3.3 Screw Threads, Gears & Splines, Angular Surfaces, Tapers & Statistical Tolerancing

3.3 Screw Threads, Gears & Splines, Angular Surfaces, Tapers & Statistical Tolerancing

Quick Answer: ASME Y14.5-2009 paras. 2.9 through 2.17 hold the General Tolerancing topics that candidates most often skip. Para. 2.9: every tolerance of orientation or position and every datum reference specified for a screw thread applies to the axis of the thread derived from the pitch cylinder, unless an exception such as MAJOR DIA or MINOR DIA is stated beneath the feature control frame or beneath the datum feature symbol. Para. 2.10: for gears and splines, the specific feature (MAJOR DIA, PITCH DIA, or MINOR DIA) must always be stated — there is no default. Para. 2.12: a directly toleranced linear-plus-angular dimension produces a wedge-shaped zone between two nonparallel planes. Paras. 2.13 – 2.14: conical taper = (D − d)/L; flat slope = (H − h)/L. Para. 2.17: statistical tolerancing requires a specific drawing note and, where the ⟨ST⟩ symbol is used, the necessary statistical indices should be specified.

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Screw Threads (Para. 2.9): The Pitch-Cylinder Default

Each tolerance of orientation or position and datum reference specified for a screw thread applies to the axis of the thread derived from the pitch cylinder. Where an exception is necessary, the specific feature of the screw thread — such as MAJOR DIA or MINOR DIA — shall be stated beneath the feature control frame, or beneath or adjacent to the datum feature symbol, as applicable.

Three consequences the exam tests:

1. There is a default for threads. Say nothing, and the control applies to the pitch cylinder axis. This is the only one of the three thread-related diameters that is not a physical surface, which is why threaded-hole inspection normally uses a thread gage with a functional plug rather than a plain pin.
2. The exception must be written in a specific place. A note reading MINOR DIA floating anywhere on the drawing is not the specified method; it goes beneath the feature control frame (for the controlled feature) or beneath or adjacent to the datum feature symbol (for a thread used as a datum feature).
3. Datum references follow the same rule. If datum feature B is a tapped hole, datum axis B is derived from the pitch cylinder unless MAJOR DIA or MINOR DIA is stated adjacent to the datum feature symbol.

Gears and Splines (Para. 2.10): No Default At All

For features other than screw threads — gears and splines — each tolerance of orientation or position and datum reference shall designate the specific feature at which it applies, such as MAJOR DIA, PITCH DIA, or MINOR DIA. The information is stated beneath the feature control frame or beneath the datum feature symbol.

The classic two-option trap: a stem shows a position tolerance on a splined bore with no note. The tempting answer is "pitch diameter, by analogy with threads." The correct answer is that para. 2.10 provides no default, so the specification is incomplete.

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Angular Surfaces (Para. 2.12): The Wedge Zone

Where an angular surface is defined by a combination of a directly toleranced linear and an angular dimension, the surface must lie within a tolerance zone represented by two nonparallel planes. The zone widens as the distance from the apex of the angle increases. Where a tolerance zone with parallel boundaries is desired, angularity or profile tolerance may be used.

      DIRECTLY TOLERANCED ANGLE (2.12)        BASIC ANGLE + ANGULARITY (Section 6)
            ╱ ── zone widens ──►                    ╱╱ ── uniform width ──►
      apex ●────────────────────              ────╱╱────────────────────
            ╲ ── zone widens ──►                    ╲╲ ── uniform width ──►
      Two NONPARALLEL planes                   Two PARALLEL planes
      Width depends on distance                Width is 't' everywhere

The practical read: the wedge is not a drafting flaw so much as an ambiguity engine. At the apex the requirement is unreasonably tight; at the far end it is unreasonably loose. Boxing the angle and adding angularity converts the same intent into a constant-width zone.

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Conical and Flat Tapers (Paras. 2.13 – 2.14)

Conical taper is the ratio of the difference in diameters of two sections of a cone to the distance between them:

$\text{taper} = \frac{D - d}{L}$

Para. 2.13 lists four acceptable ways to specify a conical taper:

• (a) a basic taper and a basic diameter;
• (b) a size tolerance combined with a profile of a surface tolerance applied to the taper (see para. 8.4.2);
• (c) a toleranced diameter at both ends of the taper and a toleranced length — the standard notes this method is applicable to noncritical tapers, such as the transition between shaft diameters;
• (d) a composite profile tolerance.

Standard machine tapers — the American Standard Self-Holding and Steep Taper series covered by ASME B5.10 — are usually dimensioned by specifying the taper name and number, with the gage-line diameter and length optionally added and the taper in inches per foot shown as reference.

Flat taper (para. 2.14) is specified by a toleranced slope and a toleranced height at one end, where slope is the inclination of a surface expressed as a ratio of the difference in heights at each end to the distance between them:

$\text{slope} = \frac{H - h}{L}$

Worked Example

A shank tapers from ⌀40.00 at one end to ⌀31.00 over a 180 mm length. The conical taper is $(40.00 - 31.00)/180 = 9/180 = 0.05$, commonly written 1:20. If the designer needs the surface form controlled as well as the taper, method (b) — a size tolerance plus a profile of a surface tolerance — is the correct specification, because a toleranced-diameter-at-each-end callout (method (c)) leaves the intermediate surface form uncontrolled.

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Statistical Tolerancing (Para. 2.17)

Statistical tolerancing is the assigning of tolerances to related components of an assembly on the basis of sound statistics — for example, where the assembly tolerance is the square root of the sum of the squares of the individual tolerances:

$T_{\text{asm}} = \sqrt{T_1^2 + T_2^2 + \cdots + T_n^2}$

• 2.17.1 Application to assemblies: tolerances assigned by arithmetic stacking simply divide the assembly tolerance among the components. Where arithmetic stacking is restrictive, statistical tolerancing may be used to enlarge the component tolerances.
• 2.17.2 Identification: a note such as "FEATURES IDENTIFIED AS STATISTICALLY TOLERANCED SHALL BE PRODUCED WITH STATISTICAL PROCESS CONTROLS" shall be placed on the drawing. Alternatively, the dimension may carry both the statistical tolerance and the more restrictive arithmetic limits, with a note permitting production to either. The standard adds a CAUTION: where the statistical tolerancing symbol is used, the necessary statistical indices should be specified.

The point of the note requirement: a statistical tolerance is a contract about process capability, not merely a wider number. Without an SPC obligation on the drawing, a supplier could deliver parts distributed anywhere inside the enlarged limits, and the statistical assumption behind the root-sum-square collapses.

Arithmetic vs. Statistical Stack — Same Four Parts