## 3 Results
### Determination of the Tire Steering Resistance Torque of an Unlocked Steered Wheel in Static State
#### 3.2.3 Study of the Position of the Center of Relative Motion of the Contact Patch  
Experimental studies of the position of the center of relative motion of the contact patch were carried out on a bench (see Section 6, item 2) with a special rim, which is shown in Figure 7. At the same time, the radius of the trajectory of the contact patch of the tire is determined by the trajectory of the center of relative motion. An analysis of Figure 7 shows that the special rim consists of two parts: the main rim 1 and the extension 2. The tire is installed on the main rim. The main rim 1 is a diskless wheel (size 440-533) for a wide-profile tire size 1300 \(\times\) 530-533 mod. BI-3 with flange 3 welded to the inner landing ring. Extension 2 consists of the base of the rim of a diskless wheel (size 440-533) and flange 4 welded to it. Flanges 3 and 4 are connected to each other with bolts 5. On the main rim and the extension, in addition to the solid landing cone 6, which provides a knuckle length value of 0.225 m when the wheel is installed on the bench, four rows of three evenly spaced landing cones 7, 8, 9, and 10 are additionally welded. These cones facilitate the installation of the steered wheel on the bench to discretely change the knuckle length by values of 0.295, 0.365, 0.68, and 0.82 m, respectively. At the same time, installing the wheel only with the main rim provides a length of 0.225, 0.295, and 0.365 m,  
Figure 6: Dependence of the radius of the trajectory of the contact point of the rigid false wheel on the angle of rotation, with \(\alpha_{k}=9.50\), \(\beta_{k}=5.50\), \(\gamma_{k0}=-0.50\), and \(l_{k}=0.225\) m.  
Figure 7: Special rim. and the installation of the main rim with an extension allows the knuckle length values to be increased to 0.68 and 0.82 m.  
The bench (see Section 6, item 2) includes a strain gauge complex, which consists of measuring equipment and a set of sensors for measuring the steer angle and the spin angle of the wheel about the knuckle axis. Experimentally determined tire contact patch dimensions and values of static wheel radii are given in Table 3.  
The radius of the trajectory of the tire contact patch is determined by the relative motion center trajectory. Knowing the angles of rotation of the wheel about the kingpin axis and the knuckle axis and the radius of its rolling, we determine the trajectory radius of the relative motion center according to the following expression:  
\[R_{t}=\frac{r_{w}\theta_{w}}{\theta} \tag{57}\]  
where \(R_{t}\) is the trajectory radius of the relative motion center, m; and \(\theta_{w}\) and \(\theta\) are the experimental values of wheel rotation angles, respectively, about the knuckle axis and the kingpin axis, rad. The amount of displacement of the center of relative motion of the contact patch is determined by dependence (41). The dependencies of the displacement of the relative motion center of the tire contact relative to its geometric center \(\Delta_{t}\) and the edge of the contact patch \((b/2)-\Delta_{t}\) on the knuckle length (Figure 8). The experimentally obtained values of \(\Delta_{t}\) and \((b/2)-\Delta_{t}\) are well approximated by polynomial functions of the third and fourth order, respectively. The processing of these data by means of MS Excel gave the following regression equations:  
\[\Delta t= f(l_{k})=0.1722\;{l_{k}}^{3}-0.524\;{l_{k}}^{2}+0.5178\;l_{k}+0.0001,\,R^{2}=0.9982 \tag{58}\] \[\mathrm{b}/2-\Delta t= f(l_{k})=0.3819\;{l_{k}}^{4}-0.8172\;{l_{k}}^{3}+0.8636\;{l_{k}}^{2}- 0.5719l_{k}+0.1671,\,R^{2}=0.9983 \tag{59}\]  
From an analysis of Figure 8, it can be seen that with an increase in the knuckle length, the relative movement center of the contact patch shifts to the its edge. When the knuckle length \(l_{k}=0.82\) m, it moves to the edge of the contact.