# Measurement and Modeling of a Cargo Bicycle Tire for Vehicle Dynamics Simulation
## 3 Results
### Post-Processing
Further, \(F_{t,x}\) and \(F_{t,y}\) show an oscillatory force characteristic for the ranges \(\kappa>15\%\) and, respectively, \(\alpha>8^{\circ}\) in the nonlinear region. As already explained, it can be assumed that the measurement system suffers from crosstalk. For this reason, test measurements were carried out to identify the crosstalk and its effects. By applying an increasing force in the x-direction, whether all other channels show a change as well or whether they remain unchanged is unexamined. The results of the investigation are shown in Figure 7.  
As can be seen from Figure 7, all other channels except \(T_{t,x}\) show increasing or decreasing behavior, which rises with a higher force in x-direction, although they should not undergo a significant force or torque change. For this reason, the confirmed crosstalk is compensated. \begin{table}
\begin{tabular}{c c c c} \hline
**Test Case** & **Force Channel** & **Force before Test in N** & **Force after Test in N** \\ \hline \multirow{3}{*}{**drive**} & \(F_{x}\) & \(-5.875\) & \(-4.491\) \\  & \(F_{y}\) & \(5.702\) & \(-106.491\) \\  & \(F_{z}\) & \(-2.891\) & \(11.616\) \\ \hline \multirow{3}{*}{**brake**} & \(F_{x}\) & \(-11.230\) & \(-5.473\) \\  & \(F_{y}\) & \(-0.397\) & \(-27.325\) \\  & \(F_{z}\) & \(-8.052\) & \(14.288\) \\ \hline \multirow{3}{*}{**steer**} & \(F_{x}\) & \(-5.180\) & \(-0.403\) \\  & \(F_{y}\) & \(3.108\) & \(-85.590\) \\ \cline{1-1}  & \(F_{z}\) & \(-0.890\) & \(32.541\) \\ \hline \end{tabular}
\end{table} 
Table 2: Captured force outputs before and after measurement series for test no. 3.1. Measurements with the MoReLab are normally made with a measurement rim with an offset of 60 mm, so the use of the adapter rim with an offset of 5 mm results in a different behavior, with a crosstalk effect that has to be corrected. For this reason, the crosstalk of the force and torque measurements is evaluated more closely in the subsequent section. Since [22] describes similar effects for this kind of measurement device, the method he described for crosstalk compensation of force sensors is also used in the proposed research. Therefore, according to [22], a correction matrix \(K\) is created by applying a defined force in one direction, while the effects on all other channels that measure forces and torques are recorded. The introduced force or torque is applied via an adapter that geometrically corresponds to the adapter rim, so that all existing lever ratios that will appear during the tire measurements are considered. The procedure is carried out on all axes by applying a force, followed by a defined torque on all axes. Because the measurement hub of the test truck does not have a brake and is only driven by a hydraulic driveshaft, the torque of the y-axis cannot be measured. For this reason, the correction matrix of [22] is reduced by one column and one row. The objective is to determine the effects that the introduction of a static force or torque to adapter rims geometry have on the measurements of the remaining axes. From uncorrected tire measurements, a maximum force of 1000 N and a maximum torque of 15 Nm can be expected. Based on these expected values, a slightly larger input force and torque were used in these experiments to cover the range needed for the tire measurements. The input forces and torques, as well as the resulting output values on all other channels, can be seen in Table 3.  
Figure 7: Crosstalk according to input \(F_{t,x}\). Subsequently, the correction matrix \(K\) was obtained from the crosstalk data listed in Table 3 by dividing each output value of a column by the applied input force or torque. \[K= \begin{pmatrix}0.969&0.019&-0.043&0.152&0.430\\ -0.027&0.920&0.013&0.092&-0.753\\ -0.032&-0.011&1.029&-0.210&-0.010\\ 0.001&0.011&0.003&0.959&-0.023\\ 0.007&0.0000476&-0.003&-0.048&0.995\end{pmatrix}  \tag{7}\]  
Finally, the inverse of the \(5\times 5\) correction matrix \(K\) was determined to solve Equation (8).