Tolerances, fits, and variation

• Compute worst-case clearance from mating-part limits and distinguish clearance, transition, and interference fits.
• Design a calibration coupon and revise nominal dimensions from measurements.

• measurement-instruments

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.

Problem

A shaft is specified 5.96–5.99 mm and a printed hole 6.05–6.12 mm. Find the clearance range and classify the fit under these limits.

Steps

1. Minimum clearance uses smallest hole and largest shaft: 6.05 mm - 5.99 mm = 0.06 mm.
2. Maximum clearance uses largest hole and smallest shaft: 6.12 mm - 5.96 mm = 0.16 mm.
3. Because even minimum clearance is positive, the limits specify a clearance fit.

Result

Diametral clearance is guaranteed between 0.06 mm and 0.16 mm.

Sanity check

The midpoints differ by about 0.11 mm, exactly the midpoint of the clearance range.

A hole ranges from 9.98 to 10.04 mm and a pin from 10.00 to 10.02 mm. Which fit is guaranteed?

A. Clearance B. Interference C. Transition D. Line-to-line only

Your answer: ______________________________

Reasoning:

Goal

Calibrate a fabrication process with a fit coupon and diagnose geometry-dependent error.

Equipment

• Printed or laser-cut hole/slot coupon
• Known pins or drill shanks
• Calipers
• Marker

Procedure

1. Label candidate holes or slots in 0.1 mm nominal increments and predict the smallest free-running size.
2. Measure each feature in at least two directions and record actual values separately from CAD labels.
3. Test the same pin gently in each feature; classify loose, running, snug, or interference without forcing.
4. Deliberate fault: compare a round feature with one intentionally oval or printed in a different orientation; diagnose whether average size alone explains binding.

What to observe

• Expected: actual dimensions show systematic offset plus feature-to-feature variation.
• Measure: directional sizes, fit class, material, process, and orientation; the coupon does not establish universal compensation.

Transfer challenge

Set a compensated hole size and tolerance note for a removable sensor mount, including how it will be verified.

Cautions

• Do not use sharp rotating tools as gauges; use unpowered smooth shanks or purpose-made pins.

Learner: ____________________ Date: ____________________

Evidence artifact or file: ____________________________________________

Notes: