Fastener Position Tolerance Calc

Fastener Position Tolerance Calculation (cross-cutting/tolerancing/fastener-position-tolerance-calc)

Use when the task is the design-side sizing of positional tolerances and clearance holes for bolted and screwed joints with the ASME Y14.5 fixed and floating fastener formulas: total positional tolerance budget from the clearance hole MMC diameter and the fastener maximum diameter, the budget split between two mating members, the projected tolerance zone variant for the threaded or stud side, and the inverse sizing of the minimum clearance hole MMC diameter. The leaf implements the Y14.5 fastener design method in pure Python, stdlib only. It pairs with cross-cutting/tolerancing/position-tolerance-calc for the verification side (checking a drawn callout from measured coordinates) and cross-cutting/tolerancing/gdandt-basics for frame interpretation context.

Domain quick reference

• Total positional tolerance budget: T_total = H - F, where H is the clearance hole MMC diameter and F is the fastener maximum diameter at MMC. The hole is smallest and the fastener is largest at MMC, so the difference is the worst-case clearance available to absorb both member tolerances.
• Floating fastener case: both members carry clearance holes, so each member takes a share of the budget as its own positional tolerance, H = F + T1 + T2, with T1 the clearance member tolerance and T2 the other member tolerance. The total budget is independent of the split.
• Fixed fastener case: one member is threaded or carries a stud, so the same budget H - F applies and the other member share acts through a projected tolerance zone whose height defaults to the full mating part thickness (projected_zone_height), keeping the engaged threads inside the zone.
• Minimum clearance hole MMC: invert the formula, H_min = F + T1 + T2, to size the hole for a given fastener and member tolerance split.
• Equal split is the default: split_tolerance divides the total with T1 = total * first_share and T2 = total - T1, so the pair sums back to the total; any first_share strictly between 0 and 1 is allowed.
• All diameters and tolerances are millimeters, reported at 0.01 mm.
• ASME Y14.5 is referenced, not reproduced; the relations above are the standard engineering method, summary only.

Workflow

1. Record the joint inputs: the case (floating fastener for two clearance members, fixed fastener for a clearance member against a threaded or stud member), the fastener maximum diameter F at MMC, and the clearance hole MMC diameter H where one is already set.
2. Budget traverse: compute the total positional tolerance budget with floating_fastener_total_tolerance (floating case) or fixed_fastener_total_tolerance (fixed case): the clearance H minus F available to the two member tolerances.
3. Split traverse: divide the total budget between the two mating members with split_tolerance, default equal shares (0.20 and 0.20 in the worked example) or any first_share between 0 and 1 for an unequal allocation.
4. Projected zone traverse: in the fixed case, assign the threaded member share to a projected tolerance zone with projected_zone_height, whose default height is the full mating part thickness; the multiplier variant gives a shorter zone where the drawing calls one out.
5. Minimum hole traverse: when the hole must be sized instead of checked, invert the formula with minimum_clearance_hole_mmc: F plus the two member tolerances gives the minimum clearance hole MMC diameter.
6. Report bookkeeping: assemble the sizing record with fastener_report: case, total tolerance, clearance member tolerance, other member tolerance, hole diameter, minimum hole when solving, and the projected zone height for the fixed case.
7. Confirm the callout values with the deterministic contract test scripts/test_fastener_position_tolerance_calc.py.

Worked example

Fastener F = 6.35 mm with a clearance hole MMC H = 6.75 mm.

• Floating case, total positional tolerance budget: floating_fastener_total_tolerance(6.75, 6.35) = 0.40 mm.
• Equal split: split_tolerance(0.40) = (0.20, 0.20), and the pair sums back to 0.40 mm; an unequal split such as split_tolerance(0.40, 0.75) = (0.30, 0.10) keeps the same 0.40 mm total.
• Fixed case, same F and H: fixed_fastener_total_tolerance(6.75, 6.35) = 0.40 mm, the same budget as the floating case; with the hole tolerance 0.25 mm and the stud side tolerance 0.15 mm, the minimum hole is minimum_clearance_hole_mmc(6.35, 0.25, 0.15) = 6.75 mm.
• Projected zone: projected_zone_height(12.0) = 12.0 mm for the full 12 mm mating part thickness, and projected_zone_height(12.0, 0.75) = 9.0 mm for a 0.75 multiplier zone.
• Full record for the fixed joint on a 12 mm stack: fastener_report("fixed", fastener_max=6.35, tol_clearance_member=0.25, tol_other_member=0.15, mating_thickness=12.0) returns the case, total tolerance 0.40 mm, clearance member tolerance 0.25 mm, other member tolerance 0.15 mm, hole MMC 6.75 mm, minimum hole 6.75 mm and projected zone height 12.0 mm.

Verification

• Confirm floating_fastener_total_tolerance(6.75, 6.35) returns 0.40 mm and fixed_fastener_total_tolerance(6.75, 6.35) returns the same budget.
• Confirm split_tolerance(0.40) returns (0.20, 0.20) and that the pair sums back to the total within 0.01 mm.
• Confirm the split independence identity: split_tolerance(0.40, 0.75) and split_tolerance(0.40, 0.25) give (0.30, 0.10) and (0.10, 0.30), both summing to the same 0.40 mm total.
• Confirm minimum_clearance_hole_mmc inverts the budget: minimum_clearance_hole_mmc(6.35, 0.20, 0.20) = 6.75 mm, and feeding that hole back to floating_fastener_total_tolerance recovers 0.40 mm; a larger fastener at a fixed hole leaves a smaller budget.
• Confirm projected_zone_height(12.0) = 12.0 mm and the multiplier variant projected_zone_height(12.0, 0.75) = 9.0 mm.
• Confirm the fastener_report key contract: base keys in every record, minimum_hole_mmc only when solving, projected_zone_height only for the fixed case with a mating thickness, matching the documented key sets.
• Confirm every non-physical input raises ValueError: hole MMC not larger than the fastener maximum, zero or negative fastener, zero or negative total tolerance, first share 0 or 1, negative member tolerance, and zero mating thickness.
• Run the contract test offline: python3 scripts/test_fastener_position_tolerance_calc.py.

Related leaves

• cross-cutting/tolerancing/position-tolerance-calc: the verification side, checking a drawn positional callout from measured coordinates instead of sizing the hole pattern.
• cross-cutting/tolerancing/gdandt-basics: frame interpretation and modifier context for the callouts this leaf sizes.
• cross-cutting/tolerancing/tolerance-stackup: assembly-level fit assessment that consumes the sized hole and tolerance values.

Pitfalls

• Sizing on nominal instead of MMC diameters: the budget H - F uses the clearance hole at MMC (smallest hole) and the fastener at MMC (largest fastener), the worst-case clearance, so nominal-minus-nominal understates the required hole or overstates the budget.
• Splitting the budget without the sum property: report T2 = total - T1 at two decimals so the pair always sums back to the total instead of rounding each share independently and losing 0.01 mm.
• Dropping the projected zone in the fixed case: the threaded or stud member share must act through a projected tolerance zone whose height is the full mating part thickness by default, or the engaged thread length is not controlled.
• Sizing the hole from one member tolerance alone: H_min = F + T1 + T2 needs both shares, so a joint that only assigns the clearance member tolerance leaves the other member uncontrolled.
• Using this leaf to verify a drawn callout from measured coordinates: that is the position-tolerance-calc role; this leaf sizes the callout before the drawing exists.
• Feeding a hole equal to the fastener maximum diameter: H must exceed F for any clearance, and the module raises ValueError rather than returning a zero budget.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_fastener_position_tolerance_calc.py

The test covers the worked-example sizing contract (total budget 0.40 mm within bounds, equal split 0.20 and 0.20, fixed budget equal to the floating budget at the same diameters, minimum hole 6.75 mm, projected zone 12.0 mm), the split independence identity, the inverse round trip between minimum_clearance_hole_mmc and floating_fastener_total_tolerance, larger-fastener budget scaling, the documented fastener_report key sets, determinism across repeated calls, and ValueError rejection of every non-physical input listed in Verification.

Compliance

• Standards referenced, not reproduced: ASME Y14.5 is proprietary; the fixed and floating fastener relations above are standard engineering methodology, name and paraphrase only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.