PSI - Issue 59

Andrii Senyk et al. / Procedia Structural Integrity 59 (2024) 508–515

511

4

Andrii Senyk et al. / Structural Integrity Procedia 00 (2023) 000 – 000

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Fig. 2. Circlegrams of deviations from the roundness of the bushing ICS obtained after rolling the blank - cards for the j-th bushings.

Z

Z

a b



2 

10

10

1

2 k     2 k

( ) ji

{

(

)

[ ( ) ( )]} z z

1     1 k k k C 

M

C

2 e e

 



,

2

1

k

k

k

k

2



2

Z

2 a ab b  

2



n

n

1

k

( ) ji

{

[(

2 )   

(

2 )   

1     C k k k 1 

D

C

z

e

z

 













2

1

2

k

k

k

k

k

3

2



2

Z

2

k

( ), [ ( )        z M z e  ( )]} ) ( 2 2 2 2

2

1

k

k

k

b



a



,

; [ a, b ] is the interval of change in the value ∆ , it is considered to be known and

where

z

k  2

k

z

k

k  1





such that max k  are, respectively, the smallest and largest values among the deviations from roundness of the individual i -th position of each of the j -th bushings obtained as the result of processing the experimental data of deviations from roundness for 10  n bushings (sample size)). min k a  , max k b  ( min k  and

1

,

(1)

C

k

a

b

( ) k   k

( ) k   k

1 [ 

] [ 

]





b a

6 

ji  , ( ) 1 k z  ( ) 2 k z  are Laplace functions.

is mean square deviation of the random variable

( ) k   

( ) ij M  і ( ) ij D  for the sample of 10 bushings according to the Student ’ s criterion

Knowing

(

, 1       j j i , 2 i

1,2...10) 1,2...10)

D D

3| ( M

,       j j i 1,2...10) , 1 1 i

1,2...10) 1,2...10)

,        D j M i j ( , ( 2

1,2...10) |

and Fisher ’ s test

, where

F



t



(

k

(

1,2...10)

D

2

i



, ( 1    j D i , we determined the significance of the differences in terms of both mathematical expectations and dispersions, i.e., the stability of the technological process for forming deviations from roundness, where , 1,2...10) ( 1    j M i і , 1,2...10) ( 2    j M i - are, respectively, the mathematical expectations of deviations from roundness in the first and second positions of all j -th rolling bushings; , 1,2...10) ( 1    j D i і , 1,2...10) ( 2    j D i - are, respectively, the dispersion of deviations from roundness in the first > , ( 2    j D i 1,2...10)