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

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

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

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

Tolerance Analysis Given Find Component Tolerances Assembly Tolerance LL UL Assembly Function Acceptance Fraction

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

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

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

CATS Modeler Milestones 1986 CADAM 1-D graphical modeler 1987 GE Calma 1-D graphical modeler 1988 HP ME-10 2-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

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

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)

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

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

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

3-D Propagation of Surface Variation K 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

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

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-

CE/TOL Modeler

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

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

CATS Analyzer Milestones 1984 1-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 1989 2-D analysis with GD&T form variation 1990 Mating hole pattern statistical analysis 1991 3-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

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

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

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

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

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

Current Research

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)

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

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

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

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

Curve Fit Polynomial Covariance

Association for the Development of Computer-Aided Tolerancing Systems Dr. Ken Chase Brigham Young University 435 CTB Provo, Utah 84602 Tel: (801) 378-6541 FAX: (801) 378-5037 email: chasek@byu.edu website: adcats.et.byu.edu

Tolerance Analysis of Compliant Assemblies Airplane skin panels Automotive body panels

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

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

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

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