Nonlinear Dynamics Research Of Spiral Bevel Gear Pair With Random Assembly Backlash

As one of the most complex gear transmission, spiral bevel gear system is widely used in aerospace, ships, cars, etc. And it plays an important role in the transmission system due to its significant advantages:1) It transmits smoothly; 2) It can work under extremely heavy load; 3) The efficiency of transmission is high. Spiral bevel gear dynamic performance has an enormous impact on the entire driving system performance, so the analysis about spiral bevel gear system is very important. Dynamic model is set up considering backlash, time-varying meshing stiffness as well as a number of factors, then the dynamic equation is solved and analyzed, and a method is provided as a theoretical basis to choose spiral bevel gear backlash which can help engineers ensure good dynamic performance of a series of gears.Focused on the advanced helicopter reducer research project and based on the transmission system of spiral bevel gear as research object, this paper established a bend-twist-multi-axis direction vibration coupling model, then the dimensionless equations-process is executed considering various dynamic stimulation. In order to facilitate model analysis as well as the response data handling, the model is simplified. Then the inherent characteristics of the system is analyzed through numerical method, the result is compared with bevel gear model characters constructed in three-dimensional software to testify the validity of models proposed in this paper. This paper presents numerical solution of nonlinear equations, then solves nonlinear equations, and detail analysis method of nonlinear dynamic characteristics.This paper introduces random assembly backlash method into the result of spiral bevel gear backlash nonlinear equations. For a number of spiral bevel gears, the backlash values are randomly distributed. Through the chaotic index, system can be used to found connection between the variance and mean of the backlash, which can be fitted to match the appropriate critical backlash mean variance to ensure the entire batch of spiral bevel gear pair stable dynamic performance.