A unified approach to the measurement analysis of nominally circular and cylindrical surfaces
The customary procedures of roundness measurement have been developed in response to particular needs as they have arisen, incorporating approximations as appropriate. Consequently, the direct extension of these procedures to more complex measurements such as “cylindricity” is a questionable exercise. The present work develops a mathematically consistent description of the processes underlying the measurement and analysis of roundness. From this are derived analytical methods appropriate to measurements for which instrumentation is, in some cases, yet to become available. New, highly efficient algorithms for solving the minimum circumscribing, maximum inscribing and minimum zone reference figures are also produced. The method adopted identifies important features of roundness measurement such as eccentricity and radius suppression as translations between co-ordinate frames associated with the workpiece and instrument. Reference figure fitting is expressed formally as a problem in optimisation and the standard methods of Operations Research applied to it. All four standard reference circles are re-examined in this way leading to generalisations of measurement conditions and improved solution methods. Earlier advocacy of the limacon as a reference figure is confirmed and extended. The relationship of circular and limacon references is studied and an eccentricity ratio shown to be a suitable control over the approximations used in practice. The use of “limacon cyndroids” seems to provide a working approximation for the measurement of cylindricity. It is recommended that cylindrical reference figures be fitted by standard techniques of linear programming rather than by special algorithm.