直齿圆柱齿轮传动设计的全局优化方法  

Global optimization design of spur gear drive

作　　者：张少军[1] 万中[1] 刘光连[2] 

机构地区：[1]中南大学数学与统计学院,湖南长沙410083 [2]中南大学机电工程学院,湖南长沙410083

出　　处：《中南大学学报（自然科学版）》2013年第7期2736-2743,共8页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(71221061;70921001)

摘　　要：分析现有齿轮传动优化设计方法在全局优化方面的不足。针对一类载荷系数一定的直齿圆柱齿轮传动设计的体积优化问题,建立非线性优化模型。基于模型特点的分析,采用变量组合与取自然对数的变量变换方法,将原非线性问题等价地转化为含混合变量的线性规划模型,并设计一类求解混合变量的线性规划问题的全局优化方法。将这一系列方法应用于研究典型的直齿圆柱齿轮传动优化设计案例,并与已有设计优化方法比较。结果表明:该全局优化方法得到的大小齿轮分度圆柱体积小于其他方法得到的圆整最优值。The deficiency of global optimization for the current optimal design of gear drive was analyzed.A nonlinear optimization model was constructed to minimize the volume of spur gear drive with a fixed load coefficient.Based on the analysis on the structural characteristics of the model,the original nonlinear optimization problem was converted into a binary linear programming with some continuous and discrete variables by a method of variable transformation.Then,a class of global optimization methods for linear programming with mixed variables were developed.The proposed method was applied into a typical case study on the optimal design of gear drive,and compared with the existent ordinary optimization methods available in the literature.The obtained results show that the optimal total volumes of pinion and wheel by the global optimization method are smaller than the rounded optimal values by the other four local methods.

关 键 词：齿轮传动 非线性规划 混合变量 全局优化 

分 类 号：TH122[机械工程—机械设计及理论] TH132.41