# Validation of a Manual Methodology for Measuring Roundness and Cylindicity Tolerances
## 4 Discussion  
After having obtained the results using MM and CME, some technological considerations should be pointed out. The first feature focuses on the measurement process fundamentals. The CME method is a one-point measurement system as the workpiece is supported vertically on one of its front faces, the stylus contacts at a point on the workpiece surface, and positive or negative variations with respect to an initial reference are registered. In other words, there is no influence of any point of the surface on the one that is being measured at the moment. Comparatively, the manual procedure consists of a three-point measurement, as the workpiece is supported on two points on the V-blocks. These contact points vary for each position during the rotation of the part influencing the signal of the dial indicator [27], see Figure 9. This becomes important when analyzing lobed forms as the actual measurement of the dial indicator can be slightly varied. This influence is really a measuring error source that might be more important for high-angled V-blocks. To compensate for this effect, correction factors based on the number of sides of the lobed shape are traditionally applied [28]. Fortunately, although measurement correction is necessary, the three-point measurement with V-blocks makes it possible to evaluate lobe forms, which would not be noticeable if a two-point measurement method, i.e., diameter measurements, was applied. Figure 8: Result obtained for the cylindricity analysis of a whole part using the CME. The second aspect that can be established is related to the minimum number of points that are necessary to be considered in the manual procedure. Regarding this issue, it was decided to measure three cross sections of one of the parts using the CME, see Figure 10. For this purpose, several points used for the roundness analysis according to the analytical procedure established by Excel(r) have been filtered out. The evolution of the relative error with respect to the total measured number of points of the profile (i.e., 3600 points) is shown in Figure 11. No significant variations were found as the number of points decreased up to 1000. Thereafter, slight variations occur as the number of measured points decreases up to 40 points, as the maximum difference in the results is less than 1% in any case. To consider a lower number of points leads to an unstable behavior of the roundness tolerance value. Particularly, for only eight points, the differences found among readings were higher than 12%. Logically, using fewer points for the measurement leads to lower roundness tolerance values. This is due to the lower probability of detecting the position of the furthest and closest points of the profile from the center of the LSC, which are the ones that really define the tolerance value. It is concluded that it would be possible to obtain good measurement accuracy using the manual procedure by taking at least 40 equidistant points. Figure 10: Cross sections selected for the analysis. Figure 9: Contact point variation when assessing deviations of lobed forms in V-blocks (Adapted from [28]). Arrows represent the contact part-dial indicator. The shape of the profile also influences the error made as the number of points is reduced, which is established as the third conclusion. Cross section 3 in Figure 12 has the smallest roundness tolerance as the points of the profile are closer to LSC. However, the value of the tolerance is mostly defined by the deviated zone of LSC. Therefore, as the probability of registering this zone with a smaller number of points decreases, the error made in the measurement increases significantly. On the contrary, oval or lobed profiles, such as cross sections 1 and 2, respectively, that differ from LSC in several zones, are more likely to be correctly defined with a smaller number of points. MM methodology presents clear advantages to the understanding and clarifying of the concepts involved.