gdt-tolerancing

name	gdt-tolerancing
description	GD&T and tolerancing — ASME Y14.5, fits and limits (ANSI/ISO), flatness/roundness/cylindricity/straightness, position/runout/concentricity, datum reference frames, MMC/LMC, tolerance stack-up analysis.
metadata	{"priority":7,"promptSignals":{"phrases":["GDT","GD&T","tolerance","fits","clearance fit","interference fit","datum","position tolerance","runout","stack-up"],"minScore":4}}

GD&T & Tolerancing — Complete Skill (ASME Y14.5-2018)

Limit Fits (ANSI B4.1 / ISO 286)

Terminology:

• Basic size: nominal dimension
• Deviation: algebraic difference from basic size (ES=upper dev shaft, EI=lower dev hole)
• Tolerance: algebraic difference between max and min limits (IT = fundamental tolerance)

ANSI Standard Fits:

Class	Symbol	Description
Running/sliding	RC1-RC9	Clearance, precision to heavy
Locational clearance	LC1-LC11	Accurate location, some play
Locational transition	LT1-LT6	Clearance OR interference
Locational interference	LN1-LN3	Rigid location, no clearance
Force/shrink	FN1-FN5	Heavy interference

ISO System (Hole-basis, preferred): Hole: 50H7 = 50mm, H (fundamental deviation=0), IT7 Shaft: 50g6 = 50mm, g deviation, IT6

IT grades (tolerance values): IT6: precision machine components IT7: normal precision (H7/h6, H7/f7) IT8: medium service IT9-IT11: general manufacturing

Fundamental Tolerances Quick Reference (mm, 50mm basic size)

IT6: 0.016mm (16μm) IT7: 0.025mm (25μm) IT8: 0.039mm (39μm) IT9: 0.062mm (62μm)

Common fit combinations: H7/h6 → sliding fit (clearance 0-0.041mm) H7/f7 → free running (clearance 0.025-0.066mm) H7/k6 → transition fit (pushfit, -0.002 to +0.023mm) H7/n6 → light press fit (interference 0.004-0.029mm) H7/p6 → press fit (interference 0.015-0.040mm) H7/s6 → shrink/force fit (interference 0.027-0.052mm)

GD&T Symbols (ASME Y14.5)

Form controls (no datum needed): ⏤ Flatness: all points within two parallel planes ○ Roundness (circularity): all points on circle within two coaxial circles ⌭ Cylindricity: all points within two coaxial cylinders ⌇ Straightness: all points on line within tolerance zone

Orientation controls (datum required): ⊥ Perpendicularity ∠ Angularity ∥ Parallelism

Location controls: ⊕ Position: center of feature within cylindrical/zone tolerance ◎ Concentricity (deprecated in 2018): coaxial medial points ⊚ Symmetry (deprecated in 2018)

Runout controls: ↗ Circular runout: single cross-section, one revolution ↗↗ Total runout: all cross-sections, one revolution

Profile controls: ⌒ Profile of a line ⌓ Profile of a surface

Feature Control Frame

[Symbol | Tolerance | Datum A | Datum B | Datum C] Example: [⊕ | ⌀0.5 M | A | B | C]

MMC, LMC, RFS

MMC (Maximum Material Condition): ⓜ — most material (smallest hole, largest shaft) LMC (Least Material Condition): ⓛ — least material (largest hole, smallest shaft) RFS (Regardless of Feature Size): default when no modifier shown

Bonus tolerance at MMC: Actual tolerance = stated tolerance + (actual size - MMC size) If hole 10H7 (+0.025/0): MMC = 10.000 If pin ⊕⌀0.2 M: at MMC (10.000) = 0.2; at LMC (10.025) = 0.2+0.025 = 0.225

Datum Reference Frame (DRF)

6 degrees of freedom: 3 translation + 3 rotation Primary datum (3 points): constrains 3 DOF Secondary datum (2 points): constrains 2 more DOF Tertiary datum (1 point): constrains last DOF

Datum feature simulator: perfect form at MMC (e.g., perfect plane, perfect cylinder)

Tolerance Stack-Up Analysis

Worst-case (arithmetic): Gap_min = Nominal_gap - Σ|tolerances| Gap_max = Nominal_gap + Σ|tolerances| Use when: safety-critical, small numbers of parts

Statistical (RSS — Root Sum Square): σ_total = √(σ₁² + σ₂² + ... + σₙ²) Gap_min = Nominal - k·σ_total (k=3 for 99.73%) Use when: large assemblies, statistical process control

Steps:

1. Identify loop of dimensions forming the gap
2. Assign tolerance to each dimension (+/-)
3. Calculate: worst-case or RSS
4. Verify gap_min > 0 (no interference) and gap_max < allowable

Press Fit Stress Analysis (Interference)

Interference δ = (R_i,shaft - R_o,hole) [must be positive for press fit] Contact pressure: p = δ·E/(2r·(... thick wall formula ...)) For two steel cylinders of same material (E, ν): p = δ·E/(2r·((r_o²+r²)/(r_o²-r²) + (r²+r_i²)/(r²-r_i²))) Hub outer hoop stress: σ_θ,hub,outer = p·(r²+r_o²)/(r_o²-r²) Torque capacity: T = μ·p·2πr²L (μ ≈ 0.12-0.15 dry steel)

Surface Finish (Ra, Rz)

Ra = arithmetic average roughness (CLA) Rz = 10-point average (peak-to-valley) Rz ≈ 4·Ra (approximately)

Process	Ra (μm)
Grinding	0.1-0.8
Turning (fine)	0.4-1.6
Milling (fine)	0.8-3.2
Drilling	1.6-6.3
Casting	6.3-25
Hot rolling	12.5-50

Output

Provide: specified dimensions with limits, GD&T callout if needed, fit type and clearance/interference range, tolerance stack-up result.