A linear actuator assembly that jammed. The actuator was a lead screw, two end plates, and a carriage. Every part was within print tolerance. The drawing said “all dimensions per ASME Y14.5.” The QC inspector checked every dimension and signed off. The assembly jammed when the carriage hit the end stop. The lead screw was binding against the nut. Every part was in spec. The assembly didn’t fit.
This is the classic stacked tolerance failure. Each part has a tolerance band. The assembly has a chain of dimensions that add up. If every part is at the extreme of its tolerance in the same direction, the assembly exceeds its design envelope. The parts are all “correct” and the assembly is still wrong.
The arithmetic stack
Consider the actuator: the lead screw length is 300 ± 0.1 mm. The end plate thickness at the bearing mount is 12 ± 0.05 mm (two plates). The carriage travel is 280 ± 0.1 mm. The nut position on the carriage is 10 ± 0.05 mm. The bearing bore is 8 + 0.02 / -0 mm.
Worst case: the screw is at 300.1 mm, both plates at 12.05, the carriage travel at 279.9, the nut at 9.95, and the bearing bore at 8.00. The total stack is:
300.1 + 12.05 + 12.05 + 279.9 + 9.95 + 8.00 = 622.05 mm
The design envelope was 620 ± 0.15 mm. The stack at worst case is 622.05 — 1.9 mm over the upper limit. The carriage hits the end stop 1.9 mm early. It jams.
The probability of every part being at the extreme in the same direction is low for a one-off build. But for 1000 units, some will hit it. And if the process is biased (the screw maker always lands on the high side, the plate maker always on the high side), the assembly is systematically oversized.
Worst case vs statistical stacking
Worst-case (arithmetic) stacking adds all the tolerances. It’s the safe assumption — if the worst case fits, all assemblies fit. But it over-constrains the design. The statistical (root-sum-square, RSS) method takes the square root of the sum of the squares of the tolerances. For independent, centered processes, RSS gives a more realistic stack. For the actuator:
Worst case: ±(0.1 + 0.05 + 0.05 + 0.1 + 0.05 + 0.02) = ±0.37 mm
RSS: √(0.1² + 0.05² + 0.05² + 0.1² + 0.05² + 0.02²) = √(0.01 + 0.0025 + 0.0025 + 0.01 + 0.0025 + 0.0004) = √0.0279 = ±0.167 mm
The RSS stack (±0.167 mm) is within the ±0.15 mm envelope if the parts are centered. The worst case (±0.37 mm) is not. The design was released based on an RSS calculation. The parts were not centered — the screw maker’s process ran high, and the plate maker’s process ran high. The RSS assumption (centered processes) was wrong, and the worst case came home.
What actually fixed it
Three changes. First, the end plate thickness tolerance was tightened from ±0.05 to ±0.02 mm. The plate was a machined part — the tighter tolerance added $1.50 per plate. Second, the carriage travel dimension was made a “reference” dimension, and the design was changed so the end stop is adjustable — a 5 mm adjustment slot absorbs the stack. Third, the lead screw length tolerance was kept at ±0.1 mm but the screw is now cut to length after assembly, not before. The assembly is measured, then the screw is cut.
The combination eliminated the jam. The assembly now fits regardless of the individual part extremes. The lesson: when an assembly is sensitive to tolerance stacking, don’t fight it by tightening every dimension. Add an adjustable feature or a “fit at assembly” step. It’s cheaper and more robust.
Designing for tolerance stack — the rules
- Identify the critical assembly dimension (the one that makes or breaks function).
- Draw the tolerance chain. Every part that contributes to that dimension is in the chain.
- Calculate worst case and RSS. If worst case doesn’t fit but RSS does, you’re betting on centered processes. Verify the processes are centered, or add a gap.
- Prefer adjustable features (slots, shims, threaded adjusters) over tight tolerances.
- Consider a datum strategy: dimension from the same datum on all parts so the stack doesn’t accumulate.
- For high-volume assemblies, run a Monte Carlo simulation with the actual process distributions. It’s a one-hour job in any CAD system and it shows you the real failure rate.
The datum problem
A big source of stack errors is inconsistent datums. If part A is dimensioned from its left edge and part B from its right edge, the assembly dimension between them has double the uncertainty. The fix: dimension both parts from the mating feature, or add a datum reference that ties them together. On the actuator, the end plate holes were dimensioned from the plate center, but the plate center wasn’t the mating datum. Moving the dimensions to the mating surface removed 0.04 mm from the stack.
The measurement trap
QC measured every part and signed off. The inspector measured the screw length, the plate thickness, the carriage travel — all within tolerance. What the inspector didn’t do was measure the assembly. The assembly dimension is the one that matters. The fix in QC: measure a sample of assembled units, not just parts. The assembly measurement catches the stack error that part inspection misses. It’s the difference between “every part is good” and “the product works.”
Tolerance stacking turns good parts into bad assemblies. Calculate the stack, keep the processes centered, and add adjustability where the stack is critical. The jammed actuator wasn’t a QC miss — every part was in spec. The assembly was 1.9 mm over because five tolerances lined up in the same direction. A slot, a shim, or a “cut to fit” step absorbs the stack that tight tolerances can’t.
