Evolution of the Residual Stresses Formation from FeC0. 15Cr12Ni2 ...

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ScienceDirect Procedia Engineering 176 (2017) 355 – 362

Dynamics and Vibroacoustics of Machines

Evolution of the residual stresses formation from FeC0.15Cr12Ni2 steel in the part surface during the diamond smoothing Shvetcov A.N.*, Skuratov D.L. "Samara National Research University, 34 Moskovskoye Shosse, Samara, 443086, Russian Federation"

Abstract The study devoted to investigation of influence of such diamond smoothing characteristics as: indenter pressing effort, smoothing rate, length feed value, and diamond indenter sphere radius, on the evolution of the residual stresses formation in the part surface from FeC0.15Cr12Ni2 heatproof wrought steel. The diamond smoothing is one of the most effective and simple technologies of the finishing-and-reinforcing machining of the complete, provided the residual stresses formation of the part surface, considerably influenced on fatigue and corrosion resistance of the part. The mathematical models, binding the diamond smoothing process characteristics with the residual stresses value and occurrence depth, were received as a result of factorial experiment in the study. Result inaccuracy of the residual stresses value and occurrence depth results of the calculation, based on the models, is within 20%. Accuracy proof of the tests, homogeneity of variances, and models adequacy were implemented by Student's test, Kokhren’s test, and Fisher’s test, respectively. © 2017 2017The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of (http://creativecommons.org/licenses/by-nc-nd/4.0/). Machines. under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines Peer-review Keywords: Diamond smoothing; Complete factorial experiment; Residual stresses; Occurrence depth; Mathematical model; Model adequacy

1. Introduction The diamond smoothing process, from the moment of its implementation in production up to present, is one of the most effective and simple technologies of the surface plastic deformation became widespread in air-engine technology, automobile production, shipbuilding, and other industry fields [1]. In the smoothing process hardening of the surface and the residual stresses formation, take place which has a beneficial effect on the part fatigue

* Corresponding author. Tel.: +7-927-704-9527; fax: +0-000-000-0000 . E-mail address: [email protected]

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines

doi:10.1016/j.proeng.2017.02.332

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A.N. Shvetcov and D.L. Skuratov / Procedia Engineering 176 (2017) 355 – 362

resistance rise [1, 2, 3, 4, 5]. As the result the quality indicators of the surface layer improve and the part resource increase. [6, 7]. Optimization of diamond smoothing process requires availability of a mathematical model that forms interrelation of the diamond smoothing process parameters to the parameters that determine the quality of the surface, such as roughness, microhardness, the depth of hardened layer, residual stresses, etc. Some of the existing models that enable to determine the rational machining conditions are given in the studies [2, 8-17]. The residual stresses of the plane, ring, and other sample forms are more particularly determined by Davidenkov N.N. approach [18], which consists in layer-by-layer removal of the material. In the general case, a triaxial stress state takes place in the thin-walled cylinders. Meanwhile, the stresses radial component is insignificant and has not much influence on surface qualitative index. So it is conditionally considered that the surface has biaxial stress state. Results of many research studies [1, 2, 4, 19] shows that, after the diamond smoothing, compression axial and peripheral residual stresses are formed at the detail surface and the axial stresses have greater value than peripheral ones [1]. Thus, as a criterion for evaluation of the surface layer stress state of parts after diamond smoothing, peripheral residual stresses can be used so far as the value of the peripheral stresses will be greater than the axial ones. In addition, the peripheral stresses measurement requires fewer inputs for the sample preparation for the investigation. 2. Methods The complete factorial test was carried out for the investigation of diamond smoothing condition characteristics influence on the value and occurrence depth of the peripheral residual stresses. FeC0.15Cr12Ni2 heatproof wrought steel was used as a tested material. An experimental determination of the locked-up stresses was carried out at ASB-1 facility, had been was designed by professor Bukaty S.A., using his author methodology. The tested samples were collars with an outer diameter 108 mm, inside diameter 96.6 mm, and width 10.5mm. Before the diamond smoothing, every collar was machined by turning conditions:   107 m/min, S o  0.04 mm/rpm, and t  0.5 mm, by the pass-through cutter with T15K6 cemented carbide, which has geometry

parameters: r  1.5 mm   45 ; 1  42 ;   10 ;   7 ;   5 . The sample roughness an characteristic Ra , after the turning operation, ranged between 0.581 μm and 0.855μm. Turning and smoothing processes were carried out on the screw-cutting lathe 1V616, using specially designed workholders. The workholder for the outer turning makes it possible to machine 16 collar samples simultaneously; workholder for smoothing process makes it possible to machine 3 collar samples with 5 false collars, placed along the samples edges. Using of the false collars is necessary for machining of the whole surface of the samples on the equal conditions and exclusion of the edge effect. In the capacity of diamond smoothing process characteristics were taken: smoothing tool radius R , smoothing force Py , smoothing speed  , and feed value S o . In the capacity of smoothing tool was used indenter from synthetic diamond grade of ASB-1. 3. Experimental design

 *

In order to receive the mathematical models, binding the maximal values of the peripheral residual stresses      o and the occurrence depth a with the diamond smoothing process characteristics, of type:

max

max

 *

max

max

 C S oy Pyx R m  z ;

a  C a S oy Pyx R m  z , a

a

a

a

(1)

the complete factorial experiment (CFE) of 24 type was carried out. Using of the experimental design method means transformation of the equations (1) to the equation (2) by taking the logarithm:

357


M y  0 1 Xˆ 1   2 Xˆ 2   3 Xˆ 3   4 Xˆ 4 ,

(2)



here y - is the mathematical model of the valuation parameter  

max

  o

max

, a ;

M y - true value alteration on

the logarithm scale; X 1 , X 2 , X 3 , X 4 - logarithms of the So , Py , R respectively, and  ;  0 , 1 ,  2 ,  3 ,  4 coefficients, which should be estimated during the analysis process. The equation (2) is submitted in a form: yˆ b 0  b1 X 1  b2 X 2  b3 X 3  b4 X 4 ,

(3)

yˆ - valuation of the mathematical expectation of repercussion M y from the equation (2); b0 , b1 , b2 , b3 , b4 coefficients valuation  0 , 1 ,  2 ,  3 ,  4 respectively. or the The equation (3) shows the empirical dependence of the relevant valuation parameter     o occurrence depth a on diamond smoothing process characteristics. Meanwhile, the alteration of the unknown variable Xˆ i is realized by using of relevant alteration equation, which has expression 12 ln Xˆ i max  ln Xˆ i min  as a unit for a new scale.



Xi 

max

2ln Xˆ i  ln Xˆ i max  1 . ln Xˆ i max  ln Xˆ i min

max



(4)

During the experiment, the number of the tests was N  16 and number of the iterative tests was M  6 . The variation rates of the smoothing process characteristics are given in Table 1. Table 1. Variations rate of factors

Smoothing force Py, N Feed Sо, mm/rpm Revolutions n, rpm Tool radius R, mm

Variation range

Rates

Factor

Xˆ 1 ln Xˆ 1 Xˆ 2 ln Xˆ 2 Xˆ 3 ln Xˆ 3 Xˆ 4 ln Xˆ 4

upper

basic

200

135

lower 50

75

5.3

4.9

3.9

4.32

0.08

0.06

0.02

0.02

-2.53

-2.81

-3.91

-3.91

250

156.5

63

93.5

5.52

5.05

4.14

4.54

2.5

2

1.5

0.5

0.41

0.69

0.92

-0.69

4. Experiment analysis The experimental procedure in coded variables, also values of the maximal peripheral residual stresses and the occurrence depth are referenced in Table 2. Distribution diagram of residual stresses by the surface layer depth are represented in Fig. 1 and Fig. 2. Figures 1 and 2 show that the stress pattern of residual stress distribution corresponds to the results from the research works [1, 8].

358

A.N. Shvetcov and D.L. Skuratov / Procedia Engineering 176 (2017) 355 – 362 Table 2. The experimental procedure in coded variables, also the values maximal peripheral residual stresses and the occurrence depth №

Х0

X1

X2

X3

X4

y

ln y

ya

ln ya

1

+1

+1

+1

+1

+1

392

5.97

137

4.916

2

+1

+1

-1

+1

+1

424

6.05

148

4.999

3

+1

-1

+1

+1

+1

321

5.77

67

4.202

4

+1

-1

-1

+1

+1

410

6.02

72

4.272

5

+1

+1

+1

-1

+1

427

6.06

154

5.034

6

+1

+1

-1

-1

+1

510

6.23

155

5.046

7

+1

-1

+1

-1

+1

448

6.11

52

3.948

8

+1

-1

-1

-1

+1

499

6.21

65

4.174

9

+1

+1

+1

+1

-1

326

5.79

143

4.959

10

+1

+1

-1

+1

-1

415

6.03

169

5.128

11

+1

-1

+1

+1

-1

335

5.82

74

4.309

12

+1

-1

-1

+1

-1

374

5.92

75

4.311

13

+1

+1

+1

-1

-1

464

6.14

157

5.054

14

+1

+1

-1

-1

-1

515

6.24

170

5.138

15

+1

-1

+1

-1

-1

446

6.10

75

4.320

16

+1

-1

-1

-1

-1

491

6.20

70

4.253

bk

6.041

0.023

-0.073

-0.121

0.012

bk

4.629

0.405

-0.036

0.008

-0.055

Increase of force Py leads to a shift of maximum peripheral residual stresses deep into the part and feed decrease S o - increasing of the residual stresses value due to the number increase of the diamond indenter impact on the processed surface. Valuation coefficients of the regression relations (3), binding     o and a with the diamond smoothing process characteristics, are determined by formula:



N

bk 

X

ki

1

N

max

max



 yi

,

here N - number of tests, in this case N =16, yi  ln y or ln yа , will be the following: for the maximal values of peripheral residual stresses  *

max

 

max

  o

max

: b1  0.023 , b2  0.073 , b3  0.121 ,

b4  0.012 ; for the occurrence depth of the maximal values of peripheral residual stresses a : b1  0.405

,

b2  0.036 ,

b3  0.008 , b4  0.055 . Thereby, the regression relations in converted variables will be presented in the following form: for  *  yˆ  6.041  0.023  X 1  0.073  X 2  0.121 X 3  0.012  X 4 ;

(5)

for a  yˆ  4.629  0.405  X 1  0.036  X 2  0.008  X 3  0.055  X 4 .

(6)

max

359

A.N. Shvetcov and D.L. Skuratov / Procedia Engineering 176 (2017) 355 – 362 a

b

Fig. 1. Diagrams of residual peripheral stress when smoothing: speed   86 m/mim and length feed values S o  0.08 mm/rpm (a) and S o  0.02 mm/rpm (b): 1 – Py = 200 N, R = 2.5 mm; 2 – Py = 200 N, R = 1.5 mm; 3 – Py = 50 N, R = 2.5 mm; 4 – Py = 50 N, R = 1.5 mm

a

b

Fig. 2. Diagrams of residual peripheral stress when smoothing: speed   22 m/min and length feed values S o  0.08 mm/rpm (a) and S o  0.02 mm/rpm (b): 1 – Py = 200 N, R = 2.5 mm; 2 – Py = 200 N, R = 1.5 mm; 3 – Py = 50 N, R = 2.5 mm; 4 – Py = 50 N, R = 1.5 mm

Substituting values X i from (4) into equations (5) and (6), we will receive the regression equations in natural variables: for  *  yˆ  5.2  0.034  Xˆ 1  0.105  Xˆ 2  0.175  Xˆ 3  0.045  Xˆ 4 ;

(7)

for a  yˆ  3.056  0.588  Xˆ 1  0.049  Xˆ 2  0.015  Xˆ 3  0.224  Xˆ 4 ;

(8)

max

5. Adequacy verification of the regression equations Student’s criterion was used for verification of the test operation accuracy, it is determined by formula:

t 

yn, m  yn Sn

,

here y n , m - value of every repeated test; yn - average value of the test; S n - square root of the dispersion.

360


In turn, calculation of the rowwise dispersions, defined the tests error, is realized by use of the following expression: S n2 

1 M 1

 y M

1

 yn 

2

n, m

.

 - is the tabulated It is considered that the test were carried out with sufficient accuracy, if t   t max , where the t max value of Student’s criterion. The tabulated value of Student’s test is defined by number of degrees of freedom f , which is determined from the expression: f  N  K  1  16  4  1  11 , here K - number of factors. The tabulated value of Student’s  .  2.2 [20]. criterion for f  11 equal to t tab Values of Student’s criterion for the test results, on definition of maximum values of peripheral residual stresses   1.9945 and t max   1.8737 respectively. As the values of Student’s criterion are and the occurrence depth, are t max less than the tabulated values, therefore, the test results have an adequate accuracy. Verification of the homogeneity of variance is carried out with the help of Kokhren’s criterion as the numbers of the repeated tests are equal in all positions of the experimental procedure. The hypothesis of homogeneity of variance is taken in case of Gtab.  G , here Gtab. - the tabulated value of Kokhren’s criterion; G - calculated value of Kokhren’s criterion. The tabulated value of Kokhren’s criterion, with f 1  M  1  5 , f 2  N  16 for significance level of 5%, is equal to Gtab.  0.3645 , in accordance with the data from research study [20]. The calculated value is by expression: G  S n2(max)

N

S

2 n

1

Calculated values of Kokhren’s criterion for dependences of maximum value of the peripheral residual stresses and the occurrence depth by on the diamond smoothing process characteristics are equal G  0.04085 0.2032  0.201 and G  0 .0244 0.1269  0.117 , respectively. In both cases Gtab.  G that confirms. So the hypothesis of the homogeneity of variance is corroborated. For verification of the mathematical model adequacy, the calculated values of output parameters yˆ are calculated upon equations (7) and (8). For which the rowwise maximal and minimal values of X~ are taken from Table 1 k

considering their signs. In order to test the hypothesis about the adequacy of the model it is sufficient to estimate the deviation, characterized by the regression equation of yˆ output value from experimental results y at different points in the factor space Scattering of the experiment results regarding the constraint equation approximating the required functional dependence is characterized by the residual variance or dispersion adequacy calculated by the following formula:

S ad2 

N 1  y  yˆ 2 .  N  K  1 n 1

The number of degrees of freedom for the adequacy variance is defined as f ad  N  j , here j - number of members of the polynomial approximant, including free member f ad  16  5  11 . The adequacy verification consists of determination of relation between the S ad2 and reproducibility variance

S 2 y . The hypothesis verification of the model adequacy is carried out by Fisher’s F-test. F-test for degree of freedom f 1  11 and f 2  1 at significance level 5% table value criterion will be Ftab.  4.84 [20].

361


The calculated values of the tests for the models, binding the maximal peripheral residual stresses and the occurrence depth with diamond smoothing process characteristics, are equal F  0.704 and F  2.77 respectively. These values are less than critical value Ftab.  4.84 . Thereby, the adequacy of the mathematical models is proved. The general empirical dependences, binding the stresses residual value (9) and the occurrence depth (10) with diamond smoothing process characteristics, are received by the results the multifactorial experiment which have the following view:

 *  190  Py0.034 So0.175 0.045 R 0.105 ,

(9)

max

a  16.5  Py0.588 So0.015v 0.224 R 0.049 .

(10)

According comparing results experimental investigation with the results, calculated upon the received empirical dependences, and given in Table 3 it should be noted that divergence does not exceed 20%. Table 3. Results of the experimental and calculation value № test

Machining conditions

Experimental results

Calculation results

Tolerance

Py, N

R, mm

S, mm/rpm

n, rpm/min

 * , MPa

а, μm

 * , MPa

а, μm

 *

а

1

200

2.5

0.08

250

-392

137

-393

126.51

0%

8%

2

200

1.5

0.08

250

-424

148

-414

129.72

2%

12%

3

50

2.5

0.08

250

-321

67

-374

55.992

17%

16%

4

50

1.5

0.08

250

-410

72

-395

57.411

4%

20%

5

200

2.5

0.02

250

-427

154

-500

123.91

17%

20%

6

200

1.5

0.02

250

-510

155

-528

127.05

4%

18%

7

50

2.5

0.02

250

-448

52

-477

54.839

7%

5%

8

50

1.5

0.02

250

-499

65

-504

56.229

1%

13%

9

200

2.5

0.08

63

-326

148

-369

172.27

13%

16%

10

200

1.5

0.08

63

-415

169

-389

176.64

6%

5%

11

50

2.5

0.08

63

-334

74

-352

76.245

5%

3%

12

50

1.5

0.08

63

-374

75

-371

78.177

1%

4%

13

200

2.5

0.02

63

-464

157

-470

168.73

1%

7%

14

200

1.5

0.02

63

-515

170

-496

173.01

4%

2%

15

50

2.5

0.02

63

-446

75

-449

74.675

1%

0%

16

50

1.5

0.02

63

-491

70

-473

76.568

4%

9%

The received dependences can be used as the engineering constraints in mathematical model for determination of the reasonable conditions of machining for the diamond smoothing process [17]. 6. Summary 1. Mathematical models were received for determination of the maximal value of the peripheral residual stresses and the occurrence depth subject to characteristics of the diamond smoothing process during machining the heatproof wrought steel FeC0.15Cr12Ni2. 2. It is indicated that the calculated values of the residual stresses and depth of then occurrence obtained by using of the given models, differ from experimental values not more than 20%.The models adequacy was verified by Fisher’s criterion.

362


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