Rolling-Bearing Load, Static Rating and L10 Life Suite

Content

Screen equivalent loads, static capacity, and rating life for rolling-bearing selection.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Single-row deep-groove ball bearing

Use current catalog C₀ and f₀ values. The X/Y interpolation is limited to q ≤ 6.89.

Load screening

Equivalent dynamic load P— kN
Equivalent static load P₀—kN
Static safety factor s₀——
q = f₀Fₐ/C₀——
Limit e——
Factor X——
Factor Y——

How to use

  1. Select Equivalent loads, L10 and modified life, or Hertz static rating.
  2. For equivalent loads, enter positive radial load Fr, nonnegative axial load Fa, current catalog f0 and C0, and the actual clearance class. This mode applies only to the documented single-row deep-groove ball-bearing table.
  3. For life, enter compatible catalog rating C and equivalent load P in kN, speed n in rpm, rolling-element type, reliability R, and an authorized current aISO. Do not derive aISO from obsolete charts.
  4. For Hertz screening, enter elastic properties, signed principal radii, whole-number ball count, then choose prescribed bearing load or prescribed maximum pressure. Positive radii are convex and negative radii are concave.
  5. Select Calculate to update the one result panel. Correct any red range or geometry warning before interpretation.
  6. Use Reset example to restore the supplied values for the active mode and recalculate.
  7. Interpret L10 as a population rating at 90% reliability, not guaranteed service life. Review s0, pressure, lubrication, contamination, mounting, duty cycle, shock, and temperature separately.
  8. Do not use the table mode for another bearing type, use constant-load life for strongly variable duty, or use the Hertz approximation for plasticity, edge loading, misalignment, thin races, or safety-critical qualification.

Worked example

1. In the life mode, use C = 7.28 kN, P = 1 kN, n = 2800 rpm, ball bearing, R = 95%, and aISO = 1.1. The result is L10 ≈ 386 × 106 rev, a1 ≈ 0.618, and Lnm ≈ 262.6 × 106 rev (about 1,563 h). The lower modified life reflects the 95% reliability target despite aISO slightly above one.

FᵣFₐabHertz contact ellipse

Equations used

q = f₀Fₐ/C₀; interpolate e and Y by clearance; X = 0.56, 0.46, or 0.44 in the combined-load branch
P = Fᵣ when Fₐ/Fᵣ ≤ e; otherwise P = XFᵣ + YFₐ
P₀ = max(Fᵣ, 0.6Fᵣ + 0.5Fₐ); s₀ = C₀/P₀
L₁₀ = (C/P)ᵖ; p = 3 for balls or 10/3 for rollers; L₁₀h = 10⁶L₁₀/(60n)
a₁ = 4.48[ln(100/R)]^(2/3); Lₙ = a₁L₁₀; Lₙₘ = a₁aISO L₁₀
1/E′ = (1−ν₁²)/(2E₁) + (1−ν₂²)/(2E₂)
Rₓ = (1/R₁ₓ + 1/R₂ₓ)⁻¹; Rᵧ = (1/R₁ᵧ + 1/R₂ᵧ)⁻¹; R′ = (1/Rₓ + 1/Rᵧ)⁻¹
λ = min(Rₓ/Rᵧ, Rᵧ/Rₓ); K = {1 + √[ln(16/λ)/(2λ)] − √ln4 + 0.16lnλ}⁻¹
A = K[1 + 2(1−K²)/(πK²) − 0.25lnK]^(1/3); B = A/K
F = 5P_H/z; a = A(3FR′/E′)^(1/3); b = B(3FR′/E′)^(1/3)
pₘ = F/(πab); pmax = 1.5pₘ; prescribed pressure: F = (πABpmax/1.5)³(3R′/E′)²; C₀,H = Fz/5

Definitions and units: Fr and Fa are radial and axial loads (kN); f0, e, X, Y, q, s0, p, a1, and aISO are dimensionless; C and C0 are catalog ratings (kN); n is rpm; R is reliability in percent; L is in millions of revolutions and Lh in hours. E1, E2, and E′ are elastic moduli; ν is Poisson ratio; signed Rij are principal radii; λ is curvature ratio; K, A, and B are ellipse intermediates; z is ball count; PH is total Hertz-mode bearing load; F is maximum ball load; a and b are contact semi-axes; and pm, pmax are compressive pressure magnitudes. Hertz equations use SI internally.

Theory and method

Equivalent-load screening reduces combined radial and axial load to one constant dynamic load. The deep-groove table interpolates clearance-dependent factors only within q ≤ 6.89. Basic rating life follows the ISO 281 load-ratio power law. The reliability relation reproduces the implemented Weibull-style conversion; the modified result multiplies by a user-entered current aISO. Static screening follows the ISO 76 equivalent-static-load structure. The geometry mode treats each ball/raceway pair as smooth, elastic, frictionless, nonconforming Hertz contact and approximates the maximum ball load as 5PH/z.

Assumptions and limits

Loads and speed are constant; catalog ratings and factors are compatible with the selected bearing; load sharing is idealized; material response is linear elastic; surfaces are smooth; and thermal growth, mounting clearance changes, lubrication starvation, contamination, wear, residual stress, edge loading, misalignment, plasticity, shock, and resonance are omitted. Manufacturer calculations and current licensed standards govern final selection.

References

  • ISO 281, Rolling bearings — Dynamic load ratings and rating life, current authorized edition.
  • ISO 76, Rolling bearings — Static load ratings, current authorized edition.
  • Harris and Kotzalas, Rolling Bearing Analysis, for bearing load distribution and life context.
  • Johnson, Contact Mechanics, Cambridge University Press, for Hertz contact theory.

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