3D Tolerance Analysis with GD&T

Overview

TDT's 3D tolerance analysis lets you work with familiar GD&T symbols from your drawings. Enter your position, perpendicularity, runout, and other callouts, and TDT automatically converts them to a 6-DOF analysis.

What You Get

• Automatic DOF mapping - GD&T symbols map to the correct degrees of freedom based on geometry
• Material condition bonuses - MMC/LMC bonus calculations are automatic
• Datum reference frames - ASME Y14.5 3-2-1 rule is applied automatically
• Validation - TDT warns if your GD&T changes but torsor bounds are stale

GD&T Symbol Reference

TDT supports these GD&T symbols. The table shows which degrees of freedom each symbol affects based on your geometry type.

Position and Location

Orientation

Form

Runout

Profile

Material Condition Modifiers

Quick Start Workflow

Here's the typical workflow for 3D tolerance analysis with GD&T:

tdt feat new --title "Bore" --component CMP@1 --feature-type internal --no-edit

Then edit the feature file to add GD&T:

title: Bore
feature_type: internal
geometry_class: cylinder
geometry_3d:
  origin: [0.0, 0.0, 0.0]
  axis: [0.0, 0.0, 1.0]
  length: 25.0

dimensions:
  - name: diameter
    nominal: 20.0
    plus_tol: 0.021
    minus_tol: 0.0

# GD&T from drawing
gdt:
  - symbol: position
    value: 0.25
    datum_refs: [A, B]
    material_condition: mmc
  - symbol: perpendicularity
    value: 0.05
    datum_refs: [A]

# Preview the computed bounds
tdt feat compute-bounds FEAT@1

# Compute and save to feature file
tdt feat compute-bounds FEAT@1 --update

# Include MMC bonus (if you know actual size)
tdt feat compute-bounds FEAT@1 --actual-size 20.015 --update

# Create stackup
tdt tol new --title "Shaft-Bore Fit" --target-name "Clearance" \
  --target-nominal 0.02 --target-upper 0.05 --target-lower 0.005 --no-edit

# Add contributors
tdt tol add TOL@1 +FEAT@1 ~FEAT@2

# Run 3D analysis
tdt tol analyze TOL@1 --3d

# Check for stale bounds
tdt validate

# Auto-fix stale bounds
tdt validate --fix

Feature Setup

Features need geometry information for 3D analysis. This tells TDT what type of geometry and where it is in your assembly.

Required Fields

Geometry Examples

Cylinder (Bore or Shaft)

geometry_class: cylinder
geometry_3d:
  origin: [0.0, 0.0, 0.0]    # Center at one end
  axis: [0.0, 0.0, 1.0]      # Along Z axis
  length: 25.0               # Depth of bore

Plane (Face or Datum Surface)

geometry_class: plane
geometry_3d:
  origin: [0.0, 0.0, 0.0]    # Point on surface
  axis: [0.0, 0.0, 1.0]      # Surface normal

Sphere (Ball or Locating Feature)

geometry_class: sphere
geometry_3d:
  origin: [50.0, 25.0, 10.0] # Center point
  axis: [0.0, 0.0, 1.0]      # Reference direction

Coordinate System

Use a consistent coordinate system for all features. A common convention:

Datums

Add datum_label to features that serve as datums:

title: Mounting Face
geometry_class: plane
# ... geometry ...

# This feature is datum A
datum_label: A

TDT applies the ASME Y14.5 3-2-1 rule automatically:

• Primary datum (A) - Constrains 3 DOF
• Secondary datum (B) - Constrains 2 additional DOF
• Tertiary datum (C) - Constrains final 1 DOF

When you specify datum_refs: [A, B] in your GD&T, TDT only applies tolerances to DOFs not already constrained by those datums.

Running Analysis

tdt tol analyze TOL@1 --3d

Example Output

How Bounds Are Used

The 3D analysis uses torsor bounds to determine geometric deviation for each contributor:

• GD&T torsor_bounds - If a feature has torsor_bounds (computed from GD&T via compute-bounds), these are used directly
• Derived bounds - If no torsor_bounds exist, bounds are derived from the contributor's dimensional tolerance

The analysis output shows which source was used:

Analysis Options

Understanding Results

• WC [min, max] - Worst-case deviation range
• RSS ±3σ - Statistical 3-sigma spread
• Cp/Cpk - Process capability indices
• Zero DOFs - Fully constrained by geometry or datums

Theory Deep Dive

This section explains the underlying math for those who want to understand how TDT works internally.

Small Displacement Torsor (SDT)

A torsor represents the small deviation of a feature from its nominal position using 6 parameters:

Geometry Class DOF Constraints

Different geometry types constrain different degrees of freedom:

Jacobian Propagation

TDT uses Jacobian matrices to propagate deviations through the tolerance chain. For each contributor, the deviation at position P is:

GD&T to Torsor Mapping

The compute-bounds command applies these rules:

1. Parse GD&T controls from feature
2. For each control, determine affected DOFs based on geometry class
3. Compute bounds: translation tolerances → ±(tol/2), angular tolerances → ±(tol/length)
4. Apply material condition bonus if actual size provided
5. Merge multiple controls (tightest bound wins for same DOF)

Reference

CLI Commands

GD&T Field Format

gdt:
  - symbol: position           # GD&T symbol name
    value: 0.25                # Tolerance value
    datum_refs: [A, B, C]      # Datum references (optional)
    material_condition: mmc    # mmc, lmc, or rfs (default)

Supported Symbols

position, concentricity, symmetry, perpendicularity, parallelism, angularity, flatness, cylindricity, circularity, straightness, circular_runout, total_runout, profile_line, profile_surface

Further Reading

• Feature Entity Reference
• Stackup Entity Reference
• Tolerance Analysis Overview