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Mathematical model of cylindrical form tolerance
Min Cai1, Jiang-Xin Yang, Zhao-Tong Wu
1Department of Mechanical Engineering, Zhejiang University, Hangzhou 310012, China. caim@fulltop.com
Journal of Zhejiang University. Science
|October 21, 2004
Summary
This study develops a mathematical model for form tolerance in cylindrical features, enabling precise computer interpretation of national standard tolerances. This advances the integration of Computer-Aided Design (CAD) and Computer-Aided Manufacturing (CAM) systems.
Area of Science:
- Mechanical Engineering
- Computational Geometry
- Metrology
Background:
- Traditional tolerance representation in national standards lacks computer adaptability.
- Integrating CAD and CAM requires precise, machine-readable tolerance semantics.
- Current methods struggle with accurate interpretation of form tolerances.
Purpose of the Study:
- To establish a mathematical model for form tolerance of cylindrical features.
- To enable exact and complete semantic interpretation of tolerances for computer processing.
- To bridge the gap between national standards and digital manufacturing.
Main Methods:
- Mathematical definition of form tolerance based on ANSI Y14.5.1M-1994.
- Formulation of vector equations for each tolerance type.
- Development of mathematical models using inequalities based on feature degrees.
- Derivation of the variance area for each tolerance zone.
Main Results:
- A precise mathematical model for cylindrical form tolerance was established.
- Vector equations accurately represent national standard tolerances.
- Inequality-based models define tolerance zones effectively.
- The derived variance area provides a complete semantic interpretation.
Conclusions:
- The developed mathematical model accurately interprets the semantics of form tolerance.
- This model facilitates seamless data transfer and processing in CAD/CAM integration.
- It offers a robust foundation for computational tolerance analysis.