# Design of tractor gear transmission mechanism based on mathematical analysis

In the process of tractor gear transmission, the transmission load is large, the running speed is low, and the transmission load changes greatly, so it is unable to take effective mathematical expression to express the transmission law. Due to the particularity of tractor working environment, the tractor is required to be small in size and light in weight. At the same time, the power of tractor transmission system is high, which puts forward higher requirements for the strength and service life of gears. In the process of transmission, it bears greater impact resistance and has higher requirements for tooth wear strength. In order to meet the economic and safety requirements of tractor gear transmission, it is necessary to ensure that the tooth profile of tractor gear transmission system can bear greater impact and the tooth surface wear is minimum.

For this reason, the planetary gear transmission system model is established based on dynamics. Through the dynamic modeling of the planetary gear transmission system under the standard design state, and assuming that all parameters meet the design requirements, the failure mode of the planetary gear transmission system is not analyzed. The existing research literature does not take the vibration mechanism as the starting point to analyze and study the fault vibration characteristics of gear transmission system. The failure mode dynamic model of planetary gear transmission system established by various scholars is only to model and analyze a possible mode failure without considering the time-varying effect of vibration.

The design and calculation process of planetary gear transmission system includes selection of transmission form (i.e. determination of transmission type and transmission diagram of planetary gear transmission system), calculation of gear matching and gear related geometric parameters according to transmission ratio and assembly space, as well as efficiency calculation of the whole transmission gear system, and checking calculation of gear strength after meeting the design requirements.

Although the conventional design can meet the requirements of transmission function, the design scheme is not the optimal design scheme when considering the economy and safety. It can not meet the requirements of minimizing the tractor volume and mass at the same time, and the tooth profile of the gear transmission system can withstand greater impact and tooth wear optimization. Therefore, it is of great practical significance to make full use of different constraints and computer-aided technology to optimize the design scheme.

1) With the support of computer-aided technology, the optimal design of planetary gear transmission system is carried out by using the optimal design method. Under the condition of meeting the requirements of strength and structure, the optimal design of structure is achieved.

2) The dynamic model of tractor planetary gear transmission system is established, and the influence of the comprehensive error in the meshing process of the gear pair and the time-varying meshing stiffness of the ulnar clearance is considered.

3) The time-varying meshing stiffness of gear pair is expressed by Fourier series, and the meshing stiffness of planetary gear under different fault degrees is derived.

After the completion of the structure design, in order to further obtain the meshing stiffness of the planetary gear transmission system, the concept of gear pair meshing comprehensive error and backlash caused by the design and processing in the process of gear meshing is introduced, and the mathematical model of the planetary gear transmission system is established in the field of transmission system dynamics; Considering the time-varying effect of vibration transmission path on vibration signal, the mathematical model of meshing stiffness of planetary gear transmission in fault mode is deduced, and the meshing stiffness under different fault degrees is obtained, which provides reference for fault monitoring of tractor planetary transmission system.

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