# Mathematical model of Tractor Gear Optimization Based on mathematical analysis

According to the large power of tractor transmission system, higher requirements are put forward for the strength and service life of gears. Therefore, it is necessary to comprehensively consider the relevant constraints to accurately calculate the load-bearing capacity of the gears in the working process of the tractor.

The objective function of gear transmission can be found from many different angles to establish the optimization process model, such as the smallest volume or the lightest mass, the highest bearing capacity, the largest transmission power and so on.

The constraint condition of the objective mathematical model in this optimization design process is to minimize the volume of the planetary gear transmission system. The mathematical model is as follows

For the planetary gear transmission system, the total volume of the planetary gear transmission system can be expressed as the sum of the volume of the sun gear and the volume of all the planetary gears

Where, VA is the volume of the sun gear; Da is the diameter of the pitch circle of the sun gear; Za is the number of sun gear teeth; VC is the volume of a single planet gear; DC is the diameter of the pitch circle of the planet gear; ZC is the number of planet gear teeth; m is the modulus; B is the width of the teeth; C is the number of planet gears. 