A Model for Rolling Bearing Life with Surface and Subsurface Survival—Tribological Effects

Figures & data

Fig. 1 Schematics of surface and subsurface von Mises stress fields of a Hertzian contact. Surface stresses are related to surface microgeometry and lubrication conditions of the rolling contact. Typically surface stresses are constrained in a narrow layer at the raceway of depth comparable to the surface roughness.

Fig. 2 Inner ring sample roughness of a radial ball bearing 6217, as used in the calculations. The ball surface was assumed smooth.

Fig. 3 Calculated surface traction (along rolling direction), pressure, and stress τ_xz profile at y = 0. Surface stress τ_xz at overrolling position of maximum mean pressure. Low kappa case, κ = 0.1. Rolling direction from left to right.

Fig. 4 Calculated surface traction (along rolling direction), pressure, and stress τ_xz profile at y = 0. Surface stress τ_xz at overrolling position of maximum mean pressure. High kappa case, κ = 4. Rolling direction from left to right.

Table 1 Comparative Surface and Subsurface Stress Ratios for the Example of the 6217 Bearing, Stress Amplitude (Pa)

		Subsurface Stress Amplitude	Surface Stress Amplitude, Poor Lubrication	Surface/Subsurface Life Ratio, Poor Lubrication	Surface Stress Amplitude, Good Lubrication	Surface/Subsurface Life Ratio, Good Lubrication
Pu/P	po, (GPa)	⟨τxz − τu⟩	⟨τxz.s − τu.s⟩, κ = 0.1		⟨τxz.s − τu.s⟩, κ = 4
0.005	7.74	1.7 × 10^9	0.43 × 10^9	2.806 × 10^− 6	0.32 × 10^9	1.798 × 10^− 7
0.05	3.59	0.599 × 10^9	0.45 × 10^9	6.99 × 10^− 2	0.25 × 10^9	0.294 × 10^− 3
0.2	2.26	0.25 × 10^9	0.47 × 10^9	3.54 × 10^2	0.20 × 10^9	0.125
0.5	1.66	0.09 × 10^9	0.45 × 10^9	3.16 × 10^6	0.14 × 10^9	60

Fig. 5 Illustration of the roughness relative movement inside the contact; the local analysis of the topography is done by varying the mean pressure following to the local Hertz value; see Morales-Espejel and Brizmer (18).

Fig. 6 Flowchart of the advanced surface distress model used to solve the surface related failure modes; see Morales-Espejel and Brizmer (18).

Table 2 Range of Parameters Used in the Advanced Model for Surface Distress for the Derivation of Eq. [31[31] ]

ParameterMean Bearing Diameter dm (mm)	Minimum Value87.5	Maximum Value400
Hertzian contact pressure, po (GPa)	0.3	3.55
Lubrication quality parameter κ	0.1	4
Sliding/rolling ratio, S	0.02	0.05
Number of loading cycles, N	10^5	10^9

Fig. 7 Normalized surface damage function (R_s = I_su^eL^e_10.BR/[KLn(1/0.9)]) versus bearing load (P/P_u) and the lubrication conditions (κ) as defined in ISO 281 (15) for conditions of no contamination. Notice that, for higher values of κ better lubrication, the surface damage function is reduced, and it is also nearly constant with load.

Fig. 8 Calculated damage function ratio from Eq. [32[32] ] for different κ values and for variable load P/P_u for a deep-groove ball bearing typical case. The importance of the surface damage function with respect to the subsurface is reduced when the lubrication conditions are enhanced.

Fig. 9 Pictures of in-house tested bearing raceways showing surface- and subsurface-initiated failures. Overrolling direction from left to right.

Fig. 10 Comparison the surface damage limiting curves of the ball and roller bearings; for example, Eq. [31[31] ] and the back-calculated surface damage obtained from endurance testing of bearing population samples.

Table 3 Test Conditions Used for Bearing Life Testing, as Given in (14)

Bearing Type	Designation	Load Ratio, C/P	Lubrication, κ
Deep-Groove Ball Bearings	6305, 6205, 6206, 6207, 6309, 6220	1, 2.8, 2.4, 2.1, 3.1, 3.5, 4, 6	4, 3.4, 2.1, 2, 1
Cylindrical roller bearings	NU 207 E, NU 309 E	2.5, 2.77, 2.82	4, 1, 0.8
Spherical roller bearings	22220 E, 22220 CC	2.22, 2.3, 2.5, 2.7, 3, 4.7	4, 3.6, 1.8, 0.37, 0.28
Tapered roller bearings	331274, K-LM11749, K-HM89449, K-580/572	1, 1.1, 1.3, 2.5, 3.5	4, 2.9, 0.9

Table 4 Deep-Groove Bearing Example (6309) Results from the Present Approach to Illustrate the Use of the Model

ISO Viscosity Ratio κ	Surface Damage Function Rs	Contribution of the Surface Eq. [32[32] ] (%)	Surface–Subsurface Life Eqs. [29[29] ] and [25[25] ] L10 (Mrev)
0.1	12.2	100	17
0.4	2.2	96	81
2.9	0.02	23	1,656

Morales-Espejel, G. E. and Brizmer, V. (2011), “Micropitting Modelling in Rolling–Sliding Contacts: Application to Rolling Bearings,” Tribology Transactions, 54, pp 625–643.

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ISO 281 (2007), “International Standard, Rolling Bearings—Dynamic Load Ratings and Rating Life,” Geneva, Switzerland.

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Gabelli, A., Morales-Espejel, G. E., and Ioannides, E. (2008), “Particle Damage in Hertzian Contacts and Life Ratings of Rolling Bearings,” Tribology Transactions, 51, pp 428–445.

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