CAD Clearance at Temperature: A Small Gap Can Nearly Disappear

Disclosure: Prepared on behalf of CADProps with AI assistance. This is an original, idealized calculation using assumed expansion coefficients, not a customer case, material datasheet, physical test or CADProps simulation result.

A CAD assembly can show a positive clearance at its reference temperature and still need a separate thermal check. If a shaft expands faster than the surrounding bore, heating can consume most of the gap without changing either part's nominal design.

A reproducible example

Assume a circular shaft and an unconstrained, uniformly heated housing. At the reference temperature, the shaft diameter is 20.000 mm and the bore diameter is 20.020 mm. The initial diametral clearance is therefore 0.020 mm; the radial gap is half that, 0.010 mm.

For illustration, assign constant linear expansion coefficients of 23 × 10^-6 per kelvin to the shaft and 12 × 10^-6 per kelvin to the housing. These are assumptions, not specifications for a particular alloy or heat treatment. Raise both temperatures by 80 K.

For free, isotropic expansion, use D_hot = D_reference × (1 + alpha × delta_T). A hole in a freely expanding, homogeneous body grows with the body; it does not automatically shrink because material surrounds it.

Shaft: 20.000 × (1 + 0.000023 × 80) = 20.036800 mm.

Bore: 20.020 × (1 + 0.000012 × 80) = 20.0392192 mm.

Hot diametral clearance: 20.0392192 - 20.036800 = 0.0024192 mm.

The nominal gap is still positive, but only about 2.42 micrometres diametrally, or 1.21 micrometres radially. Calling this a comfortable clearance based only on the room-temperature model would be misleading.

Add manufacturing variation

Now assume each reference diameter has an independent ±0.005 mm size tolerance. For minimum clearance, combine the smallest bore (20.015 mm) with the largest shaft (20.005 mm), then apply their respective thermal factors.

20.015 × 1.00096 - 20.005 × 1.00184 = -0.0075948 mm.

The negative result indicates nominal geometric interference in this worst-case, simplified calculation. It does not calculate contact pressure, friction, seizure or structural damage. Those require additional material, surface, load and constraint information.

A useful review checklist

Record the reference temperature and whether a quoted gap is radial or diametral. Use coefficients appropriate to the actual materials and temperature range. Check the smallest permitted bore against the largest permitted shaft, not just nominal dimensions. Evaluate separate component temperatures if heat sources differ. Include coatings, roundness, alignment and restraints when they matter. A pressed-in housing or thermal gradient does not meet the free-expansion assumptions used here.

CADProps (https://www.cadprops.com/) is a related option for inspecting supported CAD geometry. Geometry inspection can establish nominal dimensions, but this article does not claim that a viewer certifies a hot fit or performs thermal/contact analysis. Keep the calculation assumptions beside the CAD revision, and have the responsible engineer validate the operating fit before manufacture.

The practical distinction is simple: a visible gap in CAD is a geometric observation at a defined state, not an operating-temperature guarantee.