10.4 Location, Profile, and Runout Controls with Modifiers

10.4 Location, Profile, and Runout Controls with Modifiers

Anatomy of the Feature Control Frame (FCF)

The Feature Control Frame (FCF) is the standardized rectangular box that conveys all geometric requirements for a controlled feature under ASME Y14.5. Every compartment in the frame carries precise metrological meaning and must be read strictly from left to right:

ANATOMY OF A FEATURE CONTROL FRAME:

+-------------------------------------------------------------------------+
| Comp 1: | Comp 2:               | Comp 3:   | Comp 4:     | Comp 5:     |
| Symbol  | Tolerance & Modifiers | Primary   | Secondary   | Tertiary    |
|---------+-----------------------+-----------+-------------+-------------|
|   ⌖     |  DIA .010  (M)        |    A      |    B  (M)   |    C        |
+-------------------------------------------------------------------------+
    ^           ^       ^              ^           ^            ^
    |           |       |              |           |            |
 Geometric   Diameter  Material     Primary    Secondary    Tertiary
 Control     Zone      Modifier     Datum      Datum with   Datum
 (Position)  Symbol    (MMC)        Plane      MMC Modifier Plane

• Compartment 1: Geometric Characteristic Symbol: Identifies the control type (e.g., Position, Profile of a Surface, Total Runout).
• Compartment 2: Tolerance Value and Modifiers:
  • The Diameter Symbol ($\varnothing$): Present when the tolerance zone is a cylinder or circle (such as for a hole or pin centerline). Omitted when the tolerance zone is bounded by two parallel planes (such as for a slot or surface).
  • The Numerical Tolerance Value: Specifies the total width or diameter of the tolerance zone.
  • Material Condition Modifiers: Maximum Material Condition ($\textcircled{M}$), Least Material Condition ($\textcircled{L}$), or Regardless of Feature Size (RFS default).
  • Special Modifiers: Projected Tolerance Zone ($\textcircled{P}$), Tangent Plane ($\textcircled{T}$), Free State ($\textcircled{F}$), Unequal Bilateral Profile ($\textcircled{U}$).
• Compartments 3, 4, and 5: Datum References: The primary, secondary, and tertiary datum references defining the Datum Reference Frame, listed in strict order of precedence from left to right. Datums representing features of size may also carry material condition modifiers (e.g., $[, B \textcircled{M} ,]$).

ASME Rule #2: The Default Material Condition

Under earlier standards (ANSI Y14.5M-1982), the symbol $\textcircled{S}$ was required to specify Regardless of Feature Size. In modern standards (ASME Y14.5-2009 and ASME Y14.5-2018), Rule #2 dictates:

[!IMPORTANT] ASME Rule #2 (Default RFS): Regardless of Feature Size (RFS) is the automatic default condition for all geometric tolerances and datum references. If no material condition modifier ($\textcircled{M}$ or $\textcircled{L}$) is present, the specified tolerance applies strictly at the indicated value, regardless of the produced size of the feature. The modifier $\textcircled{S}$ has been formally abolished.

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Location Controls: Position, Concentricity, and Symmetry

Location controls specify the placement of features of size relative to each other or to a datum reference frame.

1. Position (True Position)

Position is the most widely utilized and versatile control in GD&T. It defines the allowable deviation of the center, axis, or center plane of a feature of size from its theoretically exact location.

• Basic Dimensions: The theoretically exact location is established by Basic Dimensions (boxed numbers, e.g., $[2.000]$). Basic dimensions have zero tolerance of their own; the total allowable location error is governed entirely by the feature control frame.
• Cylindrical Tolerance Zone: For a drilled or bored hole, position establishes a cylindrical tolerance zone of diameter $\varnothing t$ centered at the true position. The extracted centerline of the hole must lie entirely within this cylinder.

The 57% Bonus Area: Why Position Outperforms Coordinate Tolerancing

Prior to GD&T, drawings relied on traditional plus/minus coordinate dimensioning (e.g., $X = 2.000" \pm 0.005"$, $Y = 1.500" \pm 0.005"$). This created a square tolerance zone of $0.010" \times 0.010"$:

SQUARE COORDINATE ZONE VS. CIRCULAR GD&T POSITION ZONE:

          Square Coordinate Zone (+/- .005")      Circular Position Zone (DIA .01414")
                +---------------+                     /~~~~~~~~~~~~~~~\
                | * Corner pass |                    /                 \
                |   (0.0071")   |                   |         +         |  <-- 57% More
                |       +       |                   |      (Target)     |      Tolerance Area!
                |               |                    \                 /
                +---------------+                     \~~~~~~~~~~~~~~~/ 
             Diagonal = 0.01414"                    Circumscribes Square!

1. In a square coordinate zone, a hole located at the extreme corner ($\Delta X = +0.005"$, $\Delta Y = +0.005"$) is accepted. The distance from the center is: $r = \sqrt{(0.005)^2 + (0.005)^2} = \sqrt{0.000050} \approx 0.00707"$
2. If a hole is acceptable at a radial offset of $0.00707"$ in the corner, it is functionally acceptable at that same radial distance in any direction!
3. A circular tolerance zone of diameter $\varnothing 0.01414"$ circumscribes the square zone. Comparing their areas: $\text{Area of Square} = 0.010" \times 0.010" = 0.000100\text{ in}^2$ $\text{Area of Circle} = \frac{\pi \times (0.01414")^2}{4} \approx 0.000157\text{ in}^2$ $\text{Percentage Increase} = \frac{0.000157 - 0.000100}{0.000100} \times 100\% = \mathbf{57.1\%}$ GD&T position provides $57%$ more usable tolerance area without compromising functional clearance, significantly reducing manufacturing scrap!

Diametral Position Error Formula

When an inspector measures a hole on a Coordinate Measuring Machine (CMM), the CMM reports Cartesian coordinates ($X_{\text{actual}}, Y_{\text{actual}}$). To compare against the basic dimensions ($X_{\text{basic}}, Y_{\text{basic}}$), the technician must calculate the Actual Diametral Position Error:

$\Delta X = X_{\text{actual}} - X_{\text{basic}}$ $\Delta Y = Y_{\text{actual}} - Y_{\text{basic}}$ $\text{Radial Distance } r = \sqrt{(\Delta X)^2 + (\Delta Y)^2}$ $\mathbf{\text{Actual Diametral True Position Error} = 2 \times \sqrt{(\Delta X)^2 + (\Delta Y)^2}}$

[!WARNING] The Factor of 2 Exam Trap: Candidates frequently compute the radial hypotenuse $\sqrt{\Delta X^2 + \Delta Y^2}$ and forget to multiply by 2! The feature control frame specifies a diametral zone ($\varnothing$). The radial offset $r$ is only the radius of the zone; the actual error is the full diameter ($2r$).

2. Concentricity and Symmetry

• Concentricity: Controls the central axis of all diametrically opposed median points of a cylinder relative to a datum axis. It requires dynamic mapping of opposing point pairs. Because it is exceptionally difficult and expensive to inspect, ASME Y14.5 recommends replacing concentricity with Position or Runout.
• Symmetry: Controls the derived median plane of opposing features relative to a datum center plane. (Note: Both Concentricity and Symmetry were formally eliminated in ASME Y14.5-2018 in favor of Position and Profile, but remain prevalent on legacy prints and the ASQ CQT exam).

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Material Condition Modifiers and Bonus Tolerance

MATERIAL CONDITION DEFINITIONS (SHAFT VS. HOLE):

                     EXTERNAL FEATURE (Shaft)        INTERNAL FEATURE (Hole)
   -------------------------------------------------------------------------
   MMC (Circled M):  MAXIMUM DIAMETER (USL)          MINIMUM DIAMETER (LSL)
                     Most metal / Heaviest part!     Most metal / Smallest hole!
   -------------------------------------------------------------------------
   LMC (Circled L):  MINIMUM DIAMETER (LSL)          MAXIMUM DIAMETER (USL)
                     Least metal / Lightest part!    Least metal / Largest hole!
   -------------------------------------------------------------------------
   RFS (Default):    Tolerance is FIXED at stated value; NO bonus tolerance!

1. Maximum Material Condition (MMC - $\textcircled{M}$)

The condition where a feature of size contains the maximum amount of material within its stated limits:

• External Feature (Shaft, Pin): Maximum allowable diameter (Upper Specification Limit, USL).
• Internal Feature (Hole, Bore): Minimum allowable diameter (Lower Specification Limit, LSL).

2. Least Material Condition (LMC - $\textcircled{L}$)

The condition where a feature contains the minimum amount of material:

• External Feature (Shaft): Minimum diameter (LSL).
• Internal Feature (Hole): Maximum diameter (USL).
• Application: Used to guarantee minimum wall thickness to prevent bursting or cracking under hydraulic pressure.

3. Bonus Tolerance Mechanics

When the MMC modifier ($\textcircled{M}$) is specified in the feature control frame, the stated position tolerance applies only when the feature is produced at its MMC size.

• As the actual produced size departs from MMC toward LMC, the clearance between mating parts increases.
• This additional clearance is converted directly into Bonus Tolerance:

$\mathbf{\text{Bonus Tolerance} = |\text{Actual Produced Size} - \text{MMC Size}|}$ $\mathbf{\text{Total Permissible Position Tolerance} = \text{Specified Tolerance} + \text{Bonus Tolerance}}$

4. Virtual Condition ($VC$)

The Virtual Condition is the constant worst-case boundary generated by the combined effect of the feature's MMC size and its geometric tolerance. Mating functional hard gages (Go plug gages) are manufactured to the Virtual Condition boundary:

• For an Internal Feature (Hole): $\mathbf{VC_{\text{hole}} = \text{MMC Size} - \text{Specified Geometric Tolerance}}$
• For an External Feature (Shaft): $\mathbf{VC_{\text{shaft}} = \text{MMC Size} + \text{Specified Geometric Tolerance}}$

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Profile Controls: Surface and Line

Profile controls define a uniform boundary along the true, theoretically exact contour of a part as defined by basic dimensions or CAD models.

PROFILE TOLERANCE ZONES & THE UNEQUAL BILATERAL MODIFIER (Circled U):

1. BILATERAL EQUAL (Default: [Profile | 0.020 | A | B]):
         +0.010" Outside
   ----------------------------  Outer Boundary
   ============================  TRUE NOMINAL CAD PROFILE
   ----------------------------  Inner Boundary
         -0.010" Inside
   (Tolerance zone divides equally: +/- 0.010" on each side of nominal)

2. UNEQUAL BILATERAL MODIFIER (ASME Y14.5-2009/2018: [Profile | 0.030 (U) 0.010 | A | B]):
         +0.010" Adding Material (Outside)
   ----------------------------  Outer Boundary
   ============================  TRUE NOMINAL CAD PROFILE
   ............................
   ----------------------------  Inner Boundary (-0.020" Inside Material)
   (Total zone = 0.030"; exactly 0.010" adds material; remaining 0.020" removes material)

1. Profile of a Surface

• Definition: A three-dimensional tolerance zone extending across the entire surface.
• Capability: Profile of a surface is the most powerful control in GD&T. It can simultaneously control Size, Form, Orientation, and Location relative to a datum reference frame.

2. Profile of a Line

• Definition: A two-dimensional tolerance zone applied to individual cross-sectional line elements along the profile.

3. The Unequal Bilateral Modifier ($\textcircled{U}$)

In legacy drafting, unequal or unilateral profile tolerance zones required phantom lines drawn on the print. Modern standards (ASME Y14.5-2009 and Y14.5-2018) utilize the $\textcircled{U}$ modifier:

• In a callout reading $[, \cap \mid 0.030 \textcircled{U} 0.010 \mid \mathbf{A} \mid \mathbf{B} ,]$:
  1. The first number ($0.030"$) is the total width of the tolerance zone.
  2. The number following the $\textcircled{U}$ symbol ($0.010"$) indicates the portion of the tolerance that adds material (displaced outward from nominal).
  3. The remaining balance ($0.030" - 0.010" = 0.020"$) subtracts material (displaced inward from nominal).
  4. If the callout reads $[, \cap \mid 0.030 \textcircled{U} 0 \mid \mathbf{A} \mid \mathbf{B} ,]$, the tolerance is strictly unilateral inward (material subtraction only).

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Runout Controls: Circular Runout versus Total Runout

Runout is a composite rotational tolerance that controls the relationship of features constructed around or perpendicular to a datum axis of rotation.

CIRCULAR RUNOUT VS. TOTAL RUNOUT INSPECTION:

CIRCULAR RUNOUT (Single Arrow: ↗):          TOTAL RUNOUT (Double Arrow: ⇗):
Indicator stays at fixed station;            Indicator traverses entire axial length;
Part rotates 360 degrees:                    Part rotates 360 degrees:

        Dial Indicator                              Dial Indicator TRAVERSES Axially
             [ v ]                                       [ v ] ===> ===> ===>
      +-----------------+                         +-----------------+
  ==> |   ( Shaft )     |  Rotates            ==> |   ( Shaft )     |  Rotates
      +-----------------+  360 deg                +-----------------+  360 deg
   - Checked cross-section by cross-section!   - Continuous surface sweep!
   - Controls circularity & coaxiality!        - Controls circularity, straightness,
                                                 coaxiality, taper, & waviness!

1. Circular Runout (Symbol: $\nearrow$)

• Operational Setup: The part is mounted between bench centers or precision V-blocks to establish the datum axis. A dial test indicator is placed at a fixed axial station perpendicular to the surface.
• Measurement: The part is rotated $360^\circ$ about the datum axis. The indicator registers the Full Indicator Movement (FIM). The indicator is then lifted and moved to a new axial position, and the test is repeated independently.
• What it Controls: Circularity (roundness) and Coaxiality at that specific circular element.

2. Total Runout (Symbol: $\nearrow!!\nearrow$)

• Operational Setup: The part is mounted on its datum axis. The dial indicator is placed in contact with the surface.
• Measurement: While the part is rotated $360^\circ$, the dial indicator is traversed continuously along the entire axial length of the cylindrical surface (or radially across a flat face).
• What it Controls: Simultaneously controls Circularity, Straightness of surface elements, Coaxiality, Taper, Hourglass/Barrel distortion, and Surface Waviness across the entire 3D surface.

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Step-by-Step Worked Numerical Examples

Worked Example 1: Full True Position and Bonus Tolerance Calculation

Scenario: An aerospace component drawing specifies a clearance hole with the following requirements:

• Size Dimension: $\varnothing 0.500" \pm 0.005"$
• Feature Control Frame: $[, \text{Position} \mid \varnothing 0.010 \textcircled{M} \mid \mathbf{A} \mid \mathbf{B} \mid \mathbf{C} ,]$
• Basic Dimensions: $X = 3.000"$, $Y = 2.000"$

A quality technician measures the hole on a calibrated CMM, obtaining:

• Actual Diameter $= \mathbf{0.503"}$
• Actual $X$-Coordinate $= \mathbf{3.004"}$
• Actual $Y$-Coordinate $= \mathbf{1.997"}$

Determine whether the hole conforms to the engineering drawing.

Step 1: Calculate Coordinate Deviations

$\Delta X = X_{\text{actual}} - X_{\text{basic}} = 3.004" - 3.000" = +0.004"$ $\Delta Y = Y_{\text{actual}} - Y_{\text{basic}} = 1.997" - 2.000" = -0.003"$

Step 2: Calculate Actual Diametral Position Error

$\text{Radial Offset } r = \sqrt{(\Delta X)^2 + (\Delta Y)^2} = \sqrt{(0.004)^2 + (-0.003)^2} = \sqrt{0.000016 + 0.000009} = \sqrt{0.000025} = 0.0050"$ $\text{Actual Diametral Error} = 2 \times r = 2 \times 0.0050" = \mathbf{0.0100"}$

Step 3: Determine MMC Size and Bonus Tolerance

For an internal hole, Maximum Material Condition occurs at the smallest allowable hole diameter: $\text{MMC Size} = 0.500" - 0.005" = \mathbf{0.495"}$ $\text{LMC Size} = 0.500" + 0.005" = 0.505"$

Since the actual hole was produced at $0.503"$ (larger than MMC): $\text{Bonus Tolerance} = |\text{Actual Size} - \text{MMC Size}| = 0.503" - 0.495" = \mathbf{0.0080"}$

Step 4: Calculate Total Permissible Position Tolerance

$\text{Total Permissible Tolerance} = \text{Specified Tolerance} + \text{Bonus Tolerance} = 0.0100" + 0.0080" = \mathbf{0.0180"}$

Step 5: Evaluate Conformance

• Actual Position Error: $0.0100"$
• Total Permissible Tolerance: $0.0180"$
• Actual Hole Size: $0.503"$ (within size limits $0.495"$ to $0.505"$)
• Conclusion: Because $0.0100" \le 0.0180"$ and the hole size is within limits, the feature passes inspection.

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Worked Example 2: Virtual Condition of a Precision Mating Assembly

Scenario: A precision assembly consists of a cylindrical locating pin that must press into a mating bushing hole:

• Pin Callout: $\varnothing 0.375" \pm 0.002"$, with $[, \text{Position} \mid \varnothing 0.003 \textcircled{M} \mid \mathbf{A} \mid \mathbf{B} ,]$
• Bushing Hole Callout: $\varnothing 0.380" \pm 0.003"$, with $[, \text{Position} \mid \varnothing 0.004 \textcircled{M} \mid \mathbf{A} \mid \mathbf{B} ,]$

Calculate the Virtual Condition for both features and determine the minimum clearance at worst-case assembly.

Step 1: Calculate Pin Virtual Condition (External Feature)

$\text{Pin MMC} = 0.375" + 0.002" = 0.377"$ $\mathbf{VC_{\text{pin}} = \text{MMC} + \text{Geometric Tolerance}} = 0.377" + 0.003" = \mathbf{0.3800"}$

Step 2: Calculate Bushing Hole Virtual Condition (Internal Feature)

$\text{Hole MMC} = 0.380" - 0.003" = 0.377"$ $\mathbf{VC_{\text{hole}} = \text{MMC} - \text{Geometric Tolerance}} = 0.377" - 0.004" = \mathbf{0.3730"}$

Step 3: Evaluate Worst-Case Assembly Clearance

$\text{Clearance} = VC_{\text{hole}} - VC_{\text{pin}} = 0.3730" - 0.3800" = \mathbf{-0.0070"}$ Conclusion: The calculation reveals an interference of $0.0070"$ under worst-case virtual condition! The parts will jam during automated assembly. The quality technician must flag this drawing to design engineering to enlarge the hole or tighten tolerances before production tooling is released.

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Technician Inspection Scenarios & Common Exam Traps

Real-World Shop Scenario: The Illegal Bonus Tolerance Rejection

A quality technician at a defense contractor inspects an internal bore with a feature control frame reading $[, \text{Position} \mid \varnothing 0.008 \mid \mathbf{A} \mid \mathbf{B} \mid \mathbf{C} ,]$. The actual hole diameter is produced near LMC ($0.004"$ larger than MMC). The CMM operator calculates a position error of $0.010"$ and applies $0.004"$ of bonus tolerance, reporting a total allowable tolerance of $0.012"$ and accepting the part. The quality auditor overrides the operator and scraps the lot! Why?

• Root Cause Analysis: The feature control frame had no material condition modifier (no circled M). Under ASME Rule #2, Regardless of Feature Size (RFS) is the automatic default! Bonus tolerance is strictly illegal under RFS. The allowable position tolerance was fixed at exactly $0.008"$. The hole error of $0.010"$ exceeded the specification, making the part nonconforming.

Common Exam Traps for CQT Candidates

• Exam Trap 1: Forgetting to Multiply by 2: When converting CMM coordinate deviations into diametral position error, remember: $\text{Actual Error} = 2 \times \sqrt{\Delta X^2 + \Delta Y^2}$. Missing the factor of 2 is the single most frequent calculation error on the CQT exam!
• Exam Trap 2: Determining MMC for Holes vs. Shafts: Remember: MMC means the most material (heaviest part). For a shaft, MMC is the maximum diameter. For a hole, MMC is the minimum diameter (removing the least material leaves the most metal behind!).
• Exam Trap 3: Bonus Tolerance under RFS: Bonus tolerance applies only when $\textcircled{M}$ (or $\textcircled{L}$) is explicitly present in Compartment 2 of the feature control frame. Under RFS, bonus tolerance is zero.
• Exam Trap 4: Circular Runout vs. Total Runout Indicator Movement: In Circular Runout, the indicator is stationary during part rotation; it does not travel along the part axis. In Total Runout, the indicator traverses axially across the entire length of the rotating surface.