Effect of Filter Type and Filter Size on Roundness/Circularity Measurement Using Different Mathematical Algorithms

Abstract

In the manufacturing industry, it is almost inconceivable to produce a rotating component without a minimal amount of roundness tolerance. The importance of studying roundness form deviations of circular and cylindrical features is to avoid the excessive lateral or axial runout deviations of the rotating and reciprocating parts during dynamic operations. Considering the precision that industries require now and will require in the future, the authors of this article have chosen roundness (also called circularity per ASME Standards) as the measurable parameter. In order to arrive at precise results, the roundness of a near-to-perfect cylinder is measured on an accurate spindle and turn-table type measuring instrument. Roundness profile, when measured, can be filtered in various ways to reduce or eliminate unwanted details, with a cut-off value set in terms of undulations per revolution (UPR), which gives valuable information about how the component may function, under specific conditions. Looking at real-life roundness graphs it is clear that information exists in the data at different frequencies. A classic example is ovality, which indicates an irregularity that occurs two times in one complete revolution. The workpiece would be said to have two lobes or two UPR. Multiple lobes may be present on a component, a condition contributing to either problems of fit with mating components or part functionality. Additionally, usage of recommended or generalized filter, yields data that approximately lies in the range of acceptability. Thus, there is a strong need to thoroughly understand the effect of filter size and type on roundness (form error for fit) and part functionality. Many published articles have investigated novel filters to accurately and efficiently calculate roundness. However, no work was found in literature that would present the filter size and type selection criteria and correlate it with roundness depending on mathematical method of calculating roundness and further to part functionality. This paper focusses on the investigation of filter type and size effect on roundness based on different mathematical methods of roundness error calculations. By varying parameters like the filter type (Gaussian 50%, 75% and RC Filters), the filter sizes (1 through 500 UPR) and the methods of measuring the roundness — (Least Squares Circle (LSC), Minimum Circumscribed Circle (MCC), Maximum Inscribed Circle (MIC) and Minimum Zone Circles or Separation (MZC or MZS)), roundness at different heights of the workpiece is evaluated. A clear trend is observed from the results, which can further help one to choose filters and their respective sizes for the respective design intent or the application in question.