Transcript Document

SKF Experience with
Extreme Value Analysis
Presented to 4th Conference on Extreme Value Analysis, Gothenburg
Presented by Aidan Kerrigan
2005-08-16
2015-07-17 ©SKF Slide 2 [Code]
SKF [Organisation]
1
ASTM E2283-03 on 52100
bearing steel
2015-07-17 ©SKF Slide 3 [Code]
SKF [Organisation]
Cleanliness assessment of modern bearing steels
Heat
Sulphur
Aluminium
Titanium
Oxygen
A
0.006 %
0.029 %
18 ppm
6 ppm
B
0.011 %
0.024 %
26 ppm
6 ppm
Established metallographic methods do not differentiate for very clean steels
Established metallographic methods do not facilitate bearing life modelling
2015-07-17 ©SKF Slide 4 [Code]
SKF [Organisation]
ASTM E2283 EVA methodology
x6
E3 Table 6
Hardened
Specimens
2015-07-17 ©SKF Slide 5 [Code]
SKF [Organisation]
Complex oxysulphide in an application
‘D’-type globular inclusions, < 3:1
2015-07-17 ©SKF Slide 6 [Code]
SKF [Organisation]
EVA methodology
Mean =
Sdev =
Length
(Y)
Data
15.1
15.3
15.8
16.4
16.5
17.5
18.3
19.1
19.6
19.8
20.4
20.6
21.1
22
23.4
23.4
23.8
24
24.5
27.2
28.3
33.1
44.3
47.6
23.213
8.277
Moments Method
Delta =
6.45
Lambda = 19.49
Rank ProbabilityRed. Var.
(X)
RV
1
0.04
-1.169
2
0.08
-0.927
3
0.12
-0.752
4
0.16
-0.606
5
0.20
-0.476
6
0.24
-0.356
7
0.28
-0.241
8
0.32
-0.131
9
0.36
-0.021
10
0.40
0.087
11
0.44
0.197
12
0.48
0.309
13
0.52
0.425
14
0.56
0.545
15
0.60
0.672
16
0.64
0.807
17
0.68
0.953
18
0.72
1.113
19
0.76
1.293
20
0.80
1.500
21
0.84
1.747
22
0.88
2.057
23
0.92
2.484
24
0.96
3.199
0.999
6.91
Ln ( f (x,,  ))
-3.287
-3.221
-3.075
-2.931
-2.910
-2.744
-2.660
-2.613
-2.599
-2.597
-2.601
-2.605
-2.622
-2.672
-2.792
-2.792
-2.835
-2.857
-2.916
-3.295
-3.472
-4.329
-6.535
-7.200
SUM (LL) = -78.159
2015-07-17 ©SKF Slide 7 [Code]
SKF [Organisation]
Max. Likelihood
Lambda 19.955
Delta
4.937
X
X
14.18
15.38
16.24
16.96
17.61
18.20
18.76
19.31
19.85
20.39
20.93
21.48
22.05
22.65
23.27
23.94
24.66
25.45
26.34
27.36
28.58
30.11
32.22
35.75
54.07
Solver
X low
X_low
11.9
13.2
14.2
14.9
15.6
16.2
16.7
17.2
17.7
18.2
18.7
19.2
19.6
20.1
20.6
21.1
21.7
22.3
23.0
23.7
24.6
25.7
27.2
29.7
42.4
x High
X_high
16.5
17.5
18.3
19.0
19.6
20.2
20.8
21.4
22.0
22.6
23.2
23.8
24.5
25.2
25.9
26.7
27.6
28.6
29.7
31.0
32.5
34.5
37.2
41.8
65.8
Give a working
example:
1, 2, 3, …, 24
‘Reduced Variate
Function’
Cleanliness assessment of modern bearing steels
Heat
Sulphur
Aluminium
Titanium
Oxygen
A
0.006 %
0.029 %
18 ppm
6 ppm
B
0.011 %
0.024 %
26 ppm
6 ppm
Traditional metallographic methods do not differentiate for very clean steels
Traditional metallographic methods do not facilitate bearing life modelling
2015-07-17 ©SKF Slide 8 [Code]
SKF [Organisation]
Extreme Value Analysis (ASTM E2283)
Reduced Variate Function
4
3
2
1
Prob.
Red.Var
.
0
80%
1.50
90%
2.25
95%
2.97
99.9%
6.91
-1
-2
0
20
40
60
Inclusion Length (µm)
2015-07-17 ©SKF Slide 9 [Code]
SKF [Organisation]
80
Heat A
Heat B
100
Supplier C - outliers
Reduced Variate
4
3
2
Heat 1
95% CI
1
0
-1
-2
10
20
30
40
50
Inclusion Length (µm)
2015-07-17 ©SKF Slide 10 [Code]
SKF [Organisation]
60
70
80
Supplier C
Reduced Variate
4
3
2
Heat 1
95% CI
Heat 2
95% CI
1
0
-1
-2
10
20
30
40
50
Inclusion Length (µm)
2015-07-17 ©SKF Slide 11 [Code]
SKF [Organisation]
60
70
80
Supplier D
Reduced Variate
4
3
2
Heat 1
Heat 2
1
0
-1
-2
0
10
20
30
Inclusion Length (µm)
2015-07-17 ©SKF Slide 12 [Code]
SKF [Organisation]
40
50
60
Supplier D
Reduced Variate
4
3
2
Heat 1
Heat 2
1
0
-1
-2
0
10
20
30
Inclusion Length (µm)
2015-07-17 ©SKF Slide 13 [Code]
SKF [Organisation]
40
50
60
Supplier E
Reduced Variate
4
3
2
Heat 1
Heat 2
Heat 3
1
0
-1
-2
0
10
20
30
Inclusion Length (µm)
2015-07-17 ©SKF Slide 14 [Code]
SKF [Organisation]
40
50
60
Supplier F
Reduced Variate
4
3
2
Heat 1
Heat 2
Heat 3
1
0
-1
-2
0
10
20
30
40
Inclusion Length (µm)
2015-07-17 ©SKF Slide 15 [Code]
SKF [Organisation]
50
60
70
Comparison of suppliers
Reduced Variate
4
3
2
E
F
1
0
-1
-2
0
10
20
30
Inclusion Length (µm)
2015-07-17 ©SKF Slide 16 [Code]
SKF [Organisation]
40
50
60
Comparison of suppliers
Reduced Variate
4
3
2
E
F
1
0
-1
-2
0
10
20
30
Inclusion Length (µm)
2015-07-17 ©SKF Slide 17 [Code]
SKF [Organisation]
40
50
60
Pooling of results from multiple heats
Reduced Variate
5
4
3
2
E
F
1
0
-1
-2
0
10
20
30
40
50
Inclusion Length (µm)
2015-07-17 ©SKF Slide 18 [Code]
SKF [Organisation]
60
70
80
Pooling of results from multiple heats
Reduced Variate
5
4
3
2
E
F
1
0
-1
-2
0
10
20
30
40
50
Inclusion Length (µm)
2015-07-17 ©SKF Slide 19 [Code]
SKF [Organisation]
60
70
80
Fraunhofer analysis of 19 heats of 52100
No evidence for a non-Gumbel GEV
2015-07-17 ©SKF Slide 20 [Code]
SKF [Organisation]
2
EVA and rolling contact
fatigue life of bearings
2015-07-17 ©SKF Slide 21 [Code]
SKF [Organisation]
Endurance test conditions (Pheonix 2001)
Low reduction ratio material
Turned inner rings
• Inner rings turned from ± 100 mm ø bar material
Increased running temperature
• 83°C instead of 53°C
• Full film conditions
Additional tensile hoop stress applied to inner ring
• Increased interference fit
2015-07-17 ©SKF Slide 22 [Code]
SKF [Organisation]
Material quality bearing life test
Variant
Oxygen
Sulphur
Bearing Life
Remelt
4.3 ppm
Zero
230 MRevs
Std 1
3.5 ppm
0.003 wt%
74 MRevs
Std 2
5.8 ppm
0.005 wt%
37 MRevs
Std 3
4.8 ppm
0.003 wt%
15 MRevs
Untreated
39 ppm
0.014 wt%
3 MRevs
2015-07-17 ©SKF Slide 23 [Code]
SKF [Organisation]
Extreme Value Analysis (EVA) results
Reduced Variate
4
3
2
Rem elt
Std_1
Std_2
Std_3
Untr eated
1
0
-1
-2
0
10
20
30
40
50
Inclusion Length (µm)
2015-07-17 ©SKF Slide 24 [Code]
SKF [Organisation]
60
70
80
90
Extreme Value Analysis (EVA) results
Reduced Variate
4
3
2
Rem elt
Std_1
Std_2
Std_3
Untr eated
1
0
-1
-2
0
10
20
30
40
50
Inclusion Length (µm)
2015-07-17 ©SKF Slide 25 [Code]
SKF [Organisation]
60
70
80
90
Methodology to link EVA to performance
EVA ratings on inner rings turned from ±100 mm ø bar
Life calculation using ‘virtual’ steel by randomly selecting
inclusions from the EVA population and randomly
positioning them in the rings
• Actual life for one variant (Std_2) used to locate the predicted lives
2015-07-17 ©SKF Slide 26 [Code]
SKF [Organisation]
Predicted versus actual bearing L10 life
Predicted Bearing L10 Life (MRevs)
1000
Factors not accounted for:
- Reduction ratio
- Ring forming process
- Stressed volume
- etc.
100
10
Rem elt
Std_1
Std_2
Std_3
Untr eated
1
1
10
100
Actual Bearing L10 Life (MRevs)
2015-07-17 ©SKF Slide 27 [Code]
SKF [Organisation]
1000
Predicted versus actual bearing L10 life
Predicted Bearing L10 Life (MRevs)
1000
100
Rem elt
Std_1
Std_2
Std_3
Untr eated
10
1
1
10
100
Actual Bearing L10 Life (MRevs)
2015-07-17 ©SKF Slide 28 [Code]
SKF [Organisation]
1000
Inclusion assessment methods
Inspected Area or Volume
LF UST
HF UST
EVA
ASTM E45
ISO 4967
1
DS
10
100
Inclusion Size (µm)
2015-07-17 ©SKF Slide 29 [Code]
SKF [Organisation]
1000
Experience to date
ASTM E2283 EVA for comparison
• Heat to heat
• Not measure every heat
ASTM E2283 EVA for characterisation
• Multiple heats over short timeframe
• Compare steelmaker process routes
Compliments other techniques
• Need to use a combination of techniques to evaluate the inclusion population
Next: ESIS round robin
2015-07-17 ©SKF Slide 30 [Code]
SKF [Organisation]