Computer-Aided Fixture Design Verification (CAFDV)

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Computer-Aided Fixture Design Verification(CAFDV)
Presented by Yuezhuang Kang December 7,
2001 Worcester Polytechnic Institute
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Introduction Fixture and CAFDV
Fixture the device that locates and holds the
workpiece during its machining process.
Fixture design has large impact on product
quality, manufacturing lead time and cost.
Computer-Aided Fixture Design (CAFD) uses
computer to reduce lead time and ensure fixture
design quality.
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Introduction 4 Stages of CAFD

• Setup Planning
• determines number of setups
• determines machining features of each setup
• Fixturing Planning
• finds fixturing surfaces and positions
• Configuration Design
• constructs detailed fixture geometries
• Verification (CAFDV)
• verifies (and improves) fixture designs

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CAFDV Overview
CAFDV is studied systematically for the first
time.
This presentation is organized by levels above.
Introduction Modeling Applications Implementatio
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Literatures Geometric Model

• The Jacobian Matrix (Asada and By, 1985)
• Workpiece DOFs constrained by fixture
• Locating completeness

• The Grasp Matrix (Xiong 1998, 1999)
• Locating Performance Index (Stability Index)
• Locator Layout Optimization

• In this study
• The Jacobian Matrix is extended for tolerance
  analysis
• An algorithm of finding the Jacobian Matrix is
  implemented

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s Literatures
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Literatures Kinetic Model
All previous stability related studies consider
no deformation or only workpiece deformation.
This study fills the blank with consideration on
fixture deformation.
Workpiece deformation has been and can only be
solved with FEA.
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Literatures Tolerance Analysis

• Datum Establish Error (Choudhuri and DeMeter
  1999)
• Used planar bounding surfaces for simple and
  fast estimation
• For planar datum and machining surfaces only

• Reference Planes three orthogonal planes (Rong
  et al, 1996)
• Works with any type of datum surface
• Includes only predefined locating modes

• This work uses the Jacobian Matrix and contact
  points
• Works with any type of surface and locating mode
• Defines surface tolerance by surface sample
  points
• Calculates sensitivity for tolerance assignment

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Literatures Locator Types
Most earlier studies all locators are assumed
to be points. Wu et al (1995) used lines and
surfaces to represent locators, however,
non-geometry information are lost.
This study allows any type of locator, which is
converted into equivalent locating points with
all necessary information.
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Literatures Summary

• The Geometric Model (the Jacobian Matrix)
• The Jacobian Matrix is extended for tolerance
  analysis
• An algorithm of finding the Jacobian Matrix is
  implemented

• The Kinetic Model
• Fixture deformation is considered for the first
  time
• The Fixture Stiff Matrix is created to link
  external forces with fixture deformation (and
  workpiece displacement)

• Tolerance Analysis
• Uses the Jacobian Matrix
• Locator tolerances are assigned based on
  sensitivity analysis

• Locator Types
• All types of locators are allowed, and they are
  converted into locating points with all necessary
  information

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Modeling for CAFDV
Geometric Fixture Model Describes the
relationship between workpiece displacement and
locator displacements. Kinetic Fixture
Model Describes the relationship between external
forces and workpiece displacement.
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Geometric Fixture Model
?d J ? ?q
?q J-1 ? ?d
J the Jacobian Matrix
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s Geometric Fixture Model
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The Jacobian Matrix
?d J ? ?q
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Kinetic Fixture Model Overview
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s Kinetic Fixture Model
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Three Types of Coordinate Systems

• Global coordinate system (GCS) the fixed CS in
  3D space.
• Workpiece coordinate system (WCS) the CS
  attached to each workpiece.
• Local coordinate system (LCS) the CS attached
  to each contact point.

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s Kinetic Fixture Model
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Finding Fixture Stiffness Matrix Step 1. Find
Contact Point Displacement in GCS
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Finding Fixture Stiffness Matrix Step 2.
Transform Point Displacement into LCS
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Finding Fixture Stiffness Matrix Step 3. Find
Contact Forces in LCS
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Finding Fixture Stiffness Matrix Step 4.
Transform Contact Forces into GCS
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Finding Fixture Stiffness Matrix Step 5.
Combine Contact Forces into Internal Wrench
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Finding Fixture Stiffness Matrix Result
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Contact Forces
Contact Force in LCS (essential in stability
verification)
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Fixture Modeling Summary
Geometric Model
?d J ? ?q
?q J-1 ? ?d
Kinetic Model
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CAFDV Applications
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Locator Tolerance Verification
Verifies if the locator tolerances can ensure
machining surface accuracy.
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Surface Deviation
Step 1.
Find machining surface sample points
Step 2.
Find workpiece displacement
Step 3.
Find sample point displacements
Step 4.
Find point displacements along surface normal
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Surface Deviation and Accuracy
Definitions follow ANSI Y-14.5 standards.

• Surface and Line Profile

• Parallelism, Perpendicularity and Angularity

• True Positioning Deviation

Machining Surface Accuracy
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s Tolerance Verification
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Tolerance Verification Summary

• Locator Error
• ? Locating Point Displacements
• ? Workpiece Displacement
• ? Sample Point Displacements
• Machining Surface Deviations
• Machining Surface Accuracy

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Stability Verification
To verify if the workpiece remains stable under
external forces (gravity, clamping and cutting
forces).
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Stability Criteria
Workpiece Stability Criteria No slippery at any
contact point, i.e., the reaction force at each
contact point should fall within its friction
cone.
Contact Force in LCS
Friction Cone
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s Machining Stability
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Contact Stability Index (CSI)
CSI is a normalized measurement of a contact
point stability.

• -1 ? CSI lt 0 outside the friction cone,
  unstable
• CSI 0 on the friction cone, marginally
  stable
• 0 lt CSI ?1 inside the friction cone, stable

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Stability Verification Summary
Stability Criteria All contact forces should
fall within its friction cone, i.e., CSI gt 0.
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Locating Performance
How to measure this intuitive stability?
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s Locating Performance
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Locating Performance Index (LPI)
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s Locating Performance
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CAFDV Applications Summary
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CAFDV Implementation Issues

• Conversion between locator and locating points
• Software Design
• Software User Interface

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Locator and Locating Points
Seven types of locators are implemented. Locators
are converted into points for fixture models.

• Conversions between locator and its equivalent
  locating points
• geometry conversion
• tolerance conversion
• stiffness conversion

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s Locator Conversion
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Geometric Conversion
A locator and its equivalent locating points
constrain the same number of DOFs of the
workpiece.
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Tolerance Conversion V-Block Type
A locator and its equivalent locating points
provide the same level of locating accuracy.
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s Locator Conversion
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Stiffness Conversion V-Pad Type
A locator and its equivalent locating points
provide the same level of stiffness.
Note The results are based on ANSYS FEA results,
with material as steel.
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s Locator Conversion
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Software Design System Architecture
Modularized Design to maximize the portability
and reusability
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User Interface Integration with CAD
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CAFDV Task Menu
This implementation contains five modules.
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Accessibility Panel and Locator Selection
Seven types of locators and equivalent locating
points
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Locator Selection
CAD interaction
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Locator Details
Each locator has its own tolerance specification
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Tolerance Analysis and Tolerance Types
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Tolerance Assignment and Locator Tolerance
Locator with assigned tolerances
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Stability Analysis
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Summary

• The first systematic study of CAFDV
• Reformulation of fixturing problems with two
  models
• Establishment of the Jacobian Matrix and the
  Fixture Stiffness Matrix
• CAD Integration successfully integrated with
  CAD package
• Tolerance analysis
• Tolerance analysis with the Jacobian Matrix
• Tolerance assignment with sensitivity analysis
• Stability analysis
• Handling of 3-D, frictional, and
  over-constraint problems
• Consideration of clamping sequence
• Optimization for minimal clamping forces

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Future Work

• Loading/Unloading accessibility
• Stability dynamics and workpiece deformation
• Tolerance consideration of fixture deformation

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Questions?