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UDC 625.173.2
O. M. PATLASOV1, S. O. TOKARIEV2*
'Dep. «Track and Track Facilities», Dnepropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 42, e-mail am_patlasov@ukr.net, ORCID 0000-0003-2081-5648
2 Dep. «Track and Track Facilities», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 42, e-mail tokarevsergeyaleks@yandex.ua, ORCID 0000-0002-2607-3123
THE MEASUREMENT METHODOLOGY IMPROVEMENT OF THE HORIZONTAL IRREGULARITIES IN PLAN
Purpose. Across the track superstructure (TSS) there are structures where standard approach to the decision on the future of their operation is not entirely correct or acceptable. In particular, it concerns the track sections which are sufficiently quickly change their geometric parameters: the radius of curvature, angle of rotation, and the like. As an example, such portions of TSS may include crossovers where their component is within the so-called connecting part, which at a sufficiently short length, substantially changes curvature. The estimation of the position in terms of a design on the basis of the existing technique (by the difference in the adjacent arrows bending) is virtually impossible. Therefore it is proposed to complement and improve the methodology for assessing the situation of the curve in plan upon difference in the adjacent versine. Methodology. The possible options for measuring horizontal curves in the plan were analyzed. The most adequate method, which does not contradict existing on the criterion of the possibility of using established standards was determined. The ease of measurement and calculation was took into account. Findings. Qualitative and quantitative verification of the proposed and existing methods showed very good agreement of the measurement results. This gives grounds to assert that this methodology can be recommended to the workers of track facilities in the assessment of horizontal irregularities in plan not only curves, but also within the connecting part of switch congresses. Originality. The existing method of valuation of the geometric position of the curves in the plan was improved. It does not create new regulations, and all results are evaluated by existing norms. Practical value. The proposed technique makes it possible, without creating a new regulatory framework, to be attached to existing one, and expanding the boundaries of its application. This method can be used not only for ordinary curves, but for very short sections, the curvature of which changes abruptly to its opposite value.
Keywords: methodology; irregularity; measurement; plan of a railway track; curve assessment in plan
Introduction
On the Ukrainian railway network for the past several decades has been a tendency to increase the speed of motion [9], which obviously leads to the revision of existing and the creation of new regulatory documents. This applies to rail transport as a whole and of its individual farms. In particular, the track facilities directly involved in the maintenance and repair of road infrastructure.
Quite a significant impact on the performance of traffic safety, smooth running and ride comfort passengers in the general case affects not only the plan and profile of the railway track, but also the presence of geometric and strength irregularities. Existing regulations govern not only work to prevent occurrence of malfunctions during operation, but also the necessary course of action
to eliminate them. For the track state establishment in accordance with the maintenance norms the instrumental methods was used to evaluate its status.
In practice, the geometric position of the curve in plan is checked by means of traditional methods. These include: versine method [8], Hoffer's method [4] and the method of Honikberg [6]. The first two methods, can be usually use in the operation portion of the curve, the latter is the design of the reconstruction and repairs of the road.
The above mentioned versine method based on the measurement of deflections f (Fig. 1) when fixed value of the chord length through a specific length [8].
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Fig. 1. The bend versine measurement scheme
Method of Hoffer, which was forgotten over the last few decades, has been modified (Fig. 2) and found further application in practice [3].
Fig.3. Curve measurement scheme by the Honikberh method:
BC - beginning of curve; EC - end of curve
methods linked with can be listed in one
All above-mentioned geometric point of view another.
On foreign railways, the assessment of the
position of curves in the plan is treated similarly to that in the domestic railways using the versine method [12, 10].
The modern methods of valuation of railway track plan include [5, 7]:
- survey using modern total stations;
- the use of track measuring cars;
- survey using the benchmark system;
- plan survey with track measuring cars;
- use of track measuring trolleys.
Fig.2. The Hoffer modified method
For the design of the second track and reconstruction of the existing railway survey curves can also be performed using the method of Honikberg (Fig.3).
Fig.4. The crossover general scheme:
S1 - first switch; S2 - second switch
Therefore it is necessary to create a methodology that would give the opportunity to get versine to any position on the track section in the plan and to assess its state according to the difference obtained in related deflections.
Purpose
It is important quickly, efficiently and timely to perform routine maintenance and repairs for workers of track facilities. Based on this principle, it is necessary to develop a methodology for assessing the phase position of the road in such a way as to reduce the time spent on measurement and processing of the results. Thus as much as possible to use the existing regulatory framework relating to the issue of determining the position of the curve in the plan.
Methodology
- First, it is necessary to analyze the possible methods of assessing the position of the curve in the plan and to identify their main advantages and disadvantages. The following methods are taken into account:
- the position of the joints of rails using diagonals;
- method of linear serifs (polar method);
- position of connecting track ordinates of the basic line, that is broken outside of the track;
- measurement of horizontal angles in the plan;
- the position of the curve with the ordinate from the baseline, that is located between the rail thread.
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As a primary or reference, the most extensively used on the railways of Ukraine is the versine method. All other proposed methods will be theoretically checked and compared with the versine method.
Method of assessment of the joints using diagonals is to measure the distances d1, d2, d3, d4 (Fig. 5).
The measured diagonals in pairs should be compared (dj i d4, d2 i d3).
Fig. 5. The joints measuring position scheme
The diagonals must have the following value:
d =V a + Bf,
(1)
-B+
(2)
i+1 V ^i+1 i+1
In turn: ' A = Ro-(R - S,) cos a,
Ai+1 = Ro -(Ro - Si+1 )cos a
<
Bi =(Ro - Si +1 )sin ^
B,+1 =(Ro -St)sina, i = 1, 3,5..., 2n +1.
where Ro - the radius of the outer rails; St - track width, measured in the appropriate section; a - the
angle formed the normals to the curve at the
measurement points:
I,
a =-
Ro
(3)
where lo - the length of the outer rails between the measurement points.
If the pair of the measured diagonals are not equal, there are horizontal irregularities. The difference of pairwise diagonals characterizes irregularities in plan or disagreements rail joints.
But to evaluate geometric inequalities, their length lineq and amplitude bineq placed between the joints or between the cross-sections are almost not possible. Therefore, the assessment method application of the joints using diagonals makes it impossible to get the versine at intermediate points
in the future. In this case it is necessary to identify the additional points on the irregularities. If the joints are not on squares (overlapping joints on the value of (a), the task on the assessment of horizontal irregularities is complicated. Moreover, as the source the radius and length of the outer and inner rail filaments between the points of measurement should be known. This method is appropriate to use in areas where the rails have the same length, i.e. in a straight line.
When using the method of linear serifs (the so-called polar method) the base with the length S should be set outside of the track. The checkpoints
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divided the track into segments of any length (Fig. 6). From the first base station the distance ai is measured to control points. From the second base station the distance bi is measured to the same checkpoint.
Tha angles a, fa can be found with the formula:
( S2 + a,2 - b2 Л
a, = arccos
ß, = arccos
2a, S
( S2 - a,2 + b 2b, S
/ 2 Л
(4)
The coordinates Xi and Yi for each point of measurement can be set from the expression:
X,. = S-
tg ß,
Y, = S
tg a,+ tg ß,
tg a- tg ß, tg a,+ tg ß,
(5)
The test measured coordinates for each point can be done on the other side of the curve, with the set on the new basic line and following the same procedure.
The measurement error increases with increasing distances ai and bi, therefore, the basis S should be placed as close as possible to the track. The main disadvantage is the fact that when determining the curvature of the track in adjacent points, it may suddenly change due to the measurement errors.
Next on the list for comparison is a method of ordinate measuring from the baseline, set outside of the track. For this purpose it is necessary to fix a baseline, if it is possible, within the subgrade. For further measurement of ordinates a baseline should be divided into a control point for measurement, the distance between which a1, a2, a3, ..., an they are not necessarily identical (Fig. 7).
Fig. 6. The linear serif method
Fig. 7. The ordinate measurement scheme from the basic line is broken on the sidelines
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From control points perpendicular to the baseline the segments are laid before crossing with a rail thread of the track.
During the survey the great attention should be paid to the deposition of the perpendicular line from the baseline. To perform such an operation is difficult, especially when the ordinate value is more than 1 000 mm. The geometric position of the curve is determined by the results of the measured ordinates.
The problems of measurement of this method is that the values of ordinates are set according to the outside edge of the rail. And therefore, it is also necessary to determine the wear of the rail head at each point. And also the fact that the stations for baselines need to fix reliably it cannot be ignored, because during the crossing of trains on a site is not only by their displacement. This all leads to significant thief of working time.
Alternatively, the position of the curve in the plan can be measured with horizontal angles. Usually these cases arise within the seam zone during the connecting of two rails (Fig. 8).
The angular displacement of the rails during operation may occur due to insufficient lateral stability of a rail-sleeper grid, due to the stiffness of the rails, which are trying to recover the initial shape to the bending, the reducing the regulatory pressing force of the terminals, hijacking ways and the presence of temperature forces in the rails in the summer, that can lead to a zero gaps and incorrect location of the sleepers in the curve.
<o = V 2sin2 ß
imp '
(6)
The maximum angle of impact, in turn, is formed by a number of other factors:
cos ß,mp = cos ßn --
*0
(7)
where pn - initial arrow angle; S - the gap between the crest of the wheel and rail; R0 - the initial radius of switch rail. The radius value is:
R =
VI
Jo
(8)
Fig. 8. Plan angle measurement scheme
The question how to measure the value of the angle of impact arises immediately. To date, the only value that characterizes the so-called angle of impact, is the rate of loss of kinetic energy at impact in switch rail [1]:
where j0 - fast (pulsed) centrifugal acceleration.
At the present time in different countries of the instantaneous magnitude of centrifugal acceleration in the design adopted in the range from 0.4 to 1.0 m/s2 [13]. However, as shown the theoretical and experimental studies, these values can reach 2-2.5 m/s2 [11]. It is also necessary to take into account the fact that the conditions of interaction within the switch and curve are significantly different. This is, firstly, the speed of movement. Secondly, the presence or absence of superelevation. Thirdly, the design features of the switch rail which, unlike conventional rail in a curve are not fixed. And there are more many other factors that affect the interaction of track and rolling stock. Therefore, to assess the position of the curve in terms of the magnitude of impact angles is possible, but not entirely correct. The speed limit in the zone of angles arise in the plan can be set by changing the width S2 relative to the regulated value Si [2].
The latest from considered methods is the position of the curve with the ordinate from baselines rail that is located between the filaments (Fig. 9). The ordinate dimension from the rails to the base line, broken on the outside of the track or between the track is taken as bases(see Fig. 7).
The problem of using this method is that current regulations do not regulate the procedure for the use of the measured ordinates.
The authors propose to estimate the position of the horizontal curve on the ordinate, the value of which is mathematically given by the deflections, comparing which can get the status of the curve.
where V - speed.
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Fig. 9. The ordinate measurement scheme from the basic line is located between rails
Fig. 10 shows the calculated scheme of the transition from the axis, measured along the
perpendicular to the baseline, omitted at the points
A, F, B, to the versine FE, measured from the center of the chord length a.
Denote the versine of FE in i point using f Ordinates, measured in the i-th and neighboring points, in accordance Fi and Fi-1, Fi+1. From geometrical considerations we can write the formula for the determination of versine fi, measured from the center of the chord length a.
Given the fact that in real conditions, the angle a has a value close to zero, so cos a« 1, then we can write:
f, = F -2(F+1 + F-1 ).
(9)
where Fi, Fi-1, Fi+1 - ordinates, measured from bais line, mm.
For testing the methods it is necessary to conduct field measurements in real conditions. In
practice, to fix the base for the measurements (see Fig. 9) between the rails is difficult. It is proposed to consolidate and remove ordinates track template (Fig. 11). Obtained values of the ordinates must be transformed into the versine at the value of the chord a. Actually, the question arises about the chord length when this method will provide accurate information.
According to [2] the curves are estimated by the difference in adjacent deflections only when the chord length is a=20 m. Show that for short irregularities in plan, the length of which is less than the length of the chord, it makes no difference how long the chord to assess the condition of the curve is. The allegations are originate from the following calculations.
Consider the case depicted in Fig. 12. Let there exist a curve, which in the i point has a horizontal inequalities with amplitude bineg and length lineq< a.
Fig. 10. Design scheme of transition from the measured ordinates F to versine f
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Fig. 11. Measuring with the track pattern ЦУП-2 Д
Fig. 12. The determine correlation scheme between versine differences at different chord length
For an ideal (theoretical) curve = ft2 0 and
fi-j = f1 . In case of occurrence of irregularities
and offsets of the i-th point on the value bineq the following relations are fair:
Then, the difference of the deflections at 20 meter chord would be:
f20 = f20 - f -2 =T W
3 —/ 2
(11)
f20 - ft
20 ■ bt b
' ti ' ~ineq 20 20
20 20 Ji-2 ~ Jt i-2
ineq
f10 « f1U + b
Ji Jti
■10 ti
f10 ~ J10 _ Ji-1 « Jt i-1 "
(10)
For the 10 meters chord the result is similar:
3 2
f10 = f10 - fi-0 =т bmeq.
(12)
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Therefore, the difference in adjacent versine at 20-and 10-meter chord are the same, that gives grounds to assert the requirement of assessing the state of the curve only on the statutory regulations of the chord length. Accordingly, the phrase in paragraph 2.1.2 [2] «...the difference of adjacent versine, measured from the midpoint of the chord length of 10 m shall be no greater than 5 mm» is incorrect and inappropriate.
The section was divided in 1 m and the dimensions of the versine was carried out at 10-meter chord (the curve radius R»300 m).
Table 1
The measurement results of the curve position in plan
№ of point Fi, mm fi mes,mm fi calc,mm Absolute error, mm
1 302
2 326
3 344
4 362
5 374
6 388 37 35 2
7 401 38 39 1
8 405 37 38 1
9 402 34 31 3
10 401 33 31 2
11 405 34 35 1
12 398 29 30 1
13 390 28 30 2
14 381 27 28 1
15 366 27 28 1
16 352 21 20 1
17 336 19 18 1
18 315
19 304
20 275
21 260
22 239
Table 1 shows the actual Fi ordinate measured versine f™eas and calculation versine ftcal, obtained by the ordinate transformation using the proposed method.
Findings
A comparison of the calculated with the proposed method and measured versine showed a small absolute error, which is well within the measurement error. Thus, it can be assume that the technique can be used to assess the status of the curve track section with an abrupt change of curvature.
Originality and Practical value
The proposed improved method of estimating the position of the curve in plan, quickly changes its curvature and has bumps that are shorter than the chord length.
The results showed that this method is quite simple and convenient to use to perform naturals measurements using the least amount measuring means. And also thanks to the simplified method for data processing and the lack of controversy regarding the existing regulatory framework the speed limit on a given stretch of road can be set at once.
Conclusions
1. The existing methods of estimating the geometric position of the normal curves in plan in the operation and design of repairs to the track are analyzed.
2. A comparative analysis was realised and the main advantages and disadvantages, limits of the application of existing methods were determined. The most suitable option for detailed analysis was determined.
3. The mathematical combination of the existing and proposed methods was developed.
4. The qualitative and quantitative verification were conducted. The results showed the adequacy of the proposed methodology and the absence of contradictions.
5. The suggestions regarding the editing of paragraph 2.1.2 Instructions on the device and maintenance of the tracks of the Ukrainian Railways [2] were provided.
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А. М. ПАТЛАСОВ1, С. А. ТОКАРЕВ
2*
'Каф. «Путь и путевое хозяйство», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел./факс +38 (056) 373 15 42, эл. почта am_patlasov@ukr.net, ORCID 0000-0003-2081-5648
2*Каф. «Путь и путевое хозяйство», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел./факс +38 (056) 373 15 42, эл. почта tokarevsergeyaleks@yandex.ua, ORCID 0000-0002-2607-3123
УСОВЕРШЕНСТВОВАНИЕ МЕТОДИКИ ИЗМЕРЕНИЯ ГОРИЗОНТАЛЬНЫХ НЕРОВНОСТЕЙ В ПЛАНЕ
Цель. В масштабах всего верхнего строения пути (ВСП) существуют такие конструкции, где стандартные подходы к принятию решения о дальнейшей их эксплуатации не совсем корректны или приемлемы. В частности, это касается участков пути, которые достаточно быстро меняют свои геометрические параметры: радиус, кривизну, угол поворота и тому подобное. В качестве примера, к таким участкам ВСП
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2015, № 4 (58)
можно отнести те стрелочные съезды, в пределах которых находится составляющая, так называемая соединительная часть, на достаточно короткой длине существенно меняющая кривизну. Оценить положение в плане такой конструкции на основе существующей методики (по разнице в смежных стрелах изгиба) практически невозможно. Поэтому в исследовании предлагается дополнить и усовершенствовать методику оценки положения кривой в плане по разнице в смежных стрелах изгиба. Методика. Проанализированы возможные варианты измерения горизонтального положения кривых в плане. Определена наиболее адекватная методика, которая не противоречит существующей по критерию возможности использования установленных нормативов. Во внимание также принималась простота измерений и расчета. Результаты. Качественная и количественная верификация предложенной и существующей методик показала очень хорошее совпадение результатов измерений. Это дает основания утверждать, что данную методику можно рекомендовать работникам путевого хозяйства в оценке горизонтальных неровностей в плане не только в кривых, но и в пределах соединительной части стрелочных съездов. Научная новизна. Усовершенствована существующая методика оценки геометрического положения кривых в плане. При этом не создаются новые нормативы, а все полученные результаты оцениваются по существующим нормам. Практическая значимость. Предлагаемая методика дает возможность, не создавая новую нормативную базу, привязываться к существующей, и расширяет границы ее применения. Данную методику можно применять не только для обычных кривых, но и для очень коротких участков, кривизна которых резко меняет свое значение на противоположное.
Ключевые слова: методика; неровность; измерения; план пути; оценка состояния кривых в плане
О. М. ПАТЛАСОВ1, С. О. ТОКАРЕВ2*
'Каф. «Ктя та колшне господарство», Дшпропетровський нацюнальний ушверситет затзнпчного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Укра!на, 49010, тел./факс +38 (056) 373 15 42, ел. пошта am_patlasov@ukr.net, ОКСШ 0000-0003-2081-5648
2*Каф. «Колш та колшне господарство», Дшпропетровський нацюнальний ушверситет затзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Украша, 49010, тел./факс +38 (056) 373 15 42, ел. пошта tokarevsergeyaleks@yandex.ua, ОКСШ 0000-0002-2607-3123
УДОСКОНАЛЕННЯ МЕТОДИКИ ВИМ1РЮВАННЯ ГОРИЗОНТАЛЬНИХ НЕР1ВНОСТЕЙ У ПЛАН1
Мета. В масштабах вае! верхньо! будови коли (ВБК) юнують так конструкци, де стандарты пвдходи до прийняття ршення щодо подальшо! !х експлуатацп не зовам коректш або прийнятш. Зокрема, це стосуеть-ся дмнок коли, яш досить швидко змшюють сво! геометричш параметри: радус, кривизну, кут повороту тощо. Як приклад, до таких дмнок ВБК можна вщнести п стрiлочнi з'!зди, в межах яких е складова, так звана з'еднувальна частина, котра на досить коротай довжинi суттево змшюе кривизну ще! частини. Оцiнити положения у плат тако! конструкци за юнуючою методикою (за рiзницею в сумiжних стрiлах вигину) практично неможливо. Тому в дослiдженнi пропонуеться доповнити та удосконалити методику оцiнки положення криво! у планi за рiзницями в сумiжних стрiлах вигину. Методика. Проаналiзовано можливi варiанти вимiрювання горизонтального положення кривих у плат. Визначено найбшьш адекватну методику, яка не суперечить юнуючш за критерiем можливосп використання встановлених нормативiв. До уваги також приймалась простота вимiрювань та розрахунку. Результати. Якiсна й кшьшсна верифiкацiя приведено! методики показала дуже добрий збiг результатiв вимiрювань запропоновано! та iснуючо! методик. Це дае тдстави стверджувати, що дану методику можна рекомендувати працiвникам колiйного господарства щодо оцшки горизонтальних нерiвностей у плат не лише в кривих, а й у межах з'еднувально! частини стршочних з'!здiв. Наукова новизна. Вдосконалено юнуючу методику оцiнки геометричного положення кривих у планi. При цьому не створюються новi нормативи, а все базуеться на юнуючих. Практична значимкть. Запропонована методика дае можливють, не створюючи нову нормативну базу, прив'язуватись до iснуючо!, та розширюе меж1 !! застосування. Дану методику можна застосовувати не тшьки для звичайних кривих, а й для дуже коротких дмнок, кривизна яких рiзко змiнюе свое значення на протилежне.
Ключовi слова: методика; нерiвнiсть; вимiрювання; план колi!; оцiнка стану кривих у плат
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2015, № 4 (58)
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Prof. V. D. Petrenko, D. Sc. (Tech.) (Ukraine); S. V. Ivanchak, (Ukraine), Chief engineer of the Track
service of Prydniprovska Railway recommended this article to be published
Received: June 15, 2015
Accepted: Aug. 14, 2015
