9.3 Coaxial Holes, Counterbored Holes, Non-Parallel Axes, Spherical Features & Bidirectional Position

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

9.3 Coaxial Holes, Counterbored Holes, Non-Parallel Axes, Spherical Features & Bidirectional Position

Key Takeaways Explain This Topic AI

Where positional tolerances locate holes and counterbores relative to common datum features, two feature control frames are used, one under the hole note and one under the counterbore note, and the two may reference the same or different datum features.

Bidirectional positional tolerancing under para. 7.4.4 produces a noncylindrical tolerance zone, so the diameter symbol is omitted, and the standard notes that a further refinement of perpendicularity within the positional tolerance may be required.

The polar coordinate method of para. 7.4.4.2 applies one dimension line radially and the other perpendicular to the line of centers, with the tolerance values representing distances between two concentric arc boundaries in the radial direction.

Spherical features are located with the spherical diameter symbol per para. 7.4.6, producing a spherical tolerance zone about the center point rather than a cylindrical zone about an axis.

Para. 7.4.7 permits positional tolerancing of hole patterns whose axes are neither parallel to each other nor normal to the surface, with each cylindrical zone oriented along its own basic axis rather than along the surface normal.

Last updated: September 2026

9.3 Coaxial Holes, Counterbored Holes, Non-Parallel Axes, Spherical Features & Bidirectional Position

Quick Answer: Para. 7.4 collects the position applications that do not fit the simple round-hole-in-a-plate model. Counterbored holes : two feature control frames are used — one beneath the note specifying the hole requirements and one beneath the note specifying the counterbore — and the counterbore may reference the same datum features as the hole or different ones. Bidirectional positional tolerancing (7.4.4) applies where a greater tolerance is wanted in one direction than another ; it produces a noncylindrical zone, so the diameter symbol is omitted , and it has a rectangular coordinate method (7.4.4.1) and a polar coordinate method (7.4.4.2) . Spherical features (7.4.6) use the spherical diameter symbol S⌀ . Non-parallel axis hole patterns (7.4.7) may be positionally toleranced even where the axes are neither parallel to one another nor normal to the surface. Repetitive patterns related to a repeated datum reference frame (7.4.8) are handled with notes stating the number of places.

Counterbored and Counterdrilled Holes

A counterbore is a separate feature of size from the hole it surrounds, and the standard treats it that way. Where positional tolerances are used to locate holes and counterbores relative to common datum features, two feature control frames are used: one placed under the note specifying the hole requirements and the other under the note specifying the counterbore requirements.

Design Intent Datum References Result

Counterbore must line up with the same mating pattern as the hole Both frames reference the same datums, typically with a tighter value on the hole Fastener head clearance and shank clearance both controlled to the same frame

Counterbore must line up with the hole itself , not with the part datums The counterbore frame references the hole as a datum feature Coaxiality of counterbore to hole guaranteed regardless of where the pair lands

Hole and counterbore serve different mating parts The two frames reference different datum features Each feature is located to whatever it actually mates with

Recall from para. 1.8.11 that where the thickness of remaining material has significance, that thickness rather than the counterbore depth is dimensioned , and that the relationship of the counterbore and the hole shall be specified — the second feature control frame is how that relationship gets specified.

Bidirectional Positional Tolerancing (Para. 7.4.4)

Where it is desired to specify a greater tolerance in one direction than another , bidirectional positional tolerancing may be applied. Bidirectional positional tolerancing results in a noncylindrical tolerance zone for locating round holes; therefore, the diameter symbol is omitted from the feature control frame in these applications.

The standard adds a NOTE that is easy to miss and frequently tested: a further refinement of perpendicularity within the positional tolerance may be required — because a two-parallel-plane zone in each direction does not automatically constrain the hole's tilt the way a cylindrical zone does.

7.4.4.1 Rectangular Coordinate Method

Two feature control frames, each without a diameter symbol, each associated with the dimension line in its own direction: ⌀8.0 ± 0.1

┌───┬─────┬───┬───┬───┐ applies in the X direction
│ ⌖ │ 0.4 │ A │ B │ C │ zone: two parallel planes 0.4 apart
└───┴─────┴───┴───┴───┘
┌───┬─────┬───┬───┬───┐ applies in the Y direction
│ ⌖ │ 0.2 │ A │ B │ C │ zone: two parallel planes 0.2 apart
└───┴─────┴───┴───┴───┘
Combined: a 0.4 × 0.2 rectangular zone at true position
7.4.4.2 Polar Coordinate Method

Bidirectional positional tolerancing may also be applied to features located by polar coordinate dimensions relative to specified datums. Where a different tolerance is desired in each direction, one dimension line is applied in a radial direction and the other perpendicular to the line of centers . The positional tolerance values then represent distances between two concentric arc boundaries (for the radial separation) and between two parallel planes (for the tangential separation).

This is the correct control for a bolt circle where radial position matters more than angular position , or vice versa — a common requirement on rotating machinery flanges.

Spherical Features (Para. 7.4.6)

A positional tolerance may be used to control the location of a spherical feature relative to other features of a part. The symbol for spherical diameter precedes the tolerance value to specify a spherical tolerance zone .

⌖ | S⌀0.3 | A | B | C locates the center point of the ball within a sphere 0.3 in diameter. Note the symbol discipline required by para. 3.6: ⌀ gives a cylinder, S⌀ gives a sphere, and no symbol at all gives two parallel planes. A spherical feature of size also establishes a datum point rather than an axis when used as a datum feature.

Non-Parallel Axis Hole Patterns (Para. 7.4.7)

Positional tolerancing may be applied to a pattern of holes where axes are not parallel to each other and where axes are not normal to the surface.

Radial holes around a hub, angled coolant passages in a manifold, and compound-angle mounting holes all fall here. The mechanics do not change — basic dimensions locate each true position and each true orientation, and a cylindrical zone is established about each true position along its own basic axis direction , not along the surface normal.

The trap to watch: candidates assume the zone must be perpendicular to the entry face. It is not. The zone follows the basic axis of the hole , which is why the drawing must supply a basic angle for each non-normal hole.

Repetitive Patterns and Repeated Datum Reference Frames (Para. 7.4.8)

Where positional tolerances locate patterns of features of size relative to repetitive datums , a note is placed beneath or adjacent to the datum feature symbol and another beneath or adjacent to the feature control frame , indicating the number of places each applies on an individual basis . To associate a note with one line of a multiple-segment feature control frame , the note shall be placed adjacent to the applicable segment . Where the individual requirements are shown on a main view or in a CAD model without a detail view, the indication of the number of occurrences shall be shown .

This is how one detail view can define a boss that repeats eight times around a housing, each instance carrying its own local datum reference frame rather than being located to a single global frame.

Application Para. Key Specification Rule
Holes and counterbores 7.4 (Figs. 7-25, 7-26) Two feature control frames; datums may match or differ
Closer control at one end 7.4.3 Different values at the extremities ⇒ conical zone
Bidirectional, rectangular 7.4.4.1 No diameter symbol ; a frame per direction
Bidirectional, polar 7.4.4.2 Radial and tangential values; concentric arc boundaries
Noncircular FOS 7.4.5 Locates the center plane ; boundary concept for irregular shapes
Spherical features 7.4.6 S⌀ ⇒ spherical zone about a center point
Non-parallel axes 7.4.7 Zones follow the basic axis , not the surface normal
Repeated datum frames 7.4.8 Notes state the number of places , adjacent to the applicable segment