Unified approach for tolerance analysis, synthesis, and compensator selection

Area of Science:

• Engineering
• Mechanical Design
• Computational Geometry

Background:

• Tolerancing is critical for the feasibility of real-world engineering designs.
• Existing methods for tolerance analysis, allocation, and synthesis can be complex and computationally intensive.
• The system Jacobian is a powerful tool for analyzing system behavior under perturbations.

Purpose of the Study:

• To present a unified approach to tolerance analysis, allocation, and synthesis using the system Jacobian.
• To develop an algorithm for automatic tolerance allocation (synthesis) by fitting an orthotope within an ellipsoid.
• To introduce metrics for evaluating the effectiveness of compensator sets in managing manufacturing tolerances.

Main Methods:

• Utilizing the system Jacobian to evaluate perturbed systems for tolerance analysis.
• Implementing an algorithm that fits an orthotope inside an ellipsoid for automatic tolerance allocation (synthesis).
• Developing and presenting metrics to assess the looseness of allocated tolerances and the efficacy of compensator selection.

Main Results:

• The system Jacobian effectively supports the three key sub-tasks of tolerancing: analysis, allocation, and synthesis.
• The orthotope-ellipsoid fitting algorithm provides a method for automated tolerance synthesis.
• New metrics enable the selection of optimal compensator sets by correlating with tolerance looseness.

Conclusions:

• The proposed system Jacobian-based methodology offers a comprehensive framework for addressing critical tolerancing tasks.
• The developed algorithm facilitates automated error budgeting and tolerance synthesis.
• The introduced metrics aid in optimizing compensator selection for improved design robustness.