Tolerance Analysis - TDT Tessera Design Toolkit

Tolerance Workflow

TDT models tolerances using three entity types. Features define dimensions on components. Both Mates and Stackups use features for different analyses: Mates calculate fit between two mating features, while Stackups analyze cumulative tolerance chains.

FEAT

Features

→

MATE

Fit Analysis

TOL

Stackups

Building a Tolerance Chain

# Create features on components
$ tdt feat new --title "Housing Bore" -c CMP@1 -t internal
✓ Created feature FEAT@1

$ tdt feat new --title "Shaft OD" -c CMP@2 -t external
✓ Created feature FEAT@2

# Create a stackup and add contributors
$ tdt tol new --title "Bearing Clearance" --target-nominal 0.05 \
    --target-upper 0.10 --target-lower 0.02
✓ Created stackup TOL@1

$ tdt tol add TOL@1 +FEAT@1 ~FEAT@2
✓ Added 2 contributors to stackup TOL@1

Analysis Methods

TDT calculates three different analyses, each providing unique insights into your tolerance chain's behavior.

Method	Description	Best For
Worst-Case	All dimensions at their extreme limits simultaneously. Most conservative.	Safety-critical, 100% yield requirement
RSS (Root Sum Square)	Statistical combination assuming normal distributions. Calculates Cpk.	Production planning, capability analysis
Monte Carlo	10,000+ random samples from actual distributions. Most realistic.	Complex chains, non-normal distributions

Running Analysis

$ tdt tol analyze TOL@1 --iterations 50000 --verbose

⚙ Analyzing stackup TOL@1 with 3 contributors...
✓ Analysis complete for stackup TOL@1

   Target: Clearance = 0.05 (LSL: 0.02, USL: 0.10)

   Worst-Case Analysis:
     Range: 0.01 to 0.09
     Margin: 0.01
     Result: pass

   RSS (Statistical) Analysis:
     Mean: 0.05
     ±3σ: 0.018
     Margin: 0.012
     Capability: Cp=1.33, Cpk=1.33
     Yield: 99.99%

   Sensitivity Analysis (% variance contribution):
     Housing Depth:  45.2%
     Cover Height:   32.1%
     Gasket:         22.7%

   Monte Carlo (50000 iterations):
     Mean: 0.0501
     Std Dev: 0.0061
     Range: 0.027 to 0.074
     95% CI: 0.038 to 0.062
     Performance: Pp=1.31, Ppk=1.30
     Yield: 99.87%

Distribution Visualization

The --histogram flag displays an ASCII histogram showing the Monte Carlo distribution with spec limits marked. In-spec samples appear in green, out-of-spec in red.

tdt tol analyze TOL@1 --histogram --bins 20

   Distribution Histogram (10000 samples, 20 bins):

      0.425 │░░                                              │    67
      0.445 │░░░░░░░░                                        │   278
      0.465 │░░░░░░░░░░░░░░░░░░░░                            │   722 ◄LSL
      0.485 │██████████████████████████████████████          │  1347
      0.505 │██████████████████████████████████████████████████│  1823
      0.525 │█████████████████████████████████████           │  1318 ◄USL
      0.545 │░░░░░░░░░░░░░░░░░░░░░░                          │   785
      0.565 │░░░░░░░░░░                                      │   342
      0.585 │░░░                                             │   112
            └──────────────────────────────────────────────────┘
   Legend: LSL=0.480  USL=0.520  (█ in-spec, ░ out-of-spec)

✓ Configurable bin count with --bins N

✓ LSL/USL limits clearly marked

✓ Color-coded in-spec vs out-of-spec

✓ Sample counts per bin

CSV Export for External Analysis

Export raw Monte Carlo samples to CSV for analysis in Excel, Python, R, or any statistical tool. Perfect for custom visualizations or deeper analysis.

Export to CSV

# Export Monte Carlo samples
$ tdt tol analyze TOL@1 --csv > samples.csv

$ head -10 samples.csv
sample,value,in_spec
1,0.515109,1
2,0.473383,1
3,0.506680,1
4,0.530796,0
5,0.498786,1
6,0.471828,0
7,0.525510,0
8,0.501505,1
9,0.487642,1

# Import into Python for custom analysis
$ python3 -c "
import pandas as pd
df = pd.read_csv('samples.csv')
print(f'Yield: {df.in_spec.mean()*100:.2f}%')
print(f'Mean: {df.value.mean():.4f}')
print(f'Std: {df.value.std():.4f}')
"
Yield: 66.99%
Mean: 0.5002
Std: 0.0207

3D SDT Analysis

TDT supports full 3D tolerance analysis using Small Displacement Torsor (SDT) theory. Propagate 6-DOF geometric deviations through kinematic chains with Jacobian matrices. Integrates with ASME Y14.5 GD&T controls for familiar datum-based analysis.

🎯

6-DOF Torsors

3 translations (u, v, w) + 3 rotations (α, β, γ) per feature

⚙️

Jacobian Propagation

Transform deviations through kinematic chains with 6×6 matrices

📐

Geometry Classes

Plane, Cylinder, Sphere, Cone - each with DOF constraints

📊

Braille Visualization

Terminal-based chain schematics and deviation ellipses

3D Tolerance Analysis

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

⚙ Running 3D SDT analysis for stackup TOL@1...
✓ 3D Analysis complete

   Result Torsor (6-DOF):
     Translation:  u=±0.15  v=±0.12  w=±0.08 mm
     Rotation:     α=±0.002 β=±0.001 γ=±0.003 rad

   Sensitivity by DOF:
     Housing Bore:    u=45%  v=38%
     Shaft OD:        u=32%  v=28%
     Bearing Race:    u=23%  v=34%

# 3D analysis with visualization
$ tdt tol analyze TOL@1 --3d --visualize

Chain Schematic:
  ┌────┐       ┌────┐       ┌────┐
  │CMP1│──||───│CMP2│──||───│CMP3│ → Functional
  └────┘       └────┘       └────┘    Direction

Geometry Class	Description	Constrained DOF
Plane	Flat surface (datum A typical)	w, α, β
Cylinder	Holes, shafts, pins	u, v, α, β
Sphere	Ball features	u, v, w
Cone	Tapered features	u, v, α, β

GD&T Integration (ASME Y14.5)

TDT's 3D analysis integrates seamlessly with ASME Y14.5 GD&T controls. Define features with standard callouts - position, perpendicularity, parallelism - and TDT automatically converts them to torsor bounds for chain analysis. Supports MMC/LMC bonus tolerance calculation.

⊕

Position

Document true position tolerance with material modifiers

○

Concentricity

Document coaxiality requirements

⌭

Cylindricity

Document form tolerance for cylindrical features

Parallelism

Document parallelism requirements to datum

⟂

Perpendicularity

Document perpendicularity requirements to datum

↗

Runout

Document runout requirements for rotating parts

Quick Reference

Common Commands

# Create stackup
tdt tol new --title "Gap Analysis" --target-nominal 0.5 \
    --target-upper 0.8 --target-lower 0.2

# Add features (+ positive, ~ negative direction)
tdt tol add TOL@1 +FEAT@1 +FEAT@2 ~FEAT@3

# Run analysis with histogram
tdt tol analyze TOL@1 --histogram --bins 30

# Run with more iterations for better accuracy
tdt tol analyze TOL@1 --iterations 100000

# Verbose output (shows Cp, Cpk, Pp, Ppk, sensitivity)
tdt tol analyze TOL@1 --verbose

# Include GD&T position tolerances in calculations
tdt tol analyze TOL@1 --with-gdt

# Custom sigma level (4σ = more conservative)
tdt tol analyze TOL@1 --sigma 4.0

# Mean shift factor (Bender method for process drift)
tdt tol analyze TOL@1 --mean-shift 1.5

# Export for external analysis
tdt tol analyze TOL@1 --csv > tolerance_data.csv

# 3D SDT analysis (requires features with geometry_3d)
tdt tol analyze TOL@1 --3d

# 3D analysis with braille visualization
tdt tol analyze TOL@1 --3d --visualize

# 3D Monte Carlo simulation
tdt tol analyze TOL@1 --3d --method-3d monte-carlo

# List all stackups with results
tdt tol list

# Show stackup details
tdt tol show TOL@1