Tolerance Stack-Up in Machined Assemblies
Short answer: a tolerance stack-up is the sum of every part and process variation that affects one dimension in an assembly. If you add the individual tolerances directly you get the worst-case stack, which is conservative and usually too pessimistic. If you combine them statistically in root-sum-square you get a realistic stack, but it assumes the variations are independent and centered. Machining to ±0.005 mm per part does not guarantee a ±0.005 mm assembly — the numbers add. At BQUQ we hold ±0.005 mm in production and inspect against your datum scheme, so send the drawing and get a quote within 12 working hours.
The single most common assembly failure in precision work is not a bad part. It is parts that were each in tolerance but did not fit when stacked. Understanding how tolerances combine lets you set part-level limits that actually deliver the assembly limit you need.
What a Tolerance Stack-Up Actually Is
An assembly dimension depends on several parts and processes. Each contributes variation. The stack-up is what all those contributions do to the final dimension. Two questions matter: which direction each contribution pushes the result, and how much variation each contributes.
Contributors to a typical stack include: the machining tolerance on each part feature, the tolerance on any sub-assembly, and process variation such as fixture repeatability and thermal growth. If your assembly has a clearance fit, the stack decides whether the gap ever closes.
Worst-Case vs Statistical Stack
| Method | How it combines | Result | When to use |
|---|---|---|---|
| Worst-case (arithmetic) | Add all tolerances | Largest possible, very conservative | Safety-critical, low volume |
| RSS (root-sum-square) | Square, sum, square-root | Realistic, tighter | High volume, independent causes |
| Modified RSS | RSS plus a safety factor | Practical compromise | Most production work |
Worst-case says the gap could close if every part sits at its extreme. In practice, parts center near nominal and the extremes rarely coincide, which is why RSS is often 40–60% smaller than worst-case for a five-part stack.
The catch: RSS assumes the contributors are independent and roughly centered. If two dimensions are cut in the same setup or share a datum, their errors correlate and RSS understates the risk. Use worst-case for correlated contributors and RSS for the rest.
A Worked Stack
Suppose a shaft (bore diameter tolerance ±0.01 mm), a housing bore (±0.02 mm), and a bearing outer diameter (±0.008 mm) combine to set a radial clearance.
| Contributor | Tolerance (±) | Squared value |
|---|---|---|
| Shaft OD | 0.010 mm | 0.0001 |
| Housing bore | 0.020 mm | 0.0004 |
| Bearing OD | 0.008 mm | 0.000064 |
| Fixture repeatability | 0.005 mm | 0.000025 |
Worst-case sum: 0.010 + 0.020 + 0.008 + 0.005 = 0.043 mm.
RSS: √(0.0001 + 0.0004 + 0.000064 + 0.000025) = √0.000589 ≈ 0.024 mm.
Same parts, very different predicted variation — 0.043 mm worst-case versus about 0.024 mm statistical. Which number you design to depends on how much risk you are willing to carry.
Why Machining Capability Sets the Floor
You cannot stack tighter than the process can hold. If a feature needs ±0.005 mm and the shop holds ±0.005 mm, that feature alone can consume a large share of the assembly budget. BQUQ machines ±0.005 mm in production on stable materials, verified with CMM, but that is a per-feature capability — it does not mean every dimension on the drawing earns it.
The practical move is to allocate the tightest tolerances to the few functional features that need them, and let cosmetic or clearance features take looser calls. This keeps the stack budget available where it matters.
Datum Strategy First, Math Second
Stack-up math on a bad datum scheme is wasted. Choose functional datums — the surfaces that actually locate the part in the assembly or in the fixture — and dimension from them. When every part in the stack uses datums that correspond to how it is assembled, the contributions are what you expect. When they do not, unexpected errors appear that no calculation predicted. Our guide to roundness and concentricity shows how datum choice drives functional results, and our tolerance standards guide covers callout conventions.
How to Set Part Tolerances From an Assembly Limit
Work backward. Start with the assembly tolerance you need. Subtract the contributions you cannot control, such as thermal effects and fixture repeatability. What remains is your parts' budget. Split it across parts in proportion to how hard and expensive each is to hold tight. Then verify with a first-article report and, on critical stacks, a CMM check of the assembled condition.
Two practical rules: never let one part consume more than half the assembly budget, and always leave a margin for the process variations you cannot see. Assemblies fail at the edges, not at nominal.
Frequently Asked Questions
Q: Is worst-case or RSS the right method?
A: Use worst-case when failure is unsafe or the contributing tolerances are correlated, and RSS when contributors are independent and volume is high. Many teams run both and design to a point between them with a safety factor.
Q: If my parts are each within ±0.005 mm, will my assembly be within ±0.005 mm?
A: No. Tolerances stack. Three parts at ±0.005 mm can produce an assembly variation of ±0.015 mm worst-case, or about ±0.009 mm by RSS. The assembly limit is always looser than the individual limits.
Q: Why did my assembly fail when all parts passed inspection?
A: Usually because the parts were individually in tolerance but the stack was not analyzed, or because the datum scheme did not match how the parts assemble. Check both before blaming the supplier.
Q: Can BQUQ help with a stack-up on my assembly?
A: Yes. Send the assembly drawing and we will review datum strategy and the per-part tolerances we can hold, usually flagging where a looser call is safe and where a tighter one is required.
Q: How does a supplier prove a tolerance is real?
A: With a first-article inspection report and, for critical features, CMM data per batch. Ask for the report on your first order and confirm the numbers yourself. Send drawings to sc@bquq.com or WhatsApp +86 13713157787 for a quote in 12 working hours.
Related Resources
- CNC machining tolerances guide: ISO 2768, GD&T, and what a shop can actually hold.
- CNC precision components: the tight-tolerance parts where stack-up discipline matters most.
- About BQUQ: an ISO9001-certified source factory in Dongguan running CNC, stamping, springs, and heat sinks under one roof.
- Contact us: assembly stack-up review and quotes within 12 working hours.
Authored by the BQUQ Engineering Team. BQUQ is an ISO9001-certified source factory in Dongguan, China, running CNC machining, metal stamping, custom springs, heat sink and collet lines under one roof. Send drawings to sc@bquq.com or WhatsApp +86 13713157787 for a quote within 12 working hours. www.bquq.com
