Cubic Mean Load (Bearing)
Calculate the equivalent mean load of a bearing under a cycle with two different loads, P_m = ∛(P₁³·U₁ + P₂³·U₂), from the loads P₁ and P₂ (N) and the time (or revolution) fractions during which they act U₁ and U₂ (with U₁ + U₂ = 1). Many bearings do not work under CONSTANT load: the load varies over the operating cycle (a press loading and unloading, a motor accelerating and decelerating, a machine with different work phases). To compute life in this case, the variable cycle is replaced by an equivalent CONSTANT load causing the same fatigue damage — the mean load. But the mean is NOT arithmetic: since fatigue damage is proportional to load CUBED (the life exponent p=3), the mean load is a time-fraction-weighted mean, but with the loads cubed (then cube-rooted) — the so-called cubic mean or 'fatigue-weighted mean'. This makes HIGH loads weigh disproportionately more (a double load causes 8× more damage), so even a small fraction of time at high load dominates the result. This formula (here for two load levels; it generalizes to several) is essential to size bearings in variable-load machines, avoiding underestimating the damage. Enter the two loads and their time fractions.
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Cubic mean load (bearing)
The equivalent mean load on a bearing running a duty cycle with two different loads is P_m = ∛(P₁³·U₁ + P₂³·U₂), from the loads P₁ and P₂ and the fractions of time U₁ and U₂ over which they act (with U₁ + U₂ = 1). Many bearings never see a constant load: it changes through the cycle (a press that loads and unloads, a motor that accelerates, a machine with distinct phases). To calculate bearing life in that situation, the variable cycle is replaced by an equivalent constant load that would cause the same fatigue damage — the mean load. But this mean is not the arithmetic one: since fatigue damage is proportional to the load raised to the third power (the exponent p=3), the mean load is a time-weighted average taken with the loads cubed (and the cube root applied at the end) — the so-called cubic mean, or 'fatigue-weighted average'. That makes the high loads count disproportionately (twice the load does 8× the damage), so even a short spell at high load dominates the result. This formula (written here for two steps; it generalises to any number of them) is essential for sizing bearings in machines with variable loading, and it keeps the damage from being underestimated. Enter the two loads and their time fractions.
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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.
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.
Equivalent Dynamic Load (Bearing)
Calculate a bearing's equivalent dynamic load under combined loading, P = X·F_r + Y·F_a, from the radial load F_r (N), the axial load F_a (N) and the factors X and Y (dimensionless, tabulated by the maker per bearing type and the F_a/F_r ratio). Most bearings actually carry RADIAL (perpendicular to shaft) and AXIAL (along shaft) loads at once, but catalog life and capacity formulas are defined for an equivalent pure radial load. The equivalent dynamic load is that fictitious radial load that would give the SAME bearing life as the real load combination. The X and Y factors depend on the bearing type (deep-groove ball, angular contact, self-aligning, tapered roller) and the axial-to-radial ratio — for mainly radial loads, X≈1 and Y≈0 (axial negligible); when axial grows past a limit (the e factor), Y starts to contribute. Computing P correctly is the first step in any bearing design, since P enters the life formula L10 = (C/P)^p and the capacity check. Wrong factors (or ignoring axial load) give an incorrect life estimate. Enter the radial load, axial load and the X and Y factors.
Equivalent Static Load (Bearing)
Calculate a bearing's equivalent static load, P_0 = X_0·F_r + Y_0·F_a, from the radial load F_r (N), the axial load F_a (N) and the static factors X_0 and Y_0 (tabulated by the maker). Unlike the equivalent dynamic load (related to FATIGUE under rotation), the equivalent static load is used to check the bearing under loads with the bearing STOPPED or turning very slowly, or under PEAK loads (shocks, momentary overloads). The risk here is not fatigue but PERMANENT DEFORMATION (indentation) of the races by the rolling elements: an excessive static load 'dents' permanent marks (brinelling) into the races, which then cause noise, vibration and early failure when the bearing turns again. The equivalent static load is the pure radial load that would cause the same maximum permanent deformation (at the most-loaded contact) as the real radial-axial combination. It is compared with the bearing's static load rating C0 (also tabulated) via the static safety factor s0 = C0/P0. This check is especially important in bearings carrying loads with the machine stopped (shafts of equipment parked under load) or subject to shocks. Enter the radial load, axial load and the static factors X0 and Y0.
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.
Bearing Mean Diameter
Calculate a bearing's mean (pitch) diameter, d_m = (D + d) ÷ 2, from the outer diameter D (mm, of the outer ring) and the inner diameter d (mm, of the bore, fitting the shaft). The mean diameter is the average of the bore diameter (seating on the shaft) and the outer diameter (seating in the housing), and roughly represents the diameter of the CIRCLE described by the rolling-element centers (the pitch diameter). It is a fundamental bearing geometric parameter, used in several calculations: in the SPEED FACTOR n·d_m (governing limit speed and heating), in estimating the rolling-element peripheral velocity, in the characteristic defect frequencies (used in vibration analysis for diagnosis — the ball-pass frequencies of inner/outer race, BPFI/BPFO, depend on d_m), and in the cage rotation speed. The mean diameter is the compact way to characterize a bearing's 'size' for these kinematic and dynamic calculations, without needing the internal details (number and diameter of rolling elements, contact angle). The outer D and inner d diameters are the basic catalog dimensions of any bearing (with the width), and d_m derives directly from them. Enter the outer and inner diameters.
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.