesnykh poyezdov [About motion of lightweight cars in the heavy trains]. Dnipropetrovsk, 1966. 38 p.
14. Danovich V.D., Rybkin V.V., Myamlin S.V., Reidemeister A.G., Tryakin A.G., Halipova N.V. Opredeleniye dopuskayemykh skorostey dvizheniya gruzovykh vagonov po zheleznodorozhnym putyam kolei 1520 mm [Determining the permissible speed of freight cars on railroad tracks of 1520 mm]. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu imeni akademika V. Lazariana [Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan], 2003, issue 2, pp. 7786.
15. Zheleznov K.I., Akulov A.S., Yevdomakha H.V., Zabolotnyi O.M., Chabaniuk Ye.V., Shvets A.O. Trenazher dlia navchannia mashynista mahistralnoho lokomotyva [Simulator for driver training of the main locomotive]. Patent UA, no. u 2013 09075, 2014.
16. Posmitiukha A.A. Analiz stanu bezpeky rukhu poizdiv u lokomotyvnomu hospodarstvi zaliznyts Ukrainy za
2008 rik [Analysis of traffic safety in railway locomotive economy of Ukraine in 2008]. Lokomotiv-Inform -Locomotive-Inform, 2009, no. 3/4, pp. 27-30.
17. Pravyla vyznachennia pidvyshchennia zovnishnoi re iky i vstanovlennia dopustymykh shvydkostei v kryvykh diliankakh kolii. TsP 02336 [The rules for superelevation determining of an outer rod and permissible speeds in curved sections of the track. TsP 02 336]. Kyiv, Ukrzaliznytsia Publ., 2013. 44 p.
18. Vershinskiy S.V., Lazaryan V.A., Lvov A.A., Blokhin Ye. P. Prodolnaya i poperechnaya dinamika 2-osnykh avtostsepnykh vagonov v tyazhelovesnykh poyezdakh i pri povyshennykh skorostyakh [Longitudinal and perpendicular dynamics of two axle automatic coupling cars in heavy trains and at the high speeds]. Moscow, VNIIZhT Publ., 1954. 312 p. No. I-05-54.
19. Vershinskiy S.V., Lazaryan V.A., Lvov A.A., Konashenko S.I., Korotenko M.L. Prodolnaya i poperechnaya dinamika 2-osnykh avtostsepnykh vagonov v tyazhelovesnykh poyezdakh i pri povyshennykh skorostyakh [Longitudinal and perpendicular dynamics of two axle automatic coupling cars in heavy trains and at the high speeds]. Moscow, VNIIZhT Publ., 1953. 351 p. No. I-05-54.
20. Pustovhar V.A. Analiz stanu bezpeky rukhu poizdiv u lokomotyvnomu hospodarstvi zaliznyts Ukrainy za
2009 rik [Analysis of traffic safety in railway locomotive economy of Ukraine in 2009]. Lokomotyv-inform -Locomotive-Inform, 2010, no. 3, pp. 14-17.
21. Zheleznov K. I., Akulov A. S., Yevdomakha H. V., Zabolotnyi O. M., Chabaniuk Ye. V., Shvets A. O. Kompiuterna prohrama «Obucheniye vozhdeniyu poyezdov mashinistov magistralnykh lokomotivov» [Computer program «Learning to drive trains of drivers in mainline locomotives»]. Certificate UA, no. 54184,
2014.
22. Shadur L.A. Vagony. Konstruktsiya, teoriya i raschet [Cars. Design, theory and calculation]. Moscow, Transport Publ., 1980. 440 p.
23. Anyakwo A., Pislaru C., Ball A. New Method for Modelling and Simulation of the Dynamic Behaviour of the Wheel-rail Contact. Intern. Journal of Automation and Computing, 2012, vol. 9, issue 3, pp. 237-247. doi: 10.1007/s11633-012-0640-6.
24. Kurhan D.M. Features of perception of loading elements of the railway track at high speeds of the movement. Nauka ta prohres transportu. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu - Science and Transport Progress. Bulletin of Dnipropetrovsk National University of Railway Transport,
2015, issue 2 (56), pp. 136-145. doi: 10.15802/stp2015/42172.
25. Marquis B., Greif R. Application of Nadal limit in the prediction of wheel climb derailment (JRC2011-56064). Proc. of the ASME/ASCE/IEEE. 2011 Joint Rail Conf. (16.03.-18.03.2011). Pueblo, Colorado, USA, 2011. pp. 1-8. doi: 10.1115/jrc2011-56064.
Prof. S. V. Miamlyn, D. Sc. (Tech.), (Ukraine); Senior Associate M. M. Khachapurydze, PhD (Tech.), (Ukraine); Senior Associate M. O. Radchenko, PhD (Tech.), (Ukraine) recommended this article to be published
Received: Aug. 21, 2015 Accepted: Oct. 20, 2015
