Tolerance Stack-Up Analysis for Machined Assemblies
A part can measure perfect on the inspection bench and still refuse to go together on the assembly line. In our experience, that gap usually comes from tolerances that were each reasonable on their own drawing but were never added up across the full assembly. Tolerance stack-up analysis is the calculation that catches this before the first part is cut. This guide explains how the math works, which method to request, and what a buyer should expect from a machining partner who claims to handle assembly fit, not just individual dimensions.
Table of Contents
Quick Takeaways
Key Insight | Explanation |
|---|---|
Stack the loop, not the drawing | Every dimension can be in tolerance while the assembly still fails. Add each contributing dimension in the closed loop from one mating surface to the other. |
Worst case is the safe default for low volume | Adding every tolerance at its limit guarantees fit if the parts are in tolerance, but it forces tighter individual callouts and higher machining cost. |
RSS only works with a stable, centered process | Root-sum-square assumes random, centered variation. Ask for capability data on every critical feature before you accept it on a production part. |
Machining sequence is a stack contributor | Each setup, re-clamp, and datum change adds error. Put the datum reference frame and the features that must share one setup on the drawing. |
Tighten only where the function demands it | Tight bands raise cost and scrap risk. Keep the tight tolerance on mating features and loosen the rest of the part. |
Ask for measured evidence, not promises | Request CMM data on the mating features and a first article that checks the actual gap or fit, not only the individual dimensions. |
Why Stack-Up Analysis Matters for Machined Assemblies
Tolerance stacking, sometimes called tolerance stack-up, is the combined effect of dimensional tolerances across every part that sits between two mating surfaces. Tormach's guidance on the topic makes a practical point: a dimension's tolerance has to be checked against what the cutting tools and the machine can actually hold, at both the upper and lower limits. Skip that check and the assembly inherits errors that nobody planned for.
The cost side is where buyers feel the problem first. Tighter tolerances make a machined part harder to produce and usually more expensive, so the goal is to find the point where manufacturability, function, and cost agree. A stack-up analysis shows where that point sits for a given assembly, instead of letting every feature default to the tightest band on the drawing.
In practice, the failure shows up as a shop floor surprise. A bore is in tolerance, a pin is in tolerance, and the fit still binds or leaves a gap. Nobody made an error on a single dimension. The error lives in the sum. JLCCNC's overview of stack-up describes the same pattern, where several small dimensional differences add together in one assembly, which is why we treat stack-up as an assembly-level question from the first quote review.
Consider an illustrative example, not a customer job. A machined aluminum housing has a pocket depth of 25.00 mm, a mating plate of 12.00 mm, and a spacer of 12.50 mm, each with a plus or minus 0.05 mm tolerance. The nominal gap is 0.50 mm, and the worst-case total is 0.15 mm, so the gap can run from 0.35 mm to 0.65 mm. If the function needs at least 0.40 mm, a worst-case check exposes the problem before the first part ships, while a single-dimension inspection would pass every piece.
Defining the Stack: Loops and Contributors
Drawing the Closed Loop from Mating Surface to Mating Surface
Every stack-up starts with a closed loop. You pick the functional requirement, such as a running clearance or a bearing preload, and trace a path through the assembly from one mating surface to the other that returns to the start. Each dimension the path crosses is a contributor. If the loop misses a feature, the analysis is wrong before the first calculation.
The most common mistake we see is drawing the loop through the datums that are easiest to dimension rather than the faces that actually determine the fit. A bore located from a surface that never touches the mating part will look fine on paper and drift on the floor. Trace the path through the surfaces that contact each other, not the ones that are convenient to call out.
Separating Direct Contributors from Indirect Ones
Direct contributors sit inside the loop: a pocket depth, a boss height, or a thread engagement length. Indirect contributors affect the loop through the process, such as a fixture locating surface that moves between setups, or a clamp load that compresses a gasket. Direct contributors go into the math immediately. Indirect ones need either a measured value or an explicit allowance, or the analysis will look tidier than the real assembly.
A closure check helps here. Once the loop is drawn, confirm that the sum of contributors describes the actual gap or fit, using the nominal values from the drawing. If the nominal result does not match the assembly model, the loop is missing something.
Pro tip: Count the features in the loop before you count the tolerances. If one loop has more than about eight contributors, check whether two of them can be machined as a single feature or referenced from one datum.
Worst-Case, RSS, and Monte Carlo: Choosing a Method
Worst-Case Addition: When Guaranteed Fit Is Non-Negotiable
Worst-case analysis adds every tolerance at its limit in the direction that closes the gap. If the assembly fits under that condition, it fits every time, provided the parts actually sit within their tolerances. For low-volume aerospace hardware, precision fixtures, and any assembly where a field failure is expensive, that guarantee is worth the tighter part tolerances it demands.
The downside is cost. Worst-case stacks often force tolerances tighter than the function needs, which pushes a job toward extra passes, slower feeds, or additional inspection. Use worst-case to find the bottleneck, then decide whether to tighten one feature or change the design.
Root-Sum-Square: Cheaper Tolerances with a Process Condition
Root-sum-square (RSS) combines tolerances as the square root of the sum of their squares. That gives a narrower total than worst-case when contributors are independent and centered, which lets designers loosen individual callouts. The catch is that RSS assumes a stable, centered process. A machine with a drifting offset, or a fixture that shifts between lots, breaks that assumption, and the stack fails without warning.
Our rule is simple: do not accept an RSS-based tolerance on a production part unless you can see process capability data for each critical feature. Ask for the Cpk or equivalent data, and ask whether the process was centered during the study.
Monte Carlo Simulation for High-Volume Programs
Monte Carlo simulation samples thousands of random assemblies from distributions you define, then reports how many meet the requirement. PatSnap's engineering comparison describes worst-case as guaranteeing 100 percent assemblability, while Monte Carlo targets a 99.73 percent yield at three sigma with looser individual tolerances. That trade makes sense for high-volume programs where a small scrap rate is acceptable and tolerance cost is large.
Monte Carlo is only as good as its input distributions. If the inputs are guessed, the simulation produces a precise-looking answer built on a guess. Ask whether the inputs came from measured process data before you trust the yield figure.
Use the table below to match the method to the program. The right choice depends less on the math and more on what a failed assembly costs and how stable the process is.
Method | What It Guarantees | Where It Fits Machined Assemblies |
|---|---|---|
Worst-case addition | Fit under every combination of limits, provided parts are in tolerance | Low-volume, safety-critical, or high-cost-of-failure assemblies |
Root-sum-square | Statistical fit for stable, centered processes | Production runs with capability data on every critical feature |
Monte Carlo simulation | A predicted yield, such as 99.73 percent at three sigma | High-volume programs with measured input distributions |
How Machining Sequence Changes the Stack
A stack-up analysis on paper assumes each feature is made exactly as drawn, but a machined part is made in steps. The order of operations, the number of setups, and the datums used at each step decide how errors accumulate. An ASME paper on automatic tolerance analysis for manufacturing reaches a related conclusion: the tolerance stackup is dictated by the sequence in which machining errors accumulate.
Datum Shifts Between Setups
Each time a part is removed and re-clamped, the surface you machine from may not be the one the designer used. A feature cut in a second setup from a re-located surface inherits the error of that re-location. On a five-axis job, several faces can often be machined in one setup, which removes that transfer error. On a job that needs three or four flips, the same part can carry a stack the drawing never showed.
Specify the datum reference frame on the drawing, and state which features must be machined in one setup. That single instruction often does more for fit than tightening several callouts.
Fixturing and Workholding as Hidden Contributors
Fixtures locate the part, but they also bring their own tolerance, wear, and repeatability. A locating pin that wears across a production run changes every part downstream of it. Clamping force can distort thin walls, so the part relaxes after release, and a bore that measured in tolerance on the machine may not measure that way on the bench.
Ask your machining partner how workholding is controlled, whether fixtures are verified, and how often locating surfaces are checked. A credible answer names specific checks, not general assurances.
Buyer Checklist for Stack-Up Requests
What to Put on the Drawing
Give the machining partner the functional requirement, not only the dimensions. A note that says a bearing bore needs a specific running clearance tells the shop what matters, and it lets them choose the right process to hold it. Also mark the mating features, the datum scheme, and the features that must be checked on the CMM.
Include an assembly sketch with the loop marked. A shop that sees the loop can spot a contributor you missed, such as a shim or gasket, before any material is cut.
Questions to Ask a Machining Partner Before the Quote
Ask which method the shop uses to check stack-up, whether it runs worst-case checks on its own process, and how it handles RSS assumptions on critical features. Ask whether the shop can hold the tighter bands on mating features with its current equipment, such as 5-axis milling, lathe turning, or wire EDM for features that need it.
Ask what will be measured and how. A supplier should explain which features get a CMM report, which get gauge checks, and how measurement uncertainty compares with the tolerance being held.
Pro tip: Request a short written stack-up summary with your quote. If the supplier cannot list the critical loop and its contributors in writing, expect surprises at assembly.
Verifying the Stack with CMM, FAI, and PPAP
First Article Inspection Across the Full Stack
A first article inspection proves the process can make the part, and it proves more when the inspection plan follows the stack. Measure the mating features and the datums they rely on, then assemble a sample set and check the actual gap or fit. A passing report on each dimension alone does not prove the assembly works.
At SCPM, CMM programming is part of first article work, and we prefer inspection plans built around the functional loop rather than a list of isolated dimensions. When measured values and the predicted stack disagree, the gap usually points to a contributor nobody modeled.
Using PPAP Documentation to Track Stack Risk
PPAP packages give buyers a record of what was measured, how the process was controlled, and which characteristics were classified as critical. Used well, they show whether the stack assumptions held in production, not only in the first article run. If an RSS tolerance was accepted, the control plan should name the process metric that protects it.
SCPM is A2LA accredited, and its MetroLab division supports calibration. For a buyer, that matters because a stack-up analysis is only as credible as the measurements that test it.
Pro tip: Ask for the calibration status of any gauge used on a critical stack feature. A measurement system that cannot resolve a fraction of the tolerance cannot confirm the fit.
Frequently Asked Questions
What is tolerance stack-up analysis in simple terms?
It is the calculation of how individual dimensional tolerances combine across an assembly to set the final gap, fit, or clearance. It answers whether parts that are each in tolerance will still assemble and function together.
Should I request worst-case or RSS analysis for my machined parts?
Request worst-case for low-volume or safety-critical assemblies where a failed fit is expensive. Use RSS only when the supplier can show stable, centered process data for each critical feature.
Does stack-up analysis add significant cost to a machined assembly?
The analysis itself is engineering time, which is usually small compared with scrap and rework on a locked-in design. The bigger cost lever is the tolerance you choose, so the analysis pays off by loosening the callouts that do not affect function.
Does a passing CMM report prove the assembly will fit?
No. A CMM report confirms individual features against the drawing. Fit depends on how those features combine in the loop, so you also need a check of the assembled gap or a stack model that uses the measured values.
When do I need a stack-up analysis for a machined assembly?
Run one whenever two or more machined features must mate, when function depends on a clearance or preload, or when parts come from multiple setups, fixtures, or suppliers.
Can my machining shop run the analysis for me?
Many shops include stack-up review as part of design for manufacturability. Confirm who owns the loop, which method is used, and whether the results are documented in the quote.
Share with us which stack-up method your team relies on and the assembly that surprised you most, since real field cases are what shape the next round of practical guidance.
References
Tormach guide to best practices for tolerance stacking in CNC machining
PatSnap Eureka comparison of deterministic and Monte Carlo tolerance stack-up methods
ASME article on automatic tolerance analysis and how machining errors accumulate
JLCCNC overview of tolerance stack-up analysis methods, examples, and cost
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