Four mathematical models of oil film pressure

contact force of asperity

axial force of synchronizer ring and cone torque are established by means of average Reynolds equation and asperity friction principle. The coupling number of oil film thickness and speed difference of synchronization is solved by using 4-Runge-Kutta method. The changing rule of oil film thickness

speed difference

viscous torque

asperity friction torque and total torque are analyzed. After verification of the mathematical model of synchronization

the effects of structure factors such as the width of synchronizer ring

radius of synchronizer ring

cone angle and thickness of friction material of synchronizer are studied by the model. The results show that the increase of the width of synchronous ring results in increasing viscous torque and asperity friction torque

decreasing the decline rate of oil film thickness

the response of asperity friction torque is delayed and the synchronization time is increased. With the increase of the radius of synchronous ring

the viscous torque and asperity friction torque increase

the oil film thickness descends and the synchronization time is shortened. When the friction angle increases

the viscous torque increases

the asperity friction torque decreases

the speed difference descends slowly and the synchronization time prolongs. With the increase of friction material thickness

the asperity friction torque and the changing rate of oil film thickness increase correspondingly

but the minimum oil film thickness and the synchronization time decrease.