Analysis of optimal periodicity of preventive maintenance of rail service car taking into account operational technology Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

Secton 6. Mechanics

Yakubov Mirdjalil Sagatovich, Mukhamedova Ziyoda Gafurdjanovna, "Tashkent Institute of Railway Transport Engineers, Department of Transport Logistics Tashkent, Uzbekistan Mukhamedova Ziyoda, E-mail: ziyoda.mukhamedova@email.com

ANALYSIS OF OPTIMAL PERIODICITY OF PREVENTIVE MAINTENANCE OF RAIL SERVICE CAR TAKING INTO ACCOUNT OPERATIONAL TECHNOLOGY

Abstract: Analysis of the nature, causes of damage and modes that led to a failure of rail service car operated by JSC "Uzbekiston Temir Yollari" has shown that 50% of the damage falls on mechanical equipment, 31.8% on electrical and 18.2% on hydraulic equipment. The result of the search and elimination of the failure of a rail service car, assessment of the possibility of its failure, monitoring of operation quality of technological process with complex mechanical, electrical and hydraulic equipment should be a clear, well-coordinated static and dynamic stability of the assembly site allowing the basic operations of the overhead contact system. For this purpose, a certain maintenance schedule is carried out to reduce the flow parameter (intensity) of failures. Based on the carried out analysis and calculations, the authors managed to obtain the optimal periodicity of scheduled preventive maintenance separately for mechanical, electrical and hydraulic equipment, which is, 372.8 hours, 500 hours, and 620.2 hours, respectively.

Keywords: railcar, main frame of the body, analytical-numerical method, preventive maintenance, hydraulics, mechanics.

1. Introduction

Analysis of the nature, causes of damage and modes that led to a failure of rail service car operated by JSC "Uzbekiston Temir Yollari" has shown that 50% of the damage falls on mechanical equipment, 31.8% on electrical and 18.2% on hydraulic equipment.

The result of the search and elimination of the failure of a rail service car, assessment of the possibility of its failure, monitoring of operation quality of technological process with complex mechanical, electrical and hydraulic equipment should be a clear, well-coordinated static and dynamic stability of the assembly site allowing the

basic operations of the overhead contact system. For this purpose, a certain maintenance schedule is carried out to reduce the flow parameter (intensity) of failures. It is known that three principles of assignment of operation periods between preventive maintenance are distinguished: regular, calendar and combined ones [1, 2]. For rail service car, a combined principle, or a so-called mixed mode, is used; it includes scheduled precautionary repair and unplanned preventive maintenance.

To calculate the periodicity of preventive maintenance of a rail service car, it is necessary to know the effects of the periodicity of preventive maintenance. It

is necessary to mention that the maintenance requires a certain amount of time and resources, which generally reduce the technical and economic efficiency. Therefore, reliability assessment is performed taking into account financial, labor and other operating costs. Equations linking the reliability and maintenance costs can be obtained while investigating maintenance processes, taking into account some acceptable ranges of quantitative reliability indicators at minimum costs; that is, an optimal period of preventive maintenance is calculated, separately for mechanical, electrical and hydraulic equipment taking into account the technological nature of maintenance.

For a rail service car used for the assembling and repair of the overhead contact system, which is the most important part of the speed and high-speed electrified railway, the limit state of the resource is established, that is, the service life for reasons of safety, of economic and other indicators when the maintenance system is installed.

2. Determination of optimal periodicity

Below we consider and determine the optimal periodicity of each type of equipment, taking into account their physical characteristics, that is, the determinant parameters and extrapolating the changes in their value by the operating time until the limiting parameter is reached. For the rail service cars, it is advisable to use as determinant parameters the accuracy of load-carrying capacity limiter of the rotary crane, the frame strength mechanism, the tightness of the hydraulic equipment and the insulation failure, as well as the failure of connectors and contacts of electrical equipment during long service cycles. When the predetermined rates of resource production determined from the failure rate curves x (t) or the failure flow parameters o (t), are reached, the time comes from which the unacceptable increase of A and w begins [4].

It is known that conducting scheduled preventive repairs at increasing deviations from the adjusted parameters and the failure flow o (t), caused by aging and changing parameters due to deviation from the established operating conditions of the object, reduces the average frequency of loss of the normal mode of operation [5, 6].

Taking into account that each mechanical, electrical and hydraulic equipment of a rail service car is subjected to several types of failures, characterized by A (t) and o (t), the periodicity of scheduled preventive maintenance TnA can be optimized according to the criteria for a minimum of resource costs for the type of equipment and

mode losses of electric trains traffic, due to failures of the equipment elements of the rail service cars.

Analysis of the average cost of preliminary inspections and routine repairs of the main parts of the equipment of the rail service cars shows that the cost of their labor expenditures "LCm.p - is less than the losses from its emergency work =1 Cae, leading to a decrease in its resource and loss from the established traffic of electric rolling stock (electric locomotives). Therefore, it can be corrected in order to minimize the total specific costs by solving this problem by the method of Lagrange undetermined multipliers, which allows us to reduce the conditional optimization problem to the simpler problem of unconditional optimization based on the criterion of minimum annual costs including losses from the accidents, i.e., finding an absolute extremum [7].

3 = S(c

1 ■

n .m .3 rSi

casi )

min

(1)

i=i

were - ^l"_1Cn n 3 iKi - is the total costs for preventive maintenance of the i-th type of equipment of a rail service car;

- is an intensity of the i-th type of equipment failures of a rail service car;

Caei - a total cost of emergency repair of the i-th type of equipment;

\ei - is an intensity of accidents from the i-th type of equipment.

The condition (1) is adequate to the criterion of the minimum of unit costs:

f n \

^Cn .n .3.

3 =-

C

■ = 1 =

i=1

Here:

Kaii ^

^^ Cai

V i=i

i V

Km ^ min

(2)

T

V nmi

m

m (t)dt

From (2) follows the equality:

=T

i=i

T

V nmi,

¡•T ■

J0 nm' ^ (t )dt+ T

_i=1

n

T .

/ J aei

(3)

Realization and volumes of maintenance of mechanical, electrical and hydraulic equipment of a rail service car to the permissible error within their operating range is justified economically if the cost of its specific expenses

i=i

1

3

per unit of time is less than the cost of elimination of

accidents and production costs. Therefore, the relative minimum of the objective function (3) should be sought under the limitations:

n n

Yen.R.3.i — Y Casi i=1 i=1

n

l=1

T

+L

T n n

J0 ^ ai eXP(bi )dt + Zen-R.3.i / XCa

+

(5)

^ mm

or

n .R .3 .i

- (4)

Teas, ^ 1 i=1

Taking into account the limitation (4), the failure flow parameter o (t) for a given object can be written in the first approximation in the form co (t) = a exp (bt), where a and b are the coefficients that take into account the failure parameters for equipment types, and k is a given coefficient of the current cost of scheduled maintenance. For the objective function (3), the Lagrange function is written as:

. i=1 i=l In the formula (5) we will point out that the average

statistical growth of the failure parameter of metal structure (mainly due to the weakening of the bearings in the axial direction, cracks and curvature of the beams) can be approximated by the function (Figure 1):

(t ) = 0.007 exp (0.3f) (6)

and for electrical equipment due to the predominant wear of their insulation, failure of the connectors and contacts, the failure flow is approximated as

(t ) = 0.005 exp (0.2t) (7)

and for hydraulic equipment due to wear of the rod or piston consolidation, as well as the presence of air in the system, etc. the failure flow is expressed as

(t ) = 0.003 exp (0.13t) (8)

œ

Figure 1. Change in the failure flow parameter of metal equipment 2. - electrical equipment. 3. - hydraulic equipment

We denote the first term of (5) by F (t). The minimum value of this function is determined by equating the derivatives on all variables to zero:

dL _ dF dK«i (TnRi ) àœi (Tasi )

dT

nR1

dL

dT

dTnR 1 dTnR1 dTnR 1 j

dF + dK®2 (TnR2 ) d®2 (Tas2 )

nR 2

dL

dT

nR2

dF

dT

nR2

dT

nR2

dK®3 (TnR3 ) d®2 (Tas3 )

(9)

dTnR 3 dTnR 3 dTnR 3 dTnR 3

dL = dF + dKœpnx ) _ doTi) dl dl dl dl ,

Solving the obtained system, with respect to T, TnA2, T , with the above numerical parameters of failures and given Cn.n.3A and Caei we obtain the optimal periodicity of scheduled preventive maintenance separately for mechanical, electrical and hydraulic equipment, which is, 372.8 hours, 500 hours, 620.2 hours, respectively.

3. Conclusion

When designing, manufacturing and using the assembly site of a rail service car, it is necessary to be guided by both technical and economic measures aimed at ensuring not only a generalized reliability standard but also reliability indices for certain types of equipment

1

that provide the specified efficiency of operation with minimum operating costs. The expediency of calculating the maximum permissible values of the failure rate is shown taking into account the complexity of the existing reliability ratio of mechanical, electrical and hydraulic equipment, which is coordinated by the results of theoretical study and the recommended provisions for maintenance periodicity.

Taking into account the operational technology of assembly site and the average cost of routine repairs as well as the costs of emergency recovery work, a mathematical model for determining the optimal periodicity of maintenance with the use of Lagrange undetermined multipliers has been developed.

Mathematical models could be used in design and study of the main characteristics of the reliability of assembly sites.

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