Determination of Traction Characteristics of Diesel Locomotives by Least Square Method Applied to Experimental Data

Determination of traction characteristics of diesel locomotives by least square method applied to experimental data

A. Radosavljevic Mechanical Engineering Department, Institute of Transportation CIP,

Neman]ina 6, 11000 Belgrade, Yugoslavia EMail: [email protected]

Abstract

A common situation on the railways is that numerous vehicle data are experimentally defined. But for numerical and computational calculations it is necessary to present this data in functional forms. This paper defines methods for the determination of basic traction characteristics of railway traction vehicles: basic resistance and tractive effort produced on the wheel tread, provided we have experimental data. The well-known method of least squares is used for determining coefficients of function and correlation coefficients which best represent experimental measurements and are applied to experimental data. All calculations are conducted on the basis of the data received during test runs of diesel-electric locomotive series JZ 641-300. As a result we have basic traction characteristics in functional forms and very small deviation of experimental data and values calculated from functions.

1 Introduction

Computer-aided calculations are now ordinary practice in traction-energy calculations on railway. That is why better accuracy of calculations is very important. On railways, we are faced with the fact that certain values can be experimentally determined so that such data, in order to be used in traction- energy calculation should be substituted by the curves that represent them best.

68 Computational Methods and Experimental Measurements

When compiling a model of a traction vehicle running on a line it is also advisable to start with the data (for example for traction motor, diesel motor, main generator etc.) given in graphic or tabular forms. The values given in such a way are not suitable for computer calculation and should be transformed into analytical expressions.

Such an approach gives us the possibility to analytically present the most important characteristics of electrical or diesel locomotives: basic resistance and traction characteristic (tractive effort). It is necessary to mention that accuracy of curve determination to replace experimentally obtained points depends on the fact that locomotive tractive effort values are expressed in kN and minor deviations from experimentally obtained values are important in traction-energy calculations (those of train running time and energy consumption). If in approximation, desired accuracy is not achieved for a certain train running speed interval, then the interval of speed change should be altered (reduced) and approximation repeated. Experimental determination of values for basic resistance and traction characteristic were carried out on a diesel-electric locomotive,series JZ 641-300.

2 Diesel electric locomotive series JZ 641-300

Diesel electric locomotives, series JZ 641 (subseries 300) are manufactured in Ganz Mavag Co., Hungary ( Fig. 1). The inventory of these locomotives counts

3 1 in the Railway Transport Enterprise "Beograd" which is a part of Yugoslav Railways (JZ).

Figure 1: Diesel electric locomotive, series JZ 641-300

The locomotives are four axle units with individual axle drives, Bo-Bo axle arrangement, used for shunting operations in passenger stations and marshalling yards and haul of goods and lightweight passenger trains, but without train heating facilities. They are designed for maximum speed of 80 km/h, the ratio of smaller gear teeth to bigger gear teeth being 17:77. They are equipped with eight-cylinder, four-stroke, water-cooled diesel motor with a V-

designed antechamber combustion system and cylinder axes at the angle of 90° (SEMT-PIELSTICK 8 PA4V185 VG). In the original design, the motor had nominal power of 982 kW at 1500 1/min. However, in the locomotives in this series, for the purpose of harmonizing it with the main generator characteristics, the diesel motor power was damped to nominal power of 660 kW± l%at 1500 1/min.

The power distributor is electrical with direct current main generator (ED 800) and four direct current electric traction motors (Tc 32.44a/14-K) placed in pairs in each bogie. The torque of the traction motors is transmitted to axles via axle gears, that are designed as single-step reducing gears.

3 Determination of basic resistance

Basic resistance of a locomotive means the resistance occurring when a locomotive runs at a constant speed V on tangent and level track under average weather conditions. Basic resistance of a locomotive JZ 641-300 was measured by the method of runway of a locomotive with a dynamometer car on tangent and level track (gradient was 0 %o on the longest section of it, while the maximum deviations from the horizontal line were -0.6 %o) recording speed and effort on buffers. When the speed of 80 km/h was achieved, the controlling handle in the locomotive was pushed into neutral position and the locomotive ran until it stopped without brake application. With the speed decrease, the basic resistance of locomotive WOL [daN], was derived from the following formula

WOL = WOL - + Fod + WiL (1)

where, WOL = AV • L [daN]; AV = V: - V, [km/h-30s] = WOL [daN/t], AV is 30s deceleration; L = 64 t locomotive mass; Fod [daN] effort on buffers of the dynamometer car, WJL = w, • L [daN] is resistance force due to track gradient;

Wj [daN/t] specific resistance due to track gradient.

Table 1. The experimental values of the basic resistance V [km/h] 0 10 20 30 40 50 60 70 80

Wou [daN] 294 304 316 333 361 400 443 494 556

The experimental values of speed and basic resistance of a diesel locomotive are shown in the Table 1.

In order to carry out as adequate as possible analytical interpretation for the locomotive basic resistance and curve coefficients that best represent the experimental values, least square method was used. It is known in practice that the curve for the locomotive basic resistance (diesel or electric) is a square parabola having the form of:

70 Computational Methods and Experimental Measurements

OL = a • V" + b • V + c (2)

The parameters a, b and c are determined from the condition that a sum of the square deviation has minimum value, Krsmanovic [1], Simonovic [2].

S (a,b,c) = [Woy - (a • Vi + b • Vi +c)f = min (3)

For that purpose we will differentiate the function S (a,b,c) by a, b and c and equalize to zero.

= 0 (4) Sa Sb Sc

By calculating partial derivatives we obtain the following system of equations to determine parameters a, b and c (n presents a total number of experimental data).

, oLi

The calculation of parameters a, b and c is made easier by a program for personal computer written in Turbobasic. Based on the given measurements, the values obtained for a, b and c are as follows: a-0.03931832, b=0.08620139 and c=296.4304, correlation coefficient is 0.9995, so that the square function (parabola) for the basic resistance of diesel locomotive ]Z 641-300 has the following form which is suitable for analytical calculations:

= 0.0393 1832 + 0.08620139 • V + 296.4304 (6)

In order to verify the a, b and c coefficients, another program CURVEFIT was used. It gave the same results (Table 2.)

Table 2. V [km/hi 0 10 20 30 40 50 60 70 80

WOL' fdaN] 294 304 316 333 361 400 443 494 556 WoLfdaN] 296.4 301.2 313.9 334.4 362.8 399 443.1 495.1 555

Computational Methods and Experimental Measurements 71

4 Determination of traction characteristics

A traction characteristic for the locomotive series JZ 641-300 consists of seven curves each corresponding to a position of the running controller, namely to respective diesel motor power (range from 85 to 660 kW). The traction characteristic corresponding to the full diesel motor power is most important for traction calculations (position 7 of the running controller) so that experimental measurements will be generally carried out for that purpose.

Depending on the locomotive speed we distinguish three intervals in traction characteristic variations (Fig. 2): I: From the critical speed (minimum constant speed) V=10.9 km/h to V=26 kin/h when the traction motor inductor field is attenuating - shunting.

II: From the speed when deshunting is done V=23 km/h to speed of V=63.5 km/h when the main generator power starts to be limited. Ill: From the speed V=63.5 km/h to the maximum locomotive speed.

Ft, Wol [kN] F,

i j r i\ \ \

h j \ L j \ \ L. \ II 1 K L III

) 109 20 40 60 80 1C V[km/h]

Figure 2: Tractive characteristics and basic resistance of the JZ 641-300

diesel locomotive

Experimental data of traction characteristic were recorded by an inspection instrument train formed of the following vehicles: diesel locomotive JZ 641-325

72 Computational Methods and Experimental Measurements

+ JZ dynamometer car + electrical locomotive JZ 461-136 for braking + 5 four- axle passenger coaches. The total mass of the inspection train (without the JZ

641-325 diesel locomotive) was 388 tons and the number of axles 30. The applied method involved measurement of the locomotive traction characteristic with the braked instrument train in the whole speed range (0-^80 km/h). An electric rheostat brake was used on the electrical locomotive. When the traction characteristic was tested at higher speeds, the four-axle passenger cars were uncoupled from the instrument train in order to minimize train mass and achieve maximum speed. This mass was 170 tons and the number of axles was 10. The ambient air temperature was +19 °C, the weather was calm, no wind, and the rails were dry. In the course of testing, the following values were measured in the dynamometer car: traction characteristic (tractive effort) at the draw bar, specific resistances during acceleration and deceleration, main generator current and voltage, inspection train speed, fuel temperature and consumption in the diesel motor. The values of specific resistance were read out from the longitudinal profile of the line and the line gradient. Before testing, locomotive mass and wheel diameters of locomotive and dynamometer car were found. When the traction characteristic was recorded a fuel sample was taken for a chemical analysis (density and low heat power of fuel). The fuel characteristics were checked in order to determine the locomotive efficiency at the draw bar and the wheel rim. The measured values of tractive effort are given in Table 3. The traction characteristic (tractive effort) of the locomotive at the wheel rim Ft was calculated from the following formula:

where: Fk [daN] is the locomotive tractive effort at the draw bar; WOL [daN] basic locomotive resistance; Wa= a-L [daN] resistance force from acceleration and deceleration; L [t| locomotive mass; a [daN/t] specific resistance from the acceleration and deceleration; i [daN/t] specific resistance from track gradient; WR [daN/t] specific resistance from curved track; W, = i-L [daN] resistance force from track gradient; FWR = WR-L [daN] resistance force from curved track.

Table 3. V [km/h] 9.66 9.66 10.15 11.11 15.94 15.94 16.43 16.43 16.43 16.43 16.43 19.32 Ft [kN] 196.06 188.95 179.8 165.62 125.4 123.36 121.01 121.2 120.19 120.19 119.63 102.77 V [km/h] 19.32 19.32 19.32 19.32 19.81 24.15 24.64 24.64 24.64 24.64 25.12 31.4 Fi [kN] 102.77 102.77 101.76 101.76 92.63 77.47 77.99 78.51 77.49 75.97 75.47 61.18 V [km/h] 32.37 32.85 33.33 33.82 33.82 35.26 34.78 35.26 35.26 38.16 38.65 52.65 Ft [kN] 59.69 61.41 58.68 58.18 57.39 56.43 57.42 56.21 57.42 53.99 52.98 37.65 V [km/h] 53.14 53.14 53.62 62.32 63.28 63.28 63.77 64.73 65.7 67.63 71.01 66.66 Fi [kN] 37.68 38.59 37 32.1 30.88 30.86 30.9 28.75 26.1 24.28 21.26 27.71 V [km/h] 77.3 77.77 78.26 78.26 79.71 80.19 80.19 81.16 81.16 81.16 Fi [kN] 17.43 18.2 18.48 18.95 19.61 18.7 17.93 18.36 18.05 18.12

Computational Methods and Experimental Measurements 73

The least square method applied to measurements through the program CURVEFIT gives the following function as the most convenient form of representing tractive effort:

F = a + b - V + - (8) V

where coefficients a, b and c of the locomotive tractive effort differ for the three intervals of speed change (Table 4.), correlation coefficients are 0.9955, 0.9966 and 0.9782. Figure 3 shows traction characteristics and basic resistance of the JZ 641-300 diesel locomotive with experimental values.

Table 4. AV fkm/h] a b c 10-25 66.744 -1.8346 1365.605

25-615 22.5102 -0.2383 1492.4797 63.5-80 -472.7856 3.0889 19519.7517

Ft, Wol [kN] 200

150

100

o/ 0 20 40 60 80 100 V [km/h] Figure 3: Traction characteristic and basic resistance of the JZ 641-300 diesel locomotive with experimental values

74 Computational Methods and Experimental Measurements

5 Conclusions

By checking the functions representing values of basic resistance and traction characteristic of diesel locomotive, series JZ 641-300 it can be stated that the applied least square method has given very satisfactory values for the analytical presentation of the main curves for this locomotive. Highly accurate approximation is indispensable because the , traction characteristic is a domineering parameter in all traction and energy calculations for locomotives, and the accuracy of the calculation mostly depends on the accuracy of that parameter. Besides applying the least square method to experimental values, we can mention its further applications on railways such as for various diagrams of operation of some units (diesel motor, tractive motor, main generator etc.) which are also to be presented in form of functions for computer processing by the least square method.

References

1. Krsmanovic, Lj. & Vuskovic, I., Method of Laboratory Measurement, Faculty of Mechanical Engineering University of Belgrade, Belgrade, pp. 61-96, 1984.

2. Simonovic, V., Introduction in Theory of Probability and Mathematical Statistics^ Gradjevinska knjiga, Belgrade, pp.92-96, 1988.