9.5 LMC Applied to Position: Wall Thickness, Breakout Protection & Boundary Calculations

9.5 LMC Applied to Position: Wall Thickness, Breakout Protection & Boundary Calculations

Quick Answer: Para. 7.3.5 applies the least material condition modifier Ⓛ to positional tolerancing where the functional requirement is preserving material rather than guaranteeing clearance. Under Ⓛ, the stated tolerance applies when the feature is at LMC, and bonus tolerance accrues as the feature departs from LMC toward MMC. The governing constant boundary is the LMC virtual condition: for an internal feature $VC_{\text{LMC}} = \text{LMC} + T$; for an external feature $VC_{\text{LMC}} = \text{LMC} - T$. Para. 2.8.2 adds the reciprocal rule that follows: where a geometric tolerance is applied on an LMC basis, perfect form at LMC is required and perfect form at MMC is not.

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Why LMC Exists

MMC protects assembly: it guarantees a worst-case clearance boundary that a mating part is designed against. LMC protects material: it guarantees a worst-case boundary of remaining stock. The two are mirror images, and confusing their direction is the single most common LMC error.

Typical LMC applications named by the standard and by practice: minimum wall thickness between a hole and an adjacent surface or cavity, preventing machining breakthrough into an internal fluid passage, maintaining structural edge distance on castings, and guaranteeing minimum stock for a subsequent machining operation.

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The Arithmetic

For an internal feature (hole) with ⌖ | ⌀T Ⓛ | A | B | C:

$$VC_{\text{LMC}} = \text{LMC} + T \qquad \text{Bonus} = \text{LMC} - \text{Actual Size} \qquad T_{\text{total}} = T + \text{Bonus}$$

For an external feature (boss, pin) with ⌖ | ⌀T Ⓛ | A | B | C:

$$VC_{\text{LMC}} = \text{LMC} - T \qquad \text{Bonus} = \text{Actual Size} - \text{LMC} \qquad T_{\text{total}} = T + \text{Bonus}$$

Worked Example: Protecting a Wall

A cored passage runs parallel to a drilled port. The port is ⌀12.00 – ⌀12.40 with ⌖ | ⌀0.25 Ⓛ | A | B | C.

• LMC = ⌀12.40 (largest hole = least material)
• MMC = ⌀12.00
• LMC virtual condition $= 12.40 + 0.25 = \mathbf{\varnothing 12.65}$ — this is the constant outer boundary the designer used when setting the wall thickness

The outer boundary never moves. A smaller hole is safer for wall thickness, so the standard rewards it with position tolerance — the exact inverse of the MMC case, where a larger hole is safer for assembly.

        MMC (Ⓜ) — protects CLEARANCE      LMC (Ⓛ) — protects MATERIAL

     bonus grows as hole gets BIGGER    bonus grows as hole gets SMALLER
              ▲                                   ▲
              │        ●                     ●    │
              │   ●                               │   ●
              │●                                       │●
        ──────┴──────────►                ◄────────────┴──────
        MMC            LMC                MMC            LMC
     Inner boundary constant            Outer boundary constant
        = MMC − T                          = LMC + T

Worked Example: An External Feature

A cast alignment boss is ⌀20.00 – ⌀20.30 with ⌖ | ⌀0.30 Ⓛ | A | B | C, protecting a minimum section between the boss and a nearby pocket.

• LMC = ⌀20.00 (smallest boss = least material)
• LMC virtual condition $= 20.00 - 0.30 = \mathbf{\varnothing 19.70}$
• Boss produced at ⌀20.22: bonus $= 20.22 - 20.00 = 0.22$; $T_{\text{total}} = 0.30 + 0.22 = \varnothing 0.52$
• Check: $20.22 - 0.52 = 19.70$ ✓ — the inner boundary is invariant

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The Reciprocal Form Rule (Para. 2.8.2)

Where a geometric tolerance is applied on an LMC basis, perfect form at LMC is required. Perfect form at MMC is not required. This is the reciprocal of the MMC concept. Where a geometric tolerance is applied on an LMC basis, the allowed tolerance is dependent on the unrelated actual minimum material envelope of the considered feature. The tolerance is limited to the specified value if the feature is produced at its LMC limit of size.

This is the LMC counterpart of Rule #1's envelope requirement, and it catches candidates who assume Rule #1 is universal. Under a normal size-only specification, Rule #1 requires perfect form at MMC and imposes none at LMC. When an LMC geometric tolerance is applied, that expectation flips: form must be perfect at LMC, and the MMC envelope stops being the controlling boundary.

LMC Applied to a Radial Pattern (Para. 7.4.5.2)

The standard illustrates LMC on a radial pattern of slots located relative to an end face and a center hole, where LMC is specified to protect the material between the slots and the outside of the part. The same logic scales to any pattern where the concern is what is left, not what fits.

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Verification Consequence

MMC controls are cheap to verify: a functional gage at the virtual condition is a physical embodiment of the requirement. LMC controls are not gageable in that way, because the boundary being protected is a minimum material boundary that no hard element can represent. Expect CMM verification with the actual minimum material envelope computed from the measured surface, and expect an exam item that tests exactly this asymmetry.