Left panel shows the gap between each pair of mating surfaces plotted against temperature. A positive gap is clearance (green region); a negative gap is interference (red region). The red dashed zero line is the transition — crossing it means the fit changes character. The dotted vertical line marks your reference (nominal) temperature.
Right panel shows how much each individual surface diameter grows or shrinks from its nominal value. This tells you why the gap is changing — e.g., an aluminum bore expanding faster than a steel shaft widens the clearance on heating.
[S] in a label = split bushing model: the bore ID shrinks inward and OD expands outward by the wall thickness, not the full hoop diameter. A shaded band = tolerance stack (max clearance to min clearance).
Theory & Limitations
Thermal expansion model.
For a closed-ring (solid or tube), the thermally expanded diameter is
d(T) = d_nom × (1 + α × ΔT)
where α is the coefficient of thermal expansion (CTE) and ΔT = T − T_ref.
The gap between two mating surfaces is the difference in their expanded diameters.
Split bushing model.
A slit ring, C-clip, or open-arc bushing cannot develop hoop stress, so it does not expand circumferentially.
Instead, each radial face moves by t_wall × α × ΔT where t_wall = (OD − ID) / 2.
The bore ID shrinks inward; the OD grows outward. This models radial growth only.
Real split bushings may partially constrain depending on housing fit — use engineering judgment.
Tolerance stacking. When tolerances are entered, the tool computes worst-case max clearance (outer surface at +tol, inner surface at −tol) and worst-case min clearance (outer −tol, inner +tol) at each temperature. Tolerances and thermal expansion are treated as independent — no statistical combination is applied.
Limitations. The model assumes uniform temperature through the cross-section (no thermal gradients), linear CTE (no temperature dependence), and isotropic expansion. For tight fits, consider elastic deformation of the housing/shaft not captured here. CTE values are nominal room-temperature values; consult MMPDS or material data sheets for cryogenic or elevated temperature applications.