**Study on the Cross Sectional Deformation of Double-ridged Rectangular H96 Tube in E-type Bending considering Anisotropic Constitutive**

Author:Zhang Hong Lie

Supervisor:liu yu li

Database:Doctor

Degree Year:2018

Download:5

Pages:146Size:7946K

Keyword:Anisotropy，cross sectional deformation，Double-ridged rectangular H96 tube，E-type rotary draw bending，finite element simulation，multi-objective optimization

The double-ridged rectangular bent tube has been widely applied in aviation,aerospace,radar,and satellite for its advantages of lower cutoff frequency,wider operation bandwidth,lower characteristic impedance,and smaller loss.However,in rotary draw bending,the cross sectional deformation inevitably occurs due to the structural characteristics of the tube and the complexity of multi-die bending.Serious cross sectional deformation would change the transmission characteristics of double-ridged rectangular tube and affect the transmission efficiency of electromagnetic wave.With the increasingly high requirement for the transmission performance of ridge waveguide,it is needed to form a high-precision double-ridged rectangular bent tube.Therefore,by means of theoretical analysis,finite element simulation and experiment,the cross sectional deformation of double-ridged rectangular H96 tube in rotary draw bending are studied systematically and deeply.The main research content and results are as follows:With considering Hill’48,Barlat/Lian and Karafillis/Boyce yield criteria,the anisotropic constitutive model of double-ridged rectangular H96 tube was established.By using the inversion method combining three-point bending experiment and response surface method,the parameters of anisotropic constitutive model were determined.Based on the semi-implicit backward Euler return algorithm,the VUMAT subroutine of anisotropic constitutive model of double-ridged rectangular H96 tube was developed.After the reasonable simplification of mandrel and the selection of mass scaling factor and mesh density,a 3D FE model of E-bending of double-ridged rectangular H96 tube was established.The distributions of anisotropy index r and function shapes for Hill’48,Barlat/Lian and Karafillis/Boyce yield criteria determined by double-ridged rectangular H96 tube were compared.It was found that the distributions of anisotropy index r for the three yield criteria have little difference,but the difference of yield function shape is large,and the influence of the yield function shape on the prediction of cross sectional deformation of double-ridged rectangular H96 tube in rotary draw bending is slightly greater than that of anisotropy.By comparing with the experimental results,the prediction accuracy of the three anisotropy yield criteria on the cross sectional deformation were evaluated.It was found that the prediction values by using Hill’48 yield criteria are lower than those of the experiment ones,while the values obtained by using Barlat/Lian and Karafillis/Boyce yield criteria are very close to the experimental ones.Based on the plastic deformation theory,the analytical model of cross sectionaldeformation of double-ridged rectangular tube in rotary draw bending was established through the force analysis on the plates of double-ridged rectangular tube during the bending process,and the mechanism of cross-section deformation was revealed: the width deformation of ridge groove is caused by flange sagging,web deflection and variation of flange width.The contribution of flange sagging on the width deformation of ridge groove is usually small and can be omitted.The web deflection and variation of flange width have different contributions to the width deformation of outer and inner ridge grooves.For outer ridge groove,the web deflection decreases its width deformation and the variation of flange width increases it.For inner ridge groove,the two parts all increase its width deformation.In addition,combining with theoretical analysis and finite element method,the influence of web deflection and variation of flange width on the cross sectional deformation of double-ridged rectangular tube in rotary draw bending under different conditions was revealed:with the increase of bending angle,the effects of web deflection and variation of flange width on width deformation of outer ridge groove cancel each other out,so the width deformation of outer ridge groove changes little.The increase in the absolute values of width deformation of inner ridge groove is mainly induced by the variation of flange width.As the bending radius decrease,the variation of flange width is the main factor resulting in the increase in the absolute values of width deformation of outer and inner ridge grooves.With the increase of core number,the width deformation of outer ridge groove changes from shrinking to widening,which is mainly resulted from web deflection,While the width deformation of inner ridge groove change little.Based on the established FE model,the characteristics of cross sectional deformation of double-ridged rectangular tube in rotary draw bending were obtained,it was found that the maxima of height deformation of section and space deformation between ridges for the typical section are located at the opening of ridge groove and middle of the back of ridge groove,respectively,while the maxima of width deformation of inner and outer ridge grooves are situated at the opening of inner and outer ridge grooves,respectively.The maxima of height deformation of section and space deformation between ridges along bending direction were all obtained at 60° section,while the maxima of width deformation of outer and inner ridge grooves along bending direction were all obtained at 20° section.And then the significant process parameters on the cross sectional deformation were obtained,it was found that the number of core,the clearance between mandrel and tube,the clearance between bending die and tube and the boosting level of pressure die have the most significant impact on the cross sectional deformation.The space deformation between ridges and width deformation of outer and inner ridge grooves were selected as the objectives,by using a multi-objective optimization algorithm based on response surface method and genetic algorithm NSGA-II,a optimization model describing the relationship between significant factors and objectives was established,and the optimal Pareto solution was obtained.It was found that in the space of Pareto optimal solution,there is always a clear conflict between the space deformation between ridges and the width deformation of outer ridge groove.The TOPSIS method was used to determine the final unique solution of multi-objective optimization,which ensures that the width deformation of outer ridge groove satisfies the aviation standard and the space deformation between ridges and width deformation of inner ridge groove reduces by 13.17% and 17.97%,respectively.In order to overcome the disadvantages of mandrel-core die used in the rotary draw bending of double-ridged rectangular tube,a new PVC mandrel only supporting the back of ridge grooves was proposed,and the cross sectional deformation of double-ridged rectangular tube in bending by using the two mandrels was studied.It was found that compared with mandrel-core die,PVC mandrel can well control the flange sagging,space deformation between ridges and width deformation of inner ridge groove.The only drawback is that the width deformation of outer ridge groove increases,but its maximum value is only 3.21%larger than that by using mandrel-core die.In addition,it was found that this PVC mandrel is only suitable to be used in the bending of double-ridged rectangular tube whose size is not larger than 36JS5000(20.36(b)×9.47(h)×3.57(w)×2.87(d)×1.27(t)).