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Bearing axial displacement allowance is the axial movement available in a stated shaft/support arrangement before an unintended restraint is encountered. A non-locating bearing support accommodates relative shaft/housing displacement while a locating bearing establishes axial position. The required movement includes thermal changes and assembly variation, rather than shaft expansion alone.^[ref]

For a simple uniformly heated shaft and housing, estimate relative free displacement asusing the applicable linear thermal expansion coefficients and distances from their common axial reference. A shaft extension0.30mm and housing extension0.12mm give relative movement0.18mm. Assuming the housing stationary would overstate that thermal contribution in this example.

The complete bearing axial travel interval can be asymmetric. Suppose the operating states require relative motion between $-0.12$ and $+0.18\mathrm{mm}$, with an independent assembly offset between $-0.05$ and $+0.05\mathrm{mm}$. Adding the intervals gives required travel from $-0.17$ to $+0.23\mathrm{mm}$ about the nominal reference. Its total span is0.40mm, but centering a0.40mm travel range symmetrically at zero would miss the positive endpoint by0.03mm.

Once available movement is exhausted, additional expansion can generate a bearing thermal end-stop load. Movement may be accommodated inside a bearing or at a suitable seat, depending on the actual design. This interval model is bookkeeping for a specified support arrangement; the relevant travel limits must correspond to that physical mechanism and its permitted direction.

A bearing thermal end-stop load is the axial reaction that appears when relative thermal expansion exhausts the free travel of a support arrangement. In a quasistatic one-direction model, let free thermal mismatch be ${\delta }_{\mathrm{th}}$, initial travel to the stop be $g$, shaft compliance be $C_b$ and restraining support compliance be $C_s$. The engaged reaction magnitude isThe gap first closes; additional mismatch is taken up by elastic deformation of the shaft and support. This explains why the bearing axial displacement allowance matters. The locating/non-locating arrangement is intended to accommodate relative motion rather than create an unintended thermal restraint.^[ref]

For hypothetical $C_b=2.5\times 10^{-8}m/N$, $C_s=10^{-7}m/N$, $g=0.10\mathrm{mm}$ and ${\delta }_{\mathrm{th}}=0.30\mathrm{mm}$, the effective stiffness is $1/(C_b+C_s)=8MN/m$ and the load is1.6kN. The stored elastic energy in this combined linear compliance isThis is stored energy; the frictionless elastic model does not itself predict heat loss during a complete reversible cycle.

If the housing is fixed and free mismatch is $\alpha L\Delta T$, the bearing end-stop engagement temperature increment is $\Delta T_{\ast }=g/(\alpha L)$. With hypothetical $\alpha =12\times 10^{-6}{\mathrm{K}}^{-1}$ and $L=0.50\mathrm{m}$, the0.10mm gap closes at about16.67K temperature increase. Further heating raises the load according to the engaged stiffness.

The positive-part relation is a simple instance of unilateral contact complementarity: the stop supplies a reaction only when the corresponding clearance is exhausted. Shaft inertia, impact, friction or bearing preload require a more complete model. In particular, this static compatibility calculation does not determine a collision force when a moving assembly first hits the stop.

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.^[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 isUsing hypothetical $\alpha =12\times 10^{-6}{\mathrm{K}}^{-1}$, $L=0.50\mathrm{m}$ 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 $A=100\mathrm{m}{\mathrm{m}}^2$, 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.