8.2 Virtual and Resultant Condition

8.2 Virtual and Resultant Condition

Once position tolerancing and the material condition modifier are in place, two worst-case boundaries fall out of the math: virtual condition (VC) — the mating boundary used for assembly and functional gaging — and resultant condition (RC) — the boundary on the opposite side used for wall thickness and minimum material. Senior exam questions routinely ask you to compute both for a pin or a hole.

Virtual Condition (VC)

Virtual condition is the boundary generated by the collective effect of size and the position (or other geometric) tolerance at the stated material condition. It is the worst-case mating boundary: the boundary the feature can never violate while still being in-spec, and the boundary a mating part must clear.

The VC formulas depend on whether the feature is external (pin, boss, tab) or internal (hole, slot):

Where t is the position tolerance value in the FCF.

For an external feature at MMC, the pin at its largest (MMC) with the maximum allowed position error produces the largest mating boundary — that's the worst case for the hole it has to fit into, so the two worst-case effects add: VC = MMC + t.

For an internal feature at MMC, the hole at its smallest (MMC) with the maximum position error produces the smallest effective hole — the worst case for the pin that has to pass through it, so the position eats into the hole: VC = MMC − t.

Resultant Condition (RC)

Resultant condition is the boundary at the other end of the size range — the boundary generated by the feature at the opposite material condition plus the position tolerance (and any bonus available there). RC is used for minimum wall thickness, minimum material between features, and similar calculations.

For a feature controlled at MMC, the RC formulas are:

Where bonus_at_LMC is the bonus tolerance available when the feature is at LMC — for an MMC-controlled feature, bonus_at_LMC = |MMC − LMC| = the full size tolerance range.

Why VC and RC Are Different Boundaries

VC fixes the mating boundary — it is the worst case for assembly, computed from the small end of the size range plus the worst position. RC fixes the opposite boundary — it is the worst case for material left between the feature and an edge or another feature, computed from the large end of the size range plus the worst position plus the bonus available there.

A produced in-spec feature has its actual mating surface somewhere between RC and VC. For a pin, VC is the larger, outer boundary and RC the smaller, inner one, so the surface lies inside VC and outside RC. For a hole, VC is the smaller boundary and RC the larger one, so the surface lies outside VC and inside RC — the VC gage pin passes through, and the hole never opens beyond RC. Wall-thickness problems use RC; assembly problems use VC.

Using VC for Gaging and Assembly

Functional gaging is built on VC. A Go gage for a hole at MMC has a pin of diameter = VC; if the gage pin enters the hole, the hole's VC is respected (it can assemble). For a pin at MMC, the Go gage is a ring of bore = VC; if the pin passes the ring, the pin's VC is respected. Because VC is the worst-case mating boundary, designing the mating part to clear VC guarantees assembly.

Worked Example 1: Pin at MMC

Pin specified ⌀10.0 ± 0.2 with position ⌀0.3 at MMC to A | B | C.

• MMC = 10.2 (largest pin), LMC = 9.8 (smallest pin), size tolerance range = 0.4.
• Virtual condition = MMC + t = 10.2 + 0.3 = ⌀10.5. This is the worst-case mating boundary; a hole must be at least 10.5 to guarantee the pin fits.
• Bonus at LMC = MMC − LMC = 0.4. Effective position zone at LMC = 0.3 + 0.4 = 0.7.
• Resultant condition = LMC − (t + bonus_at_LMC) = 9.8 − 0.7 = ⌀9.1. This is the smallest the pin's effective boundary can be on the material side; use it for minimum wall thickness from the pin's outer surface to an edge.

Worked Example 2: Hole at MMC

Hole specified ⌀12.0 ± 0.1 with position ⌀0.2 at MMC to A | B | C.

• MMC = 11.9 (smallest hole), LMC = 12.1 (largest hole), size tolerance range = 0.2.
• Virtual condition = MMC − t = 11.9 − 0.2 = ⌀11.7. This is the worst-case mating boundary; a pin must be at most 11.7 to guarantee it passes through.
• Bonus at LMC = MMC − LMC magnitude = 0.2. Effective position zone at LMC = 0.2 + 0.2 = 0.4.
• Resultant condition = LMC + (t + bonus_at_LMC) = 12.1 + 0.4 = ⌀12.5. This is the largest the hole's effective boundary can be on the material side; use it for minimum wall thickness from the hole's inner surface to an edge or to a neighboring feature.

Formulas Table (MMC-controlled features)

Senior-Level Trap: Wrong Sign on the Hole VC

The most common Senior exam mistake on VC is treating a hole like a pin. A hole's VC is smaller than its MMC, because the worst case for mating is the smallest effective hole — the position tolerance eats into it. If you add the position tolerance to a hole's MMC, you have computed the wrong boundary (you've moved toward RC instead of VC). Memorize: internal features subtract at MMC, external features add at MMC.