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Table of contents
1 Introduction
1.1 Placement and Importance of Variation Management in Design Process
1.2 Positioning of Work
1.3 Layout of the Thesis
2 State of the Art
2.1 Product Design Process
2.1.1 Prevailing design models and their stages
2.1.2 Concurrent design process
2.1.3 Decision based design perspective
2.1.3.1 Point based design
2.1.3.2 Set based concurrent engineering
2.2 Robust Design
2.3 Tolerancing
2.3.1 Displacement accumulation
2.3.2 Tolerance accumulation
2.4 Synthesis
3 Formalization For Variation Management
3.1 Formalization of Theory
3.1.1 Expression of product design in terms of constraint satisfaction
3.2 Main Theoretical Basis in Terms of Logic
3.2.1 Quantifiers
3.2.2 Constraint satisfaction problem (CSP) limitations .
3.2.3 Quantified constraint satisfaction problem (QCSP)(Verger & Bessiere, 2006)
3.3 General Theory
3.4 Formulation of Set Based Robust Design
3.4.1 Variable definition for Robust Design
3.4.2 Domain
3.4.3 Constraints
3.4.4 Quantifier based expression for the robust set based design exploration
3.4.5 Consistency evaluation for solutions
3.4.5.1 Existence of a solution
3.4.5.2 Existence of a robust solution
3.5 Formulation of Tolerance Analysis
3.5.1 Variable definition for Tolerance analysis
3.5.2 Domain
3.5.3 Constraints
3.5.4 Quantifier based expression for the Tolerance Analysis for Mechanical Assemblies
3.5.4.1 Respect of assemblability of the mechanism
3.5.4.2 Respect of functional requirements
3.6 Synthesis
4 Application to Set Based Robust Design
4.1 Considerations for Application of Robust Design Formalization
4.2 Design Space Representation
4.3 Consistency Evaluation
4.3.1 Transformation
4.3.2 Basic notations and definitions
4.3.2.1 Interval operations
4.3.2.2 Extension of constraints
4.3.2.3 Interval Analysis
4.3.3 Consistency for the existence of a solution
4.3.4 Consistency for the existence of a robust solution
4.4 Space Exploration Tools
4.5 Illustrative Example
4.5.1 Problem Description
4.5.2 Conversion to interval arithmetic for consistency
4.5.3 Results
4.5.3.1 Results verification
4.6 Application to Examples
4.6.1 Embodiment design of a two bar structure
4.6.1.1 Results
4.6.1.2 Results verification
4.6.2 Embodiment design of a rigid flange coupling
4.6.2.1 Problem description
4.6.2.2 Design constraints
4.6.2.3 Flange design
4.6.2.4 Design model
4.6.2.5 Results
4.6.3 Design of a 6 Bar Mechanism
4.6.3.1 Problem Description
4.6.3.2 Design Constraints
4.6.3.3 Design Model
4.6.3.4 Algorithm improvements
4.6.3.5 Results
4.7 Conclusion and Discussion
5 Application to Tolerance Analysis
5.1 Considerations for the Application of Tolerance Analysis Formalization
5.2 Representation of the Geometric Variation
5.2.1 Explanation of geometrical description
5.2.1.1 Geometric description in 1D
5.2.1.2 Geometric description in 3D
5.3 Constraint Expression Via Hulls
5.4 Development Of Analysis Methods
5.4.1 Approach for the worst case tolerance analysis
5.4.1.1 QCSP
5.4.1.2 Formulation of tolerance analysis for QCSP solver
5.4.2 Statistical tolerance analysis based on formalization and Monte Carlo simulation
5.4.2.1 Monte Carlo simulation
5.4.2.2 Transformation for statistical tolerance analysis .
5.4.2.3 Results
5.5 Application
5.5.1 Geometric description
5.5.2 Geometric behavior and constraint model
5.5.2.1 Compatibility Hull (Hcompatibility)
5.5.2.2 Interface Hull HInterface
5.5.2.3 Functional Hull HFunctional
5.5.3 Optimization
5.5.4 Assembly Example Results
5.5.5 Error Control and Revalidation
5.6 Conclusion
6 Conclusion And Perspectives
6.1 Conclusion
6.2 Perspectives
A Appendix 1
A.1 Description of FOL terms and symbols
A.2 Constraints For Flange Coupling Example
A.2.1 Nomenclature
A.2.2 Constraints for flange coupling design
A.2.2.1 Bolt design
A.3 Constraints For Six Bar Mechanism
A.3.1 General Considerations
A.3.2 Assemblability Constraints
A.3.2.1 Fitting and Framing Constraints
A.3.2.2 Path generation constraints
References
