Abstract: Various factors affecting the fatigue life of rolling bearings are reviewed, including various fatigue-induced stresses (maximum shear stress, maximum dynamic shear stress, Von Mises stress and octahedral shear stress), tangential force, residual stress and hoop The effects of stress, fatigue limit stress, surface roughness, elastohydrodynamic lubrication, surface treatment, contamination particles in lubricating oil, temperature, speed, non-failure life and steel purity (oxygen content) provide a reference for accurate prediction of bearing life.
1 Fatigue crack induced stress
Since Swedish scientists Lundberg and Palmgren proposed the maximum dynamic shear stress theory in 1947 and 1952, it is generally believed that the maximum dynamic shear stress parallel to the rolling direction under the contact surface is the main cause of bearing fatigue failure, that is, the crack first occurs in the maximum dynamic shear stress. The stress occurs and then spreads to the surface, resulting in contact fatigue spalling.
In rolling point contact, the maximum value of τmises appears at a depth of z/a = 0.7 below the surface; when the lubricant on the contact surface has contamination particles, the maximum value of τmises appears in the area adjacent to the contact surface, as shown in Figure 3 shown.
In rolling contact, like the maximum static shear stress, the value of the octahedral shear stress τOCT also cycles between 0 and the maximum value. The maximum static shear stress under the raceway is greater than the maximum octahedral shear stress. On the surface, τyz has a value of 0. For general point contact ball bearings, τOCT is about 0.28Pmax, which is about 15 % smaller than τyz. And the depth below the surface is about the same ( zOCT =0.73b, zyz=0.79b). On the contact surface, τOCT is non-zero, approximately 0.17Pmax. In the absence of large surface shear stress, fatigue failure always begins below the surface, so it is reasonable to use τyz as the fatigue-induced stress. But almost all experiments show that when the film thickness ratio is less than 1, the surface friction force is large, and the fatigue cracks are induced from the surface, so it is inappropriate to use τyz as the fatigue-induced stress. Instead, τOCT should be taken as the fatigue-induced stress. Figure 4 is a comparison of the corresponding values of τ0, τyz, τOCT with respect to the depth z/b.
2 Four Stress Calculations under Line Contact Conditions (No Friction)
Cheng Wangquan and Zheng Xuyun  mentioned that τ and τf can be the maximum alternating shear stress, maximum shear stress, Mises
Select either of equivalent stress and octahedral shear stress. Under frictionless line contact conditions,
3 Influence of tangential force
In the actual operation of the bearing, there is inevitably a tangential friction resistance along the contact surface; in the case of elastohydrodynamic lubrication, there is a tangential friction force. The existence of tangential force increases the value of static shear stress and orthogonal shear stress, and the depth from the surface decreases. In line contact, when the friction coefficient is greater than 0.11, the maximum static shear stress occurs on the contact surface; in point contact, and when the friction coefficient is 0.25, the maximum static shear stress occurs on the contact surface  .
4 Influence of residual stress and hoop stress
During the heat treatment of bearing steel, residual stress will be generated during the transformation from retained austenite to martensite. In addition, an increase in the number of stress cycles also affects the measured surface residual compressive stress values.
 et al first published the analysis results of residual stress, indicating that the existence of residual compressive stress at the depth of maximum shear stress will reduce the maximum shear stress and increase the life. If the residual stress can reduce the maximum shear stress by 10%, the fatigue life of the rolling bearing can be doubled. Tallian
[6, 7] The results of fitting a large number of bearing test data in the past three decades also show that residual compressive stress can improve bearing life, while residual tensile stress can reduce bearing life.
When the interference fit of the bearing is too tight, or the rotational speed is too high to generate centrifugal force, hoop stress will be generated in the rolling elements and rings. Coe et al.
 have systematically studied the effect of hoop stress on the life of the inner ring and the entire set of bearings. Their results show that for an angular contact ball bearing with an inner diameter of 45 mm, when the speed is 1 500 r/min, the life is reduced by about 11% ~ 17%, and at 3 000 r/min speed, the life can be reduced by about 21% ~ 22%. This extra stress has the potential to reduce bearing life by as much as 90 percent.
Zaretsky used finite element to analyze the stress distribution under the raceway surface, and compared and verified the life-stress index of many life models, pointing out that the L-P model tends to underestimate the fatigue life of the bearing, and the residual stress and ring The radial stress has a large effect on the life, and the additional fatigue limit added to the I-H model may be caused by insufficient knowledge of residual and hoop stress.
5 Fatigue limit stress
Ioannides and Harris proposed the concept of fatigue limit of matrix materials, and considered that the failure volume should not only consider the volume above the maximum alternating shear stress, but should take the influence of this stress volume into account; The maximum stress is less than the fatigue stress of the material, the material will not fatigue, and the part will show an almost infinite fatigue life. A material has a finite amount of fatigue life only when the maximum stress within the stressed volume is greater than the material’s fatigue limit stress. However, Zaretsky  put forward a different view on the fatigue limit stress introduced in the model. It is believed that the introduction of the fatigue limit will increase the life-load index and thus overestimate the life of the bearing.
6 Influence of Surface Roughness and EHL Lubrication (Film Thickness Ratio)
The effect of surface roughness and EHL lubrication on life is obtained by the film thickness ratio, as shown in Figure 5. When Λ>3, the life of the bearing is longer than the rated life, this state can be called a complete elastohydrodynamic state, and in practice most bearings in the industry work under a partial elastohydrodynamic state ( Λ=1 ~ 2) .
7 Effect of surface treatment
The surface treatment technology of rolling elements and rings can change the hardness of the roller surface, residual stress distribution and the overall strength of the material, thereby increasing the bearing life. For high-frequency quenching, laser quenching, and carburizing-hardened rollers, the deeper the hardened layer, the higher the rolling fatigue strength. For this reason, there is a problem of optimal hardening depth for this type of surface treatment technology. For nitrided and nitrocarburized rollers, the rolling fatigue strength increases with the depth of hardening. In addition, the surface hardening treatment should also consider the influence of surface roughness and residual stress .
8 Effects of contaminating particles in lubricating oils
The mechanism of the influence of the contaminant particles in the lubricating oil on the life can be explained as follows. At first, the contaminant particles enter between the two contact surfaces, and indentations are generated on the surface of the raceway. When the rolling elements pass through the indentations, stress concentration will occur at the edges of the indentations. And the cracks are generated, and the cracks gradually expand with the repeated stress cycle, and finally the surface spalling occurs. Most of the bearings in actual industrial use eventually fail due to this kind of surface fatigue spalling.
It has been found that when the diameter of the contamination particles in the lubricating oil is larger than 3 μm, the rolling fatigue life can be significantly reduced to 1/2 to 1/7 or less. The larger the diameter of the pollution particles, the more the lifespan is reduced; the higher the hardness of the pollution particles, the more the lifespan is reduced. In addition, the impact of pollution particles on life must be combined with the contact ellipse parameters. The smaller the contact ellipse, the greater the impact of pollution particles on life.
9 Effect of temperature on fatigue life
Neither the fatigue model based on the subsurface stress nor the model starting from the defects on the surface has taken into account the influence of the heat generation in the bearing contact area on the fatigue life. In fact, after continuous operation of the bearing, there will inevitably be a certain temperature rise, and the magnitude of this temperature rise should be related to the thickness of the lubricating oil film between the contact pairs, the surface characteristics of the contacting parts, and parameters such as load and running speed. . At the same time, after the temperature rises, there must be a temperature distribution in the bearing ring and the rolling body. To date, this effect on fatigue life due to temperature rise and heat distribution has not been reflected in the main models.
10 Effect of running speed on fatigue life
The study of Miller et al. shows that the bearing fatigue life is directly related to the instantaneous contact time. Instantaneous contact time refers to the time required for the rolling elements to roll over the inner ring and the inner ring raceway to contact the width of the ellipse under maximum load. As the instantaneous contact time increases, the fatigue life of the bearing also increases. The slower the bearing, the longer its life in revolutions. On the other hand, the length of the instantaneous contact time will also affect the surface residual compressive stress, thereby indirectly affecting the fatigue life. However, all existing life models do not account for these influencing factors. This is a subject to be studied.
11 Influence of non-failure life on life
After analyzing 2250 sets of bearing life test data in 1962, Tallian found that when the survival rate was in the range of 0.4 to 0.93, the life of the bearing approximately obeyed the two-parameter Weibull distribution. big deviation. Later, when Shimizo and Izawa  conducted fatigue tests of linear motion ball bearings, they found that in the low-life region and the high-life region, the test data did not follow the linear relationship predicted by the classical two-parameter Weibull distribution. According to the early theory, when the failure probability is 0, the fatigue life of the bearing should also be 0, but in practice, the existence of non-failure life is indeed observed. This no-failure life is the minimum life of the bearing, which can be introduced into the life distribution as the third parameter, thereby obtaining the three-parameter Weibull life distribution.
Recently, Shmizu  analyzed the three-parameter Weibull distribution with fatigue limit combined with fatigue test data and confirmed that bearing steel does not have a fatigue limit, while structural steel has a definite fatigue limit. For bearing steel, when the fatigue limit is 0, it is indeed necessary to introduce the no-failure life, and from this, the three-parameter Weibull distribution function is derived. His experimental data were in fairly good agreement with the three-parameter Weibull distribution.
12 Influence of material purity (oxygen content)
In the past half century, steel smelting technology has made great progress, especially the successful development of modern high-cleanness steel, which greatly improves the fatigue life of bearings.
The changing trend of oxygen content of carbon bearing steel in 1985 and the relationship between oxygen content and fatigue life of AISA52100 steel and case-carburized steel.
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