8.5 Surface vs. Axis Interpretation of Position & the Boundary Concept for Slots, Tabs & Noncircular Features

8.5 Surface vs. Axis Interpretation of Position & the Boundary Concept for Slots, Tabs & Noncircular Features

Quick Answer: ASME Y14.5-2009 gives position at MMC two explanations that are not always numerically identical: the requirement stated in terms of the surface of a hole (no element of the surface may violate the virtual condition boundary) and the requirement stated in terms of the axis of a hole (the feature axis must lie within a cylindrical zone). Where they differ, the surface interpretation governs — it is the one a functional gage enforces. For noncircular features of size such as open-end slots, tabs, and elongated holes, para. 7.4.5 applies the same principles, using a positional tolerance to locate the center plane established by the parallel surfaces, with the diameter symbol omitted because the zone is two parallel planes. The boundary concept extends this to irregular shapes such as a D-shaped hole where a center is not conveniently identifiable — see also para. 8.8.

---

Two Explanations of the Same Requirement

Para. 7.3 explains a position tolerance at MMC in two ways:

• (a) In terms of the surface of a hole — while maintaining the specified size limits, no element of the hole surface shall be inside a theoretical boundary located at true position. That boundary is the virtual condition.
• (b) In terms of the axis of a hole — where a hole is at MMC, its axis must fall within a cylindrical tolerance zone whose axis is at true position, of diameter equal to the specified tolerance. As the hole departs from MMC, the zone diameter grows by the amount of the departure.

     SURFACE INTERPRETATION                    AXIS INTERPRETATION
   (boundary must stay clear)                (axis must stay in the zone)

     ╭──────────────────╮                        ╭──────────────────╮
     │   ╭──────────╮   │                        │   ╭──────────╮   │
     │   │  hole    │   │                        │   │  hole  ⋮ │   │
     │   ╰──────────╯   │                        │   ╰────────⋮─╯   │
     │ ┈┈┈ VC boundary  │                        │      zone ⌀t+bonus│
     ╰──────────────────╯                        ╰──────────────────╯
     NO surface element may                    The derived AXIS must lie
     encroach inside the VC.                   entirely within the zone.
     What a functional gage checks.            What a CMM typically reports.

Where the Two Diverge

For a perfectly straight hole the two interpretations agree exactly. They separate when the hole has form error — a bow, a taper, or a barrel:

When the two interpretations conflict, the surface interpretation is the governing requirement. This is the technical reason a part can be accepted by a CMM report and then refuse to accept a functional gage pin — the CMM reported an axis, the gage tested a boundary.

Practical rule for the exam: if a stem mentions a functional gage, a boundary, or a part that "will not assemble despite passing CMM inspection," reason with the surface interpretation and the virtual condition.

---

Noncircular Features of Size (Para. 7.4.5)

The fundamental principles of true position dimensioning and positional tolerancing for circular features of size, such as holes and bosses, apply also to noncircular features of size, such as open-end slots, tabs, and elongated holes. For such features of size, a positional tolerance is used to locate the center plane established by the parallel surfaces of the feature of size.

Two consequences follow immediately:

1. The diameter symbol is omitted. Per para. 3.6, a value without the diameter symbol is the distance between two parallel planes. A slot controlled ⌖ | 0.4 | A | B | C has a zone 0.4 wide, centred on the true position of the slot's center plane.
2. The tolerance applies in the direction that matters. A slot has a width direction and a length direction; the center-plane zone constrains the width direction. Where both directions need control, two feature control frames or a bidirectional scheme is used.

Bonus Tolerance on a Slot

The MMC arithmetic is identical to a hole, just applied to a width rather than a diameter. For a slot 12.00 – 12.30 wide with ⌖ | 0.2 Ⓜ | A | B | C:

• MMC = 12.00 (the narrowest slot contains the most material)
• Virtual condition $= 12.00 - 0.20 = \mathbf{11.80}$ — the width of the functional gage element that must pass through
• Slot produced at 12.10: bonus $= 12.10 - 12.00 = 0.10$, total tolerance $= 0.20 + 0.10 = \mathbf{0.30}$. Check: $12.10 - 0.30 = 11.80$ ✓
• Slot produced at 12.25: bonus $= 12.25 - 12.00 = 0.25$, total tolerance $= 0.20 + 0.25 = \mathbf{0.45}$. Check: $12.25 - 0.45 = 11.80$ ✓
• Slot produced at 12.30 (LMC): bonus $= 0.30$, total tolerance $= \mathbf{0.50}$. Check: $12.30 - 0.50 = 11.80$ ✓

The boundary is invariant at 11.80 in every row, exactly as it is for a hole. Use that invariance as your arithmetic check: if produced size − total tolerance does not return the virtual condition, the bonus was computed from the wrong limit.

---

The Boundary Concept for Irregular Shapes

The standard notes that the boundary concept can also be applied to other irregularly shaped features of size — such as a D-shaped hole with a flattened side — where the center is not conveniently identifiable, and cross-references para. 8.8, Combined Controls.

The mechanism: instead of describing a center plane or an axis, the drawing establishes a theoretical boundary of identical shape to the true profile, located at true position, that the feature surface may not violate. Under para. 8.8, basic dimensions and a profile tolerance establish the zone controlling the shape and size of the feature, while the positional tolerance establishes a theoretical boundary shaped identically to the true profile. For an internal feature the surface may not encroach inside that boundary; for an external feature it may not extend outside it.

The unifying idea. Every one of these controls, whatever the zone geometry, ultimately guarantees the same thing: a constant worst-case boundary that the mating part is designed against. Once you can name the boundary, the rest of the arithmetic follows.

Closer Control at One End (Para. 7.4.3)

Where the design permits, different positional tolerances may be specified for the extremities of long holes, which establishes a conical rather than a cylindrical tolerance zone. This is how a designer keeps a deep bore tightly located where a bearing seats while relaxing it where nothing mates.