The vibration frequency of a cylindrical coil spring is critical when it is subjected to high-frequency cyclic loading. If the load cycle frequency, denoted as $ f_g $, approaches or equals the natural frequency $ f $ of the spring’s self-excited vibration, resonance occurs, which can lead to structural damage. This problem falls under the category of a three-dimensional nonlinear programming problem with multiple inequality constraints. It can be directly solved using methods like the random direction exploration approach or indirectly through techniques such as the penalty function method (SUMT).
In this study, we utilize the MATLAB Optimization Toolbox to address the problem efficiently. During the design process, several key parameters must be carefully selected based on specific operational conditions. These include the excitation amplitude $ a_1 $, excitation frequency $ a_2 $, mass $ a_3 $, and the number of springs $ a_4 $. By adjusting these variables according to different application requirements, a general and flexible optimization model can be established.
As shown in the table, under the same output speed and torque conditions, the volume of the fuzzy optimization design is reduced by 26.56%, and the total tooth width sum decreases by 29.91%. The strength and reliability of the design meet the required standards with a significant safety margin. This demonstrates that fuzzy reliability optimization can produce a more compact and efficient structure, highlighting its practical benefits and potential for real-world applications.
From the calculation results, it is evident that: 1) The vibration stiffness and stability are effectively solved under the constraints of spring strength and stability, achieving a good vibration reduction effect; 2) by incorporating comprehensive constraints, the influence of various parameters on the spring’s dimensions is fully considered, thereby improving the accuracy of the design; 3) using the MATLAB toolbox allows for an intuitive and user-friendly optimization process without requiring advanced programming skills, making it easier to control and adjust parameters during the solution phase.
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