# Validation of a Manual Methodology for Measuring Roundness and Cylindicity Tolerances
## 5 Conclusions  
This article proposes a practical activity for the evaluation of roundness and cylindricity tolerances that improves their understanding based on three approaches: mathematical analysis of the concepts involved, self-experimentation and manual measurement of the tolerances, and verification of the results with an industrial roundness measuring machine. Furthermore, an analytical procedure for the calculation of the cylindricity tolerance has been proposed from the least squares cylinder. In addition, this method has never been seen before in the literature and is easily programmable in Excel. This analytical procedure is based on the fundamentals of geometry, according to the concepts of cylindricity tolerance, hence it shows a high educational value. Therefore, it is possible to calculate the cylindricity tolerance with a manual procedure without the need for complex mathematical algorithms. The practical activity has been tested with some Mechanical Engineering students. By means of a satisfaction survey, the adequacy of the proposed methodology has been verified and users have reported a better understanding of the concepts and working procedures proposed. The authors believe that this practice-based approach can enhance the self-learning of the concepts of roundness and cylindricity through the rehearsal with simple metrological instruments and reachable programming, i.e., Excel, and can provide users with the necessary skills for the industrial environment. If a cylindricity measuring equipment is not available the manual measurement procedure may be successfully applied. Small companies and, particularly, job-shop industries, do not dispose of very modern and sophisticated media and they should ask for external services to control the shapes of the products they are producing. External dependency makes decision making and parts quality control more \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{2}{c}{**Advantages**} & \multicolumn{2}{c}{**Disadvantages**} \\ \hline \multirow{4}{*}{Manual methodology} & Better acquisition of the theoretical concepts involved & Need for prior knowledge of the procedure \\ \cline{2-3}  & More economical equipment & Need for assembly \\ \cline{2-3}  & Possibility of on-machine measurements & High accuracy is difficult to obtain \\ \cline{2-3}  & Approximate evaluation of the roundness & Punctual irregularities in the profile may \\  & tolerance by recording a few profile points & be undetected. \\ \cline{2-3}  & Possibility to obtain an approximate measure & \\  & of cylindricity tolerance & Accuracy depends on the operator’s skill \\ \hline \multirow{4}{*}{CME methodology} & No need to know the theoretical concepts & \\  & involved in the measurement of roundness & Theoretical concepts put into practice may not \\  & and cylindricity & be acquired \\ \cline{2-3}  & High measurement accuracy & High cost of equipment \\ \cline{2-3}  & Automated and rapid measurement process & Measuring capacity is limited to the length \\ \cline{2-3}  & Possibility to evaluate cylindricity tolerance & range of the machine \\ \cline{2-3}  & with high accuracy & Complex pre-calibration process \\ \cline{2-3}  & Ability to visualise results and & \\ \cline{2-3}  & singular irregularities & On-machine measurements are not available \\ \hline \end{tabular}
\end{table} 
Table 3: A comparison of MM and CME methodologies related to roundness and cylindricity tolerances. difficult. Furthermore, although the roundness and cylindricity control was subcontracted, some technical knowledge is necessary to adopt the correction lines and decisions, if necessary. In this paper, it has been demonstrated that a system composed of two V-blocks on a table and a dial indicator is adequate to obtain good results if enough points are measured and good practice rules are carried out. This system can be applied in situ and for very different part sizes, in length and diameter.