## 2 Analysis of the Influence of Friction Coefficient on Synchronous Performance
### Simulation Analysis of Synchronization Performance  
The simulation model of a synchronizer in synchronization phase was built, and the influence of friction coefficient change between the synchronizer's friction pairs on synchronization performance was analyzed. According to the value range of the friction coefficient of the locking ring synchronizer's friction pair selected in this paper, the friction coefficient was set to 0.05, 0.07, and 0.09 in the simulation process, and the rotational inertia of the synchronized partial was 0.04 Kg\(\cdot\)m\({}^{2}\). The influences of speed difference and friction coefficient on synchronization time were analyzed, as shown in Figure 2.  
The larger the friction coefficient was, the shorter the synchronization time that was needed when the initial shifting speed difference was the same. With the increase in shifting speed difference, the effect of friction coefficient on synchronization time became more and more obvious. When the shifting speed difference was 600 r/min and the friction coefficient was 0.09, the synchronization time was 0.58 s. When the friction coefficient was 0.05, the synchronization time was 0.79 s. The difference between them was 0.21 s. According to the simulation, the friction coefficient should be increased in order to shorten the synchronization time. When the inertia of the synchronized part was 0.04 Kg\(\cdot\)m\({}^{2}\), the influence of speed difference and friction coefficient on sliding-friction work was analyzed, as shown in Figure 3. The variation trend of sliding-friction work was basically the same under different shifting speed differences and friction coefficients. When the shifting speed difference was the same, the friction coefficient had no effect on the final value of sliding-friction work, but only affected the increase rate of sliding-friction work. The greater the friction coefficient was, the shorter the time it took for the sliding-friction work to reach the final value. When the shifting speed difference was 600 r/min, the sliding-friction work consumed under the three friction coefficients was 78.96 J. However, when the friction coefficient was 0.09, the time needed to reach the final value of sliding-friction work was 0.21 s shorter than when the friction coefficient was 0.05. When the final value of sliding-friction work was determined, the shorter the synchronization time was, the more heat generated per unit of time. Moreover, excessive heat generated per unit of time may have caused damage to the friction surface. When the inertia of the synchronized part was 0.04 Kg\(\cdot\)m\({}^{2}\), the influence of speed difference and friction coefficient on shock degree were analyzed, as shown in Figure 4. Since the maximum shock degree occurred at the initial stage in the synchronization process, the shock degree at the initial stage was intercepted for comparative analysis. It can be seen from the graph that the maximum shock degree decreased with the increase of friction coefficient when the shifting speed difference was the same. When the shifting speed difference was 600 r/min, the maximum shock degree was 160.3 rad/s\({}^{3}\) when the friction coefficient was 0.09, and 290.4 rad/s\({}^{3}\) when the friction coefficient was 0.05. Figure 2: Synchronization time. Figure 4: Shock degree contrast curve of synchronization early stage: (**a**) shift speed difference 600 r/min; (**b**) shift speed difference 700 r/min; (**c**) shift speed difference 800 r/min; (**d**) shift speed difference 900 r/min. Figure 3: Sliding-friction work contrast: (**a**) shift speed difference 600 r/min; (**b**) shift speed difference 700 r/min; (**c**) shift speed difference 800 r/min; (**d**) shift speed difference 900 r/min. In conclusion, with the increase in the friction coefficient, the synchronization time of the synchronizer decreased. The friction coefficient had no effect on the final value of sliding-friction work in the synchronous process, but it affected the increase rate of the sliding-friction work.