= Non-locating bearing
A <non-locating bearing> support carries the required radial load while allowing the shaft's intended axial displacement relative to the housing. It complements a <locating bearing>, which establishes axial position. The movement may occur within the bearing or through a suitable ring-to-seat arrangement; its purpose is to avoid imposing an unwanted axial constraint when dimensions change.<Rolling bearings by SKF>[Section B.2, “Arrangements and their bearing types”, printed p.70, locating/non-locating support functions]{ref}
An important cause of relative movement is <thermal expansion>. For an illustrative shaft with constant <linear thermal expansion coefficient> $\alpha$, length $L$ and uniform temperature increase $\Delta T$, free extension is
$$
\Delta L=\alpha L\Delta T.
$$
Using hypothetical $\alpha=12\times10^{-6}\,\mathrm{K^{-1}}$, $L=0.50\,\mathrm m$ and $\Delta T=50\,\mathrm K$ gives0.30mm. If the housing expands differently, the required <bearing axial displacement allowance> depends on the shaft's extension relative to that housing, as well as assembly tolerances.
For contrast within the same mechanical model, constrain both ends of an elastic bar against extension. Axial strain balance gives a compressive <bearing thermal-expansion constraint load> with magnitude $F=EA\alpha\Delta T$. With hypothetical <Young's modulus> $E=200\,\mathrm{GPa}$ and area $A=100\,\mathrm{mm^2}$, the preceding temperature change gives12kN. Real supports and housings are compliant, so this rigid-constraint calculation illustrates the mechanism rather than predicting a universal bearing load.
A <non-locating bearing> is not generally a support with no useful constraint: it can still transmit substantial transverse <forces>. Its permitted axial movement must remain compatible with the shaft's other functional requirements, including gear positioning. The actual support arrangement determines whether thermal movement is accommodated without losing the required location.
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