Roundness modeling of machined parts for tolerance analysis

Out-of-roundness of circular and cylindrical parts can greatly affect assembly accuracy. At present, the ASME Y14.5M-1994 specifies circularity tolerance based on two extreme circular boundaries to confine the highest peak and the lowest valley of a roundness profile; however, the profile variations within the two extreme boundaries are not accounted for. In this paper, we propose a harmonic roundness model using Fourier series expansion. In addition, a cutting profile model has been developed to illustrate the relationship between the radial error motion of a spindle and the resultant part profile. This relationship is then used to provide physical meanings to the harmonics generated by the proposed roundness model for a part profile, in particular those caused by fractional frequency spindle error motions. The proposed harmonic model has been verified statistically by a large number of real profiles produced by both turning and cylindrical grinding processes. The proposed roundness model is expected to provide insights into the advanced tolerance analysis of circular and cylindrical parts.