基于图论的共轴主减速器轻量化设计方法

Lightweight design method of coaxial main reducerbased on graph theory

主减速器是直升机传动系统的重要部件,其质量指标对整机性能有着重要影响。以共轴反转直升机的主减速器为对象,提出了一种基于图论的主减速器构型设计方法。1)通过对现有共轴主减速器资料的归纳,得到连接规律、边界条件和齿轮单元;2)建立主减速器对应邻接矩阵的自动生成方法,并将邻接矩阵转换为改进的图论模型;3)生成方案集合并建立筛选规则,得到主减速器的可行方案集合;4)利用序列二次规划算法建立基于齿轮强度约束的优化程序,对可行方案的齿轮质量进行筛选,得到齿轮总质量最小的主减速器方案。为验证此方法的合理性,给出了三级圆柱齿轮构型主减速器方案的设计过程,筛选出一种可行方案。

Main reducer is an important component of helicopter drivetrain,and its quality has a crucial impact on the whole transmission.In this paper,taking coaxial counter rotating helicopter’s gearbox as objective,a design method of main reducer configuration based on graph theory is proposed.Firstly,connection laws,boundary conditions and gear units are obtained by review of existing literature of the reducer.Then,automatic generation of adjacency matrix corresponding to main reducer is realized before transforming adjacency matrix to model of graph theory.After setting up rules and screening schemes to yield feasible solution set of the reducer,an optimization procedure,which aims at screening gear weight of feasible solutions and obtaining the solution of the lightest gear weight,is built by SQP(sequential quadratic programming algorithm)method based on gear strength constraints.Finally,to verify the rationality of this method,the designing and screening processes of 3-stage main gearbox schemes of cylindrical gear configuration are listed.