= Bearing axial travel margin
The <bearing axial travel margin> is the smallest remaining distance between the required axial operating range and either limit of the available <bearing axial travel interval>. It measures how much extra displacement can be accommodated before the assembly reaches a limit. The physical purpose of the non-locating support is to accommodate relative axial displacement, including thermal changes and accumulated dimensional variation.<Rolling bearings by SKF>[Section B.2, printed p.70, locating/non-locating arrangements and relative displacement]{ref}
Let physical limits be $[a,b]$, <bearing nominal axial setting> be $x_0$, and required changes range from $d_{\min}$ to $d_{\max}$. The two end margins and their worst value are
$$
m_-=x_0+d_{\min}-a,\qquad
m_+=b-x_0-d_{\max},\qquad
m=\min(m_-,m_+).
$$
A negative margin means that at least one required position is outside the available interval. Zero means touching a limit, with no reserve in that direction.
For an original example, $[a,b]=[-0.30,0.30]\,\mathrm{mm}$, changes $[-0.17,0.23]\,\mathrm{mm}$ and setting $x_0=-0.03\,\mathrm{mm}$ give $m_-=m_+=0.10\,\mathrm{mm}$. A <bearing axial setting tolerance> of $\eta\in[-0.04,0.04]\,\mathrm{mm}$ expands the possible operating range to $[-0.24,0.24]\,\mathrm{mm}$. The guaranteed margin is then0.06mm. Choosing $x_0=0$ would instead give a guaranteed margin of only0.03mm under the same uncertainty bound.
In general, a bounded setting error $|\eta|\le\epsilon$ changes the guaranteed margin to $m-\epsilon$. This follows by reducing the lower end margin with $\eta=-\epsilon$ and the upper end margin with $\eta=+\epsilon$. A required reserve $m_{\rm req}$ therefore needs $m\ge m_{\rm req}+\epsilon$. The example can retain a0.05mm reserve with the centered setting and a0.04mm error bound.
A deterministic tolerance bound and a <standard uncertainty> are different specifications. Replacing the bound by one <standard deviation> would not preserve the guarantee without additional distributional assumptions. The margin calculation also concerns geometric travel: it does not by itself establish acceptable contact stress, friction or <bearing thermal end-stop load> after a limit is reached.
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