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    TECHNICAL PAPER

    COMPARISON OF DIN 28BEARING FATIGUE LIFE PREDICTIONS

    WITH TEST DATA

    THE TIMKEN COMPANY

    By: Michael Kotzalas and Gerald F

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     Abstract

    Recent advances in rolling bearing technology have spawned a flurry of activity aimed at reassessing bearing

    life prediction algorithms. This has become particularly important for the wind turbine gearbox industry, where

    20 years of calculated bearing L10 life is a standard requirement. However, it is a common observation that

    numerous, proprietary approaches have evolved to predict bearing life, and these varying methods can provide

    significantly different predictions. In an effort to create an advanced, publicly accessible method of predicting

    bearing L10 life that might provide some uniform basis, the Deutsches Institut für Normung e.V. (DIN) has created a

    standard utilizing assumptions for what constitutes a typical bearing design, manufacturing process, as well as the

    expected damage mechanisms. Validation of the standard was only accomplished to the extent that the member

    companies shared test results or comparisons with their prediction algorithms.

    To further consider the effectiveness of the DIN algorithms to accurately predict the fatigue life of rolling bear-

    ings, this paper compares test data of standard production tapered roller bearings (TRB) from six top manufac-

    turers, including Timken, with the DIN and Timken proprietary algorithms. The test data was selected to include

    varying operating conditions in recent test programs; thick and thin lubricant films, misalignment, variable loading

    and debris denting of the raceway surfaces. The results of this investigation show a bearing manufacturer’s propri-

    etary algorithms, in this case Timken, more accurately predict the actual performance of their products. In fact, the

    DIN algorithms tended to over-predict bearing fatigue life for low load and under-predict for debris contaminated

    operating conditions.

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    Introduction

    Recently, there have been significant advances in

    rolling bearing technology. These advances can be seen

    in design and manufacturing through the use of cleaner

    steels, new surface finishing and texturing techniques as

    well as the use of tribological coatings. Also, advances

    have been made in the fundamental understanding and

    modeling of rolling bearing performance. The use of com-

    puters has increased the level of sophistication available

    for bearing analyses to the point that what used to be im-

    practical is now standard practice. As such, there has

    been a large amount of recent activity in the area of pre-

    dicting bearing performance [1-7]. This has become par-

    ticularly important for many demanding and highly sophis-

    ticated applications, such as the wind turbine gearbox

    industry where 20 years of calculated bearing L10

     life is a

    standard requirement.

    One significant problem with all of the recent activ-

    ity in bearing analyses is the numerous, proprietary ap-

    proaches that have evolved to predict fatigue life. These

    methods can vary significantly causing difficulty for engi-

    neers selecting bearings, as seemingly identical bearingscan have vastly different predicted lives depending on the

    approach used.

    In an effort to create an advanced, publicly accessi-

    ble method of predicting bearing L10

     life that might pro-

    vide some uniform basis, the Deutsches Institut für Nor-

    mung e.V. (DIN) [5 and 6] has created a standard utilizing

    assumptions for what constitutes a typical bearing design,

    manufacturing process, as well as the expected damage

    mechanisms. As with any standardization activity, vali-

    dation was only accomplished to the extent that member

    companies shared test results or comparisons with their

    prediction algorithms. As the DIN 281 Addendum 4 stan-

    dard is being utilized in a slightly modified fashion for bear-

    ing selection within the American Gear Manufacturer’s As-

    sociation (AGMA) Wind Turbine Gearbox standard 6006

    [8], an investigation of its accuracy compared to bearing

    fatigue test data is desired, and is the aim of this paper.

    Bearing Fatigue Tests

    Bearing fatigue life test results from the author’s labo-

    ratory were collected. Only tests of standard production,

    or “off the shelf” tapered roller bearings (TRB) were used,

    as more scientifically controlled tests would not be rele-

    vant to the community of bearing users. The tests were

    selected to include bearings from six top manufacturers,

    including Timken, and varied operating conditions. The

    different general operating conditions included thick and

    thin lubricant films, bearing misalignment, variable loading

    and debris denting of the raceway surfaces.

     All of the tests were conducted in the author’s labo-

    ratory using a first-in-four test scheme; See Figure 1. Inthis scheme, the center bearings are radially loaded with

    a hydraulic cylinder, while the end bearings are loaded

    through the reaction with the shaft and housing. The test

    is shut down when one bearing has a spall subtending 6

    mm2 (0.01 in2 ) in area. At this time, the remaining 3 bear-

    ings are suspended, yielding the L15.91

     life for this sample

    of four bearings.

     

    FIGURE 1. BEARING TEST SETUP

    The standard test setups use an ISO viscosity grade

    mineral oil supplied via a circulating system. The lubri-

    cants contain only rust and oxidation (R&O) additives to

    prevent any alteration of the bearing fatigue performance

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    due to the additives in fully formulated oils. The circulat-

    ing oil is filtered with a 40 mm, absolute filter. Even with

    such course filtration, due to the general laboratory envi-

    ronment, the ISO 4406 oil cleanliness level has been con-

    sistently measured at 15/12 for all test housings.

    Utilizing the previously described standard test setup,

    variable parameters within the test rigs were controlled to

    obtain the desired operating environment. Such as, the

    lubricant supply temperature was set at different values to

    produce the desired lubricant film conditions. Thick film

    tests were typically run at 37.8ºC (100ºF) oil inlet temper-

    ature while thin film tests at 82.2ºC (180ºF). To produce

    misalignment conditions, the cup-housing adapters were

    manufactured with a predisposed misalignment. Control-

    ling the hydraulic pressure applied to the loading cylinder

    created the variable load conditions.

    Finally, the debris-dented conditions were created in

    a more elaborate setup, by pre-denting the bearing as-

    semblies. This was conducted by rotating a single bear-

    ing under a 4448 kN (1000 lb) pure thrust load for 2000

    revolutions in a debris-laden lubricant. The debris parti-

    cles were hardened T15 tool steel from 25 µm to 53 µm

    in size. The debris was mixed into highly filtered ISO VG

    032 mineral oil containing only R&O additives in a ratio

    of 0.5 mg/ml. After pre-denting, the bearings were ul-

    trasonically cleaned to remove any residual dirt or debris

    from the components and then assembled into the fa-

    tigue test rig.

    The final matrix of selected tests for this study is list-

    ed in Table 1. Table 1 represents 48 different sets of bear-

    ing tests, consisting of 1228 tapered roller bearings from 6

    top manufacturers. The different sets have been grouped

    into 5 general categories of operating conditions: thick lu-

    bricant films, thin lubricant films, misaligned; varied load-

    ing and debris.

    Fatigue Life Prediction

     After the bearing fatigue test data was collected, the

    lives were predicted using the Timken catalog and Timken

    advanced proprietary methods as well as the DIN 281 Bei-

    blatt 1 and 4 algorithms. In doing such, the average mea-

    sured cup OD temperature was used for determining the

    lubricant properties, and the average measured load zone

    to determine an applied bearing thrust load for each of the

    48 test sets. The bearing misalignment was estimated

    through shaft bending analysis coupled with the pre-man-

    ufactured misalignment in the cup-housing adapters. The

    above inputs were necessary for all prediction algorithms,

    however the Timken advanced and DIN 281 Addendum 4

    methodologies also require the input of profiles and sur-

    face finishes. As the design profiles and finishes were not

    known for all of the test bearings, as is the case for most

    end users, the default profiles and finishes built into each

    tool were used. The default profiles in both algorithms use

    some form of a modified (e.g. logarithmic) profile.

     After the lives were predicted for each of the 48 test

    sets, Weibull analyses were performed to combine data

    into the 5 groups of operating conditions. To do this, theindividual bearing test lives within each test set were in-

    verted and multiplied by the corresponding predicted

    L15.91

    . Now, Weibull analyses were performed for an entire

    operating condition group to determine the effectiveness

    of each prediction algorithm. The results of the Weibull

    analyses were plotted with 90% confidence intervals in

    Figures 2 through 6. Finally, the overall total weighted er-

    ror (TWE) as defined in [4], Equation 1, was determined for

    Timken and the other top manufacturers respectively.

    (1)

     As can be seen in equation 1, the TWE represents the

    error in life prediction relative to the spread of the 90%

    confidence bands. The results for TWE are shown in fig-

    ure 7.

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    TABLE 1. SELECTED BEARING TEST DATA SETS

    Test Set Heat Treatment  λ

    Ratio

    Misalignment

    (mrad)

     Average

    Load Zone

    (deg)

     Average Cup

    Temperature (ºC)

    DPW

    (mm)K Factor P/C

    1

    Thick Film

    Through Hardened 3.7 0.09 135 48 61 1.5 0.41

    2 Case Carburized 1.6 0.02 130 59 212 1.3 0.46

    3 Case Carburized 2.2 0.02 135 57 212 1.3 0.46

    4 Case Carburized 1.4 0.02 134 61 212 1.3 0.46

    5 Case Carburized 1.3 0.05 142 59 120 1.3 0.42

    6 Through Hardened 1.5 0.09 138 78 61 1.5 0.41

    7 Through Hardened 1.7 0.22 145 46 109 1.4 0.39

    8 Through Hardened 5.0 0.31 148 45 57 1.5 0.41

    9 Through Hardened 1.1 0.18 155 60 50 1.4 0.45

    10 Through Hardened 0.9 0.31 149 43 57 1.5 0.41

    11 Through Hardened 1.4 0.31 140 46 52 1.8 0.44

    12 Through Hardened 1.0 0.31 139 48 57 1.5 0.41

    13 Through Hardened 2.0 0.51 135 46 62 1.1 0.44

    14 Through Hardened 1.2 0.37 140 51 70 1.4 0.38

    15 Through Hardened 2.7 0.31 133 40 57 1.5 0.41

    16 Case Carburized 1.3 0.80 149 46 45 1.4 0.41

    17 Through Hardened 1.6 0.51 128 49 62 1.1 0.44

    18 Through Hardened 1.2 0.31 147 48 57 1.5 0.41

    19

    Thin Film

    Case Carburized 0.5 0.17 146 79 47 1.4 0.40

    20 Case Carburized 0.4 0.00 144 84 109 1.4 0.38

    21 Case Carburized 0.5 1.00 150 77 53 1.6 0.37

    22 Case Carburized 0.5 0.07 135 91 120 1.3 0.42

    23 Through Hardened 0.5 0.20 149 96 77 1.4 0.41

    24 Through Hardened 0.6 0.07 136 88 120 1.3 0.42

    25

    Misaligned

    Through Hardened 1.6 2.00 135 76 61 1.5 0.41

    26 Case Carburized 0.8 2.00 136 86 50 1.1 0.3927 Case Carburized 0.5 2.00 153 86 47 1.1 0.39

    28 Case Carburized 2.7 1.80 144 47 56 1.1 0.40

    29 Case Carburized 0.6 2.00 146 78 52 1.8 0.40

    30 Through Hardened 2.3 1.00 144 44 53 1.6 0.39

    31 Through Hardened 1.7 0.94 147 48 47 1.1 0.42

    32 Through Hardened 2.1 1.21 126 48 56 1.1 0.45

    33 Through Hardened 1.7 0.95 152 48 50 1.1 0.44

    34 Case Carburized 3.0 1.09 141 43 39 1.6 0.40

    35

     Varied Load

    Case Carburized 0.7 0.94 175 82 63 1.7 0.39

    36 Case Carburized 0.7 0.47 170 68 63 1.7 0.20

    37 Case Carburized 0.7 0.38 140 67 63 1.7 0.16

    38 Case Carburized 0.9 0.90 175 83 43 1.7 0.3939 Case Carburized 0.9 0.45 165 57 43 1.7 0.20

    40 Case Carburized 0.7 0.18 130 89 94 1.3 0.62

    41 Case Carburized 0.7 0.10 130 82 94 1.3 0.36

    42 Case Carburized 0.7 0.06 120 74 94 1.3 0.21

    43 Case Carburized 0.7 0.04 120 66 94 1.3 0.15

    44 Case Carburized 0.4 0.12 150 86 94 1.3 0.41

    45 Case Carburized 0.9 0.06 135 68 94 1.3 0.21

    46

    Debris

    Case Carburized 1.7 0.51 119 78 62 1.1 0.39

    47 Through Hardened 1.8 0.51 148 56 62 1.1 0.39

    48 Through Hardened 1.3 0.51 151 84 62 1.1 0.39

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    FIGURE 2. THICK FILM RESULTS WITH 90% CONFIDENCE 

    FIGURE 3. THIN FILM RESULTS WITH 90% CONFIDENCE 

    FIGURE 4. MISALIGNED RESULTS WITH 90% CONFIDENCE 

    FIGURE 5. VARIABLE LOAD WITH 90% CONFIDENCE 

    FIGURE 6. DEBRIS DENTED RESULTS WITH 90% CONFIDENCE 

    FIGURE 7. OVERALL RESULTS USING TOTAL WEIGHTED ERROR

    1.25

    1.00

    0.75

    0.50

    0.25

    0.00  Timken Timken DIN 281.1 DIN 281.4  Catalog Advanced

       L   1   5 .   9

       1  -   P  r  e

       d   i  c   t  e   d

       /   L   1   5 .   9

       1  -   T  e  s   t

    1.75

    1.50

    1.25

    1.00

    0.75

    0.50

    0.25

    0.00  Timken Timken DIN 281.1 DIN 281.4  Catalog Advanced

       L   1   5 .   9

       1  -   P  r  e   d   i  c   t  e   d

       /   L   1   5 .   9

       1  -   T  e  s   t

    1.25

    1.00

    0.75

    0.50

    0.25

    0.00  Timken Timken DIN 281.1 DIN 281.4  Catalog Advanced

       L   1   5 .   9

       1  -   P  r  e   d   i  c   t  e   d

       /   L   1   5 .   9

       1  -   T  e  s   t

    3.00

    2.50

    2.00

    1.50

    1.00

    0.50

    0.00

      Timken Timken DIN 281.1 DIN 281.4  Catalog Advanced

       L   1   5 .   9

       1  -   P  r  e

       d   i  c   t  e   d

       /   L   1   5 .   9

       1  -   T  e  s   t

    7.00

    6.00

    5.00

    4.00

    3.00

    2.00

    1.00

    0.00  Timken Timken DIN 281.1 DIN 281.4  Catalog Advanced

       L   1   5 .   9

       1  -   P  r  e   d   i  c   t  e   d

       /   L   1   5 .   9

       1  -   T  e  s   t

    1.25

    1.00

    0.75

    0.50

    0.25

    0.00  Timken Other Manufacturer’s  Bearings Bearings

       T  o   t  a   l   W  e   i  g   h   t  e   d   E  r  r  o  r

    Timken Advanced

    DIN 281.4

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    Discussion of Results

    The thick and thin film results show relatively good

    agreement between the prediction methods and with the

    test data. This is expected as this type of bearing dam-

    age has been studied for many decades. The thick film

    tests typically incur inclusion damage as shown in Fig-

    ure 8A, while the thin film tests point surface origin (PSO)

    damage shown in Figure 8B. The advanced analyses (i.e.,

    Timken advanced and DIN 281.4) slightly under-predicted

    the thick and thin film data, however the 90% confidence

    bands overlapped unity. In other words, the statistical

    value of L15.91 estimated from the test data with 90%

    confidence, which lies between the dark bands shown in

    Figures 2-6, overlap unity and thus could be equal to the

    predicted value. For the simple methods (i.e., Timken cat-

    alog and DIN 281.1), the thick film predictions were con-

    servative as they underestimated the test data by 22.2%

    for the DIN 281.1 and 46.1% for the Timken catalog at

    the value of their upper 90% confidence band. Howev-

    er, manufacturers do tend to be conservative when using

    simple methods, as bearing damage from possible appli-

    cation conditions not considered can affect actual perfor-

    mance. A good example of this is bearing misalignment.

    The thin film results contained unity within the 90% con-

    fidence intervals for all analyses except the Timken cata-

    log, which was again slightly conservative.

    The misaligned results indicate a general underesti-

    mation for all analysis methods. The simple methods do

    not consider the geometric stress concentration (GSC)

    damage mode, Figure 8C, which is typical of misalign-

    ment. This leads to an assumption that the test resultshad other factors causing this under-prediction. In fact,

    most of the tests also had thick film conditions occur-

    ring, which led to a general under-prediction in the results

    in Figure 2. The advanced methods, for this condition,

    also under-predict the test results. As the thick film re-

    sults were accurate for these methods, it appears their

    consideration for the extreme values of misalignment in

    these tests are conservative. The test misalignment val-

    ues varied between 0.94 to 2.00 mrad, while most cata-

    logs list values of 0.50 mrad as the acceptable limit. Also,

    these advanced algorithms are highly dependent on ac-

    curate descriptions of the design profile, which could be

    leading to some of the error in the life predictions. In any

    case, the under-predictions were 54.2% for the Timken

    advanced and 71.2% for the DIN 281.4 at the upper val-

    ue of their 90% confidence band.

    The variable load condition results, Figure 5, showed

    a general trend of over-prediction for all methods except

    the Timken advanced. The Timken advanced algorithm

    contained unit within the 90% confidence band, and thus

    accurately predicted the fatigue data. The Timken cat-

    alog method did over-predict the test data by 12.8% at

    the lower 90% confidence band, however the over-pre-

    dictions were by 57.2% for the DIN 281.1 and 29.7% for

    the DIN281.4. The Timken algorithms consider a change

    in the damage mode from inclusion, GSC or PSO when

    loads are moderate to heavy, to peeling damage when

    the loads are light [9]; See Figure 8D. The DIN algorithms

    do not consider this change in expected damage mode

    and thus tended to over-predict the life in lightly loaded

    applications. This is shown more directly in Figure 9, in

    which the Weibull analysis was performed on subgroups

    of test results within the variable load condition with near

    identical ratios of equivalent radial load to radial dynam-

    ic capacity based on one million cycles (P/C). The Tim-

    ken advanced method is close to one for all relative load

    levels, while the DIN 281.4 factor tended to increasingly

    over-predict with decreasing load ratio. In relation to the

     AGMA standard, the lowered limit of the maximum effec-

    tive life factor was not a consideration, as all of the values

    were below 10. Thus, the AGMA standard is identical to

    the DIN 281.4 in these conditions.

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     A) INCLUSION B) PSO

    C) GSC D) PEELING

    FIGURE 8. TYPICAL DAMAGE MODES FOR ROLLING ELEMENT BEARINGS

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    7

    6

    5

    4

    3

    2

    1

    0

      0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

       L   1   5 .   9

       1  -   P  r  e   d   i  c   t  e   d

       /   L   1   5 .   9

       1  -   T  e  s   t

    P/C

    FIGURE 9. LIFE PREDICTION RATIOS VS. LOAD RATIO

    Timken Advanced

    DIN 281.4

    The debris dented operating condition results are

    shown in Figure 6. The Timken catalog method does not

    consider debris, and thus a large over-prediction, as seen

    in the results, was expected. The Timken advanced al-

    gorithm utilized Debris Signature AnalysisSM (DSA) [1, 2

    and 10], so the dent geometries associated with the size,

    shape and type of debris were considered. Using this

    methodology, the 90% confidence bands overlapped uni-

    ty. The DIN methods, however, both under-predict the

    debris damaged test results by 48.5% for DIN 281.1 and

    31.0% for DIN281.4 at the upper value of the 90% con-

    fidence band. The ISO 4406 cleanliness levels were cre-

    ated for hydraulic fluids to prevent erosive and abrasive

    damage. As such, they do not effectively account for the

    different types of debris materials (e.g. hard ductile, soft

    ductile or hard brittle) that can occur in a bearing system

    [2 and 9]. Thus, to best handle the different types of bear-

    ing damage that can occur from debris, the need to be

    overly conservative would be necessary and was evident

    in the test data.

    Overall TWE are shown in Figure 7 for Timken ad-

    vanced algorithms and DIN 281.4 predicting fatigue per-

    formance for Timken products and the other top manufac-

    turers respectively. As can be seen, the Timken algorithm

    predicts fatigue performance for Timken products much

    better than the DIN 281.4 standard. However, the DIN281.4 methodology predicts the fatigue performance of

    the other top manufacturers product better than the Tim-

    ken algorithms. This should be expected, as each man-

    ufacturer has inherently included the steel specifications,

    manufacturing processes and design attributes associ-

    ated to their products built into their prediction method-

    ologies. As such, Timken algorithms predict the fatigue

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    performance of Timken products better than other meth-

    odologies. Also, the other top manufacturers, some of

    whom worked within DIN to create the DIN 281 standard,

    are best able to predict the fatigue performance for their

    products.

    Conclusions

    The overall TWE comparison for the 48 different test

    groups shows that Timken algorithms are better at pre-

    dicting fatigue for Timken products, and the DIN standard

    was only slightly better at predicting fatigue for the re-

    maining top manufacturers. Also, when considering each

    of the five operating condition groups, the Timken ad-

    vanced algorithm was more accurate for predicting per-

    formance as evidenced by the location of the confidence

    bands with respect to unity. This is particularly important

    for low loads, where the DIN factor was over-predicting or

    for heavily debris-damaged conditions when the DIN fac-

    tor was under-predicting life.

    References

    1. Ai, X, and Nixon, H. (2000), “Fatigue Life Reduction

    of Roller Bearings due to Debris Denting: Part I – Theo-

    retical Modeling,” Tribology Transactions, v. 43, n. 2, pp.

    197-204.

    2. Ai, X, and Nixon, H. (2000), “Fatigue Life Reduc-

    tion of Roller Bearings due to Debris Denting: Part II – Ex-

    perimental Validation,” Tribology Transactions, v. 43, n. 2,

    pp. 311-7.

    3. Harris, T., and McCool, J. (1996), “On the Accuracy

    of Rolling Bearing Fatigue Life Prediction,” Transactions of

    the ASME, Journal of Tribology, v.118, n. 2, pp. 297-310.

    4. Ioannides, E., Bergling, G., and Gabelli, A., (1999),

    “An Analytical Formulation for the Life of Rolling Bear-

    ings,” Acta Polytechnica Scandinavica, Mechanical En-

    gineering Series, v. 137.

    5. DIN ISO 281 Beiblatt 1 (April, 2003), Rolling Bear-

    ings - Dynamic Load Ratings and Rating Life - Life Modi-

    fication Factor aDIN and Calculation of the Modified Rat-

    ing Life.

    6. DIN ISO 281 Beiblatt 4 (April, 2003), Rolling Bear-

    ings – Dynamic Load Ratings and Rating Life - Methods

    for Calculation of the Modified Reference Rating Life for

    Universally Loaded Rolling Bearings.

    7. ASME Tribology Division (2003), Life Ratings for

    Modern Rolling Bearings/A Design Guide for Application

    of International Standard ISO 281/2.

    8. ANSI/AGMA/AWEA 6006-A03 (2003), Design and

    Specification of Gearboxes for Wind Turbines.

    9. Hoeprich, M. (1998), “Extended Rolling Element

    Bearing Fatigue Life at Low Loads,” Presented at the 53rd

    STLE Annual Meeting, Detroit, MI.

    10. Nixon, H., Ai, X., Cogdell, J., and Fox, G. (1999),

    “Accessing and Predicting the Performance of Bearings

    in Debris Contaminated Lubrication Environment,” SAE

    Technical Paper #1999-01-2791.

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    NOTES

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     WORLDWIDE LEADER IN BEARINGS AND STEEL

    Timken® is the registered trademark ofThe Timken Company.www.timken.com

    © 2005 The Timken CompanyPrinted In the U.S.A..7M-03-05 Order No. 5866