Integrating GD&T into dimensional variation models for multistage machining processes

Abstract

Recently, the modelling of variation propagation in multistage machining processes has drawn significant attention. In most of the recently developed variation propagation models, the dimensional variation is determined through kinematic analysis of the relationships among error sources and dimensional quality of the product, represented by homogeneous transformations of the actual location of a product's features from their nominal locations. In design and manufacturing, however, the dimensional quality is often evaluated using Geometric Dimensioning and Tolerancing (GD&T) standards. The method developed in this paper translates the GD&T characteristic of the features into a homogeneous transformation representation that can be integrated in existing variation propagation models for machining processes. A mathematical representation using homogeneous transformation matrices is developed for position, orientation and form characteristics as defined in ANSI Y14.5; further, a numerical case study is conducted to validate the developed methods.

Keywords:

• GD&T characteristics
• mathematical modelling
• variation propagation
• machining process
• homogeneous transformation matrices

Acknowledgements

The authors gratefully acknowledge the financial support of the National Science Foundation award DMI-033147, UK EPSRC Star Award EP/E044506/1 and the NIST Advanced Technology Program (ATP Cooperative Agreement # 70NANB3H3054). The authors also appreciate the fruitful discussion with Mr Ramesh Kumar and Dr Ying Zhou from Dimensional Control Systems, Inc.