7.4 Location, Profile & Runout Tolerances

7.4 Location, Profile & Runout Tolerances

Position Tolerance & True Position Calculation

Position is the most widely utilized and versatile geometric control in mechanical engineering. Governed by Section 7 of ASME Y14.5-2009 (and Section 10 of ASME Y14.5-2018), position defines the allowable deviation of a feature of size (such as a drilled hole, threaded insert, dowel pin, or slot) from its theoretically exact true position, as established by basic dimensions originating from a Datum Reference Frame.

The Cylindrical Tolerance Zone

When applied to a cylindrical feature (hole or pin), the position tolerance value in the Feature Control Frame is preceded by the diameter symbol: [Position | ∅ .010 | A | B | C].

• The tolerance zone is a cylinder of diameter $0.010\text{ in}$, whose theoretical axis is located at the exact basic coordinate dimensions.
• The actual derived axis of the manufactured hole or pin must lie entirely within this cylindrical zone along the full depth of the feature.

The True Position Mathematical Formula

When an inspector measures a hole on a Coordinate Measuring Machine (CMM) or height stand, the machine reports Cartesian coordinates $(X_{\text{actual}}, Y_{\text{actual}})$. The inspector compares these against the basic drawing dimensions $(X_{\text{basic}}, Y_{\text{basic}})$:

1. Calculate Linear Coordinate Offsets: $\Delta X = X_{\text{actual}} - X_{\text{basic}}$ $\Delta Y = Y_{\text{actual}} - Y_{\text{basic}}$
2. Calculate Radial Offset ($R$): By the Pythagorean theorem, the distance from true position center to the actual hole center is: $R = \sqrt{(\Delta X)^2 + (\Delta Y)^2}$
3. Calculate Diametral True Position Deviation: Because the tolerance zone is specified as a diameter, the radial error must be multiplied by two: $\text{Actual Position Deviation} = 2 \times R = 2 \times \sqrt{(\Delta X)^2 + (\Delta Y)^2}$ $\text{Actual Position Deviation} = 2 \times \sqrt{(X_{\text{actual}} - X_{\text{basic}})^2 + (Y_{\text{actual}} - Y_{\text{basic}})^2}$

Comprehensive Step-by-Step Calculation Example

An inspector evaluates a mounting hole with the following blueprint callout:

• Basic Dimensions: $X = 3.250\text{ in}$, $Y = 1.750\text{ in}$
• Hole Size: $∅ 0.500 - 0.510\text{ in}$
• Feature Control Frame: [Position | ∅ .008 (M) | A | B | C]

CMM Inspection Data:

• Measured Diameter: $0.504\text{ in}$
• Measured Coordinates: $X_{\text{actual}} = 3.253\text{ in}$, $Y_{\text{actual}} = 1.746\text{ in}$

Step 1: Compute Linear Coordinate Deviations: $\Delta X = 3.253 - 3.250 = +0.003\text{ in}$ $\Delta Y = 1.746 - 1.750 = -0.004\text{ in}$

Step 2: Calculate Actual Diametral Position Deviation: $\text{Actual Position} = 2 \times \sqrt{(+0.003)^2 + (-0.004)^2} = 2 \times \sqrt{0.000009 + 0.000016} = 2 \times \sqrt{0.000025} = 2 \times 0.005 = 0.010\text{ in}$

Step 3: Calculate Allowable Positional Tolerance with Bonus:

• $\text{MMC Hole Size} = 0.500\text{ in}$
• $\text{Bonus Tolerance} = \text{Actual Hole Size} - \text{MMC} = 0.504 - 0.500 = 0.004\text{ in}$
• $\text{Total Allowable Tolerance} = \text{Stated Tolerance} + \text{Bonus} = 0.008 + 0.004 = 0.012\text{ in}$

Step 4: Quality Adjudication: $\text{Actual Deviation} (0.010\text{ in}) \le \text{Total Allowable Tolerance} (0.012\text{ in}) \longrightarrow \mathbf{CONFORMS / PASS}$

---

Concentricity & Symmetry vs. Position

Historically, ASME standards included Concentricity (◎) and Symmetry (⌯) to control coaxiality and balance on rotating equipment.

Concentricity (◎)

• Definition: Concentricity controls the derived median points of all diametrically opposed cross-sectional surface elements relative to a datum axis.
• Metrology Challenge: It does NOT evaluate the center of a circle or axis of a cylinder. It requires an inspector to take hundreds of paired differential surface points, compute their midpoints, and ensure every midpoint falls inside a cylindrical zone. It applies strictly at RFS.
• Status in Modern Standards: Concentricity is so difficult and costly to inspect that ASME Y14.5-2018 ELIMINATED Concentricity entirely! Modern drawings use Position (to control axis location) or Runout (to control surface coaxiality).

Symmetry (⌯)

• Definition: Controls the derived median points of opposing planar surfaces relative to a datum center plane. Also applies strictly at RFS.
• Status in Modern Standards: Like concentricity, ASME Y14.5-2018 ELIMINATED Symmetry. Symmetry is now controlled using Position with a boundary or RFS modifier.

---

Profile Tolerances: Profile of a Line vs. Profile of a Surface

Profile is the most comprehensive and mathematically robust geometric control in ASME Y14.5. It can simultaneously control size, form, orientation, and location of complex curved contours, castings, turbine blades, automotive body panels, or simple planar surfaces.

1. Profile of a Line (⌒)

• Dimensionality: A two-dimensional (2D) control evaluated element-by-element along individual cutting planes.
• Tolerance Zone: Bounded by two parallel profile lines separated by distance $t$. It controls cross-sectional slice contours independently.

2. Profile of a Surface (⌓)

• Dimensionality: A three-dimensional (3D) volumetric control extending across the entire surface area.
• Tolerance Zone: Bounded by two parallel 3D offset surfaces separated by distance $t$.

Profile Tolerance Zone Dispositions

Quality inspectors must verify how the profile tolerance zone is distributed relative to the true theoretical profile:

1. Bilateral Equal (Symmetric — Default): The tolerance zone is divided symmetrically on both sides of the true profile: $\pm t/2$. A profile tolerance of $0.020\text{ in}$ permits $+0.010\text{ in}$ of material addition and $-0.010\text{ in}$ of material removal.
2. Unilateral (All Outside or All Inside): The entire tolerance zone is positioned entirely on one side of the true profile:
   • All Outside: Permissible only to add material (no undercutting permitted).
   • All Inside: Permissible only to remove material (no outward stock allowed).
3. Unequally Disposed Profile (The Circled U Symbol — Ⓥ): Introduced in ASME Y14.5-2009 to replace confusing phantom lines, the circled U modifier defines asymmetrical tolerance zones:
   • Syntax: [Profile | .030 Ⓥ .010 | A | B | C]
   • Interpretation: The first number (.030) is the total width of the tolerance zone. The second number (.010) following circled U specifies how much of the tolerance adds material (disposed outward) from the true profile.
   • Remaining Tolerance: The remaining portion ($0.030 - 0.010 = 0.020\text{ in}$) extends inward, removing material.

Unequally Disposed Profile: [Profile | .030 Ⓥ .010 | A | B]
======================================= +0.010 in (Outer boundary - adds metal)
- - - - - - - - - - - - - - - - - - - -  0.000 in (True Theoretical Profile)
======================================= -0.020 in (Inner boundary - removes metal)
|<-------------- Total Zone = 0.030 in -------------->|

---

Runout Tolerances: Circular Runout vs. Total Runout

Runout is a composite rotational tolerance that controls surface variation relative to a datum axis as the workpiece rotates 360 degrees about that datum axis. Runout is measured exclusively in terms of Full Indicator Movement (FIM) (also called Total Indicator Reading, TIR).

1. Circular Runout (↗)

• Scope of Control: Evaluates individual circular elements of a surface independently.
• Metrology Procedure:
  1. The workpiece is mounted on bench centers or in a precision collet defining the datum axis.
  2. A dial test indicator is placed in contact with the surface at a fixed axial station perpendicular to the datum axis.
  3. The part is rotated 360 degrees about its datum axis. The indicator is HELD COMPLETELY STATIONARY along the length of the part.
  4. The maximum indicator swing (Peak minus Valley) is the circular runout FIM.
  5. The procedure is repeated at separate individual stations along the cylinder.
• What Circular Runout Controls: Simultaneously controls circularity (roundness) and coaxiality at each specific cross-section. It does NOT control axial straightness or taper across multiple stations.

2. Total Runout (⇗)

• Scope of Control: Evaluates the entire surface simultaneously across all cross-sections.
• Metrology Procedure:
  1. The workpiece is rotated 360 degrees about its datum axis on precision bench centers.
  2. Simultaneously, the dial test indicator is traversed continuously along the entire axial length of the rotating feature (forming a continuous helical scan).
  3. The Total Runout is the absolute difference between the single highest indicator peak and the single lowest valley across the entire traversed surface.
• What Total Runout Controls: Total runout simultaneously controls:
  1. Circularity (roundness)
  2. Coaxiality
  3. Straightness of surface elements
  4. Taper and barrel variations across the entire length
• Planar Shoulder Application: When applied to a flat shoulder face perpendicular to the rotation axis, Total Runout controls perpendicularity and flatness (axial wobble).

---

Real Shop Inspection Scenarios & Common Exam Traps

• Exam Trap: Forgetting to Double the Radial Offset in True Position Calculations: The most common mathematical trap on the ASQ CQI exam involves calculating radial offset $R = \sqrt{\Delta X^2 + \Delta Y^2}$ and selecting that answer. Remember: True Position is a diameter! The radial distance from true center to actual center is only half the tolerance zone. You must multiply by 2: $\text{True Position} = 2 \times R$.
• Exam Trap: Moving the Indicator Axially During Circular Runout Testing: If an inspector slides the dial indicator along the shaft while performing a Circular Runout check, the measurement is corrupted and invalid. Axial traverse is permitted strictly during Total Runout testing.
• Exam Trap: Misinterpreting the Circled U Modifier: A question states: [Profile | .020 Ⓥ .005 | A]. Candidates often assume $.005$ is the total tolerance, or that $.005$ is subtracted from nominal. Remember: $.020$ is the total tolerance band, and $.005$ is the portion extending outward (adding material), leaving $.015$ extending inward (removing material).