86 research outputs found
Rolling Bearing Life Prediction, Theory, and Application
Get PDFA tutorial is presented outlining the evolution, theory, and application of rolling-element bearing life prediction from that of A. Palmgren, 1924; W. Weibull, 1939; G. Lundberg and A. Palmgren, 1947 and 1952; E. Ioannides and T. Harris, 1985; and E. Zaretsky, 1987. Comparisons are made between these life models. The Ioannides-Harris model without a fatigue limit is identical to the Lundberg-Palmgren model. The Weibull model is similar to that of Zaretsky if the exponents are chosen to be identical. Both the load-life and Hertz stress-life relations of Weibull, Lundberg and Palmgren, and Ioannides and Harris reflect a strong dependence on the Weibull slope. The Zaretsky model decouples the dependence of the critical shear stress-life relation from the Weibull slope. This results in a nominal variation of the Hertz stress-life exponent. For 9th- and 8th-power Hertz stress-life exponents for ball and roller bearings, respectively, the Lundberg- Palmgren model best predicts life. However, for 12th- and 10th-power relations reflected by modern bearing steels, the Zaretsky model based on the Weibull equation is superior. Under the range of stresses examined, the use of a fatigue limit would suggest that (for most operating conditions under which a rolling-element bearing will operate) the bearing will not fail from classical rolling-element fatigue. Realistically, this is not the case. The use of a fatigue limit will significantly overpredict life over a range of normal operating Hertz stresses. Since the predicted lives of rolling-element bearings are high, the problem can become one of undersizing a bearing for a particular application
Rolling Bearing Life Prediction, Theory, and Application
Get PDFA tutorial is presented outlining the evolution, theory, and application of rolling-element bearing life prediction from that of A. Palmgren, 1924; W. Weibull, 1939; G. Lundberg and A. Palmgren, 1947 and 1952; E. Ioannides and T. Harris, 1985; and E. Zaretsky, 1987. Comparisons are made between these life models. The Ioannides-Harris model without a fatigue limit is identical to the Lundberg-Palmgren model. The Weibull model is similar to that of Zaretsky if the exponents are chosen to be identical. Both the load-life and Hertz stress-life relations of Weibull, Lundberg and Palmgren, and Ioannides and Harris reflect a strong dependence on the Weibull slope. The Zaretsky model decouples the dependence of the critical shear stress-life relation from the Weibull slope. This results in a nominal variation of the Hertz stress-life exponent. For 9th- and 8th-power Hertz stress-life exponents for ball and roller bearings, respectively, the Lundberg-Palmgren model best predicts life. However, for 12th- and 10th-power relations reflected by modern bearing steels, the Zaretsky model based on the Weibull equation is superior. Under the range of stresses examined, the use of a fatigue limit would suggest that (for most operating conditions under which a rolling-element bearing will operate) the bearing will not fail from classical rolling-element fatigue. Realistically, this is not the case. The use of a fatigue limit will significantly overpredict life over a range of normal operating Hertz stresses. (The use of ISO 281:2007 with a fatigue limit in these calculations would result in a bearing life approaching infinity.) Since the predicted lives of rolling-element bearings are high, the problem can become one of undersizing a bearing for a particular application. Rules had been developed to distinguish and compare predicted lives with those actually obtained. Based upon field and test results of 51 ball and roller bearing sets, 98 percent of these bearing sets had acceptable life results using the Lundberg- Palmgren equations with life adjustment factors to predict bearing life. That is, they had lives equal to or greater than that predicted. The Lundberg-Palmgren model was used to predict the life of a commercial turboprop gearbox. The life prediction was compared with the field lives of 64 gearboxes. From these results, the roller bearing lives exhibited a load-life exponent of 5.2, which correlated with the Zaretsky model. The use of the ANSI/ABMA and ISO standards load-life exponent of 10/3 to predict roller bearing life is not reflective of modern roller bearings and will underpredict bearing lives
NASA Technical Memorandum 102000
Get PDFERRATA NASA Technical Memorandum 102000 INVESTIGATION OF WEIBULL STATISTICS I N FRACTURE ANALYSIS OF CAST ALUMINUM F r e d e r i c A. H o l l a n d , Jr., and Erwin V. Z a r e t s k y Page 5, SUMMARY OF RESULTS, numbered paragraph 4 should read 4. The ASME p r e s s u r e vessel code f o r t h e d e s i g n o f s p h e r i c a l p r e s s u r e vessel s h e l l s was f o u n d t o be much more c o n s e r v a t i v e t h a n t h e p r o b a b i l i s t i c d e s i g n methodology presented. INVESTIGATION OF WEIBULL STATISTICS I N FRACTURE ANALYSIS OF CAST ALUMINUM F r e d e r i c A. H o l l a n d , J r . , and E r w i n V. Zaretsky' N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n Lewis Research Center C l e v e l a n d , Ohio 44135 ABSTRACT The f r a c t u r e s t r e n g t h s o f two l a r g e batches of A357-T6 c a s t aluminum coupon specimens w e r e compared by u s i n g two-parameter W e i b u l l a n a l y s i s . The minimum numb e r o f these specimens necessary t o f i n d t h e f r a c t u r e s t r e n g t h o f t h e m a t e r i a l was determined. The a p p l i c a -2 b i 1 i t y of three-parameter Wei b u l l a n a l y s i s was a1 so U i n v e s t i g a t e d . A d e s i g n methodology based on t h e combi
Comparison of Models for Ball Bearing Dynamic Capacity and Life
Get PDFGeneralized formulations for dynamic capacity and life of ball bearings, based on the models introduced by Lundberg and Palmgren and Zaretsky, have been developed and implemented in the bearing dynamics computer code, ADORE. Unlike the original Lundberg-Palmgren dynamic capacity equation, where the elastic properties are part of the life constant, the generalized formulations permit variation of elastic properties of the interacting materials. The newly updated Lundberg-Palmgren model allows prediction of life as a function of elastic properties. For elastic properties similar to those of AISI 52100 bearing steel, both the original and updated Lundberg-Palmgren models provide identical results. A comparison between the Lundberg-Palmgren and the Zaretsky models shows that at relatively light loads the Zaretsky model predicts a much higher life than the Lundberg-Palmgren model. As the load increases, the Zaretsky model provides a much faster drop off in life. This is because the Zaretsky model is much more sensitive to load than the Lundberg-Palmgren model. The generalized implementation where all model parameters can be varied provides an effective tool for future model validation and enhancement in bearing life prediction capabilities
Probabilistic Life and Reliability Analysis of Model Gas Turbine Disk
No full textIn 1939, W. Weibull developed what is now commonly known as the "Weibull Distribution Function" primarily to determine the cumulative strength distribution of small sample sizes of elemental fracture specimens. In 1947, G. Lundberg and A. Palmgren, using the Weibull Distribution Function developed a probabilistic lifing protocol for ball and roller bearings. In 1987, E. V. Zaretsky using the Weibull Distribution Function modified the Lundberg and Palmgren approach to life prediction. His method incorporates the results of coupon fatigue testing to compute the life of elemental stress volumes of a complex machine element to predict system life and reliability. This paper examines the Zaretsky method to determine the probabilistic life and reliability of a model gas turbine disk using experimental data from coupon specimens. The predicted results are compared to experimental disk endurance data
Life and reliability of rotating disks
Get PDFIn aerospace applications, an engineer must be especially cognizant of size and weight constraints which affect design decisions. Although designing at or below the material fatigue limit may be desirable in most industrial applications, in aerospace application it is almost mandatory to design certain components for a finite life at an acceptable probability of survival. Zaretsky outlined such a methodology based in part on the work of W. Weibull (1939, 1951) and G. Lundberg and A. Palmgren (1947a, 1947b, 1952). It is the objective of this work to apply the method of Zaretsky (1987) to statistically predict the life of a generic solid disk with and without bolt holes; determine the effect of disk design variables, thermal loads, and speed on relative life; and develop a generalized equation for determining disk life by incorporating only these variables
Effect of Roller Geometry on Roller Bearing Load-Life Relation
Get PDFCylindrical roller bearings typically employ roller profile modification to equalize load distribution, minimize stress concentration at roller ends and allow for a small amount of misalignment. The 1947 Lundberg-Palmgren analysis reported an inverse fourth power relation between load and life for roller bearings with line contact. In 1952, Lundberg and Palmgren changed their load-life exponent to 10/3 for roller bearings, assuming mixed line and point contact. The effect of roller-crown profile was reanalyzed in this paper to determine the actual load-life relation for modified roller profiles. For uncrowned rollers (line contact), the load-life exponent is p = 4, in agreement with the 1947 Lundberg-Palmgren value but crowning reduces the value of the exponent, p. The lives of modern roller bearings made from vacuum-processed steels significantly exceed those predicted by the Lundberg-Palmgren theory. The Zaretsky rolling-element bearing life model of 1996 produces a load-life exponent of p = 5 for flat rollers, which is more consistent with test data. For the Zaretsky model with fully crowned rollers p = 4.3. For an aerospace profile and chamfered rollers, p = 4.6. Using the 1952 Lundberg-Palmgren value p = 10/3, the value incorporated in ANSI/ABMA and ISO bearing standards, can create significant life calculation errors for roller bearings
Recalibrated Equations for Determining Effect of Oil Filtration on Rolling Bearing Life
Get PDFIn 1991, Needelman and Zaretsky presented a set of empirically derived equations for bearing fatigue life (adjustment) factors (LFs) as a function of oil filter ratings. These equations for life factors were incorporated into the reference book, "STLE Life Factors for Rolling Bearings." These equations were normalized (LF = 1) to a 10-micrometer filter rating at Beta(sub x) = 200 (normal cleanliness) as it was then defined. Over the past 20 years, these life factors based on oil filtration have been used in conjunction with ANSI/ABMA standards and bearing computer codes to predict rolling bearing life. Also, additional experimental studies have been made by other investigators into the relationship between rolling bearing life and the size, number, and type of particle contamination. During this time period filter ratings have also been revised and improved, and they now use particle counting calibrated to a new National Institute of Standards and Technology (NIST) reference material, NIST SRM 2806, 1997. This paper reviews the relevant bearing life studies and describes the new filter ratings. New filter ratings, Beta(sub x(c)) = 200 and Beta(sub x(c)) = 1000, are benchmarked to old filter ratings, Beta(sub x) = 200, and vice versa. Two separate sets of filter LF values were derived based on the new filter ratings for roller bearings and ball bearings, respectively. Filter LFs can be calculated for the new filter ratings
Relation Between Residual and Hoop Stresses and Rolling Bearing Fatigue Life
Get PDFRolling-element bearings operated at high speed or high vibration may require a tight interference fit between the bore of the bearing and shaft to prevent rotation of the bearing bore around the shaft and fretting damage at the interfaces. Previous work showed that the hoop stresses resulting from tight interference fits can reduce bearing lives by as much as 65 percent. Where tight interference fits are required, case-carburized steel such as AISI 9310 or M50 NiL is often used because the compressive residual stresses inhibit subsurface crack formation and the ductile core inhibits inner-ring fracture. The presence of compressive residual stress and its combination with hoop stress also modifies the Hertz stress-life relation. This paper analyzes the beneficial effect of residual stresses on rolling-element bearing fatigue life in the presence of high hoop stresses for three bearing steels. These additional stresses were superimposed on Hertzian principal stresses to calculate the inner-race maximum shearing stress and the resulting fatigue life of the bearing. The load-life exponent p and Hertz stress-life exponent n increase in the presence of compressive residual stress, which yields increased life, particularly at lower stress levels. The Zaretsky life equation is described and is shown to predict longer bearing lives and greater load- and stress-life exponents, which better predicts observed life of bearings made from vacuum-processed steel
Comparison of Life Theories for Rolling-Element Bearings
Get PDFNearly five decades have passed since G. Lundberg and A. Palmgren published their life theory in 1947 and 1952 and it was adopted as an ANSI/ABMA and ISO standard in 1950 and 1953. Subsequently, many variations and deviations from their life theory have been proposed, the most recent being that of E. Ioannides and T.A. Harris in 1985. This paper presents a critical analysis comparing the results of different life theories and discussing their implications in the design and analysis of rolling-element bearings. Variations in the stress-life relation and in the critical stress related to bearing life are discussed using stress fields obtained from three-dimensional, finite-element analysis of a ball in a nonconforming race under varying load. The results showed that for a ninth power stress-life exponent the Lundberg-Palmgren theory best predicts life as exhibited by most air-melted bearing steels. For a 12th power relation reflected by modern bearing steels, a Zaretsky-modified Weibull equation is superior. The assumption of a fatigue-limiting stress distorts the stress-life exponent and overpredicts life
- …
