Residual Stress Change Due to Rolling Contact of Ball and Roller Bearings

1980 ◽  
Vol 24 ◽  
pp. 215-220
Author(s):  
Kikuo Maeda ◽  
Noriyuki Tsushima ◽  
Hiroshi Muro
Keyword(s):  
Residual Stress ◽  
Contact Stress ◽  
Stress Measurement ◽  
Rolling Bearing ◽  
Bearing Steel ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Compressive Yield Strength ◽  
Rolling Elements ◽  
Hertzian Contact Stress

The life of a rolling bearing is predominantly determined by the contact stress between the rolling elements (ball and roller) and the raceway of inner and outer rings. The contact stress is calculated by assuming Hertzian stress distribution. The maximum Hertzian contact stress Pmax usually ranges from 2000 to 3000 MPa in actual service of rolling bearings. These figures are rather large compared to the compressive yield strength of hardened bearing steel (σys = 2000 MPa). Therefore plastic deformation sometimes occurs under the raceway, creating residual compressive stress. Several investigators have so far reported about the residual stress due to rolling contact. There were, however, few who referred to the residual stress in used bearings and application of residual stress measurement to failure analysis.

Surface Durability of Spur Gears at Hertzian Stresses Over Shakedown Limit

1974 ◽  
Vol 96 (2) ◽  
pp. 359-372 ◽  
Author(s):  
Akira Ishibashi ◽  
Taku Ueno ◽  
Shigetada Tanaka
Keyword(s):  
Fatigue Testing ◽  
Testing Machine ◽  
Carbon Steels ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Load Testing ◽  
Short Period ◽  
Hertzian Contact Stress ◽  
Surface Durability ◽  
Shakedown Limit

Using a new type of gear-load testing machine and a disk-type rolling fatigue testing machine designed and made by the authors, the upper limits of Hertzian contact stress allowable on rolling contact surfaces were investigated. It was shown conclusively that gears and rollers made of soft carbon steels could be rotated beyond 108 revolutions at Hertzian stresses over shakedown limit (≈ 0.4 HB). In the case of gears, pits having a pitting area ratio of 0.04 percent occurred during 1.16 × 108 rotations at a Hertzian stress of 0.50 HB. However, no pitting occurred on the roller rotated through 1.20 × 108 revolutions at a Hertzian stress of 0.71 HB, although appreciable changes in texture were observed at the subsurface. In order to rotate gears or rollers at Hertzian stresses over shakedown limit, their surface must either be very smooth initially or after a short period of running, and an oil film must be formed between contacting surfaces.

Effect of Lubricant on Surface Rolling Contact Fatigue Cracks

2010 ◽  
Vol 97-101 ◽  
pp. 793-796 ◽  
Author(s):  
Khalil Farhangdoost ◽  
Mohammad Kavoosi
Keyword(s):  
Fatigue Crack ◽  
Fatigue Cracks ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Element Analysis ◽  
Crack Face ◽  
Hertzian Contact Stress ◽  
Model Of Friction

This study performed the finite element analysis of the cycle of stress intensity factors at the surface initiated rolling contact fatigue crack tip under Hertzian contact stress including an accurate model of friction between the faces of the crack and the effect of fluid inside the crack. A two-dimensional model of a rolling contact fatigue crack has been developed with FRANC-2D software. The model includes the effect of Coulomb friction between the faces of the crack. The fluid in the crack was assumed not only to lubricate the crack faces and reduce the crack face friction coefficient but also to generate a pressure.

Planar Tooth Profile Synthesis for Relative Curvature

2017 ◽  
Author(s):  
Zhiyuan Yu ◽  
Kwun-Lon Ting
Keyword(s):  
Contact Stress ◽  
Tooth Profile ◽  
Hertzian Contact ◽  
Rolling Motion ◽  
Special Cases ◽  
Systematic Methodology ◽  
Hertzian Contact Stress ◽  
Curvature Theory ◽  
The Given ◽  
Tooth Pair

This paper is the first that uses the new conjugation curvature theory [1] to directly synthesize conjugate tooth profiles with the given relative curvature that determines the Hertzian contact stress. Conjugation curvature theory offers a systematic methodology to synthesize the relative curvature for a tooth pair. For any given relative curvature between the contact tooth profiles, a generating point can be located on an auxiliary body. Under the rolling motion among the pinion pitch, the gear pitch and the pitch on the auxiliary body, the generating point will trace fully conjugate profiles on the pinion and gear bodies with the given relative curvature at the instant of the contact. Full conjugation throughout the contact of the profiles is guaranteed with the three instant centers remaining coincident [1]. The methodology is demonstrated with a planar tooth profile synthesis with given relative curvature. One may find that the Wildhaber-Novikov tooth profile, which is known to have low relative curvature and Hertzian contact stress, and its variations become special cases under such methodology.

scholarly journals Study on the Steel Rail Rolling Contact Stress with Consideration of Initial Residual Stress

2015 ◽  
Vol 22 ◽  
pp. 03018 ◽  
Author(s):  
Hua Song ◽  
Jian Yang ◽  
Linbang Song ◽  
Jinkai Yao ◽  
Xinglong Du ◽  
...  
Keyword(s):  
Residual Stress ◽  
Contact Stress ◽  
Rolling Contact ◽  
Steel Rail ◽  
Initial Residual Stress

Hertzian Contact-Stress Deformation Coefficients

1969 ◽  
Vol 36 (2) ◽  
pp. 296-303 ◽  
Author(s):  
Duane H. Cooper
Keyword(s):  
Contact Stress ◽  
Digital Computer ◽  
Approximate Calculation ◽  
Transcendental Equation ◽  
Contact Stresses ◽  
Elliptic Integrals ◽  
Hertzian Contact ◽  
Stress Deformation ◽  
Hertzian Contact Stress

Formulations are given for the coefficients λ, μ, ν defined by Hertz in terms of the solution of a transcendental equation involving elliptic integrals and used by him to describe the deformation of bodies subjected to contact stresses. Methods of approximate calculation are explained and errors in the tables prepared by Hertz are noted. For the purpose of providing a more extensive and more accurate tabulation, using an automatic digital computer, these coefficients are reformulated so that a large part of the variation is expressed by means of easily interpreted elementary formulas. The remainder of the variation is tabulated to 6 places for 100 values of the argument. Graphs of the coefficients are also provided.

Hertzian Contact Stress Modeling in Railway Bearings for Assorted Load Conditions and Geometries

2014 ◽  
Author(s):  
Michael A. Mason ◽  
Charles P. Cartin ◽  
Parham Shahidi ◽  
Mark W. Fetty ◽  
Brent M. Wilson
Keyword(s):  
Finite Element ◽  
Contact Stress ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Modeling Tools ◽  
Heat Treat ◽  
Roller Bearings ◽  
Tapered Roller ◽  
Tapered Roller Bearings ◽  
Load Conditions

Increasing freight car loads demand higher performance tapered roller bearings. As the stress state on railway bearing applications continues to increase, further advancement in the modeling tools and methods used for subsurface contact stress evaluations are needed. Heat treat specifications and contact geometries for railway bearings were originally developed for ideal load conditions. However, in railroad applications, tapered roller bearings are exposed to a vast range of load conditions that are seldom perfect. Moreover, when comparing global rail markets, there are often differences in bearing loads, railcar wear conditions, maintenance practices, and reliability versus utilization expectations. Advanced modeling techniques need to be developed by bearing designers in order to meet the specific needs of each individual rail market. Prior research has shown that subsurface stresses, resulting from rolling contact, are the primary factor in the development of fatigue cracks in railway bearings. In addition, finite element modeling software has previously been used to analyze Hertzian contact stresses under rolling contact. Recent advancements in the technology and computational power of finite element methods can be used to numerically analyze more detailed simulations of complex geometries and biased load conditions in railway bearings. These improvements in the tapered roller bearing modeling methodology are necessary to determine the material, heat treat specifications, and geometry required to meet the demands of specific railway bearing applications. Furthermore, the specific risks associated with some common railway bearing design and modeling assumptions will be evaluated. An exploratory list of these assumptions include: line versus point contact, load deflection factor, zero contact angle, rigid body assumptions, linear material behavior, neglect for overload, and uniform loading on the bearing. Emphasis will be placed on potential improvements in the theoretical and finite element prediction of surface and subsurface stresses in railway bearings under rolling contact with a review of prior research on the subject.

Tooth Surface Fatigue Strength of Normalized Steel Conical Involute Gears

2000 ◽  
Author(s):  
Tatsuya Ohmachi ◽  
Koji Iizuka ◽  
Hidenori Komatsubara ◽  
Ken-ichi Mitome
Keyword(s):  
Fatigue Strength ◽  
Contact Stress ◽  
Testing Machine ◽  
Hertzian Contact ◽  
Tooth Surface ◽  
Paper Test ◽  
Surface Fatigue ◽  
Involute Gears ◽  
Conical Gears ◽  
Hertzian Contact Stress

Abstract The tooth surface fatigue strength of the conical involute gear is evaluated in this paper. Test gears are straight intersecting-axis conical gears. The material of the test gear is normalized steel. The power circulating testing machine is used in this experiment. The circulating torque is kept constant and the number of times of contact is 107. The tooth surface life is evaluated by the pitting area rate. The critical value of the circulating torque is found between 147 N·m and 157 N·m. For critical torque, the pitting area rate does not progress over 4%. The Hertzian contact stress of the test gear is calculated at the circulating torque. The contact stress should be evaluated in consideration of the wearing effects.

Hysteretic Resonances and Intermittency Chaos in Ball Bearings

2018 ◽  
Author(s):  
Zhiyong Zhang ◽  
Xiaoting Rui ◽  
Yushu Chen ◽  
Wenkai Dong ◽  
Lei Li
Keyword(s):  
Ball Bearing ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rolling Bearings ◽  
Rotor Systems ◽  
Revolute Joints ◽  
Rolling Elements ◽  
Varying Compliance

Ball bearings are essential parts of mechanical systems to support the rotors or constitute the revolute joints. The time-varying compliance (VC), bearing clearance and the Hertzian contact between the rolling elements and raceways are three fundamental nonlinear factors in a ball bearing, hence the ball bearing can be considered as a nonlinear system. The hysteresis and jumps induced by the nonlinearities of rolling bearings are typical phenomena of nonlinear vibrations in the rolling bearing-rotor systems. And the corresponding hysteretic impacts have direct effects on the cleavage derivative and fatigue life of the system components. Therefore, the behaviors of hysteresis and jumps are given full attentions and continued studies in the theoretical and engineering fields. Besides, many researchers have done a lot of calculations to depict the various characteristics of bifurcations and chaos in the rolling bearings and their rotor systems, but few researches have been addressed on the inherent mechanism of the typical intermittency vibrations in rolling bearings. With the aid of the HB-AFT (the harmonic balance method and the alternating frequency/time domain technique) method and Floquet theory, this paper will investigate deeply the resonant hysteresis and intermittency chaos in ball bearings.

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