Static Equivalent Load⚠ unverified
Mechanical / Bearings · Compute the static equivalent load for a static safety check
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Fa | Fa | N | 1.0 | Axial (thrust) load |
| Fr | Fr | N | 1.0 | Radial load |
| X0 | X0 | — | 0.5 | Static radial load factor (dimensionless). Default is 0.5 |
| Y0 | Y0 | — | 2.0 | Static axial load factor (dimensionless). Default is 2.0 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | P0 | N | Static equivalent load P0, in newtons (N) |
The science & history
Understanding the Parameters
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Radial and axial loads $F_r$, $F_a$ — here they are the peak static loads (including shock factors and the weight of stationary machinery), not the running duty loads. Static damage is set by the worst instantaneous press, so you use maxima, not averages.
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Static factors $X_0$, $Y_0$ — the static counterparts of the dynamic $X,Y$. They are generally different numbers because static damage is governed by the single most heavily loaded contact and its peak Hertzian pressure, whereas dynamic damage is governed by fatigue accumulation over the whole loaded arc. For deep-groove ball bearings ISO 76 gives $X_0 = 0.6$, $Y_0 = 0.5$; the defaults here ($0.5$, $2.0$) are placeholders — use catalogue values for your bearing.
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The $\max$ operator — a floor. When the combined term $X_0 F_r + Y_0 F_a$ comes out below $F_r$ (small thrust), the pure radial load is the more damaging case and must govern. Without the floor the formula could non-physically under-report the load at low thrust.
Derivation (Approaching a Proof)
Static capacity is defined (ISO 76) by a permissible permanent deformation: the total plastic indentation of raceway plus rolling element must not exceed $0.0001 D$ (one ten-thousandth of the ball diameter) at the most heavily loaded contact. That deformation is a monotonic function of the peak contact pressure, which by Hertz theory is a function of the peak rolling-element load $Q_{\max}$.
For a static combined load, $Q_{\max}(F_r, F_a)$ again depends nonlinearly on both components and on the contact angle. As with the dynamic case, the standard replaces the true nonlinear $Q_{\max}$ with a linear surrogate — a static equivalent radial load $P_0$ defined so that it yields the same $Q_{\max}$:
$$P_0 = X_0 F_r + Y_0 F_a.$$
The coefficients $X_0$, $Y_0$ are fitted to the static contact geometry. Because this linearisation can dip below the trivial radial-only case for small $F_a$, the standard clamps it from below with the pure radial load, giving the final form
$$P_0 = \max\!\left(F_r,\; X_0 F_r + Y_0 F_a\right).$$
Dimensional check. $X_0$, $Y_0$ are dimensionless; both branches of the $\max$ have dimension of force, so $[P_0] = \text{N}$. ✓
History and Development
The static rating framework was standardised as ISO 76 (static load ratings), a companion to ISO 281's dynamic ratings. The $0.0001 D$ permanent-deformation limit dates to mid-20th-century bearing-industry testing that correlated that level of brinelling with the onset of noticeably rough, noisy running. The static safety factor $s_0 = C_0/P_0$ is specified in design codes (e.g. $s_0 \ge 1$ to $2$ for smooth running, higher for shock or high-precision applications). It is the check that catches crane hooks, jammed mechanisms, and heavy slow-oscillating pivots that fatigue life alone would miss.
Related Concepts: Equivalent Dynamic Load Bearing, Dynamic Load Rating, Bearing Rating Life L10, Hertzian Contact Pressure, Contact Stress Basics
Notes: Use catalogue $X_0$, $Y_0$ for your bearing type; the defaults are illustrative. After computing $P_0$, form the static safety factor $s_0 = C_0/P_0$ and compare against the required minimum for the application.