= Bearing axial setting tolerance
A <bearing axial setting tolerance> specifies the permitted difference between the realized axial reference position of an assembly and its <bearing nominal axial setting>. It consumes some of the available <bearing axial travel margin>. The setting tolerance must therefore be included when deciding whether all required thermal and operating changes remain inside the physical travel limits. The bearing manufacturer's locating/non-locating arrangement discussion explicitly includes relative displacement and accumulated dimensional variation.<Rolling bearings by SKF>[Section B.2, printed p.70, relative axial displacement and tolerance accumulation]{ref}
Let physical travel be $[a,b]$, required displacement changes be $[d_{\min},d_{\max}]$, and setting error be $\eta\in[\eta_{\min},\eta_{\max}]$. To retain a prescribed margin $m_{\rm req}\ge0$ for every allowed combination, the nominal setting must satisfy
$$
a+m_{\rm req}-d_{\min}-\eta_{\min}
\le x_0\le
b-m_{\rm req}-d_{\max}-\eta_{\max}.
$$
The lower bound follows from the smallest possible realized position $x_0+d_{\min}+\eta_{\min}$; the upper bound follows from the largest. This is a worst-case guarantee over the stated ranges and needs no assumption that the errors are statistically independent.
For an original example, take $[a,b]=[-0.30,0.30]\,\mathrm{mm}$, required changes $[-0.17,0.23]\,\mathrm{mm}$, setting error $[-0.02,0.04]\,\mathrm{mm}$ and required margin0.05mm. The admissible nominal-setting interval is $[-0.06,-0.02]\,\mathrm{mm}$. Choosing $x_0=-0.04\,\mathrm{mm}$ gives worst-case operating endpoints $-0.23$ and $+0.23\,\mathrm{mm}$, leaving0.07mm at each end. The asymmetric error range has shifted the balanced nominal setting relative to a symmetric tolerance assumption.
A <bearing axial tolerance stack> combines the contributing dimensions and their signs before applying this range calculation. Two separate bounded errors of $\pm0.01$ and $\pm0.02\,\mathrm{mm}$ can add to $\pm0.03\,\mathrm{mm}$ in the worst case. Taking a square root of summed squares would answer a statistical uncertainty question under additional assumptions; it would not reproduce that deterministic bound. The distinction between a bound and <standard uncertainty> matters when a guaranteed clearance or reserve is specified.
The resulting interval can be empty. That outcome identifies incompatible travel, operating-change, tolerance and reserve requirements; adjusting the nominal setting alone cannot resolve it. A nonempty interval addresses axial geometry but does not establish acceptable friction, elastic loading or contact conditions after an end stop engages.
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