## 3 Results and Discussion
### Simulation Results and Their Discussion
The simulation with a rearward shift of the centre of gravity (b3r) shows a lower than the nominal (b1) value of the \(F_{SA}\) force (its value is at the level of 71 \(\div\) 77 kN in  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **M** & **b2** & **b3r** & **b3r** & **b4** & **b5** & **b6** & **b7** & **b6** \\ \hline \multicolumn{10}{c}{**Constant Excitation to a \(\pm\)45\({}^{\circ}\)**} \\ \hline \multirow{3}{*}{II} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} \\  & & & & & & & & & \\  & 0 \(\div\) 100 AN & 0 \(\div\) 14 AN \(\times\) & 0 \(\div\) 82 kAN \(\times\) & 0 \(\div\) 12 kAN \(\times\) & 0 \(\div\) 11 kAN \(\times\) & 0 \(\div\) 11 kAN \(\times\) & 0 \(\div\) 10 kAN \(\times\) & 0 \(\div\) 7 kAN \(\times\) & 0 \(\div\) 14 kAN \(\times\) \\ FD & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} & \multirow{3}{*}{\(>\)0} \\  & & & & & & & & \\  & 0 \(\div\) 62 kAN & 0 \(\div\) 7 kAN \(\times\) & 0 \(\div\) 61 kAN \(\times\) & 0 \(\div\) 11 kAN \(\times\) & 0 \(\div\) 71 kAN \(\times\) & 0 \(\div\) 71 kAN \(\times\) & 0 \(\div\) 71 kAN \(\times\) & 0 \(\div\) 62 kAN \(\times\) \\ FD &the phase of fully developed braking in b3r variant, where for b1 case is c.a 100 kN). This means that loading of the semi-trailer axle (as in b3r variant), resulting in an increase in the adhesion utilization rate, has a positive effect on reducing the risk of braking safety. From the other hand, in the simulation with the centre of gravity shifted forward (b3f), the horizontal force in the coupling is 8 \(\div\) 12 kN higher than the nominal variant (b1) value. The braking results with a constant deceleration of 4.5 m/s\({}^{2}\) (CD) are similar in terms of quality. Figure 16: Range of coupling force for constant excitation series (CE) for 9 braking variants (lighter colour—braking initialization phase IB, darker colour—fully developed braking phase FD). Figure 17: Range of coupling force for constant deceleration series (CD) for 9 braking variants (lighter colour—braking initialization phase IB, darker colour—fully developed braking phase FD). The highest value of the horizontal force in the coupling was obtained for the simulation with an unbraked semi-trailer (b5), in which the coupling force is a maximum of 113 kN for ABS off and 117 kN for ABS on. ABS, the maximum force in the coupling is similar to the case of b3f. However, in b5, in the phase of fully developed braking, it is even approx. 12 kN lower than in b3f. From this, it follows that case b3f (centre of gravity shifted forward) is even worse than no trailer braking (b5). In the variant with longer reaction time (b6), an increase in the maximum value of the horizontal force in the coupling in the phase of applying the brakes (IB) is noticeable. However, the increase in these forces is not significantly large (by 5 kN in the CE simulation and 9 kN in the CD simulation). From the other hand, in the phase of fully developed braking (FD), the force \(F_{sA}\) in the coupling is identical to this in the nominal variant (the maximum braking torque for the axle of the semi-trailer is reached). A greater value of the maximum force in the coupling in the brake initialization phase (IB) than in the fully developed braking phase (FD) in the nominal variant b1 (CE) did not occur, and this effect becomes visible with the increase in the response time of the semi-trailer braking system. In the moment when \(F_{sA}\) reach maximum the risk of jack-knifing phenomena is greatest. This topic will also be discussed later in this section. Also, higher than the value of the \(F_{sA}\) force in the nominal variant is shown by the variant with exceeded load mass b4 (by 4 kN for the CD case and by 9 kN for the CE case).