# Optimal design of bevel gear transmission mechanism

The function of bevel gear is to transmit the motion and power between two intersecting axes. Similar to cylindrical gears, bevel gears have many classifications. According to the appearance of gear teeth, bevel gears can be divided into straight bevel gears, helical bevel gears and spiral bevel gears. The advantages of bevel gear transmission are high transmission efficiency, stable transmission ratio, reliable operation, compact structure, space saving, wear resistance, long service life and low noise. At present, bevel gear transmission has been widely used in many fields. At present, the main objective of bevel gear transmission optimization design is to select the appropriate gear pair parameters under the condition of meeting the bearing capacity, so as to minimize the volume and structure of the transmission device.

At present, domestic scholars on the bevel gear transmission test and research is more in-depth. Ye Xiaofen and others put the size and strength design of the reducer into the constraint conditions, established the mathematical model, and used the MATLAB optimization toolbox to carry out the structural optimization design, and solved the volume of the transmission mechanism and the minimum objective function. Sun Hongjie et al. Take the gear modulus and transmission ratio as design parameter variables, take the gear tooth surface and tooth root strength requirements and non-interference between mechanisms as constraint conditions, take the minimum total transmission center distance of gear pair as objective function, and use matlab toolbox to solve the problem. Li Xuzhen integrated the gear parameters into the optimization mathematical model, combined with particle swarm optimization algorithm to solve the objective function. All of the above researches make the gear pair obtain smaller volume, but there are also some disadvantages, which can not meet the multi-objective optimization requirements of gear transmission, such as the insufficient contact degree and low strength of gear pair meshing, which leads to the decline of the stability of gear transmission.

The optimization mathematical model of bevel gear transmission mechanism is established, and the objective function is solved by genetic algorithm and Matlab toolbox. Genetic algorithm simulates the natural selection and genetic mechanism of Darwinian evolution theory. It is a kind of randomized search algorithm that continuously selects excellent individuals until the optimal individual is found in the whole situation. Genetic algorithm is widely used in engineering optimization design because of its applicability to complex multi-modal function and global optimization of objective function, especially in the fields of mechanism structure parameter optimization design, production scheduling, pattern recognition, neural network, adaptive control, etc.

This paper analyzes the characteristics of bevel gear transmission mechanism, establishes its mathematical model, obtains the optimization design variables, objective function, performance constraints and boundary constraints, and carries out the optimization design. The penalty function method is used to construct the fitness function, and the tooth surface contact strength condition and tooth root bending strength condition in the optimization design mathematical model are constructed as penalty terms in the fitness function. The genetic algorithm. M format file is compiled, and the optimal solution is obtained by using fmincon function of MATLAB optimization toolbox. After the program is finished, the design variables need to be rounded and adjusted.

The feasibility and applicability of using genetic algorithm to optimize the design of bevel gear transmission mechanism are verified by optimization examples, which provides a reference for multi-objective optimization design of bevel gear transmission mechanism.

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