Abstract
Cross-sectional deformation of double-ridged rectangular tube (DRRT) inevitably occurs due to the inhomogeneous deformation induced by external boundary conditions in rotary draw bending (RDB). Unreasonable factor combination would aggravate the cross-sectional deformation of DRRT. So, a powerful and efficient method combining Response Surface Methodology (RSM) and Non-Sorted Genetic Algorithm II (NSGA-II) was proposed to optimize the factors to control the cross-sectional deformation of DRRT in RDB. Firstly, an orthogonal experiment was used to screen out the important factors. It was obtained that three factors—clearance between DRRT and mandrel, clearance between DRRT and bending die, and boosting of pressure die—have an important influence on the cross-sectional deformation of DRRT. It can also be observed that the variation trend of flange sagging (FS) is always consistent with that of space deformation between ridges (SDR) with the changing of factors. RSM based on a Box-Behnken design was then used to establish response surface models. The proposed response surface models were used to analyze the relationship of the important parameters to the responses, such as space deformation between ridges, and width deformation of outer and inner ridge grooves (WDO and WDI). Finally, multi-objective parameter optimization for the cross-sectional deformation of DRRT in RDB was performed by using the established model and NSGA-II algorithm. The interaction of responses was revealed and the value range of each response in the space of Pareto optimal solutions was determined. It can be observed that there is always an evident conflict between SDR and WDO in the space of Pareto optimal solutions. By using this optimization method, the absolute values of SDR and WDI were significantly reduced—by 13.17% and 17.97%, respectively—compared with those before optimization, while WDO just increase only a little.
Highlights
The bent double-ridged rectangular tube (DRRT) has been widely applied in communication devices used in aviation, aerospace, radar, and satellite for its advantages of lower cutoff frequency, wider operation bandwidth, lower characteristic impedance, and smaller loss [1]
Before conducting the optimization process, the orthogonal experiment was initially adopted to Before conducting the optimization process, the orthogonal experiment was initially adopted to select the important factors from the nine factors shown in Table 3, and each factor was assigned three select the important factors from the nine factors shown in Table 3, and each factor was assigned levels (−1, 0, +1)
By using the orthogonal test design, it was obtained that M clearance, B clearance, and Boosting have an important influence on the cross-sectional deformation of DRRT in rotary draw bending (RDB)
Summary
The bent double-ridged rectangular tube (DRRT) has been widely applied in communication devices used in aviation, aerospace, radar, and satellite for its advantages of lower cutoff frequency, wider operation bandwidth, lower characteristic impedance, and smaller loss [1]. Unfavorable parameter combinations would aggravate the cross-sectional deformation of DRRT. Severe cross-sectional deformation brings about a serious loss of microwave. Controlling the cross-sectional deformation of DRRT in RDB is critical for obtaining a sound bent DRRT. There are mutual conflicting effects of the several quality indexes; that is to say, a relative small value of one quality index is obtained by using certain a parameter combination while others are probably relative large. This makes it difficult to control the cross-sectional deformation of DRRT. Considering the interaction of several quality indexes, taking the quality indexes as objectives and conducting multi-objective parameter optimization is very important to improve the forming quality of DRRT in RDB
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