## 4 Results and Discussion
### Response Time of Subassemblies in a Single Axle  
Subassemblies in a single loop consist of treadle valve, control pipeline, relay valve, brake pipeline and brake chamber. Delay time of a loop is the accumulation of the response time of each subassembly. Sensors used for measuring the response time are arranged as shown in Figure 7. \(t^{(up,down)}_{res. (f,r)j}\) (\(j=1,2,3,4\)) represents the response time of each subassembly in the front (C) or rear (E) loop in brake process or brake release process. Specifically, \(t^{(up,down)}_{res.(f,r)1},t^{(up,down)}_{res.(f,r)2},t^{(up,down)}_{res. (f,r)3}, t^{(up,down)}_{res. (f,r)4}\) represents the response time of treadle valve, controlling pipeline, relay valve and braking pipeline, respectively. Hence, the delay time of the two loops can be described as,  
\[\left\{ \begin{array}{l}\Delta t^{(up,down)}_{dd.,f}=\sum\limits_{j=1}^{n}t^ {(up,down)}_{res.(f)}\\ \Delta t^{(up,down)}_{dd.,f}=\sum\limits_{j=1}^{n}t^{(up,down)}_{res.(f)}\\ \end{array} \right., \tag{10}\]  
where \(\Delta t^{(up,down)}_{dd.,f}\), \(\Delta t^{(up,down)}_{dd.,f}\) are the delay time of the front loop C and rear loop E, respectively. The original measured data of the two loops under the testing condition of group 1 are shown in Figure 14.  
Subsequently, a method for calculating the response time of each subassembly in a single loop is given as follows. \[\left\{ \begin{array}{l}\Delta t^{(up,down)}_{dd.,f}=t^{(up,down)}_{pp.,f}-t _{start.(up,down)}\\ t^{(up,down)}_{res.,f}=\Delta t^{(up,down)}_{dd.,f_{i}}-\Delta t^{(up,down)}_{ dd.,f(i-1)}\\ \end{array} \right., \tag{11}\]  
\[\left\{ \begin{array}{l}\Delta t^{(up,down)}_{dd.,f_{i}}=t^{(up,down)}_{pp., f}-t_{start.(up,down)}\\ t^{(up,down)}_{res.,f_{i}}=\Delta t^{(up,down)}_{dd.,f_{i}}-\Delta t^{(up,down)}_{ dd.,f(i-1)}\\ \end{array} \right., \tag{12}\]  
where \(\Delta t^{(up,down)}_{dd.,f_{i}}\) and \(\Delta t^{(up,down)}_{dd.,i}\) are the delay time of each subassembly in the front and rear loop, respectively, and they are calculated in the same way as \(\Delta_{dd. (up,down)}\) mentioned in Section 4.1. \(t^{(up)}_{pp.,f_{i}}\)  
Figure 13: The variation of the brake chamber pressure with different pedal openings. (**a**) \(\psi=67\%\)**(b) \(\psi=93\%\)**. \(t_{\gamma_{p}\_ri}^{(up)}\) are the times when the pressure in a subassembly increase to 75% of its steady value in the brake process, and \(t_{\gamma_{p}\_fi}^{(down)}\), \(t_{\gamma_{p}\_ri}^{(down)}\) are the times when the pressure in a subassembly decreases to 15% of its steady value in the brake release process. These times are measured by sensors \(f_{i}\) and \(r_{i}\). Finally, the response times of each subassembly in two loops are acquired, as shown in Figures 15 and 16. Figure 14: Original pressure curves of front loop C and rear loop E under the testing condition of group 1. Figure 15: Response time of each subassembly in brake process under the testing condition from group 1 to group 5, shown in (**a–e**) respectively. Finally, the proportion of response time of each subassembly can be calculated using the following formula and the corresponding results are shown in Figure 17.  
\[\varphi_{\textit{res.}(f,r)j}^{(up,down)}=\frac{t_{\textit{res.}(f,r)j}^{(up, down)}}{\Delta t_{\textit{dd.}(f,r)}^{(up,down)}}, \tag{13}\]  
From Figure 17, it can be observed that the response time of the treadle valve and the controlling pipeline are much longer than that of the controlling pipeline and braking pipeline. The sum response time accounts for more than 80% of the total delay time of both the two loops in the brake process,  
Figure 16: Response time of each subassembly in brake release process under the testing condition from group 1 to group 5, shown in (**a**–**e**), respectively. \(j=1,\,2,\,3,\,4\). Figure 17: Average proportion of response time of each subassembly under the testing condition from group 1 to group 5.