PSI - Issue 59

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

513

6

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

j j a  0 is the average value of the deviations from the roundness of the j -th rolling bushing for 24 values (in each position; kj kj a b , are coefficients of the Fourier series of the k -th harmonic of the j -th rolling bushing; k is harmonic sequence number.

1 2



1 2



ij  ( ) cos f  

;

.

kj a 

k d

  

ij  ( ) sin f  

kj b 

k d

  

ij

ij

ij

ij





0

0

The constructed ensemble of 10 implementations of deviations from the roundness of the rolling bushings obtained after the fi rst technological operation of “rolling” is shown in Fig. 3.

Fig. 3. The ensemble of implementations of deviations from roundness of the rolling kingpin bushings for the undercarriage of UAZ vehicles after the first technological operation.

The obtained values j  were presented as random variables and the presence of outliers in the statistical series ' j  was checked using the Grebbs criterion. If such values were found for a certain rolling bushing circlegram, it was removed from the sample, and the circlegram of another rolling bushing was taken additionally. Thus, having achieved the homogeneity of the statistical series j  , we obtained the amplitude values and distribution characteristics presented in Table 2.

Table 2. Values of amplitudes Аk, approximated by the Fourier series deviations fro m the roundness of the bushing ICS, average values , μm, dispersions , μm2 and coefficients of variation .

The amplitude values

Scattering characteristics

j  , μm 79.8 51.4 49.8 78.7 64.6 70.1 61.2 86.6 67.2 51

( ) j v k 

( ) j D  μm 2

А1

А2

А3

А4

А5

А6

А7

А8

А9

А10

Bushing No

1 2 3 4 5 6 7 8 9

227

178 130 123 133 116 192 176 255 145 44

125

141 131 153 178 123 192 124 137 205 166

13 40 28 77 18 35 71 34 71 53

78 59 68 87 27 51 75 58 82 20

14 31 15 37 42 54 61 53 48 7

26 37 10 15 29 35 39 24 24 55

7 6 7

39 23

6372 2639 2479 6196 2604 4178 4920 3745 7508 4514

0.25 0.19 0.17 0.26 0.24 0.21 0.32 0.32 0.29 0.21

52 32

89 64 75 66 65

6

126 164 150

32

18

8

5

31 29 26 22 31

27 20 21 30 15

47 60 73

166 109 145 118

10

135

i y

i x

  24 1 i

  24 1 i

The method of R.S. Sprague is used to find the coordinates of the center:

,

and the

2

2

X

Y





0

0

24

24