# Evaluation of the Variability of Vibration Measurement Results in Rolling Bearing Quality Control
## 4 Results and Discussion
### Repeatability and Reproducibility of the Bearing Vibration Measurement Result  
The analysis conducted in this subchapter is based on the procedures specific to method R&R. The analysis of repeatability and reproducibility (R&R) is a component of the MSA (Measurement Systems Analysis). MSA is a method of assessing the quality and reliability of measurement systems, which is used to identify and remove measurement errors resulting from measurement system variability. In short, analysis R&R allows for analysing the impact of selected factors of an industrial measurement system on the measurement results' variation [29,30]. The main purpose of using analysis R&R is to identify the reasons for the measurement process' variation. The analysis should result in the minimisation of these reasons. The testing conducted in this chapter involved 9 measurements of a single bearing in 3 series featuring 3 measurements. Each series was preceded with the bearing's placement on the verified device, while each measurement in a series was preceded by a clamp release and application. Each measurement was conducted at the same point on the outer ring's circumference. The order of procedure was as follows: the bearing's inner ring was fitted to the spindle's rotating shaft to enable contact between the outer ring and the sensor's pin at a specific point. The first measurement was conducted after the bearing was loaded with the force applied by the clamp (selected for the given type). Then, the clamp was released and applied again to conduct the second measurement without changing the outer ring's position in relation to the sensor. The third measurement conducted at the same point was also preceded by the clamp's release and repeated application. The tested bearing was removed from the shaft after a series of three measurements. The same measurement sequence was used when the bearing was fitted onto the shaft for the second and third time. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency Range, Hz**} & \multicolumn{2}{c}{**Calculated Statistic F for System Combinations**} & \multicolumn{2}{c}{**F\({}_{\textbf{hr}}\) (\(\textbf{p}=0.95\))**} \\ \cline{2-5}  & **1**\(\leftrightarrow\)**2** & **1**\(\leftrightarrow\)**3** & **2**\(\leftrightarrow\)**3** & \\ \hline Medium & 1.50 & 2.22 & 1.48 & 1.61 \\ High & 1.42 & 1.93 & 1.35 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the comparison of variances of the obtained rolling bearing vibration measurement populations in the selected band. The testing was conducted on 10 ball bearingss type 6305. The methodology specified above allowed for obtaining 90 measurement results. Only damaged bearings were included in the testing. The structure of the experiment for rolling bearing vibration measurement systems allows for the adoption of the following definitions:  
Repeatability EV (Equipment Variation) will be the degree of conformity of subsequent rolling bearing vibration measurements taken without removing the bearing from the device's measuring shaft, whereas the reproducibility will be interpreted as the degree of conformity of subsequent vibration measurements when the bearing is removed from the device's measuring shaft and then fitted again. It is necessary to note that the bearing vibration measurement is always taken on the same side when the electromagnetic sensor's pin is in contact at the outer ring's same point. However reproducibility AV (Appraiser Variation) is in the average of measurements made by different appraisers using the same instrument when measuring the identical characteristic on the same part. The analysis results are presented in Table 7.  
The MSA analysis assumes that the value R&R is expressed as a percentage and is used as basis for specifying the tested system's efficiency.