Bearing L10 Life and Reliability Conversion
Convert rolling-bearing L₁₀ rating life to operating reliability for one bearing or a two-bearing series assembly.
Engineering screening tool—verify inputs and results independently. Use at your own risk.
Rating life and service inputs
Use a positive basic rating life, constant speed, and non-negative elapsed service life.
Operating reliability
The rating-life conversion assumes constant speed. The probability relation is the empirical model documented below.
Two-bearing series inputs
Enter each bearing’s L₁₀h rating life at one common non-negative service time.
Assembly reliability
Series operation requires both independent bearings to survive. Common-cause and dependent failures are not represented.
How to use
- Select Single bearing to convert rating life from million revolutions, or Two-bearing system when two L₁₀h values are already known.
- Enter positive rating life values and, for a single bearing, positive constant speed in rpm. Enter non-negative service life in hours.
- Select Calculate or edit a field to update the active result. Select Reset to restore the example inputs.
- Read the canonical survival probability and supporting life, ratio, or individual-bearing metrics. Values near 1 indicate higher modeled survival.
- Correct any warning before use. Do not apply this model to varying duty, modified-life factors, dependent or repairable failures, common causes, or certification and safety decisions without a validated engineering analysis.
Equations used
Time and rotation are positive magnitudes. Every reliability is dimensionless:
L₁₀h = L₁₀ × 10⁶ / (60n)
a₁ = t/L₁₀h
R(t) = exp{−[(a₁/4.48)^(3/2)]}
Rᵢ(t) = exp{−[(t/(4.48L₁₀h,ᵢ))^(3/2)]}
Rsystem(t) = R₁(t)R₂(t)
round₃(x) = Math.round(1000x)/1000
L₁₀ is basic rating life in millions of revolutions; n is constant speed in rpm; L₁₀h is rating life in hours; t is elapsed service life in hours; a₁ is the life ratio; i identifies bearing 1 or 2. Single-bearing L₁₀h displays to a whole hour. Ratios and probabilities display to three decimals; the system product uses unrounded bearing probabilities before final rounding.
Worked example
- Single bearing: L₁₀ = 500 × 10⁶ rev, n = 4000 rpm, and t = 1000 h gives L₁₀h = 2083 h, a₁ = 0.480, and R(t) = 0.966.
- Two-bearing system: L₁₀h,1 = 1000 h, L₁₀h,2 = 1500 h, and t = 800 h gives R₁ = 0.927, R₂ = 0.960, and Rsystem = 0.890. Requiring both bearings lowers assembly survival.
Theory and method
Basic rolling-bearing rating life is commonly expressed as L₁₀, the life associated with 90% reliability under the rating model. This screening calculator first converts revolutions to hours at constant speed, then applies the implemented Weibull-form survival relation with scale factor 4.48 and shape exponent 3/2. For two independent bearings in series, joint survival is the product of their individual probabilities.
Assumptions and limits
- Positive rating lives, constant speed in single-bearing mode, and one common time basis.
- Two-bearing mode assumes independent, non-repairable bearings and requires both to survive.
- Load spectra, contamination, lubrication, temperature, mounting, clearance, modified-life factors, dependence, and common-cause failure are omitted.
- The implemented empirical reliability relation is preserved as stated; it is not a replacement for a complete ISO 281 bearing selection and modified-life calculation.
References
- ISO 281:2007, Rolling bearings — Dynamic load ratings and rating life.
- Weibull, W. (1951), A Statistical Distribution Function of Wide Applicability.
Related analysis: Rolling-Bearing Load, Static Rating, and L10 Life Suite. Continue in TriboSolver when contact loads, lubrication, or operating conditions should be refined before reliability screening.