Simulated rationalization industry preset for aircraft running gantry spring
August 10 12:26:47, 2025
Geometric constraints encompass dimensional restrictions, and the upper and lower bounds of each design variable can be treated as fuzzy subsets within the design space. This approach allows for the formulation of more flexible and realistic constraints. The fuzzy reliability associated with the static strength of a spring imposes limitations on the torsional shear stress it can withstand. This relationship is typically modeled using the mean and standard deviation of the torsional shear stress limit, which accounts for uncertainties in manufacturing and processing.
The concept of fuzzy reliability also applies to fatigue strength, where the elastic load becomes a key constraint. When considering fatigue strength, the pulsating fatigue limit of the spring material is often assumed to follow a normal distribution. The mean value of this limit corresponds to the minimum working load, while the standard deviation reflects variability in the material properties. These parameters are essential in defining the fuzzy reliability of the spring’s fatigue performance.
Fuzzy reliability is further influenced by the membership function of the spring's static and fatigue strengths. This function serves as a constraint that ensures the spring meets both operational and design requirements. In addition, the diameter of the spring is constrained by the end conditions, such as the number of coils or the type of end termination.
A mathematical model has been developed to convert these common constraints into a structured optimization framework. This model can adapt to changing working conditions, making it highly versatile. The fuzzy optimization problem is transformed into a conventional optimization model using the optimal horizontal cut-off method. This technique helps in identifying the most suitable threshold values for decision-making.
To determine the optimal horizontal cut-off, a first-level comprehensive fuzzy evaluation is performed. This process involves assigning factor grades and membership degrees through expert scoring methods. The alternative set, which includes possible cut-off levels, is defined based on the design requirements. The weight set is then established to reflect the relative importance of each factor and its corresponding level in the evaluation.
The fuzzy comprehensive evaluation is calculated using matrix operations, specifically the multiplication rule. The resulting evaluation provides insights into the best possible solution, which is then used to determine the optimal horizontal cut-off value. Once the model is converted into a conventional optimization problem, it can be solved using programming tools like Turtc2.0.
In the implementation, three primary design variables—spring diameter, wire diameter, and number of active coils—are considered as unknowns. Other parameters are predefined based on typical manufacturing standards. Using a C language for loop, the program iterates through possible values, ensuring an efficient search for the optimal solution. This approach not only enhances accuracy but also improves the practicality of the design process.