# Checking and Calculation of Life of Pure Electric Vehicle Transmission Bearing System

With the rapid development of the automobile industry, the enhancement of global environmental awareness, and the energy crisis caused by the massive exploitation of non-renewable resources such as oil and coal, automobile and parts companies are forced to carry out technological revolution and develop new energy vehicles. In order to seize the opportunity and seize the commanding heights of the market, a series of electric motors and transmissions for pure electric urban public transport buses have been designed and developed. Now introduce the life check calculation of its transmission bearing system.

**1 Force analysis of transmission system**

This pure electric urban public transportation bus adopts induction AC motor, which has the characteristics of wide speed regulation range, high efficiency, high speed regulation precision, and can realize closed-loop control of speed and torque, so that the matching transmission has a structure Simple, less gear, light weight and so on. AC induction motor rated power

The power rate is 100 kW (the following analysis and calculations are based on the motor operating at rated power), the rated speed is 1 500 r/min, the rated output torque is

The torque is 640 N m, and the transmission ratios of the three gears are: 4. 06, 1. 89, 1. The transmission structure of the transmission is shown in Figure 1, and the schematic diagram of the transmission relationship of each gear is shown in Figure 2. The gear transmission parameters, used bearing types and calculation parameters are shown in Table 1 and Table 2, respectively. The gear material is 20CrMnTi, and the tooth surface hardness is 58-64 HRC.

## 1.1 Calculation of gear force

Firstly, according to the transmission gear relationship, taking the driving gear as the research object, calculate the circumferential force Fgt, radial force Fgr and axial force Fga of each gear respectively, P is the transmission power; n is the gear speed; β is the gear helix horn. The calculation results of each force of the gear are shown in Table 3. Since the 3rd gear of the transmission is a direct gear and the transmission ratio is 1:1, the circumferential force, radial force and axial force on each gear are all zero.

## 1.2 Calculation of reaction force of gear shaft support

The structure of each support shaft of the transmission is treated as a statically indeterminate problem. According to the force on the gear, the support reaction force is calculated using the force balance equation [2]. The force analysis of each gear and shaft is shown in Figure 3 and Figure 4. In the first gear, the supporting reaction forces of bearings A and C on the I-axis are FrA1 = 5. 29 kN, FrC1 = 8. 63 kN (direction angle is 4°); the supporting reaction forces of bearings D and E on the intermediate shaft are FrD1 = 8 respectively. 01 kN, FrE1 = 20. 08 kN; the support reaction forces of bearings B and C on the Ⅱ axis are FrB1 = 21. 15 kN, F’rC1 = 5. 70 kN (the direction angle is 161.15°). In 2nd gear, the supporting reaction forces of bearings A and C on the I-axis are FrA2 = 5. 29 kN, FrC2 = 8. 63 kN (direction angle is 4°); the supporting reaction forces of bearings D and E on the intermediate shaft are FrD2 = 7 respectively. 46 kN, FrE2 = 6. 58 kN; the support reaction forces of bearings B and C on the Ⅱ axis are FrB2 = 7 respectively. 05 kN, F’rC2 =9. 11 kN (direction angle is -171.6°).

**2 Calculation of bearing force and equivalent load**

The radial force that the bearing bears is equal in magnitude to the shaft end support reaction force, and the direction is opposite; the bearing axial force should include the axial force caused by the radial force of the bearing itself in addition to the axial resultant force of the gear, such as bearing E The calculation of the axial force should take into account the internal axial force FS caused by its radial force, FS = Fr2Y. In addition, since the support point C is the common support of the I and II shafts, the radial force of the C bearing should be the vector synthesis of the two forces (in the 1st gear, it is the vector synthesis of FrC1 and F’rC1; in the 2nd gear, its is the vector synthesis of FrC2 and F’rC2). The calculation of the corresponding gear bearing force and equivalent dynamic load also needs to take into account the matching installation method of the bearing and its related load conditions.

**3 Calculation of the average equivalent load of the transmission system bearing**

According to the maximum speed limit of urban public transport bus 50 km/h, combined with the motor output power and torque characteristic curve, in the process of transmission design and calculation, considering the economy of electric energy output, 25 and 37 km/h were selected as the 2nd gear and 3rd gear of the transmission respectively. The automatic shift point of the gear is adopted, and the 1st gear start mode is adopted. Combined with GB/T 18488. 1—2006 “Electric Vehicle Motor and Its Controller” Appendix B Basic Urban Cycle (the theoretical driving distance of a basic urban cycle is 1017m), the road spectrum parameters of this transmission are calculated, see Table 6. When the input speed of the motor is 1 500 r/min, according to the speed of the bearing and the road spectrum of the urban public transport bus, the average speed of the system bearing can be obtained as shown in Table 7.

**4 Calculation of life of transmission bearing system**

Substitute the relevant parameters of each bearing into the above formula to obtain L10hA =2. 13 × 106 h; L10hB = 1. 62 × 105 h; L10hC = 8. 45 × 105h; L10hD = 3. 03 × 105 h; L10 hE = 26 216 h.

According to the basic cycle conditions of relevant urban public transport passenger cars provided in Table 6, a basic cycle time is 195 s, the passenger car is loaded and travels at a constant speed for 101 s, and the actual driving distance is 1 017 m. The life of the transmission bearing system is converted into the driving distance,

The “Standard for Compulsory Scrap of Motor Vehicles” stipulates that the service life of urban public transport buses is 13 years or 400,000 kilometers, and will be forcibly scrapped according to the first comer. The theoretical life of the transmission system bearing is 796 466. 8km, which fully meets the theoretical life mileage of the vehicle.

**5 Conclusion**

The theoretical life of the typical transmission bearing system is systematically checked, and the correctness of bearing selection in the transmission design process is verified. At the same time, it can also provide reference for the calculation and verification of similar transmission design, so as to shorten the transmission design and development cycle. However, in order to fundamentally guarantee and improve the service life of the transmission bearing system, in-depth research is needed on bearing materials, heat treatment, lubrication and cleanliness of the working environment, so as to continuously meet the inherent needs of automobile manufacturers and customers.

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