Position Tolerancing Calculations Flashcards

A hole has a position tolerance of ⌀0.4 at MMC. The actual hole diameter is 10.3 mm and MMC is 10.0 mm. What is the total allowable position tolerance?

Answer: ⌀0.7

At MMC the tolerance is ⌀0.4; the hole is 0.3 mm larger than MMC, so bonus tolerance adds 0.3, giving ⌀0.7 total.

For a pattern of four holes, the True Position is defined by basic dimensions from datum A (primary), B (secondary), and C (tertiary). Which datum controls orientation of the pattern?

Answer: Datum A

The primary datum (A) controls orientation — it establishes the first degree of constraint, typically perpendicularity or parallelism.

A shaft pin has a position tolerance of ⌀0.5 at LMC. The actual pin diameter is 12.0 mm and LMC is 12.3 mm. What bonus tolerance is available?

Answer: ⌀0.3

At LMC, bonus tolerance equals the amount the actual size departs from LMC: 12.3 − 12.0 = 0.3 mm added to the stated ⌀0.5.

The formula for converting a Cartesian position deviation (Δx, Δy) to a diametral position error is:

Answer: 2√(Δx² + Δy²)

The diametral true-position error = 2 × √(Δx² + Δy²), because the cylindrical tolerance zone is centered on true position.

A hole center is measured at X = 25.08 mm and Y = 15.06 mm. Basic dimensions are X = 25.00 and Y = 15.00. What is the diametral position error?

Answer: ⌀0.10

Δx = 0.08, Δy = 0.06; radial error = √(0.08² + 0.06²) = √(0.01) = 0.10; diametral = 2 × 0.05 = ⌀0.10.

When RFS (Regardless of Feature Size) is applied to a position tolerance, bonus tolerance is:

Answer: Not applicable — no bonus is allowed

RFS means the geometric tolerance applies at every actual feature size with no bonus; the tolerance value is fixed.

A composite position callout has an upper segment of ⌀0.8 and a lower segment of ⌀0.2. What does the lower segment control?

Answer: Feature-to-feature spacing within the pattern

The lower (FRTZF) segment of a composite callout controls feature-to-feature relationship (spacing/orientation) within the pattern, not its location from external datums.

A hole is located at basic X = 40.00, Y = 30.00. The CMM measures the hole axis at X = 40.05, Y = 29.96. What is the diametral position error?

Answer: ⌀0.128

Δx = 0.05, Δy = 0.04; radial = √(0.0025 + 0.0016) = √0.0041 ≈ 0.064; diametral = 2 × 0.064 ≈ ⌀0.128.

What does the term 'virtual condition' mean for an internal feature (hole) controlled with position at MMC?

Answer: MMC size minus the position tolerance

For an internal feature, virtual condition = MMC size − position tolerance, representing the worst-case boundary for assembly.

A pin (external feature) has MMC = 12.0 mm and a position tolerance of ⌀0.3. What is its virtual condition?

Answer: 12.3 mm

For an external feature, virtual condition = MMC + position tolerance = 12.0 + 0.3 = 12.3 mm.

Projected tolerance zone is specified because:

Answer: It controls the zone where a fastener extends outside the part, preventing interference at assembly

A projected tolerance zone extends the positional control above the hole to where mating fasteners or studs will reside, preventing angular stack-up issues.

If a position callout reads ⌀0.25 (M) with a projected tolerance of 15 mm, what does '15' represent?

Answer: The minimum projection height above the part surface

The projected tolerance zone height (15 mm) specifies how far the cylindrical zone extends beyond the part surface to capture fastener axis deviation.

A zero tolerance at MMC callout (⌀0.000 (M)) means:

Answer: The entire size tolerance becomes available as bonus position tolerance when at actual size

With ⌀0.000 at MMC, there is no fixed tolerance; all allowable variation comes exclusively from bonus tolerance as the feature departs from MMC.

Which statement correctly describes the 'inner boundary' of a hole controlled with position at MMC?

Answer: MMC size minus position tolerance

The inner boundary (worst-case minimum size) = MMC − position tolerance, which equals the virtual condition for an internal feature.

In a 3D tolerance stack, three features contribute ±0.10, ±0.15, and ±0.20 positional deviations along the same axis. What is the worst-case total deviation?

Answer: ±0.45

Worst-case (arithmetic) stack = 0.10 + 0.15 + 0.20 = ±0.45 mm along that axis.

Using RSS (Root Sum of Squares) for the same three deviations (±0.10, ±0.15, ±0.20), the statistical tolerance is approximately:

Answer: ±0.27

RSS = √(0.10² + 0.15² + 0.20²) = √(0.01 + 0.0225 + 0.04) = √0.0725 ≈ ±0.27 mm.

A pattern of 6 holes must assemble with 6 clearance fasteners. MMC of holes = 10.0 mm, fastener MMC = 9.6 mm. Using the fixed fastener formula, the position tolerance is:

Answer: ⌀0.4

Fixed fastener tolerance = (MMC_hole − MMC_fastener) / 1 = 10.0 − 9.6 = 0.4; split between two mating parts gives ⌀0.2 each, but for a single part: ⌀0.4.

For a floating fastener assembly, the position tolerance formula is:

Answer: T = (H − F) / 2

Floating fastener formula: each part gets T = (H_MMC − F_MMC) / 2, splitting the clearance equally between both mating parts.

A true position callout without any modifier defaults to which condition under ASME Y14.5-2018?

Answer: RFS

Under ASME Y14.5-2018, RFS is the default implied condition when no modifier symbol (M or L) is shown.

A position tolerance is given as ⌀0.5 with datum B at MMC. If datum feature B (a pin) measures 14.8 mm and its MMC is 15.0 mm, what is the datum shift available?

Answer: 0.2 mm

Datum shift = MMC_datum − actual_datum = 15.0 − 14.8 = 0.2 mm, which may be used to relax the positional requirement.