# Measurement of Wheel Radius in an Automated Guided Vehicle
## 4 Research Outcomes and Their Analysis
### Research Results and Their Analysis  
As part of the basic research, 56 tests in four measuring series were carried out. In the individual series were the following loads: 790 N, 1093 N, 1376 N and 1800 N. On the basis of the obtained test results, the influence of the load on the rolling radii of the wheels was determined using the Statistica package. The average values and standard deviations in a given series were obtained in the individual  
Figure 11: The tested vehicle (**a**) view; (**b**) scheme.  
measurement series and were presented in Table 1. Coefficients of variation in individual measurement series were presented in Table 2. Apart from the measurements for the left wheel and the 1800 N load, the standard deviation values characterizing the dispersion of measurements are similar.  
Figure 12a,b shows the determined regression curves together with a 95% confidence interval. For the left wheel, the correlation coefficient is 0.8617, and for the right wheel, is 0.9351 The correlation coefficient for the left wheel assumes smaller values due to the greater dispersion of the measurement results. The measure of this spread is the standard deviation (Table 1).  
Figure 13 shows a comparison of the obtained rolling radius courses as a function of load for both wheels. These courses have a similar slope. Their nonparallelism is basically determined by the measurement for the left wheel loaded with 1800 N. This measurement is burdened with the largest error and the largest dispersion of the measuring points shown in Figure 12a.  
Using the data from Table 1, slip coefficients for both wheels were determined. Figure 14 shows the relationship between the load of a given wheel and slip. The obtained relationships for the slip, \(s=0.1\%\) to \(s=0.3\%\) are linear.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Force F\({}_{\text{N}}\), N**} & \multicolumn{2}{c}{**Left Wheel**} & \multicolumn{2}{c}{**Right Wheel**} \\ \cline{2-5}  & **r, m** & \(\sigma\times\mathbf{10^{-6}}\)**, m** & **r, m** & \(\sigma\times\mathbf{10^{-6}}\)**, m** \\ \hline
790 & 0.10046 & 25.632 & 0.10030 & 23.935 \\
1093 & 0.10049 & 25.103 & 0.10034 & 24.587 \\
1376 & 0.10054 & 20.679 & 0.10041 & 18.644 \\
1800 & 0.10058 & 37.081 & 0.10046 & 20.101 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Average values and standard deviations in the individual measurement series.  
Figure 12: Linear regression with a 95% confidence interval estimated for (**a**) left wheel; (**b**) right wheel.  
Figure 13: Comparison of the obtained rolling radius courses.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Force F\({}_{\text{N}}\) (N)**} & \multicolumn{2}{c}{**790**} & **1093** & **1376** & **1800** \\ \hline
**Left wheel** & 0.000255 & 0.000250 & 0.000206 & 0.000369 \\
**Right wheel** & 0.000239 & 0.000245 & 0.000186 & 0.000200 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coefficients of variation in individual measurement series.  
As part of the study also determined the deflection characteristics of a flexible bend as a function of load. The graph presenting such characteristics is shown in Figure 15.  
The graph presented in Figure 15 is a hysteresis loop, which is visible after the enlargement of the selected fragment. The dependence of the deflection on the pressure force does not differ much from the linear characteristic.