Circularity tolerance modeling, analysis, and design for high precision assemblies

Circular feature is one of the most common part features used in machines. Since it is practically impossible to make a part with perfect geometry, tolerances are specified to ensure the functionality of a final product while maintaining a low cost. This study presents fundamental treatments for circularity tolerance modeling, analysis, and design. First, a roundness profile model is presented. At present, the standard for geometric dimensioning and tolerancing, ASME Y14.5M, specifies a circularity tolerance based on the tolerance zones defined by two concentric circular boundaries. To represent profile variation within the tolerance zones, a harmonic roundness model using Fourier series expansions is proposed. A cutting profile simulation model has also been developed to illustrate the relationship between the radial error motion of a machine tool spindle and the resultant part profiles. The profile model has been verified statistically by a large number of real profiles produced by turning and cylindrical grinding. Second, the effect of out-of-roundness on positioning accuracy is investigated for various cylindrical fit conditions. Analytical approaches and computer simulations are used together to facilitate more extensive investigations. Systematic procedures are also proposed for assigning circularity tolerance by prescribing a fit condition and a desirable process capability of assembly. As a result, new circularity tolerance guidelines are suggested for fit conditions. Third, the study is further extended to spindle design analysis. The geometrical accuracy of a machine tool spindle has been investigated to examine the effect of circularity and concentricity tolerance on spindle running accuracy. The study is verified through real spindle design data obtained from a custom-built Purdue High Speed Spindle. Finally, an experimental study is provided to verify the simulation routines used in the analysis of positioning accuracy