| 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:
- Identify loop of dimensions forming the gap
- Assign tolerance to each dimension (+/-)
- Calculate: worst-case or RSS
- 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.
