Machine Design #99: Position Tolerance for Hole Patterns — Control Replaceable Assembly, Not Each Coordinate
Hole-pattern position tolerance must preserve function, manufacturability, inspectability, cost, and serviceability when the boundary changes.
Function before a number
Write the input, expected result, acceptance limit, failure symptom, and measurement method before choosing a thickness, tolerance, datum, or hole pattern. Assign an owner to every value and change.
Core checks
- Assembly function and hole-pattern requirement: record value, source, method, owner, and pass/fail evidence.
- Datum order and mobility: record value, source, method, owner, and pass/fail evidence.
- Position tolerance, MMC, and virtual condition: record value, source, method, owner, and pass/fail evidence.
- Drill, reamer, CMM, or gauge method: record value, source, method, owner, and pass/fail evidence.
- Fastener clearance and replacement part: record value, source, method, owner, and pass/fail evidence.
- Capability, acceptance, and change control: record value, source, method, owner, and pass/fail evidence.
| Failure mode | Symptom | Verification |
|---|
| Function not defined | Over-tight or weak design | Rebuild the functional stack |
| Datum not real | Inspection and assembly disagree | Try the real fixture |
| Documents out of sync | Correct number, wrong revision | Baseline every reference |
Square zone versus round zone: why the difference is 57 per cent
Giving hole centre coordinates with plus-minus tolerances, for example X = 50 plus or minus 0.1 and Y = 30 plus or minus 0.1, creates a square acceptance zone 0.2 mm across. But the function of fitting a bolt does not care in which direction the centre deviates — it only cares how far. The zone that matches the function is a circle.
The two zones differ noticeably. A circular zone whose diameter equals the diagonal of the square zone (0.2 times the square root of 2, about 0.283 mm) has roughly 57 per cent more area:
- Square zone: 0.2 x 0.2 = 0.04 square mm
- Circular zone of diameter 0.283: pi x 0.1414 squared, about 0.0628 square mm
That means the plus-minus notation is rejecting 57 per cent of the parts that would in fact assemble — while still accepting diagonally deviated parts that are actually harder to fit. This is why a position tolerance with a cylindrical tolerance zone describes the function better than plus-minus coordinates.
The three components of a position requirement
| Component | How it is written | Its role |
|---|
| Basic dimension | The number in a rectangular box | The theoretically exact position, carrying no tolerance of its own |
| Position tolerance frame | Position symbol plus zone diameter plus datum system | How far the centre may deviate, and relative to what |
| Datum system | A, B, C in order of precedence | Anchors the hole pattern to the actual mounting face |
The common mistake is writing a basic dimension with a plus-minus tolerance as well — two control methods stacked on each other, and the shop does not know which one to follow.
Maximum material condition and bonus tolerance
For clearance holes there is a simple physical relationship: the larger the hole, the easier it assembles even with more centre deviation. Maximum material condition exploits exactly that — when a hole is machined larger than its minimum size, the part is granted extra position tolerance known as bonus tolerance.
Apply it when: the hole takes a bolt or a through pin and the only function is clearance to assemble. Do not apply it when: the hole locates a component, holds a bush or a bearing, where the position decides the function rather than merely whether it fits.
Checking with a functional gauge
An under-appreciated benefit of position tolerancing with maximum material condition: the hole pattern can be checked with a functional gauge — a plate with pins at the theoretically exact positions, and if the part drops on, it passes. Far faster than measuring each coordinate on a coordinate measuring machine, and it checks exactly what the function needs: does it assemble.
See also Machine Design #30 — Geometric tolerancing for assembly function.
Maximum material condition (MMC) and bonus tolerance
For a hole pattern that takes bolts, the holes do not always need the same position accuracy at every hole size. When a hole is larger than its smallest allowed size, the clearance around the bolt grows, and that extra clearance lets the hole sit further off while the bolt still passes. That is what the Ⓜ symbol (maximum material condition) on a position tolerance means.
- A hole at its smallest size (most material) gets exactly the position tolerance stated on the drawing.
- A larger hole earns a bonus tolerance equal to how much larger it is, because the extra clearance
allows it.
Example: position stated as ⌀0.2 Ⓜ, smallest hole ⌀5.0. If the actual hole measures ⌀5.1, it earns 0.1 bonus, so the total position tolerance becomes ⌀0.3. On the same pattern, calling Ⓜ accepts more parts that still assemble, which cuts scrap.
Clearance formulas: floating and fixed fasteners
Choose the position tolerance from the real clearance between bolt and hole:
| Fastener case | Formula (T per part) | Meaning |
|---|
| Floating fastener (both parts clearance holes) | T = H − F | Both holes can shift |
| Fixed fastener (one side threaded/pinned) | T = (H − F) / 2 | The threaded side cannot shift, so clearance splits |
Here H is the smallest hole diameter and F the largest bolt diameter. A fixed fastener gives less tolerance because one side is locked — remember this when one part has a tapped hole or a locating pin.
Functional gauge: check the whole pattern at once
When Ⓜ is used, a hole pattern can be checked with a functional gauge: a plate with pins of the right size at the true nominal positions. Any pattern that drops over the gauge passes, bonus tolerance included — fast and true to the real assembly condition, instead of measuring each hole's coordinates and recomputing.
MINATA release checklist
- [ ] Function, boundary, and failure symptom are written.
- [ ] Datums, ownership, process, and mistake-proofing are clear.
- [ ] Six topic checks have evidence and pass/fail limits.
- [ ] Manufacturing, assembly, inspection, and maintenance were tried.
- [ ] Revision, supplier, material, and configuration records agree.
Good engineering is an explicit chain that survives manufacture, operation, maintenance, and change. For hole-pattern position tolerance, evidence that function and variation remain reliable is the MINATA standard.
Frequently asked questions
Why not give hole centre coordinates with plus-minus tolerances?
Because that creates a square acceptance zone, while the function of fitting a bolt needs a circular one. The equivalent circular zone has about 57 per cent more area, which means the plus-minus notation rejects many parts that would in fact assemble.
What is a basic dimension?
The theoretically exact position, written in a rectangular box and carrying no tolerance of its own. The tolerance lives in the position tolerance frame. Writing a basic dimension with an added plus-minus is stacking two control methods, and the shop does not know which to follow.
When is maximum material condition used?
When the hole only has to give clearance — a through bolt hole, a through pin hole. Then a hole machined larger than the minimum earns bonus tolerance, which is entirely sound physically. Do not use it for locating holes or holes taking a bush or a bearing.
What is a functional gauge and when is it worth making?
A plate with pins at the theoretically exact positions; if the part drops on, it passes. Worth making when the volume is high enough or the hole pattern is checked repeatedly — far faster than measuring each coordinate, and it checks what the function actually needs.
How is the datum system chosen for a hole pattern?
By the faces the part actually seats and locates on when assembled to its mating part. A hole pattern correct relative to a datum unrelated to the assembly interface is a hole pattern correct on paper that does not fit.
Frequently asked questions, continued
What does the Ⓜ symbol on a position tolerance buy?
It grants bonus tolerance: when a hole is larger than its smallest size, the clearance around the bolt grows, so the hole may sit that much further off and still assemble. The result is more accepted parts and less scrap, on patterns where the function only needs "the bolt passes".
How do floating and fixed fasteners differ in tolerance?
A floating fastener (both sides clearance holes) gives T = H − F per part. A fixed fastener (one side threaded or pinned) gives only T = (H − F)/2, because the locked side cannot shift, so the clearance splits.
What is a functional gauge?
A plate with pins of the right size at the true nominal positions. A hole pattern that drops over the gauge passes, including the bonus tolerance from Ⓜ. It checks the whole pattern at once against the real assembly condition, faster than measuring each hole.
Conclusion
Position Tolerance for Hole Patterns is not paperwork done to make a file look tidy. It is how intent becomes a result that can be manufactured, assembled and measured repeatedly. A good drawing does not need the designer standing beside it to explain it; the structure of the information has to do that work.
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