Lucian Tudose

Optimal mass minimization design of a two-stage coaxial helical speed reducer with Genetic Algorithms

The full description of a two-stage speed reducer generally requires a large number of design variables (typically, well over ten), resulting a very large and heavily constrained design space. This paper presents the specific case of the complete automated optimal design with Genetic Algorithms of a two-stage helical coaxial speed reducer. The objective function (i.e. the mass of the entire speed reducer) was described by a set of 17 mixed design variables (i.e. integer, discrete and real) and also was subjected to 76 highly non-linear constraints. It can be observed that the proposed Genetic Algorithm offers better design solutions as compared with the results obtained by using the traditional design method (i.e. a commonly trial and cut error).

Pareto Approach in Multi-Objective Optimal Design of Single-Row Cylindrical Rolling Bearings

Even if it seems simple, the design of the rolling bearings is a difficult task for mechanical engineering. Their specific structure and the involved tribological phenomena in their operation lead to many and complex calculations of rolling bearings. Consequently, to find the optimal design of the rolling bearings the Multi-Objective Optimization should be used. In this paper, two objective functions (the basic dynamic radial load rating of the bearing and the minimum thickness of the elastohydrodynamic film between rollers and raceways) are optimized using multi-objective Evolutionary Algorithms (EAs) in order to obtain the optimal design of a single-row cylindrical roller bearing. Three design variables (the complex factor γ, the roller diameter, and the roller length) were used to fully, completely, and uniquely describe the bearing geometry and to construct the objective functions and the constraints. To solve this optimal design problem the authors used Cambrian optimization platform.

Generalized Golden Ratios defined by means

Abstract Golden Ratio is defined by a proportion corresponding to the geometric mean. We introduce a generalized Golden Ratio as a fixed point of an operator defined by an arbitrary mean satisfying certain conditions. An algorithm for the evaluation of the generalized Golden Ratio is obtained using Banach’s fixed point theorem. As applications we show that some problems in shape optimization correspond to some aesthetic standards introduced in the paper.