Springback Prediction And Compensation Of Variable Curvature Bending For Minor Diameter Thick-walled Tube

With the industrial development, it requires more and more high-strength lightweight andhigh-precision complex. Tubular products are widely used in many fields such as aeronauticsand aerospace, shipbuilding, automobile, pressure vessel, oil and chemical industries, etc.Tube forming components have many desirable features, such as saving materials, reducingthe weight, strengthening the structure, absorbing the impact energy and shock. Therefore, itplays an important role in modern manufacture industry to meet the requirements of designperformance, installation space, lightweight and integration for the product. With theincreasing needs for tube forming accuracy, the spatial shape is more and more complex, andthe process is more and more difficult. The metal tube bending is a complex process withmaterial nonlinearity, geometric nonlinearity and boundary nonlinearity. The defect ofspringback appears consequentially after unloading, which leads to the difficulty of geometricand shape accuracy requirements and becomes one of the research hotspots and difficulties inthe technology field of metal plastic processing. Springback prediction and compensation oftube bending is the key point of metal tube high-efficient and precise forming.In this paper, based on the tube bending springback properties, it builds new finite elementsimulation method, analytic calculation method and experiment method. The built methodsemphasize on revealing the bending mechanism, for solving the immatureness of variablecurvature (variable curvature of the plane and space) tube bending. The theory and methods ofpractical springback prediction and compensation have been built. The above research work isto resolve the springback control of variable curvature bending problem for minor diameterthick-walled tube. It provides significant benefit to accurate forming of the variable curvaturebended tube. The main works of this research are as follows:1） The variation laws of minor diameter thick-walled tube mechanical properties areanalyzed based on tube section tensile tests, which laid the foundation for improving theprediction accuracy of forming quality. Then based on bending conditions of thick-walledtube, the mechanical equilibrium differential equations are established. The stress and strainstates of the bended tube are analyzed. The tube bending moment is derived to establish anapproximate formula for calculating springback angle, which can realize preliminaryestimation for minor diameter thick-walled tube bending springback. 2） With the finite element softwareABAQUS, the bending and springback processes of two-dimension (2D) variable curvature tube are simulated to reveal the springback laws. In thispaper,2D variable curvature tube axis is transformed into discrete constant curvature arcs.Then a recursive bending method in turn is adopted. Static implicit algorithm is employed tosimulate the non-die springback process. Its accuracy and reliability are proved throughexperiments.3） The tube axis is segmented with biarc-curve fitting. The mathematics relationship of theradius before and after springback can be built through the approximate pure bendingspringback experiment. Then the partitioned arcs after springback prediction are merged withfirst-order geometric (G1) continuity, and compensated with modified function according tothe axis complexity. The mathematic analytic model for springback prediction of2D variablecurvature tube bending is established. Two series of trials are carried out with this model. Thefeasibility, reliability and accuracy have been proved by data and analysis.4） The elasto-plastic FEM for three-dimension (3D) variable curvature tube bending andspringback is established by software ABAQUS. Displacement loading programs, namely realtime control of the tangent vectors trajectories of discrete axis nodes are adopted during tubebending. By defining connector properties as HINGE, BEAM, TRANSLATOR, SLOT,ROTATION and etc, the tube bending load displacement trajectories are controlled.5） To predict the springback of three-dimensional variable curvature tube forming quicklyand accurately, mathematic analytical model is established. In this paper, the problem isprojected onto discrete osculating planes and rectifying planes. Then the3D problem istransformed into2D. The mathematics relationship of the radius before and after springbackin the plane is built by an approximate pure bending springback experiment. Then thespringback on the special planes are transformed into3D considering a special law. Toestablish mathematic analytic model, the discrete tube axes after springback prediction aremerged with first-order geometric (G1) continuity, compensated with the modified functionaccording to the axis complexity. The feasibility of the model is verified by experiments.Finally, an automatic and modularity3D variable curvature tube bending springbackprediction system has been established by applying UG secondary development. 6） Variable curvature tube bending is strong nonlinear. The node geometric adjustmentmethod which combines two ways:(i) the displacement vectors at the nodes corresponding tobending springback,(ii) the local Frenet frames of curves before and after the springback, tomodify the die surface of tube bending. The approach based on iteratively comparing a targetpart shape with a simulated part shape, following bending and springback using mathematicanalytical models of3）and5）, is effective in reducing springback. The simulation results,engineering application examples and their analysis show preliminarily that the proposedmethod can ensure the geometric accuracy of the bending of the minor diameter thick-walledtube.Accurate prediction and compensation of springback is essential for the controlling tubebending. It provides significant benefit to accurate forming of the complex structure bendedtube.