Optimum Design Of Spiral Bevel Gear Reducer With Small Tooth Differences Based On Genetic Algorithm

The classical design method of machine structure results in large deadweight, high cost, unreasonable design parameter in excessively pursuit of the security of structure. Compared with it, modern design method introduces advanced arithmetic and means of computer aided design, which can make design result approach optimal value as perfect as possible. So the performance of machine structure can be improved greatly. At the same time it can not only increase efficiency but also economize time. Therefore science and technology personnel attach much importance to the method.This paper aims at a new kind of bevel gear planetary reduction gear with small tooth differences. The interference problem in the engagement course of bevel gear pair is analyzed and the analytical condition of tooth profile without overlap interference is gained based on the differential geometry and the theory of space engagement. The inertia moment of the balance wheel is obtained according to momentum theorem, D'Alembert's principle and Laichai theorem.The maximal contact stress between two cylinders according to Hertz contact law of elastic mechanics. Finally, the optimal mathematic model is constructed based on the characteristics of optimization variables, with consideration of bevel gears strength, the interference of profile of tooth, nutation angle etc. The Object function ensures the minimum of inertia moment and volume. Genetic algorithm is used to resolve the problem and the reasonable design parameter can be obtained relative to different input powers, rotation speeds and transmission ratios.The example indicates that genetic algorithm has the advance of rapid convergence, finer stability and so on, which can improve efficiency of design work. So it has a wide acceptance in the process of mechanical structure design practice. Compared with traditional optimization algorithms, thegenetic algorithm is more convenient in treatment of non-convex or discontinuous function, therefore, is more suitable in the solution of the global optimization. It is believed that the theory of genetic algorithm will be more perfect under the effort of researchers and thus the application of this algorithm will be more and more widely used in the field of bevel gear drive parameter optimization.