DETERMINATION OF STOPPING DISTANCE OF UNPOWERED ROLLING STOCK BY METHOD OF SEQUENTIAL BRAKING

Dep. «Car and Car Facilities», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 04, e-mail reidemeister@mail.ru, ORCID 0000-0001-7490-7180 Laboratory «Cars», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 04, e-mail v.sh91@mail.ru, ORCID 0000-0003-4701-6491


Introduction
In the current regulatory documents [8] one of the effectiveness criteria of the car automatic brake is considered stopping distance.Stopping distance is the distance traveled by train from the moment of shift of brake valve handle or emergency valve into the braking position to the full stop of train [5,12].The stopping distance is determined by means of field experiment [14,1].For the test there is formed a sample traction unit of a locomotive, a track test car and a single car.It is allowed conducting the test without a track test car if its functions are performed by the lead locomotive.The value of the stopping distance is assumed the track traveled by car from the moment of uncoupling from a sample tractive connection to the complete stop.This method of determining the stopping distance was called the «abandonment» method.In cases when the integrity of the tractive connection must not be broken, the method of sequential braking is used.One conducts a series of braking with a sample tractive connection, consisting of a locomotive, a track test car, and, if necessary, a sample car, with recording of braking distance.The values of the tractive connection stopping distance with a sample car and without it are used to calculate the stopping distance of a single car [2,10].The literature focuses on the method of sequential braking during unpowered rolling stock testing [3,6].According to the requirements of regulatory documents [8] the value of target brake application speed is selected from a range of 60 km/h and further at intervals of 20 km/h till the design speed.The tools for speed and stopping distance measurement should meet the following requirements listed in Table 1.

Purpose
To estimate the determination accuracy of a car stopping distances during the test by the method of sequential braking.

Methodology
Determination of the stopping distance of the sample car by method of sequential braking can be carried out according to the presented method.When there are set speeds one calculates the braking force of the locomotive or the tractive connection locomotive-track-test-car (L) and the tractive connection with a sample car (L-SC).Having processed the stopping distance results we determine the braking force L and L-SC by the formula: where Е і -kinetic energy; S i -braking length; W iresistance to movement; і -index indicating the set of tractive connection.Kinetic energy is determined by the formula [4] 2 (1 ) where Q i -weight; V b , -velocity at the beginning of braking; g -gravitation acceleration, g = 9.81 m/s 2 ; γ -coefficient taking into account the steadying effect.The coefficient γ assume as [9] − Locomotive -0.25; − Passenger car 0.5; − Freight car: − Loaded -0.08; − Empty -0.04.
For coupled unit the coefficient γ is determined by formula: where tc Q -weight of tractive connection.Resistance to movement is determined by the formula where w i -specific resistance to movement 0.4 0.6 where w Vb , w Ve -basic specific resistance to movement at speeds at the beginning and at the end of braking, respectively [5,12].
The braking force of a sample car is determined by the formula The braking length of the test car is calculated by the formula: To verify the proposed method there were conducted the calculations of stopping distance of the tractive connection with the sample car and without it, and of the sample car separately by the typical method [11].Then the obtained values for the tractive connections were used as input data to determine the stopping distance of sample car by the expressions (1-7).The results are shown in Table 2.The parameters of locomotives and cars are given in Table 3.
The values of stopping distance for different configurations of sample tractive connection shown in Table 4 were obtained at the initial braking speed of 120 km/h.The discrepancy between the stopping distance of a sample car by the method of «sequential braking» and the stopping distance value by the typical method does not exceed 0.84%, so I think the method accuracy is sufficient.
Every testing implies the measurement error.Evaluation of the error impact on the final results is shown in Table 5.The error was introduced into the original data and then increased.The evaluation was conducted during the simulation of 100 braking operations.
The error reduction at the input from 1% to 0.5% will result in double decreased error at the output (stopping distance of the car).

Originality and practical value
The methodology of error estimation of car stopping distances determination under tests by the method of sequential braking was proposed.Work results make it possible to replace the running brake tests by the abandonment method, under which the integrity of tractive connections is broken, with safer testing by the method of sequential braking, providing the level of result accuracy of 2-5%.

Conclusions
The conducted research allows making the following conclusions: 1) An alternative to the method of «abandonment» in determining the effectiveness of the car brakes empirically during the train testing should become the method of «sequential braking».
2) Further work should be focused on determining the ways to reduce the impact of cumulative error on the stopping distance of a sample car.
3) The proposed test method requires experimental confirmation.