**Abstract:** The five-speed 5T18 transmission gear-bearing system simulation model was established by RomaxDesigner software, and the influence of the deep groove ball bearing at the rear end of the output shaft on the dynamic performance of the system under different bearing preload and inclination was analyzed under the first gear condition. The dynamic response curves of the system bearing force, transmission error and dynamic meshing force are obtained.

** Introduction**

Transmission is one of the key components that make up the automobile powertrain, and the quality of its performance has a direct impact on the comfort and operability of the automobile. Because the helical gear has the characteristics of high coincidence and smooth transmission, it is widely used in transmission assembly, but the meshing position of the helical gear will be affected by radial force and axial force at the same time during operation. The unreasonable adjustment of bearing clearance will cause abnormal vibration, noise and premature failure of the system under the action of long-term axial force. Therefore, in order to improve the accuracy of the transmission, the ball bearing used on the output shaft needs to be preloaded. After the bearing is preloaded, the force on each rolling element will be more uniform, which can greatly improve the vibration resistance of the system. The preloading effect of the bearing will directly affect the transmission. box performance and service life [1]. There are usually two types of bearing preloading: positioning preloading and constant pressure preloading, but the positioning preloading method has a greater effect on increasing the bearing stiffness, so the positioning preloading is widely used in transmission assembly. In gearbox assembly, adjusting shims are usually used to ensure proper bearing preload on the output shaft and intermediate shaft. When an appropriate preload is applied to the ball bearing, the phenomenon of bearing deformation, bearing inclination, and axial dimension change will occur. Therefore, when selecting an adjusting shim, it is necessary to first apply a preload to the bearing to control [2]. Therefore, the study of bearing The influence of preload on the dynamic characteristics of transmission gear-bearing system is of great significance. In this paper, a gear-bearing system simulation model of the fifth-speed 5T18 transmission is established, and the dynamics of the gear-bearing system of the transmission under the conditions of different preload and inclination of the deep groove ball bearing at the rear end of the output shaft under the first gear condition is studied. influence of characteristics.

**1 Establishment of the transmission gear-bearing simulation model**

The JAC 5T18 transmission gear-bearing model is established in the RomaxDesigner software, as shown in Figure 1. The 5T18 transmission is currently mainly used in JAC Ruifeng M3 models. It is a three-shaft transmission. The front end of the input shaft is connected to the housing through deep groove ball bearings, the rear end is connected to the output shaft through needle roller bearings, and the intermediate shaft and the output shaft are two. The end is connected to the shell through deep groove ball bearings [3]. In actual assembly, due to the influence of parts manufacturing error, assembly error and other factors, the bearing clearance is unreasonable. Therefore, the 5T18 transmission selects appropriate adjusting shims for the intermediate shaft and output shaft bearings to ensure a reasonable shaft. Adjust the bearing clearance and adjust the bearing clearance, so as to control the preload of the bearing and increase the stiffness of the ball bearing. Figure 2 is a schematic diagram of gear-bearing dynamics. The driving gear and the driven gear are installed on the intermediate shaft and the output shaft respectively, and the bearings are deep groove ball bearings. The bearing can be regarded as a spring resistance model, and the force between the tooth surfaces is represented by the elastic force and damping force of the gear meshing [4].

p represents the driving gear, g represents the driven gear; ωp, ωg are the meshing speeds of the driving gear and the driven gear, respectively; Kpx, Kpy, Kgx, Kgy are the main tooth end bearing and the tooth end bearing in the x-axis and y-axis directions, respectively. Cpx, Cpy, Cgx, Cgy are the damping coefficients of the main tooth end bearing and the tooth end bearing in the x-axis and y-axis directions, respectively; Km and Cm are the instantaneous meshing stiffness and instantaneous meshing of the tooth surface when the gear meshes, respectively. damping value. Then the relative displacement of the main and passive gears along the meshing line is the dynamic transmission

## The dynamic error can be expressed as [5]:

δ(t)=Rpθp-Rgθg+(xp-xg)sinα+(yp-yg)cosα-e(t). (1)

Among them: Rp and Rg are the base circle radius of the main and passive gears respectively; θp and θg are the main and passive gear meshing angles, respectively; xp, yp, xg, yg are the main and passive gear meshing process axial and radial Relative displacement; α is the meshing angle when the main and driven gears are engaged; e(t) is the meshing error caused by the manufacturing error such as the pressure angle of the gear itself and the gear assembly error, that is, the static transmission error.

The dynamic meshing force of the gear can be expressed as the resultant force of the meshing elastic force and the meshing damping force of the gear, namely:

Fm(t)=Kmf(δ(t))+Cmδ·(t). (2)

Where: f(δ(t)) is the backlash displacement function of the main and driven gears related to the backlash jn,

In this paper, the gear-bearing model is used to simulate the working condition of the first gear of the transmission. The simulated input rated torque is 175N·m and the speed is 3000r/min. The influence of the rear bearing tilt of the transmission and the bearing preload on the system performance is analyzed. The bearing inclination and preload are realized by applying different inclination angles and displacements to the outer ring of the deep groove bearing after the output shaft. , 100μm, 150μm and other dynamic responses of the system transmission error, dynamic meshing force and bearing force.

**2 Dynamic simulation and analysis**

### 1 Dynamic Simulation Theory

According to the theory of elastic mechanics, the equation of gear system dynamics is obtained as:

mx··+cx·+kx=F(t). (4) Among them: m, x, c, k are the mass of the gear-bearing dynamic system, respectively

matrix, relative displacement vector, damping matrix, stiffness matrix; F(t) is the excitation load matrix. The dynamic response of the transmission system is analyzed in the RomaxDesigner dynamic analysis software, ignoring the influence of external excitation, and only taking the combined action of the gear mesh stiffness k(t) and the transmission error e(t) as the excitation source of the system, Therefore, the free excitation on the right side of formula (4) can be expressed as the product of the transmission error and the mesh stiffness, namely:

F(t)=k(t)e(t). (5) In formula (5), the meshing stiffness k(t) and the transmission error e(t) can be directly calculated, so formula (5) can be simplified as: mx··+cx·+kx=k(t)e(t). (6)

The solution of equation (4) is the result of the dynamic response.

### 2 Analysis of simulation results

Figure 3 shows the static transmission error diagram under different bearing preloads under the first gear condition. It can be seen that the maximum static transmission error is 45.9 μm under the first gear condition, and the static transmission error remains basically unchanged under different preloads; With the increase of preload, the peak value of transmission error is slightly reduced. Figures 4 to 9 show the frequency response of the system under the harmonics of the output gear, respectively. Figure 4 shows the dynamic transmission error of the gear transmission system under different bearing inclinations. It can be seen that different bearing inclinations have basically no effect on the dynamic transmission error of the system. When the inclination is 4°, the error peak value is slightly reduced. Figure 5 shows the dynamic transmission error of the gear transmission system under different bearing preloads. It can be seen that with the increase of preload, the peak value of dynamic transmission error decreases, and the system reaches the maximum peak at high frequency, that is, when the gear-bearing is running at high speed The system is prone to vibration.

Figure 6 shows the dynamic meshing force of the output shaft gear under different bearing inclinations, which is the actual excitation force under a given first gear condition. It can be seen that with an inclination of 4°, the maximum dynamic meshing force is approximately reduced. 100N. Figure 7 shows the dynamic meshing force of the output shaft gear under different bearing preloads, which is the actual excitation force under a given load condition. It can be seen that with a preload of 150 μm, the maximum dynamic meshing force is reduced. 500N, compared with Fig. 4, Fig. 6, Fig. 7, it can be seen that the frequency characteristics of dynamic meshing force are basically the same as the dynamic transmission error, and have nothing to do with bearing preload and inclination angle. The bearing force is the dynamic response force caused by the gear dynamic meshing force and the gear meshing error transmitted to the bearing through the gear-output shaft, and is also the excitation source of the vibration of the box. Figure 8 shows the frequency domain distribution of the dynamic bearing force of the deep groove ball bearing at the rear end of the output shaft under three bearing inclinations. Depend on

Figure 8 shows that as the inclination increases, the amplitude of the bearing force increases significantly at high speed, which will cause the vibration amplitude of the box to increase; in the low frequency band with different inclinations, the bearing force is basically the same, that is, at low The frequency band has little effect on the bearing force. Figure 9 shows the frequency domain distribution of the dynamic bearing force of the deep groove ball bearing at the rear end of the output shaft under different preloads. It can be seen from Figure 9 that with the increase of the preload, the amplitude of the bearing force at low and high speeds decreases significantly. With a preload of 150 μm, the bearing force is reduced by 270N; the peak frequency of the dynamic bearing force is related to the dynamic transmission. The error frequency is basically the same.

**3 Conclusion**

A five-speed transmission gear-bearing dynamic simulation model was established in RomaxDesigner, and the effects of different preloads and inclinations of the deep groove ball bearing at the rear end of the system output shaft on the static transmission error, dynamic transmission error, and dynamic transmission error of the gear were studied under the first gear condition. The influence of gear dynamic meshing force and bearing force. The results show that the bearing preload has an important influence on the dynamic characteristics of the system, and proper bearing preload can improve the system performance. The tilting of the bearing will increase the bearing force of the bearing and cause the vibration amplitude of the gearbox to increase. Therefore, ensuring that the bearing does not tilt when assembling the bearing is one of the effective measures to reduce the vibration of the box.