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本文用几何规划对一个中等规模的机械设计问题——减速器的最小重量(体积)——进行优化设计,这个特定问题曾经有许多人用各种其它的优化技术进行过研究。本文把用本方法得出的数值结果与以前用其它各种方法得出的结果进行了比较,说明本方法是很有效的、容易使用和通用性较大。本文还研究了约束条件与变量上下界之间的关系问题,结果指出了以前的研究结果存在的问题并导致了原问题的简化与合理化。几何规划是一个在机械设计领域中很有前途的优化技术,在这方面国内公开发表的资料不多。本文试图以这个减速器的优化设计为例说明这个问题。
This paper uses geometric programming to optimize the design of a medium-sized mechanical design - the minimum weight of the reducer - and this particular problem has been studied by many others using a variety of other optimization techniques. In this paper, the numerical results obtained by this method are compared with those obtained by other various methods before, which shows that this method is very effective, easy to use and versatile. The paper also studies the relationship between the constraints and the upper and lower bounds of the variables. The results point out the problems existing in previous studies and lead to the simplification and rationalization of the original problems. Geometrical planning is a very promising optimization technique in the field of mechanical design. There is not much information published in this field in China. This article attempts to illustrate the problem with the optimized design of the reducer.