Tolerance stack-up on fabricated machine structures

A machine frame is a chain of tolerances, and the thing the customer actually cares about — whether the spindle is square to the table, whether the rails are coplanar, whether the ballscrew runs parallel to the way — sits at the end of that chain. Every link contributes, and the contributions do not come equally.

Most over-specified frames are the result of a stack-up that was never analysed. The designer felt uncertain, tightened everything, and paid for precision on links that contributed almost nothing. The tolerance budget follows the requirement in our guide to machine frame design.

Where the links are on a welded structure

A fabricated machine base has a stack that looks roughly like this:

1. Plate flatness and thickness variation as delivered from the mill
2. Cutting accuracy — profile position and squareness from the plasma, laser or saw
3. Fit-up — gaps, offsets and squareness at assembly before welding
4. Weld shrinkage and distortion — the largest and least predictable contributor
5. Stress relief relaxation — movement during and after the thermal cycle
6. Machining setup — how the part was supported and indicated in
7. Machining accuracy — the machine’s own positioning and geometric error
8. Measurement uncertainty — the inspection process itself
9. Assembly — bolt-up, shimming, and the foundation the machine sits on

The important structural fact is that links 1 through 5 are usually removed by link 7 for any feature that gets machined. Machining a face resets its position relative to the datums, and the fabrication tolerances upstream become irrelevant to that feature — provided the allowance survived.

That is the central insight for a weldment: tolerances on unmachined features and tolerances on machined features live in different chains. Mixing them in one analysis produces nonsense, and usually produces a drawing that specifies precision on a plate edge that nothing references.

Worst case, statistical, and which to use

Worst-case (arithmetic) stack adds the extremes of every contributor. If six features each carry ±0.1 mm, worst case gives ±0.6 mm. It is guaranteed conservative and it over-builds badly on chains longer than about three links, because the probability of every contributor sitting at its extreme in the same direction is remote.

Statistical (RSS) stack takes the root sum of squares. The same six features give about ±0.245 mm — less than half. It assumes contributors are independent and roughly normally distributed, which is reasonable for machining variation and unreasonable for weld distortion, which has a strong directional bias.

The practical approach on a machine frame:

• Use worst case for short chains, for safety-critical clearances, and for anything where a single out-of-tolerance part causes an assembly that cannot be built.
• Use statistical for longer chains of independent machining variation, where you have real process data.
• Use neither blindly for weld distortion. Distortion is not a random variable centred on zero — a given weld sequence pulls a given structure in a consistent direction. Treat it as a bias to be designed out, not a tolerance to be stacked. The levers are in controlling distortion on large weldments.

The allowance question, which is the real stack on a weldment

For a fabricated and machined frame, the stack-up that most often bites is not geometric at all. It is whether there is enough material left to machine.

The chain: plate thickness tolerance, plus cutting variation, plus fit-up offset, plus weld distortion, plus stress relief movement, against the machining allowance you specified. If that sum exceeds the allowance anywhere on the surface, the cutter runs out of material and the part is scrap.

Three millimetres of allowance is a common default for medium frames and it is adequate for a competently sequenced weldment. It is not adequate for a long, lightly restrained member welded on one side, where four or five millimetres of bow is entirely achievable.

Worth doing explicitly: estimate the expected distortion for the specific geometry, add the fabrication tolerances, and check the allowance covers it with margin. Where the estimate is uncomfortable, either increase the allowance — cheap — or fix the sequence, which is cheaper still.

Spending the tolerance budget well

Given a functional requirement at the end of the chain — say, rail coplanarity of 0.05 mm over 3 metres — the question is how to distribute it.

Three principles:

Spend where the sensitivity is highest. Not every contributor affects the outcome equally. A small angular error at the base of a tall column produces a large displacement at the top; the same error at the top produces almost nothing. Identify the high-leverage links and tighten those; release the rest.

Machine features that need to be related, in the same setup. Two pads machined in one setup on one machine are coplanar to that machine’s accuracy over that distance. The same two pads machined in separate setups inherit the full setup-to-setup error. This is the single most effective tolerance-budget decision available on a machine frame, and it is a design decision about feature orientation, not a specification decision.

Use coplanarity rather than individual flatness plus position. Controlling a set of pads as a coplanar group expresses what the machine needs and gives the shop the freedom to achieve it in the way its equipment suits. Controlling each pad’s height individually over-constrains the problem and costs more for a worse functional result. The control set is covered in GD&T and datum strategy on welded structures.

Adjustment as a tolerance strategy

The other way to close a stack is to design the adjustment in.

Shims under rail seats, jacking screws, eccentric mounts, adjustable feet, and a grouted foundation all absorb accumulated error at assembly. A frame that is shimmed flat at installation does not need to be machined flat to the same precision — and on a large structure, the shim is dramatically cheaper than the machining.

This is why many very large machine tools have modest tolerances on the fabricated structure and tight tolerances only on features that cannot be adjusted. The general principle from ASME Y14.5 style functional analysis applies: control what cannot be adjusted, adjust what need not be controlled.

The trade is service labour against manufacturing cost. For one machine, adjustment usually wins. For fifty, machining precision that removes an hour of alignment per unit usually wins.

A working sequence

1. Write down the functional requirement at the end of the chain, as a number.
2. List the contributors, separating the machined chain from the fabricated chain.
3. Estimate the sensitivity of the outcome to each contributor.
4. Check the machining allowance against the fabrication chain separately.
5. Tighten the top two or three contributors; release everything else to a general tolerance such as ISO 13920 class B.
6. Ask what could be adjusted at assembly instead of controlled in manufacture.
7. Confirm the inspection method can actually measure the final requirement.

Step seven catches a surprising number of drawings. A coplanarity requirement of 0.03 mm over four metres is meaningless if nobody in the chain has a way to measure it — the measurement uncertainty swallows the tolerance. The inspection question is covered in first article inspection on large weldments.

If you want a frame drawing checked for allowance and tolerance realism before it goes out to quote, send it through — the review comes back within 24 business hours.

See also: tolerance stack-up reference with typical contributor values and a worked example.