Mathematical analysis of three-dimensional geometric tolerances of mechanical products - analysis under maximum material condition

Dimensional tolerances and geometric tolerances of three-dimensional product shapes are very important for manufacturing process control and quality control of mechanical products. The objective of the present research is to develop systematic methods for planning and analysis of the geometric tolerances of the three-dimensional mechanical products. The tolerance zones of the geometric features have been investigated, in the previous paper, based on the definitions of the geometric tolerances, and the parameters have been defined to describe the deviations of the geometric features within the tolerance zones. Mathematical methods are discussed, in the present paper, to estimate the statistical deviations of the positions and the orientations of the geometric features, based on the deviation parameters and the relationships between the datum features and the target features. In particular, emphasis is given to the analysis of the statistical deviations of the geometric features under the MMC (Maximum Material Conditions), which specifies the interaction between the dimensional tolerances and the geometric tolerances. The proposed method is applied to the analysis of the deviations of the geometric features, to which both the dimensional tolerances and the geometric tolerances are required.