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.
Result
—
Equivalent dynamic load (bearing)
The equivalent dynamic load of a bearing under combined loading is P = X·F_r + Y·F_a, from the radial load F_r, the axial load F_a and the factors X and Y (tabulated by the manufacturer according to the bearing type and the F_a/F_r ratio). In practice most bearings take radial loads (perpendicular to the shaft) and axial loads (along the shaft) at the same time, yet catalog life and rating formulas are defined for an equivalent pure radial load. The equivalent dynamic load is exactly that fictitious radial load which would give the bearing the same life as the real combination. Factors X and Y depend on the bearing type (deep groove ball, angular contact, self-aligning, tapered roller) and on the ratio between the loads — for predominantly radial loading, X ≈ 1 and Y ≈ 0; once the axial share grows past a limit (the factor e), Y starts to contribute. Getting P right is the first step in sizing any bearing, since P is what enters the life formula L10 = (C/P)^p and the rating check. Wrong factors, or a neglected axial load, produce a wrong life estimate. Enter the radial load, the axial load and the factors X and Y.
Related Tools
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.
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.
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.
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.
Belt Maximum Tension
Calculate a belt's maximum (tight-side) tension, T₁ = T_e·r ÷ (r − 1), from the effective tension T_e = T₁ − T₂ (the power-transmitting force, N) and the tension ratio r = T₁/T₂ (at the slip limit). Knowing the force the belt must transmit (the effective tension, from power and velocity) and the maximum tension ratio the belt sustains before slipping (from friction, wrap and, in V-belts, the wedge effect), the individual side tensions can be computed. The maximum tension T₁ (tight side) is the larger, and it SIZES the belt's strength (which must not break) and the load on the BEARINGS and pulley shafts (which feel the sum of both side tensions, bending the shaft). Knowing T₁ is essential to: check the belt resists (versus its tensile strength), size the bearings for the radial load imposed by the belt (which can be significant and shortens bearing life), and set the correct installation tension. The LOWER the tension ratio r (worse friction, less wrap), the HIGHER the T₁ needed for the same power — hence the advantage of V-belts (high r) in reducing loads. Enter the effective tension and the tension ratio.
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.