Erwin V. Zaretsky

Comparison of Life Theories for Rolling-Element Bearings

Nearly 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 superio...

Endurance and Failure Characteristic of Main-Shaft Jet Engine Bearing at 3 × 106 DN

Groups of thirty 120-mm bore angular-contact ball bearings were endurance tested at a speed of 12,000 and 25,000 rpm (1.44 million and 3.0 million DN, where DN is the product of the bearing bore in mm and the shaft speed in rpm) and a thrust load of 66,721 N. The bearings were manufactured from a single heat of VIM-VAR AISI M-50 steel. At 1.44 million and 3.0 million DN, 84,483 and 74,800 bearing test hours were accumulated, respectively. Test results were compared with similar bearings made from CVM AISI M-50 steel run under the same conditions. Bearing lives at speeds of 3 million DN with the VIM-VAR AISI M-50 steel were nearly equivalent to those obtained at lower speeds. A combined processing and material life factor of 44 was found for VIM-VAR AISI M-50 steel. Continuous running after a spall has occurred at 3.0 million DN can result in a destructive fracture of the bearing inner race.

Dynamic Capacity and Surface Fatigue Life for Spur and Helical Gears

A mathematical model for surface fatigue life of gear, pinion, or entire meshing gear train is given. The theory is based on the statistical approach used by Lundberg and Palmgren for rolling-element bearings. Also equations are presented which give the dynamic capacity of the gear set. The dynamic capacity is the transmitted tangential load which gives a 90 percent probability of survival of the gear set for one million pinion revolutions. The analytical results were compared with test data for a set of AISI 9310 spur gears operating at a maximum Hertz stress of 1.71 billion N per sq m (248,000 psi) and 10,000 rpm. The theoretical life predictions were very good when material constants obtained from rolling-element bearing tests were used in the gear life model.

Effect of roller profile on cylindrical roller bearing life prediction-part i : Comparison of bearing life theories©

Four rolling-element bearing life theories were chosen for analysis and compared for a simple roller-race geometry model. The life theories were those of Weibull; Lundberg and Palmgren; Ioannides and Harris; and Zaretsky. The analysis without a fatigue limit of Ioannides and Harris is identical to the Lundberg and Palmgren analysis, and the Weibull analysis is similar to that of Zaretsky if the exponents are chosen to be identical. The resultant predicted life at each stress condition not only depends on the life equation used but also on the Weibull slope assumed. The least variation in predicted life with Weibull slope comes with the Zaretsky equation. Except for a Weibull slope of 1.11, at which the Weibull equation predicts the highest lives, the highest lives are predicted by the Zaretsky equation. For Weibull slopes of 1.5 and 2, both the Lundberg-Palmgren and Ioannides-Harris (where τu equals 0) equations predict lower lives than the ANSI/ABMA/ISO standard. Based upon the Hertz stresses for line contact, the accepted load-life exponent of 10/3 results in a maximum Hertz stress-life exponent equal to 6.6. This value is inconsistent with that experienced in the field. The assumption of a shear stress fatigue limit τu results in Hertz stress-life exponents greater than are experimentally verifiable. Presented at the 55th Annual Meeting Nashville, Tennessee May 7–11, 2001

A Study of Residual Stress Induced During Rolling

Rolling induced residual stress measurements as function of depth and component Rockwell hardness for inner races from deep groove ball bearings

Component Hardness Differences and Their Effect on Bearing Fatigue

Component hardness differences of SAE 52100 steel effect on bearing fatigue, using five-ball fatigue tester and rolling element bearings

Determination of Rolling-Element Fatigue Life From Computer Generated Bearing Tests

Two types of rolling-element bearings representing radial loaded and thrust loaded bearings were used for this study. Three hundred and forty (340) virtual bearing sets totaling 31400 bearings were randomly assembled and tested by Monte Carlo (random) number generation. The Monte Carlo results were compared with endurance data from 51 bearing sets comprising 5321 bearings. A simple algebraic relation was established for the upper and lower L10 life limits as function of the number of bearings failed for any bearing geometry. There is a fifty percent (50%) probability that the resultant bearing life ill be less than the calculated. The maximum and minimum variation between the bearing results life and the calculated life correlate with the 90-percent confidence limits for a Weibull slope of 1. 5. The calculated lives for bearings using a load-life exponent p of 4 for ball bearings and 5 for roller bearings correlated with the Monte Carlo generated bearings lives and the bearing data. STLE life factors for bearing steel and processing provide a reasonable accounting for differences between bearing life data and calculated life. Variations in Weibull slope from the Monte Carlo testing and bearing data correlated. There was excellent agreement between percent of individual components failed from Monte Carlo simulation and that predicted. Presented at the 58th Annual Meeting in New York City April 28–May 1, 2003

Effect of roller profile on cylindrical roller bearing life prediction-part II comparison of roller profiles©

Four roller profiles used in cylindrical roller bearing design and manufacture were analyzed using both a closed form solution and finite element analysis (FEA) for stress and life. The analyzed roller profiles were flat, end tapered, aerospace, and fully crowned and loaded against a flat raceway. Four rolling-element bearing life models were chosen for this analysis: those of Weibull; Lundberg and Palmgren; Ioannides and Harris; and Zaretsky. The flat roller profile without edge loading has the longest predicted life. However, edge loading can reduce life by as much as 98 percent. The end-tapered profile produced the highest lives, but not significantly higher than those produced by the aerospace profile. The fully crowned profile produced the lowest lives. Except for the flat roller profile, the predicted lives with the FEA method exceed those with the closed form solution. The fatigue limit proposed by Ioannides and Harris equates to one-half the value of a compressive residual stress that may exist in a rolling bearing steel. Presented at the 55th Annual Meeting Nashville, Tennessee May 7–11, 2001

The Effect of Contact Angle on Rolling-Contact Fatigue and Bearing Load Capacity

The NASA five-ball fatigue tester was used to determine the rolling-contact fatigue life of ½-in.-diameter M-1 steel balls applicable for high-temperature bearing use, and modified 204-size angular-contact ball bearings at various contact angles. For a constant Contact stress in the five-ball fatigue tester, fatigue life decreased with increasing contact angle. In contrast, relative thrust-load capacity increased with increasing contact angle. The Lundberg-Palmgren theory correctly predicts capacity at contact angles up to 30 degrees. Presented as an American Society of Lubrication Engineers paper at the Lubrication Conference held in Chicago, Illinois, October 1961.

Parametric Study of the Lubrication of Thrust Loaded 120-MM Bore Ball Bearings to 3 Million DN

A parametric study was performed with 120-mm bore angular-contact ball bearings under varying thrust loads, bearing and lubricant temperatures, and cooling and lubricant flow rates. Contact angles were nominally 20 and 24 deg with bearing speeds to 3 million DN. Endurance tests were run at 3 million DN and a temperature of 492 K (425 F) with 10 bearings having a nominal 24 deg contact angle at a thrust load of 22241 N (5000 lb). Bearing operating temperature, differences in temperatures between the inner and outer races, and bearing power consumption can be tuned to any desirable operating requirement by varying 4 parameters. These parameters are outer-race cooling, inner-race cooling, lubricant flow to the inner race, and oil inlet temperature. Preliminary endurance tests at 3 million DN and 492 K (425 F) indicate that long term bearing operation can be achieved with a high degree of reliability.