Tolerances, fits, and variation

Two parts drawn with the same diameter are not guaranteed to fit. Every process varies: a drilled hole wanders, a printer shrinks corners, a laser kerf removes width, and caliper readings have uncertainty. A tolerance states the permitted variation around a nominal dimension. A fit describes the relationship of two mating sizes: clearance always leaves space, interference always overlaps, and transition may do either.

For a shaft between S_min and S_max and a hole between H_min and H_max, clearance C = H - S. Worst-case minimum clearance is C_min = H_min - S_max; maximum clearance is C_max = H_max - S_min. If C_min is positive, the stated limits guarantee clearance. If C_max is negative, they guarantee interference. This arithmetic is simple but powerful because it exposes whether an assembly claim survives variation.

Tolerance allocation should follow function. A rotating toy-car axle needs enough running clearance not to bind after slight frame misalignment, while a camera insert may need firm location. Excess clearance creates wobble, noise, and position error. Tight tolerances also cost time and may be impossible for the chosen process. A practical build decision is to print or cut a small coupon containing several candidate hole sizes, measure the actual results, and select a compensated nominal dimension for that machine, material, and orientation.

A common misconception is that CAD precision equals manufacturing accuracy. Displaying 6.000 mm does not make a 6.000 mm hole. Another is adding every statistical uncertainty as though all extremes always coincide, or doing the opposite and ignoring worst case when assembly must be guaranteed. Use worst-case limits for guaranteed fit, and statistical reasoning only when its assumptions and acceptable failure rate are explicit. Do not “fix” a binding assembly by forcing it until the real interference, burr, or misalignment is understood.