Desarrollo de un método numérico para la optimización multi-objetivo del diseño de resortes helicoidales a compresión
Fecha
2022-04-19
Tipo
tesis de maestría
Autores
Van Patten Rivera, Erick
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Resumen
En esta investigación se define la implementación de un método numérico que utiliza un algoritmo genético para la optimización multi-objetivo de resortes helicoidales con el objetivo de minimizar la masa mientras se maximiza la resistencia a la fatiga y la robustez de su diseño. El método numérico y los casos de estudio en los que se prueba se enfocan principalmente a los resortes utilizados en las válvulas de control de flujo, sin embargo la metodología se puede cambiar a ser aplicable a otras aplicaciones en resorte similares. Para la implementación del algoritmo se determinan los requerimientos de diseño de los resortes y las restricciones a las que estarán sometidos, después de esto se programa el algoritmo y se prueba con funciones teóricas para verificar su efectividad.
Una vez probado el algoritmo se realiza un modelo dinámico de masa amortiguador resorte con múltiples grados de libertad y se traslada esto a un conjunto de formulaciones matemáticas con las cuales se ejecuta la optimización. Finalmente se presentan y analizan tres casos de estudios con diferentes patrones de fuerza: un patrón sinusoidal, una onda de presión y una fuerza aleatoria. Para los diferentes casos de estudio se obtienen las frontera pareto-óptimas en las cuales se encuentran las combinaciones de variables de diseño para el diámetro del resorte, diámetro del alambre y número de espiras activas que tendrán una mejor relación de masa a resistencia a la fatiga y robustez del diseño.
The scope of this work is the implementation a numeric method that utilizes a genetic algorithm to do a multi-objective optimization of helicoidally springs with the intent to minimize the mass, while maximizing the fatigue resistance and the design robustness. The numeric method and the study cases that are analyzed are focused towards the optimization of springs used in flow control valves; however, the used methodology can be applied to other similar applications. In order to implement the algorithm the design requirements and restrictions were defined, then a dynamic model of the spring in the control valve was created and converted into the mathematic equations that will be optimized through the algorithm. Three study cases are presented and analyzed to assess the performances of the algorithm. One is that of a sinusoidal force applied to the spring; another is a random load that varies in time; and that of a load emulating a pressure surge. In each of the study cases, the pareto-fronts are presented along with the combination of variables for spring diameter, wire diameter and number of active coils for each of the individuals. This pareto-front will also define the combinations of design variables that provide the best ratio of mass to fatigue resistance and robust design according to the proposed mathematical model.
The scope of this work is the implementation a numeric method that utilizes a genetic algorithm to do a multi-objective optimization of helicoidally springs with the intent to minimize the mass, while maximizing the fatigue resistance and the design robustness. The numeric method and the study cases that are analyzed are focused towards the optimization of springs used in flow control valves; however, the used methodology can be applied to other similar applications. In order to implement the algorithm the design requirements and restrictions were defined, then a dynamic model of the spring in the control valve was created and converted into the mathematic equations that will be optimized through the algorithm. Three study cases are presented and analyzed to assess the performances of the algorithm. One is that of a sinusoidal force applied to the spring; another is a random load that varies in time; and that of a load emulating a pressure surge. In each of the study cases, the pareto-fronts are presented along with the combination of variables for spring diameter, wire diameter and number of active coils for each of the individuals. This pareto-front will also define the combinations of design variables that provide the best ratio of mass to fatigue resistance and robust design according to the proposed mathematical model.
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Palabras clave
OPTIMIZACIÓN, ALGORITMO, DISEÑO, ŽŒMULTI-CRITERIA ANALYSIS