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

ASME GDTP Technologist Y14.5-2009

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1 Chapter 1: Scope, Certification Logistics, Fundamental Rules & General Dimensioning

1.1 ASME GDTP Technologist Exam Scope, Prometric Logistics, & Certification Rules 1.2 Fundamental Rules of ASME Y14.5-2009 (Rules a through p) 1.3 Engineering Drawing Standards, Drawing Units, & Basic vs. Toleranced Dimensions 1.4 Dimensioning Features: Diameters, Radii, Chamfers, Countersinks, Counterbores, Spotfaces, Keyseats & Slots 1.5 Application of Dimensions & Location of Features: Lines, Leaders, Reference Dimensions, Rectangular vs. Polar Coordinates

2 Chapter 2: Features, Limits of Size, & Material Condition Principles

2.1 Features, Features of Size, & Limits of Size 2.2 Rule #1 (Taylor Principle / Envelope Rule), Its Exceptions & Overrides 2.3 Material Condition Concepts: MMC, LMC, & RFS Calculations

3 Chapter 3: General Tolerancing & Symbology

3.1 Direct Tolerancing, Limit Dimensioning, & Angular Tolerancing 3.2 The 14 Geometric Characteristic Symbols, Feature Control Frames, & Special Modifiers 3.3 Screw Threads, Gears & Splines, Angular Surfaces, Tapers & Statistical Tolerancing 3.4 Feature Control Frame Placement, Combined Frames, Tolerance Zone Definition & Tabulated Tolerances

4 Chapter 4: Datum Reference Frames & Degrees of Freedom

4.1 Theoretical Datums, Datum Feature Simulators, & Physical Datum Features 4.2 Degrees of Freedom Constraint & The 3-2-1 Datum Precedence System 4.3 Planar, Cylindrical, & Width Datum Feature Establishment

5 Chapter 5: Advanced Datum Applications: Targets, Boundary Modifiers, Customized Frames & Restrained Condition

5.1 Datum Target Points, Lines, Areas, & Movable Datum Simulators 5.2 Material Boundary Modifiers (RMB, MMB, LMB) & Datum Shift Calculations 5.3 Functional Datum Feature Selection, Multiple Datum Reference Frames & Simultaneous vs. Separate Requirements 5.4 Rotational Constraint About a Datum Axis or Point & Customized Datum Reference Frames 5.5 Irregular & Complex Datum Features, Mathematically Defined Surfaces, Restrained Condition & Datum Feature Controls

6 Chapter 6: Form Tolerances

6.1 Flatness & Straightness Controls for Surfaces & Features of Size 6.2 Circularity & Cylindricity Controls, Differences, & Inspection

7 Chapter 7: Orientation Tolerances

7.1 Parallelism Controls for Planar Surfaces & Cylindrical Features of Size 7.2 Perpendicularity & Angularity Tolerances with Basic Angles & Tangent Plane

8 Chapter 8: Location: Position Fundamentals & Calculations

8.1 Position Tolerancing Fundamentals, True Position, & Coordinate Conversions 8.2 Bonus Tolerance & Virtual Condition Calculations for Internal & External Features 8.3 Projected Tolerance Zones (Ⓟ Modifier) & Fixed vs. Floating Fastener Formulas 8.4 Zero Positional and Orientation Tolerancing at MMC and at LMC 8.5 Surface vs. Axis Interpretation of Position & the Boundary Concept for Slots, Tabs & Noncircular Features

9 Chapter 9: Location: Patterns, Composite Controls, Coaxial & Symmetrical Relationships, and Functional Gaging

9.1 Hole & Slot Patterns, Multi-Segment Frames, & Composite Position Tolerancing 9.2 Functional Gaging Principles & Inspection Verification of Position 9.3 Coaxial Holes, Counterbored Holes, Non-Parallel Axes, Spherical Features & Bidirectional Position 9.4 Concentricity & Symmetry Tolerances Under ASME Y14.5-2009 9.5 LMC Applied to Position: Wall Thickness, Breakout Protection & Boundary Calculations

10 Chapter 10: Profile Tolerances

10.1 Profile of a Line & Profile of a Surface Fundamentals & Basic Geometry 10.2 Bilateral, Unilateral, & Unequally Disposed Profile Boundaries (Ⓤ Modifier) 10.3 Composite Profile Tolerances vs. Multiple Single-Segment Profile Controls 10.4 Profile Verification, Coplanarity Controls, & Non-Rigid Parts 10.5 Profile Applications: Conicity, Extruded and Irregular Shapes, and Profile-Controlled Datum Features 10.6 Modifier Rules for Profile & Combined Controls (Profile with Position, Orientation and Runout)

11 Chapter 11: Runout Tolerances & Comparative Control Analysis

11.1 Circular Runout vs. Total Runout Interpretation & Dial Indicator Verification 11.2 Comparative Analysis: Runout vs. Form, Orientation, & Concentricity Controls

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

Key Takeaways Explain This Topic AI

ASME Y14.5-2009 para. 7.3.5 applies the least material condition modifier to position where the functional requirement is preserving material, so the stated tolerance applies at LMC and bonus accrues as the feature departs from LMC toward MMC.

For an internal feature the LMC virtual condition equals LMC plus the specified tolerance, and for an external feature it equals LMC minus the specified tolerance; that boundary stays constant across the size range.

Para. 2.8.2 states that where a geometric tolerance is applied on an LMC basis, perfect form at LMC is required and perfect form at MMC is not, which is the reciprocal of the MMC concept.

Under LMC the allowed tolerance depends on the unrelated actual minimum material envelope and is limited to the specified value when the feature is produced at its LMC limit of size.

LMC controls are not verifiable with a functional hard gage because the protected boundary is a minimum material boundary, so verification normally uses a coordinate measuring machine computing the actual minimum material envelope.

Last updated: September 2026

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 V C LMC = LMC + T VC_{\text{LMC}} = \text{LMC} + T V C LMC = LMC + T ; for an external feature V C LMC = LMC − T VC_{\text{LMC}} = \text{LMC} - T V C LMC = 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 .

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.

Requirement Worst Case Occurs When Modifier What Stays Constant
A bolt must pass through a hole Hole is smallest and most displaced Ⓜ Inner boundary = MMC virtual condition
A wall must not become too thin Hole is largest and most displaced Ⓛ Outer boundary = LMC virtual condition

A cast boss must not break out at an edge Boss is smallest and most displaced Ⓛ Inner boundary = LMC virtual condition

A press fit must not vary Any size RFS Nothing — the zone is fixed

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 .

The Arithmetic

For an internal feature (hole) with ⌖ | ⌀T Ⓛ | A | B | C : V C LMC = LMC + T Bonus = LMC − Actual Size T total = T + Bonus VC_{\text{LMC}} = \text{LMC} + T \qquad \text{Bonus} = \text{LMC} - \text{Actual Size} \qquad T_{\text{total}} = T + \text{Bonus} V C LMC = LMC + T Bonus = LMC − Actual Size T total = T + Bonus

For an external feature (boss, pin) with ⌖ | ⌀T Ⓛ | A | B | C : V C LMC = LMC − T Bonus = Actual Size − LMC T total = T + Bonus VC_{\text{LMC}} = \text{LMC} - T \qquad \text{Bonus} = \text{Actual Size} - \text{LMC} \qquad T_{\text{total}} = T + \text{Bonus} V C LMC = LMC − T Bonus = Actual Size − LMC T total = T + 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 = ∅ 12.65 = 12.40 + 0.25 = \mathbf{\varnothing 12.65} = 12.40 + 0.25 = ∅12.65 — this is the constant outer boundary the designer used when setting the wall thickness

Actual Size Departure from LMC Bonus T total T_{\text{total}} T total Outer Boundary = D + T total = D + T_{\text{total}} = D + T total

12.40 (LMC) 0.00 0.00 ⌀0.25 12.40 + 0.25 = 12.65
12.30 0.10 0.10 ⌀0.35 12.30 + 0.35 = 12.65
12.20 0.20 0.20 ⌀0.45 12.20 + 0.45 = 12.65
12.10 0.30 0.30 ⌀0.55 12.10 + 0.55 = 12.65
12.00 (MMC) 0.40 0.40 ⌀0.65 12.00 + 0.65 = 12.65

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 = ∅ 19.70 = 20.00 - 0.30 = \mathbf{\varnothing 19.70} = 20.00 − 0.30 = ∅19.70

Boss produced at ⌀20.22: bonus = 20.22 − 20.00 = 0.22 = 20.22 - 20.00 = 0.22 = 20.22 − 20.00 = 0.22 ; T total = 0.30 + 0.22 = ∅ 0.52 T_{\text{total}} = 0.30 + 0.22 = \varnothing 0.52 T total = 0.30 + 0.22 = ∅ 0.52

Check: 20.22 − 0.52 = 19.70 20.22 - 0.52 = 19.70 20.22 − 0.52 = 19.70 ✓ — the inner boundary is invariant
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 .

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.

Ⓜ at MMC Ⓛ at LMC
Protects Assembly clearance Minimum material
Bonus grows as feature moves toward LMC MMC
Constant boundary MMC virtual condition LMC virtual condition
Perfect form required at MMC (Rule #1) LMC (para. 2.8.2)
Functional hard gage Yes No — CMM with minimum material envelope