## 1 Introduction  
As one of the main components of a transmission, the synchronizer generates friction torque during friction synchronization, thereby eliminating the difference in rotational speed between the two ends of the synchronizer, to achieve shifting [1]. During the synchronization of the synchronizer, the friction coefficient of the friction cone is changed because of friction heat, which ultimately affects the shift control accuracy of the transmission [2].  
A lot of basic research has been proposed to improve shift control accuracy [3; 4]. The temperature changing regularities of the friction surface under different working conditions were analyzed by simulation and experiment [5; 6]. The influence of temperature on the synchronizer's working performance was verified in literature [7]. The friction and heat generation process of the synchronizer with different friction coefficients were analyzed in the literature [8; 9]. The results showed that the greater the friction coefficient is, within a certain range, the higher the temperature between the friction surfaces. Additionally, [PERSON] presented a model of predicting wear in the friction lining of a wet clutch and introduced that the wear mechanism is related to thermal degradation [10]. [PERSON] developed a friction model which takes temperature, speed, and nominal pressure into account for the wet clutch during boundary lubrication conditions [11]. The friction surface temperature and the friction coefficient of the friction cone are the critical influences on the shift quality, which need further study.  
Currently, research on car synchronizers has mainly focused on the influence of the geometry of the synchronizer and the synchronous inertia on the synchronous performance, and considered the friction coefficient between the friction pairs of the synchronizer as a constant. In reference [12], the ADAMS software was used to establish the virtual prototype model of the lock-ring synchronizer, and the influence of each parameter on the shift synchronization time was studied. [PERSON] regarded the friction coefficient as a constant in the process of establishing the synchronizer model [13]. In the synchronous shift phase, the synchronizer realizes the synchronization function by sliding between the friction cones. The length of the synchronization time is directly determined by the friction coefficient between the friction cones, so the calculation method of considering the friction coefficient as a constant is not accurate. Besides this, with the deepening of the research on the synchronizer by domestic and foreign research institutions, research on the friction coefficient between the friction pairs of the synchronizer has deepened. In reference [14], the dynamic model of the double-cone synchronizer was established based on the ADAMS software. On this basis, the effects of spring stiffness, the cone angle of friction ring, and the friction coefficient on shift force and the synchronization process were analyzed. [PERSON] analyzed the influence of temperature, speed difference, and shift force on the friction coefficient during synchronizer synchronization [15]. [PERSON] compared the influence of the friction coefficient on synchronizer performance and structure parameters under different inertia and speed difference [16]. [PERSON] conducted a bench test on the working process of the synchronizer. The results showed that the friction coefficient was not maintained at a constant value. In order to accurately reflect the real situation of the synchronization process, the friction coefficient must be considered [17].  
In this paper, we study the influencing factors of the friction coefficient change of the synchronizer, and explore the quantitative variation law between the friction coefficient and each influencing factor, then develop the friction coefficient compensation control strategy to maintain the friction coefficient near the expected value and shorten the synchronization time. This is important to improve the shift quality.