Bearing Life L10
Compute nominal bearing life L10 in million revs: L10 = (C/P)^p with p=3 (ball) or p=10/3 (roller).
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Bearing L10 life: L10 = (C/P)^p · 10⁶ revolutions
The L10 basic rating life of a rolling bearing tells you how many revolutions 90% of an identical batch will survive before fatigue starts to show. The math is L10 = (C/P)^p · 10⁶ revolutions. Here C is the basic dynamic load rating you read off the manufacturer catalog, P is the equivalent dynamic load actually sitting on the bearing, and the exponent is p = 3 for ball bearings or p = 10/3 for roller bearings (cylindrical, tapered, spherical). Want hours instead of revolutions? Divide: L10h = L10 / (60·n), with n in rpm. Take a deep-groove ball bearing rated C = 12 kN carrying P = 2 kN at 1500 rpm. That works out to L10 = 216·10⁶ revolutions, roughly 2400 hours. The governing standard is ISO 281, and catalogs from SKF, NSK, Timken, FAG and NTN list C, C₀ (static) and the limiting speed for every part number.
Applications
Sizing the bearings on electric motor shafts, gearboxes, pumps and fans. Setting preventive maintenance intervals from the calculated hours of service. Wind turbine main shafts and gearboxes, rail axles, heavy industrial machinery (printing presses, paper mills, mining), HVAC blowers, automotive wheel hubs and transmissions all lean on the same number. The modified lives L10m and Lna go further, folding in lubrication, contamination and reliability factors as ISO 281 lays out.
FAQ
Why "10" in L10? Because about 10% of the bearings are expected to fail by fatigue before they reach that life, which is the same as saying 90% reliability. Want a stricter number? L5 and L1 buy you higher reliability at the cost of a shorter rated life.
Will a real bearing always reach L10? Only if lubrication, alignment and load are all close to ideal. Out in the field, what actually kills a bearing is usually contamination, vibration or misalignment long before fatigue ever gets a chance.
How do I find P? When the load is a mix of radial and axial, fall back on the catalog equivalent-load formula P = X·Fr + Y·Fa. The X and Y coefficients themselves come from the bearing series and the Fa/Fr ratio.
Related Tools
L10 Life in Hours (Bearing)
Calculate a bearing's nominal L10 life in HOURS of operation, L10h = (10⁶ ÷ (60·n))·(C/P)^p, from the dynamic load rating C (N), the equivalent dynamic load P (N), the rotation n (rpm) and the exponent p (3 for ball bearings, 10/3 for roller bearings). L10 life is the core of bearing selection: the number of revolutions (or hours) that 90% of a batch of identical bearings reaches or exceeds before FATIGUE failure (spalling of races and rolling elements) — i.e., only 10% fail earlier (hence 'L10', the life with 90% reliability). The basic formula L10 = (C/P)^p gives life in MILLIONS of revolutions; dividing by the rotation (rpm × 60 min/h) converts to hours, the practical unit for machines. The result shows the huge load sensitivity: since the exponent is 3 (balls), DOUBLING the load cuts life to 1/8! So a slightly overloaded bearing lasts far less. The capacity C is tabulated in each bearing's catalog. This calculation decides whether a bearing meets the application's required life (typically 20,000-100,000 h for industrial machines) or whether a larger one is needed. Enter the dynamic capacity, the equivalent load, the rotation and the exponent.
Required Dynamic Capacity (Bearing)
Calculate the dynamic load rating C a bearing needs to reach a desired life, C = P·(L10)^(1/p), from the equivalent dynamic load P (N), the desired nominal life L10 (in millions of revolutions) and the exponent p (3 for balls, 10/3 for rollers). It is the INVERSE of the life calculation, and how bearing SELECTION is done in practice: the designer knows the load the bearing will carry (P) and the life it must reach (L10, derived from required operating hours and rotation), and computes the minimum needed dynamic capacity C. Then a bearing is chosen from the maker's catalog whose tabulated C is EQUAL OR GREATER than the required — and that fits the available dimensions (shaft and housing diameter). The dynamic capacity C is, by definition, the load giving an L10 life of exactly 1 million revolutions, and it is each bearing's 'rating' in the catalog. This calculation is the heart of sizing: it translates the application requirement (load and life) into the component spec (capacity), letting you pick the right bearing — neither undersized (early failure) nor oversized (needless cost and space). Enter the equivalent load, the desired life and the exponent.
Sacrificial Anode Life
Calculate the life of a sacrificial anode, life = (mass × capacity) ÷ (current × 8760), from the anode mass (kg), the material's current capacity (A·h/kg), the protection current drained (A) and the 8760 hours in a year. The result, in years, shows how long the anode (zinc, aluminium or magnesium) will provide protection before being consumed and needing replacement — essential in designing galvanic cathodic protection of tanks, pipelines and marine structures. Enter the mass, the material capacity and the current.
Thickness with Corrosion Allowance
Calculate the total thickness to specify for a pressure-vessel component including the corrosion allowance, t_total = t_calculated + CA, from the minimum pressure-calculated thickness t_calculated (mm) and the corrosion allowance CA (mm). The thickness from the ASME formulas is the MINIMUM needed to resist pressure — but the vessel will operate for DECADES, and corrosion (and erosion) will consume wall material over time. If the vessel were made exactly at the minimum thickness, the first corrosion would already leave it below safe. So a CORROSION ALLOWANCE (CA) is added — a 'sacrificial' over-thickness, typically 1.5 to 6 mm, sized for the expected corrosion rate times the design life (e.g., 0.1 mm/year × 25 years = 2.5 mm). Thus the thickness specified for fabrication is the structural minimum plus the corrosion allowance. Over life, inspection (by ultrasound) measures the REMAINING thickness; when corrosion consumes the whole allowance and the thickness approaches the structural minimum, the vessel must be repaired or retired. The corrosion allowance is like a 'life reserve' built into the wall. Enter the calculated thickness and the corrosion allowance.
Load-Life Ratio (Bearing)
Calculate how a bearing's life changes when the load changes, L₂ = L₁·(P₁/P₂)^p, from the initial life L₁ (under load P₁), the loads P₁ and P₂ (N) and the exponent p (3 for balls, 10/3 for rollers). This relation expresses the essence of bearing life law: life is INVERSELY proportional to load raised to the exponent p. It lets you quickly answer, without recomputing everything, 'if I change the load, what happens to the life?'. And the answer is dramatic due to the high exponent: REDUCING the load by 20% (P₂ = 0.8·P₁) INCREASES life by (1/0.8)³ = nearly DOUBLE; INCREASING the load by 26% (P₂ = 1.26·P₁) halves the life; DOUBLING the load cuts life to 1/8. This extreme load sensitivity has important practical consequences: small overloads (from misalignment, imbalance, wrong mounting or inadequate clearance, which concentrate load) drastically cut the real life versus the calculated one — explaining why many bearings fail 'too early'. Conversely, reducing parasitic loads (better alignment, balancing) greatly extends life. This formula is a valuable tool for sensitivity analysis and failure diagnosis. Enter the initial life, the two loads and the exponent.
Reservoir Life (Sedimentation)
Estimate a reservoir's useful life from sedimentation, Vu = V ÷ V_s, from the reservoir's useful (or total) volume V (m³) and the sediment volume deposited per year V_s (m³/year). Every reservoir, by impounding a river, slows the flow and makes water lose its sediment-carrying capacity — sand, silt and clay from the watershed settle on the bottom, gradually reducing storage. The useful life is the number of years until sedimentation impairs the reservoir's function (power, supply, regulation). It is a crucial design parameter in hydrology and watershed management: reservoirs in basins with erodible soils, deforestation or intensive agriculture silt up fast (decades), while well-conserved basins last centuries. The sediment inflow V_s comes from the basin's sediment yield and the reservoir's trap efficiency (Brune curve). The simple constant-rate model gives the order of magnitude. Conserving the basin and flushing through bottom outlets extend the life. Enter the reservoir volume and the annual sediment inflow.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.