UDK 622:647:621.851.6

 

prof., d.t.n. kuanyshbaev zh.m. (KarGTU)

 

Optimization of repair fund of Kazakhmys Corporation LTD

Organization of repair is a priority in the operation of self-propelled mining machine.  Let’s consider some of the definitions and concepts that characterize the reliability of machines and equipment.   Expenses for the repair and maintenance of equipment for the entire period of operation, in connection with its worn, as per long-term statistical data, exceed the cost of new fixed assets by 5-8 times. According to the different sources , 20-25% of various kinds of equipment failure caused by errors of attendants, 40-90% of transport accidents in various grids, and most of injuries at work  are the result of wrong actions of employees.

Reliability requirements of elements and machines are established in as quantitative indicators. Lets see some definitions to evaluate the concept of reliability [1]. Infallibility- is one of the basic qualities which compound the reliability, object quality to maintain the usable state during definite period or definite working ability. Longevity- quality of machine or equipment (object) to maintain usable state before the limit  condition with proper technical service and repair. Validity coefficient- the probability that the object will be in usable state in any moment of the work, except of planning period when usage of the object is not considered: integrated indicator of reliability. The coefficient of technical acceptability - the probability that the object will be in usable state in any moment of the work, except of planning period when usage of the object is not considered and starting from that period will work in proper manner within the specified term: integrated indicator of reliability. Average resource – mathematical expectations of the resource: indicator of   longevity. Average service term - mathematical expectations of service term: indicator of   longevity

Average work before operating failure-mathematical expectations of object operating before first failure; indicator of  infallibility. Service term- calendar persistence since  the begging  of object operation or her resumption after repair work of definite unit till the transmission to the limit state. A large number of self-propelled equipment are operating at enterprise LTD. “Kazakhmys Corporation”,  providing high performance of minerals mining and its transportation. Though mentioned machines are not fully adopted to the conditions of Zhazkazgan’s  fields and appears the necessity of reliability improvement. The analyses shows  that the coefficient of technical availability  and  coefficient of equipment usage vary within wide limits. The analyses  of downtime of self-propelled equipment by ZHZM in 2009 shows that the vast majority of outages in technological change (72-77%) are downtime due to lack of spare parts and circulating units. Determining the required number of spare parts and circulating units by service time  we can define as per following methods. Interconnections of required number of n parts with service term parameters T0. and σ Risk degree, α downtime due to lack of spare parts are defined as follows. While Quintile, kα, appropriate to Risk Degree will be equivalent.

 

                       = ,                                              (1)

where tc – is total service of n parts; n -quantity of parts; T0 - mathematical expectations of service term of single part; σ - magnitude of  deviation from random value (standard). These are standard values mentioned in Table 1.

 

         Table 1

Probability of proper work,p

0,70

0,75

0,80

0,85

0,90

0,95

0,99

Risk Degree, a

0,30

0,25

0,20

0,15

0,10

0,05

0,01

Quintile, k

-0,524

-0,674

-0,842

-1,036

-1,281

-1,645

-2,326

 

Wondering the value of α and quintile from Table 1, we will obtain the number of n-units which is necessary for undisturbed operation during the time tc from formula 1 :

= ,                      (2)      

Where n cp =t c /T 0 ; ν - variety coefficient  of service term of single part, ν =σ/Ň0.

 

Formula (2) holds in all cases  when  n cp > 4 and variety coefficient ν < 1,5, i.e. in all cases. The failure, as the worth, will not go up t 6,7 %.

If to take an account of  α=0,05  and quintile k α = -1,645 then requested number of spare parts will determine as bellow:

=,                        (3)

If to take an account of  α =0,10 and quintile k α = -1,281, then requested number of spare parts will determine as bellow:

= , (4)

If to ignore the first part in brackets in expression (2), formula for determination the number  of spare parts will be:

=,                                 (5)

Mentioned formulas allows to determine requested number of spare parts and circulating units and provide the probability of no-failure operation of self-propelled equipment, as per table 1.

 

Table 2

The quantity of  work failures of components and assemblies

of East mine “Zhazkazganzvetmet” in 2009

 

Weirs, impact

Arrow

DVS

Pons

Transmission

Gydrosystem

Electro equipment

Perforator

Frame

Cooling system

Compressor

Others

23

44

118

109

176

594

230

38

73

83

20

46

 

Lets determine of normal allocation law of failure flow for main elements of mining machines for WID.

1. Mathematical expectations of  random failure flow for Annen’s Mine  “Zhazkazganzvetmet” on AID-

=  = 129,5

2. Dispersion of random cargo flow-

,

Table 3

Parameters of the normal distribution law

Variance of i-flux

Variance of i-flux

1= 11342,25

7 = 10100,25

2= 7310,25

8 = 2162,25

3=132,25

9 =  3192,25

4= 2162,25

10 = 8372,25

5= 420,25

11=11990,25

6 = 215760,25

12. () = 6972,25

 

         Lets determine the dispersion of  random quantity, in this case – failure of basic  elements of mining self-propelled machines for conditions in “East” mine taking into consideration the definite deviations of failure quantity from quantity of mathematical expectation, mentioned above.

Next we will determine the quantity of root-mean-square failure deviation of basic units of mining machines, which occur at random and submit to causal distribution law, i.e we have rms deviation, and to determine  the quantity  for failure flow of basic units of equipment. The calculation is shown in Tables 2 - 3:

 

= 159,5                                    (8)

 

To determine quintile for normal law of distribution with follow with parameters a=0; b==1.

Density of standard normal distribution  (2)

                                                                                             (9)

 

The function of standard normal distribution:

 

                                              (10)

 

Function Ô(x) is called Laplas’s function. Qualities of this function allow to receive very compact tables for  calculating the probability of occasions  connecting to any normal distribution. Thus,

1. Ô(ő)=1Ô(-ő), That is why it’s enough to know the value of function  Ô(x)  when x  0.

2. If random quantity X is distributed by  normal law N (a, b),   her linear

 

function   is submitting to standard normal distribution  , N (0.1) and consequently :

                      (11)

It means that to calculate the probability of occasion for any normal distribution is enough to know her parameters a and b and the value of standard distribution

3. The probability that random quantity assume the value from x1 to x2  within examination:

               (12)

On the basis of that, to determine reliability parameters for the Mine “East”, quintile for  WID (table 4).

 

 

 

Table 4

 Availability Parameters of East Mine “Zhazkazganzvetmet” “on WID

 

mathematical expectations of random quantity, M

129,5

Standard Deviation, σ

159,5

 

ő

 

Ô(ő)=(ő-Ě)/σ

Ô(ő)

 

1

23

 

 

 

-0,6677116

-0,668

0,251

2

44

 

 

 

-0,5360502

-0,536

0,295

3

118

 

 

 

-0,0721003

-0,072

0,472

4

176

 

 

 

0,29153605

0,2915

0,386

5

109

 

 

 

-0,1285266

-0,129

0,448

6

594

 

 

 

2,91222571

2,9122

0,0018

7

230

 

 

 

0,63009404

0,6301

0,264

8

83

 

 

 

-0,2915361

-0,292

0,386

9

73

 

 

 

-0,354232

-0,354

0,363

10

38

 

 

 

-0,5736677

-0,574

0,284

11

20

 

 

 

-0,6865204

-0,687

0,245

12

46

 

 

 

-0,523511

-0,524

0,302

 

Table 5

Calculation of Quintile of East Mine “Zhazkazganzvetmet” “on WID

ą of element

Failure

Quantity

Quintile

mathematical expectations

root mean square (RMS) deviation

mathematical expectations of service term

 

Variety coefficient

Quantity of spare parts and units

1

23

0,251

129,5

159,5

162,8

0,979

24,30

2

44

0,295

129,5

159,5

162,8

1,29

46,06

3

118

0,472

129,5

159,5

162,8

1,29

123,25

4

176

0,615

129,5

159,5

162,8

1,29

184,28

5

109

0,448

129,5

159,5

162,8

1,29

113,79

6

594

0,9982

129,5

159,5

162,8

1,29

618,30

7

230

0,736

129,5

159,5

162,8

1,29

241,28

8

83

0,386

129,5

159,5

162,8

1,29

86,63

9

73

0,363

129,5

159,5

162,8

1,29

76,21

10

38

0,284

129,5

159,5

162,8

1,29

39,85

11

20

0,245

129,5

159,5

162,8

1,29

21,19

12

46

0,302

129,5

159,5

162,8

1,29

48,15

For dump trucks: 79163/486=162,8; v=159,5/162,8=0,979|

 

Table 6

Calculation of optimal quantity of spare parts of East Mine “Zhazkazganzvetmet” on WID

ą

Failure

Quintile

Variety coefficient

constant coefficient

Square root

Quantity of spare parts

1

23

0,251

1,29

0,5

4,80

24,30

2

44

0,295

1,29

0,5

6,63

46,06

3

118

0,472

1,29

0,5

10,86

123,25

4

176

0,615

1,29

0,5

13,27

184,28

5

109

0,448

1,29

0,5

10,44

113,79

6

594

0,9982

1,29

0,5

24,37

618,30

7

230

0,736

1,29

0,5

15,17

241,28

8

83

0,386

1,29

0,5

9,11

86,63

9

73

0,363

1,29

0,5

8,54

76,21

10

38

0,284

1,29

0,5

6,16

39,85

11

20

0,245

1,29

0,5

4,47

21,19

12

46

0,302

1,29

0,5

6,78

48,15

 

Perspective method of repair organization is aggregate method of repair, which is  successfully penetrated on  enterprises of “Zhazkazganzvetmet”. The basic conditions to transfer main technological mining machines to  aggregate method  of repair is practical partitioning of machines to changeable aggregates and assembly units. Partitioning of machines is aimed to develop such nomenclature of mixed parts which could guarantee the most economical way to restore working abilities and recourses of mining machines in  industrial conditions. Mentioned data of main units and aggregates failure (table2) graphically submit to normal low of distribution. In this connection for each machine should be created optimal nomenclature of mixed spare parts (table2, table 7). Preferably the repair fund should be formed in value terms, taking into consideration probabilistic approach. In addition, the optimal number of spare parts will increase the probability of no-failure of self-propelled mining machines till 0,85-0,90.

 

Distribution of the failure of the main elements of mining equipment on WID

 

 

Literature

1. Reliability and efficiency in engineering. Edited A.I. Rembeva, Reference in 10 volumes M.: machine construction, 1986

2. Ventcel E.S. theory of relativity, M.: Science , 1969. p 285