## 5 Simulation Analysis of Braking Timing Sequence Stability of Semi-Trailer Train  
According to the calculation method of permutation and combination, there are a total of seven different combinations of braking timing arrangements for three-axle semi-trailer trains. They are all axles braking at the same time, 1-2-3, 1-3-2, 2-1-3, 2-3-1, 3-1-2 and 3-2-1, respectively. Among them, one represents the steering axle of the tractor, two represents the driving axle of the tractor and three represents the semi-trailer axle. The front axle first produces braking. The semi-trailer train model is simulated and analyzed according to these seven braking timing sequences. The speed is set to 50 km/h and braking force is applied slowly until the vehicle stops. The yaw angle, lateral acceleration, driving trajectory and jackknife angle of the train are simulated and output. The data are shown in Figure 7. Vehicle braking stability evaluation is usually concerned with the maximum value of the test items, so the maximum value of the simulation output is selected as the evaluation value. The yaw angle and lateral acceleration select the sum of the tractor and semi-trailer outputs, and braking distance and braking deviation are evaluated based on the tractor. The maximum output value of each evaluation index after simulation is shown in Table 12.  
\[P_{i}=\sum_{i=1}^{5}w_{i}r_{i},\sum_{i=1}^{5}W_{i}=1\ and\ W_{i}\geq 0 \tag{13}\]  
The linear weighted sum method is used to optimize the multi-objective optimization of the braking time sequence of the semi-trailer train, as shown in Equation (13), where \(P_{i}\) is the comprehensive evaluation value corresponding to the \(i\)-type braking time sequence, \(w_{i}\) is the weight corresponding to each evaluation index, and \(r_{i}\) is the evaluation index value corresponding to different braking time sequences. The linear weighted sum method can take into account the impact of all evaluation indicators on the whole, and can better extract the integrity of the system. \(P_{1}\) = 3.981, \(P_{2}\) = 4.237, \(P_{3}\) = 3.974, \(P_{4}\) = 4.152, \(P_{5}\) = 4.195, \(P_{6}\) = 4.231 and \(P_{7}\) = 4.146 is calculated by substituting the data in Tables 3 and 8 into Equation (13). Because, when evaluating the braking stability of the semi-trailer train for different braking timing sequences, the smaller the output value of each evaluation, the better, it follows that, the smaller the \(P_{i}\) value is, the better the braking stability of the train using that particular braking timing sequence. By comparison, it can be seen that when the braking timing sequence is tractor steering axle-trailer axle-tractor drive axle, the comprehensive evaluation value is the smallest, and it can be considered that the braking \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Item** & **Simultaneous** & **1-2-3** & **1-3-2** & **2-1-3** & **2-3-1** & **3-1-2** & **3-2-1** \\ \hline Tractor yaw angle & 3.319\({}^{\circ}\) & 3.559\({}^{\circ}\) & 3.190\({}^{\circ}\) & 3.422\({}^{\circ}\) & 3.512\({}^{\circ}\) & 3.548\({}^{\circ}\) & 3.479\({}^{\circ}\) \\ Trailer yaw angle & 2.487\({}^{\circ}\) & 2.458\({}^{\circ}\) & 2.467\({}^{\circ}\) & 2.486\({}^{\circ}\) & 2.533\({}^{\circ}\) & 2.863\({}^{\circ}\) & 2.910\({}^{\circ}\) \\ Tractor lateral acceleration & 0.060 g & 0.084 g & 0.053 g & 0.097 g & 0.066 g & 0.122 g & 0.082 g \\ Trailer lateral acceleration & 0.035 g & 0.043 g & 0.040 g & 0.041 g & 0.057 g & 0.124 g & 0.098 g \\ Jackknife angle & 0.924\({}^{\circ}\) & 1.201\({}^{\circ}\) & 0.823\({}^{\circ}\) & 1.043\({}^{\circ}\) & 1.068\({}^{\circ}\) & 0.792\({}^{\circ}\) & 0.636\({}^{\circ}\) \\ Braking distance & 22.354 m & 23.736 m & 23.449 m & 23.760 m & 23.800 m & 24.421 m & 24.313 m \\ Braking deviation & 2.829 m & 2.693 m & 2.686 m & 2.696 m & 2.703 m & 2.721 m & 2.723 m \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Maximum output value for each parameter. stability of the train is the best at this time.