Weight Function Theory For Compound Forming Of Drawing And Bulging And Its Application In Solid Granule Medium Forming Technology

With the development of industrial technology and the enhancement of environmental awareness,lightweight design has become the main goal of components design,evidenced by the wide application of shells parts in aerospace and automobile industries.According to the forming die and its corresponding deformation process,shell parts forming technology can be divided into two categories,the rigid die forming(a conventional method)and the flexible die forming.As cross section shapes of shell parts become more and more complex in recent years,the conventional forming technology has seen its limitations,and the flexible die forming technology gradually becomes the mainstream for its strong applicability,widespread application and good quality.This paper studies the deep drawing process of flexible die forming by analyzing the stress-strain state diagram and the yield trajectory of the sheet metal during the forming process.The results show that the sheet forming process is the compound effect of conventional drawing and bulging.It establishes the corresponding mathematic model by bringing together the comprehensive evaluation theory and the deep drawing of compound forming of drawing and bulging,and brings up the concepts of drawing weight and bulging weight,and then the weight function theory of flexible die forming is established.The paper also studies the application and influencing factors of the drawing weight and the bulging weight with a case study of a cylindrical part,the results indicate that,the drawing coefficient,contraction ratio of flange and height-diameter ratio will have great influence on weight value of the formed workpiece.The paper establishes the theoretical calculation formulas of strain and thickness in flange region based on the basic geometrical model of sheet deformation and the weight function theory,and the concepts of single drawing and single bulging are proposed.In the female die region,the strains of spherical shell forming stage and part wall calibration stage during the cylindrical part drawing process are analyzed from the perspectives of single drawing and single bulging respectively.On this basis,the calculation model of strain theory of the two stages is established with reference to drawing weight and bulging weight.The influence of workpiece geometry parameters on strain distribution and thickness is also within this paper's study scope.In the deformation process,the height-diameter ratio only changes the absolute value of strain,while drawing weight and bulging weight not only affect the absolute value of the corresponding variable,but also has great influence on the strain distribution and the strain state of the formed workpiece.Sheet metal solid granule medium forming(SGMF)uses granules medium instead of rigid male die or female die(or elastomer,liquid)for sheet metal drawing.SGMF features both flexible die forming characteristics and its own advantages.The stress state of the sheet metal during deformation is very different from that of other flexible die forming due to the uneven pressure transmission of the granule medium.Take a cylindrical part as the research object and the stress state of the flange deformation region and the female die deformation region during the forming process are studied.The sheet metal in flange region is analyzed by using axisymmetric equilibrium equation,and the stress analysis model is established,which takes the strain hardening of the material into consideration.Based on the theory of drawing weight and bulging weight,the stress state of the female die in spherical shell forming stage and part wall calibration stage are analyzed respectively,and the theoretical models of vertical pressure of the granules medium needed during the two forming process stages are established.Under this pressure,the sheet stress calculation model in female die region considering the hardening of the material is established by the use of stress equilibrium equation and the equivalent stress equation.Based on ABAQUS 6.14 numerical simulation platform,FEM-DEM numerical analysis model of sheet SGMF is established by manual programming input.The flow law of granules medium during the drawing process is studied by a combination of experimental and numerical simulation.The influence of blank-holder gap and lubrication conditions on the sheet metal deformation during the forming process was studied by numerical simulation,theoretical analysis and experiment.Three sets of data of the thickness,strain and stress distribution curves of the deformed workpiece are obtained from theoretical calculation,numerical simulation and experimental results,respectively.The data comparison results show that,the calculated results are in agreement with experimental and numerical simulation results,and the maximum deviation is less than 10%.The results also explain the correctness and reliability of the theoretical analysis model based on the weight function.The theoretical model based on the weight function theory of compound forming of drawing and bulging provides a new theoretical support for further revealing the deformation mechanism of flexible drawing process,and provides a new analytical method for the prediction of the thickness,strain and stress of the workpiece after deformation.