Simulated rationalization industry preset for aircraft running gantry spring
August 10 11:20:14, 2025
Geometric constraints encompass dimensional limitations, 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 of a spring's static strength imposes restrictions on its torsional shear stress. The relationship can be expressed in terms of both the mean and standard deviation of the torsional shear stress limit, accounting for uncertainties in manufacturing and processing. These uncertainties are often modeled using a normal distribution, with the membership function representing the degree of compliance with the static strength requirements.
Similarly, the fuzzy reliability of the spring’s fatigue strength is governed by the elastic load it experiences. When considering fatigue, the material’s pulsating fatigue limit becomes a key factor. Assuming a normal distribution, this limit is treated as a random variable. The mean value corresponds to the minimum working load, while the standard deviation reflects the variability in the maximum working load. The probability density function of the pulsating fatigue limit is used to calculate the fuzzy reliability, which ensures that the spring meets both operational and design standards.
The spring’s diameter is constrained by the end conditions, and a mathematical model has been developed to convert general constraints into a structured optimization problem. This model can adapt based on changing operational requirements. The fuzzy optimization problem is transformed into a conventional one using the optimal horizontal cut-off method, making it easier to solve through traditional optimization techniques.
To determine the optimal threshold value, a first-level comprehensive evaluation is conducted. Expert scoring is used to assess the factor grades and their corresponding membership degrees. In this context, the alternative set refers to possible cut-off levels, typically defined within a specific price range. Based on design requirements, the alternative set can be narrowed down, and the weight set is determined to reflect the influence of each factor and its level on the final decision.
The first-level fuzzy evaluation is performed using matrix multiplication, resulting in a fuzzy relation matrix that ranks design methods based on their membership function values. The evaluation outcome determines the optimal horizontal cut-off, guiding the selection of the best design parameters.
After converting the fuzzy model into a conventional constrained optimization problem, the Turtc2.0 programming tool is used to solve it. In the code, three design variables—spring diameter, wire diameter, and number of active coils—are considered as unknowns, while other parameters are assumed to follow known distributions or are predefined. This approach simplifies the implementation, allowing the use of loops in C language to systematically explore the design space and identify the optimal solution.