THE MEASUREMENT METHODOLOGY IMPROVEMENT OF THE HORIZONTAL IRREGULARITIES IN PLAN

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, е-mail am_patlasov@ukr.net, ORCID 0000-0003-2081-5648 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, е-mail tokarevsergeyaleks@yandex.ua, ORCID 0000-0002-2607-3123


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 i (Fig. 1) when fixed value of the chord length through a specific length [8].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.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).All above-mentioned methods linked with geometric point of view can be listed in one 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. 4. The crossover general scheme: 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.
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 d 1 , d 2 , d 3 , d 4 (Fig. 5).
where R o -the radius of the outer rails; S i -track width, measured in the appropriate section; α -the angle formed the normals to the curve at the measurement points: where l o -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 l ineq and amplitude b ineq 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 socalled polar method) the base with the length S should be set outside of the track.Тhe checkpoints divided the track into segments of any length (Fig. 6).From the first base station the distance а і is measured to control points.From the second base station the distance b і is measured to the same checkpoint.
Tha angles α i , β i can be found with the formula: The coordinates X і and Y і for each point of measurement can be set from the expression: tg , tg tg tg tg .tg tg 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 а і and b і , 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 a 1 , a 2 , a 3 , …, a n they are not necessarily identical (Fig. 7).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.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 V -speed.
The maximum angle of impact, in turn, is formed by a number of other factors: where β n -initial arrow angle; δ -the gap between the crest of the wheel and rail; R 0 -the initial radius of switch rail.The radius value is: where j 0 -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 S 2 relative to the regulated value S 1 [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.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 і point using f i .Ordinates, measured in the i-th and neighboring points, in accordance F i and F i-1 , F i+1 .From geometrical considerations we can write the formula for the determination of versine f i , measured from the center of the chord length a.
Given the fact that in real conditions, the angle α has a value close to zero, so cos 1 α ≈ , then we can write: ( ) where F i , F i-1 , F i+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 b ineg and length l ineq ≤ a. ; ; Then, the difference of the deflections at 20 meter chord would be: For the 10 meters chord the result is similar: 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).f , 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 2.1.2Instructions on the device and maintenance of the tracks of the Ukrainian Railways [2] were provided.

Fig. 3 .
Fig.3.Curve measurement scheme by the Honikberh method: BC -beginning of curve; EC -end of curve