## 3 Results and Discussion  
### Considered Vehicle Sets and Braking Variants  
Several typical cases reflecting the characteristic operating conditions describing the motion of a set of a tractor with a semitrailer were adopted for the research:  
* b1: tractor + laden semitrailer, nominal set,
* b2: tractor + unladen semitrailer,
* b3r: tractor + laden semitrailer, with uneven load distribution--shifting the trailer's centre of gravity towards the rear,
* b3f: tractor + laden semitrailer, with uneven load distribution--shifting the trailer's centre of gravity towards the front,
* b4: tractor + laden semitrailer, with exceeded maximum permissible weight (GVW),
* b5: tractor + laden semitrailer, failure of the semitrailer braking system (brakes not working),
* b6: tractor + laden semitrailer, failure of the semitrailer braking system (longer reaction time),  
Figure 5: ABS operation diagrams: (**a**) Dependence of the adhesion coefficient on the slip ratio; (**b**) Change of pressure in the brake cylinder over time.  
b7: tractor + laden semitrailer, surface with reduced adhesion (wet asphalt),
* b8: tractor + laden semitrailer, surface with reduced adhesion (icy road).  
Table 1 presents the nominal values of the main parameters describing vehicles A and B (these data were adopted based on technical data of selected vehicles [71; 72] and literature data [28; 29; 38; 52; 66; 73].  
Table 2 presents the values of the coefficients of the tangential force model in the tyre-road contact. They were selected in such a way as to obtain the values of the friction coefficients as can be found, e.g., in [43; 7; 75] for the three considered road surface conditions: nominal (it corresponds to a dry asphalt surface) and with reduced adhesion (it corresponds to a wet asphalt surface and ice-covered surface). Figure 6 shows the corresponding unit characteristics of the tangential force.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Vehicle A** & **Vehicle B** & \\ \hline wheelbase & \(L_{A}=3.65\) m & & \(L_{B}=2.62\) m \\  & laden: & \(m_{B}=35.250\) kg \\ mass & \(m_{A}=7395\) kg & unladen: & 6220 kg \\  & overloaded (1): & 39,250 kg \\  & laden: & \(b_{B}=24.2\) m, \(h_{B}=223\) m \\ CG position & \(b_{A}=2.56\) m, \(h_{A}=1.13\) m & unladen: & 1.47 m & 1.15 m \\  & laden f (2): & 5 m & 2.23 m \\ coupling position & \(c_{A}=0.43\) m, \(h_{A}=0.85\) m & \(c_{B}=7.7\) m, \(h_{B}=0.85\) m \\  & tyre: 395/70R19.5 & & 395/70R19.5 \\ wheels (3) & \(r_{AA}=0.494\) m & \(r_{AB}=0.494\) m \\  & \(h_{AA}=8\) kg m\({}^{2}\) & & \(l_{AB}=8\) kg m\({}^{2}\) \\  & \(h_{pA}=1.832\) m, \(A_{A}=9.014\) m\({}^{2}\), & \(h_{pB}=2\) m, \(\Delta A_{B}=0.732\) m\({}^{2}\), \\ forces of resistance & \(c_{xA}=0.8\), \(\rho=1.2\) kg/m\({}^{3}\) & \(c_{eB}=1.\Delta c_{x}=0.2\), \\  & \(f=0.01\), & \(\rho=1.2\) kg/m\({}^{3}\) \\  & \(\Lambda_{\rm t}=4.7\times 10^{-4}\) s\({}^{2}\)/m\({}^{2}\) & \(f=0.01\), \(\Lambda_{\rm t}=4.7\times 10^{-4}\) s\({}^{2}\)/m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Technical data of vehicles.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & \(\mathbf{c_{3}}\) & \(\mathbf{c_{5}}\) & \(\mathbf{c_{p1}}\) & \(\mathbf{c_{p2}}\) & \(\mathbf{c_{p3}}\) & \(\mathbf{c_{p4}}\) \\ \hline Nominal **(dry)** & 0.87 & 26.5 & 0.19 & \(10^{-11}\) & \(-0.006\) & 1.1 & 0.016 & 0.004 \\ Reduced friction **(wet)** & 0.65 & 28.5 & 0.21 & \(10^{-11}\) & \(-0.003\) & 1.8 & 0.09 & 0.004 \\ Reduced friction **(ice)** & 0.12 & 206 & 0.031 & \(10^{-11}\) & \(-0.003\) & 1.8 & 0.016 & 0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Modified Burckhardt type-road model parameters.  
Figure 6: Tyre-road unit longitudinal force characteristics: **(a)** For different vehicle speed; **(b)** For different normal forces.