# Research on High-Speed Vibration and Structure Optimization of Multiwire Sawing Machine
## 3 Results
### Structural Optimization and Dynamics Verification
#### 3.4.3 Response Surface Based Multi-Objective Optimization Design  
The response surface model is used to obtain the influence relationship between the optimization objective and each input parameter so that structural optimization can be performed based on this mathematical model. Before constructing the response surface, a DOE test is conducted, and here, the OSF_method is used to design the test points, and 287 test points are customized for calculation. After the calculation is completed, the response surface is then constructed using the kriging method, and the correlation error for judging its convergence is set to 5%. When it cannot converge, refinement Points are automatically inserted during the refinement process, and its maximum number of refinement points is set to five. If convergence is achieved during the refinement process, the refinement will be finished. Due to there being a sufficient number of test points, the refinement error finally reached 2.0047% after using one refinement point for refinement, which satisfied the convergence accuracy requirement, at which time the response surface construction had been completed. The multi-objective optimal design was based on the constructed response surface. By defining the objective function, setting the constraints, and determining the relationship between the input parameters, the optimal solution satisfying the requirements was found. The objective function for multi-objective optimization is shown in the following equation. \[\left\{ \begin{array}{ll}find&\min\;(P_{2})\\ &\min\;(P_{3})\\ &\min\;(P_{4})\\ &\min\;(P_{5})\\ &\max\;(P_{1})\\ \textit{seek}&\det\mathrm{D}=20\\ &\det\mathrm{H}=200\end{array} \right. \tag{4}\]  
where \(P_{1}\) denotes the first-order inherent frequency of the multi-wire sawing machine; \(P_{2}\) denotes the maximum displacement of the main frame; \(P_{3}\) denotes the maximum displacement of the subframe; \(P_{4}\) denotes the maximum displacement of the electric control cabinet; \(P_{5}\) denotes the maximum displacement of the base bracket; det D denotes the change in the spindle axis diameter;and det H denotes the change in the spindle axis height, which is used to measure the lift of the machining center of gravity. The MOGA method is used for multi-objective iterative optimization search, the initial sample points are set to 100, the number of samples per iteration is set to 100, the maximum number of iterations is set to 20, the stability percentage for judging its convergence is set to 2%, and five candidate points are set to verify the error of response surface calculation, which can also be used as the optimal solution for the calculation. When the iteration occurs for the 12 th time, as shown in Figure 14, the convergence stability percentage is 1.98%, which achieves the convergence accuracy and satisfies the requirements of the optimization search. Figure 15 shows the iterative optimization process in multi-objective optimization. According to the mechanical design manual [20], the rib thickness factor is generally taken as 0.8, and it is made to be consistent with the original, while the first-order intrinsic frequency value of the machine is as high as possible. An optimal solution is selected from five groups of candidate points, and the values are fitted and rounded regarding the other four groups of candidate points. The final values of the parameters of the optimized solution were obtained, as shown in Table 3 below. Figure 14: Stability percentage convergence graph. Figure 15: Iterative optimization search process graph.