1. CAD-Based Tolerance Analysis-- Brigham Young University
An Overview C L R L
Gap
by Ken Chase
Brigham Young University
Open Loop R T e i r
Plunger  u
Pad
Arm  g
Reel a
Base
Closed Loop b h R L

2. Concurrent Engineering
Product
Release
Product
Release
Cost or
Effort
Development Time
When manufacturing considerations are
included early in the design process,
product development time may be
significantly shortened

3. Tolerance analysis is the link between design & manufacturing
Critical Link
Engineering
Design
Manufacture
Engineering
Tolerances
Tolerance analysis is the link
between design & manufacturing

4. Effects of Tolerances are Far-reaching
Engineering
Manufacturing
Design
Resultant Dimensions
Fit and Function
Design Limits
Performance
Sensitivity
Design Intent
Robust to Variation
Customer Satisfaction
Production Cost
Process Selection
Machine Tools
Operator Skills
Tooling, Fixtures
Inspection Precision
Assemblability
Scrap and Rework

5. Tolerance Analysis Given Find Component Tolerances Assembly ToleranceLL UL
Assembly
Function
Acceptance
Fraction

6. Tolerance Analysis Promotes Concurrent Engineering
Assembly
Tolerance
Analysis
Assembly
Tolerances
Component
Tolerances
Performance
Requirements
Engineering
Model
Production
Requirements
Improved Performance
Decreased Cost

7. 3 Sources of Variation in Assemblies
R +∆R 
A+∆A R
 R A A U U
U +∆U
Dimensional and
Kinematic
Geometric

8. The CATS System 3-D CAD System CATS CATS Modeler Analyzer Mfg CAD
CATS Application Interface
CATS
Modeler
CATS
Analyzer
Mfg
Process
Database
CAD
Database

9. CATS Modeler Milestones
1986 CADAM 1-D graphical modeler
1987 GE Calma 1-D graphical modeler
1988 HP ME D vector modeler
1989 Alpha 1 3-D solid modeler
X Windows CATS interface
1990 AutoCAD 2-D modeler: AutoCATS
1991 Auto loop generation
1992 CATIA & Computervision 3-D modelers
1993 Assembly tolerance requirements models
1995 Pro/E 3-D parametric modeler
Automatic joint recognition
2000 Variation modeling on ADAMS

10. Vector Assembly Model C L Plunger Arm Base R R R  Pad  Reel Gap
Open Loop R T e i r
Plunger  u
Pad
Arm  g
Reel a
Base
Closed Loop b h R L

11. 3-D Kinematic Joints Parallel Cylinders (2) Rigid (no motion)
Prismatic (1)
Revolute (1)
Cylindrical (2)
Spherical (3)
Planar (3)
Edge Slider (4)
Cylindrical
Slider (4)
Crossed
Cylinders (5)
Point Slider (5)
Spherical Slider (5)

12. Vector Path Through a Joint U2
Datum 1 
Datum 2
Datum 2 U U1
Datum 1
2-D Joint
3-D Joint

13. Vector Path Across a Part
DRF A R
DRF U
Passes through the DRF

14. 2-D Propagation of Surface Variation
Translational
Variation
Rotational
Variation
Nominal
Tolerance
Circle
Zone
Tolerance
Zone
Tolerance
Zone
Cylinder on a plane
Block on a plane

15. 3-D Propagation of Surface VariationK
Kinematic Motion F
Geometric Feature Variation F F K K y y y K K x x z F z F K K F K
Cylindrical Slider Joint
Planar Joint

16. Assembly Tolerance Specifications
DESIGN SPECIFICATIONS
Component Tolerances
Assembly Tolerances
Parallelism
Parallelism A A
Part B
Part B
-A-
Part C
-A-

17. DESIGN SPECIFICATIONS Component Tolerances Assembly Tolerances
Perpendicularity & Angularity
Perpendicularity & Angularity A A A q± d q
-A-
-A-
Concentricity & Runout
Concentricity & Runout
- A - A A A A
-A-

18. CE/TOL Modeler

19. CATS Assembly Modeler Status
Modeling Task Graphical Automation Level
Interface
1. Specify datums √ All graphical
2. Specify assembly specs √ All graphical
3. Select and locate √ All graphical
assembly joints
4. Define datum paths √ All graphical
5. Define closed vector loop √ Auto loop generation
6. Define open vector loops √ Auto loop generation
7. Specify geometric √ Auto DOF check
variations

20. CE/TOL Analyzer Predicted rejects Quality level Skewed distributions
Statistical algorithms built-in
No equations to type

21. CATS Analyzer Milestones
D stackup with cost optimization
1986 Cost optimization with process selection
CATS 1-D Analyzer v1
1987 Estimated Mean Shift Method
1988 CATS 2-D vector loop analysis; 2-D kinematic joints
Linearized solution of implicit assembly functions
D analysis with GD&T form variation
1990 Mating hole pattern statistical analysis
D vector loop analysis; 3-D joints; 3-D GD&T
1993 Analysis of library of assembly tolerance specs
1994 Nonlinear tolerance analysis by MSM
1995 Variation Polygon representation
1996 Yield prediction for multiple assembly tolerance specs
1997 Effect of surface waviness on GD&T form variation
2000 Tolerance analysis on ADAMS

22. Complex Assembly Functions
y = f(x)
Explicit
Implicit
f(x, y) = 0

23. CATS determines the % contribution by x y c a •
38%
19%
15%
10% 5%
CATS determines the % contribution by
each component tolerance to overall
assembly variation

24. Tolerance Allocation Given Find Component Tolerances Allocation Scheme
Assembly
Tolerance
Component
Tolerances LL UL
Allocation
Scheme
Acceptance
Fraction

25. Accuracy / Efficiency
3 part assembly, 6 dimensions, 9 equations

26. CATS Tolerance Analysis Status
Analysis Task Graphical Automation Level
Interface
1. Generate assembly Automatic
equations and sensitivities.
2. Set up matrices and solve Automatic
3. Calculate assembly variation √ Built-in
and percent rejects
4. Calculate and plot sensitivities √ Built-in
and percent contribution
5. Plot assembly distribution √ Automatic
6. Perform tolerance synthesis √ Built-in algorithms
7. Perform design iteration √ Interactive graphical
interface

27. Current Research

28. Equivalent Variational Mechanisms
Add dimensional variations to a kinematic model
Modify the input and output variables
Extract the tolerance sensitvities from a velocity analysis
Converts a kinematic analysis to a tolerance analysis
Even works for static assemblies (no moving parts)

29. Tolerance Analysis of Compliant Assemblies
Simple lap joint of two thin plates

30. Multiple Cases - Single FEA Model
Uniform X Gap
Twisted Gap
Uniform Y Gap
Rotated Interference / gap x y z

31. Compliant Assembly Milestones
1996 Statistical FEA for compliant assemblies
Material covariance due to elastic coupling
1998 Geometric covariance - surface continuity
Geometric covariance from Bezier curves
1999 Geometric covariance by spectral analysis
Wavelength effects on assembly variation
Spectral characterization of surface variation
2000 Geometric covariance by polynomial analysis

32. Statistical FEA Solution
Closure Force
Statistical FEA Solution:
Mean Closure Force
Closure Force Cov
where:
Equivalent Stiffness

33. Curve Fit Polynomial Covariance

34. Association for the Development of Computer-Aided Tolerancing Systems
Dr. Ken Chase
Brigham Young University
435 CTB
Provo, Utah
Tel: (801)
FAX: (801)
website: adcats.et.byu.edu

35. Tolerance Analysis of Compliant Assemblies
Airplane skin panels
Automotive body panels

36. Material Covariance Displacing one node affects the displacement
of surrounding nodes
Described by the stiffness matrix of the part

37. Geometric Covariance Nodal variations are not independently random
Part surfaces are continuous
Random surfaces must be used to include covariance effects in statistical analyses

38. Covariance from Spectral Analysis
Frequency
spectrum 2
Auto-
spectrum
IFFT
Auto-
correlation

39. Comparison of Results Standard deviation of closure force Monte Carlo
FASTA
Large sample size required
for accuracy
5,000 FE solutions
Slower
Very similar results
Smaller sample size
required for accuracy
2 FE solutions