Zhixin LI, Mei ZHAN, Xiogung FAN, Yund DONG, Luopeng XU
aSchool of Science, Civil Aviation Flight University of China, Guanghan 618307, China
bState Key Laboratory of Solidification Processing, Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072,China
KEYWORDS2219 aluminum alloy;Complex thin-walled components;Finite element analysis;Quenching distortion;Residual stress;Shear spinning
AbstractThe quenching-spinning (Q-S) process, i.e., shear spinning after blank quenching, has been increasingly utilized to form 2219 aluminum alloy complex thin-walled components.However,the changes in material property,shape and stress of the blanks after quenching will affect the spinning forming precision.In this study, the rules and mechanisms of these effects are investigated based on a combined finite element(FE)model including blank quenching and component spinning process.The results indicate that the increase of material strength and the existence of distortion of the quenched blank lead to a notable increase in the non-uniformity of the circumferential compressive stress in the spinning area and the increase of the flange swing height during spinning.These changes result in an increase in the wall thickness and component-mandrel gap of the components.The quenching residual stress has little effect on wall thickness and roundness but can noticeably reduce the component-mandrel gap.This is because that the existence of quenching residual stress of the blank can lead to the decrease of the maximum circumferential compressive stress of the workpiece in spinning and an obvious drop in the maximum compressive stress after reaching the stress peak.Quenching distortion is the main factor affecting the roundness.Moreover,the optimized installation way of the blank for spinning is obtained.
2219 aluminum alloy complex thin-walled components are widely used in the aerospace and aviation industries due to their high material and structural reliability.1–3The shear spinning is a flexible incremental forming process and has been increasingly employed to form such components.4–5During the manufacturing process of the spun components, the quenching heat treatment is required to further enhance the mechanical properties.In order to avoid the severe quenching distortion of the components in quenching and improve the final shape and dimensional precision of the formed component,6–7the quenching is usually applied to the blank, i.e.,spinning after the quenching process of the blank.However,previous studies demonstrated that the quenching process made the state of the blanks usually deviate from the ideal situation,i.e.,existing quenching residual stress and shape distortion.8These pre-existing initial residual stress and shape distortions could affect the spinning forming precision.Additionally, the material property of the blank after quenching is changed, which could significantly affect the deformation behavior of materials in the spinning process and the final forming precision of components.
Up to now, numerous researchers have investigated the effects of the material property on the spinning process.Ma et al.9investigated the effects of material properties on the power spinning process of components with transverse inner rib.It is proved that hardening exponent n and strengthening factor K were the prominent factors influencing the degree of inhomogeneous deformation.Besides, the increase of the strengthening would reduce the degree of inhomogeneous deformation of the material in spinning.Zhang10explored the effect of material properties on the shear spinning forming of large elliptical heads of D406A ultra-high-strength steel.The results demonstrated that the component-mandrel gap of the spun components increased and the roundness decreased with the increase of the material hardening exponent and yield strength.Chen et al.11reported the effect of the material property on flange wrinkling in the spinning process using an analytical model and FE simulations.The results manifested that the decrease of the hardening exponent of the initial blank made the flange better resistant to wrinkling and can improve the formability.Some researchers12–14pointed out that the heat-treatable strengthening aluminum alloys exhibited excellent formability in an as-quenched state, while the subsequent aging treatment may result in a slight deterioration of formability.Therefore, for the 2219 aluminum alloy used in this work, it is a good choice to form the components using the as-quenched 2219 aluminum alloy blank.
As for aluminum alloy thin blank, it is inevitable to distort after quenching.If the blank is quenched by immersion in water, the degree of quenching distortion is related to the immersing speed, and the distortion is smaller at a larger immersing speed.8However,the effect of quenching distortion has not yet been considered in the forming process in previous literature.For the effect of blank shape and size on the forming process, Cui et al.15researched the influence of the blank flatness caused by the rolling process on the subsequent spinning forming of thin-walled head components.The results showed that the blank flatness had an obvious impact on the spinning force, but had little effect on the difference in wall thickness of the spun component.Lam et al.16investigated the influences of machining-induced initial distortion on springback prediction of 7B04-T651 aluminum plates in creep-age forming.Their results illustrated that the conforming initial distortions of plates had a positive contribution to the final formed shape in creep-age forming,and the prediction of final plate deflections was improved by an average of 46.8%when the initial distortion of the plates was taken into account in the geometric models.
Residual stress is another factor that affects forming precision.Weiss et al.17found that the residual stress introduced by the cooled rolling process has led to the material softening and the reduction of the offset yield stress in subsequent bending operations.Abvabi et al.18established a combined model including two rolling processes to explore the influence of residual stress introduced by the thickness reduction rolling process on the roll forming process of a V-section profile.The results demonstrated that the combined model had a more accurate prediction of shape defects in a roll forming process than the model without the consideration of residual stress.Furthermore, the residual stress led to the decrease of maximum bow height and the increase of springback angle.Therefore, the residual stress is an important factor affecting both the forming process and the final forming precision of the components according to these previous investigations.However,no literature focuses on the effect of residual stress on the spinning process.
To this end, the current studies investigated the effect of blank quenching on the forming precision in the spinning process through a numerical and an experimental approach.In this study,a combined FE model including the quenching process of 2219 aluminum alloy blank and subsequent spinning forming process of the complex thin-walled components is proposed.In the simulation of the spinning process,the initial distortion and residual stresses produced in the blank quenching process are introduced into the blank.Based on this combined model,the rules and mechanisms of the effect of blank quenching on shear spinning forming precision of 2219 aluminum alloy complex thin-walled components are investigated.These results provide reliable guidance for controlling the forming precision of components in the quenching-spinning process.
A 2 mm thick 2219-O aluminum alloy sheet was used in this study.The chemical compositions(wt%)of this alloy are listed in Table 1.Before quenching and spinning, the sheet was machined to be some round blanks with an outer diameter of 290 mm and a center hole of 20 mm.
2.1.Tensile test
The uniaxial tension tests were conducted in accordance with ASTM E21-2009 and ASTM E8/E8M-2013a to obtain the material properties of as-annealed and as-quenched 2219 alu-minum alloy sheets.The shape of the sample and the true stress-true strain curves obtained from the standard tensile test are depicted in Fig.1.It can be seen that the strength of the asquenched 2219 aluminum alloy is significantly higher than that of the as-annealed alloy.Based on these true stress-true strain curves, the yield stress of the as-annealed and as-quenched 2219 aluminum alloy were identified to be 71.5 MPa and 131.2 MPa using the 0.2 % offset approach, respectively.Young’s modulus and Poisson’s ratio of 2219 aluminum alloys were 75.8 GPa and 0.33, respectively.
Table 1 Main element composition of 2219 aluminum alloy.
2.2.Quenching of blank
In the quenching experiment, as shown in Fig.2, the round blanks were held at 530 ℃in the heating furnace for 2 hours first.Subsequently, the round blanks were quickly quenched in water at 25 ℃.The transfer time from the heating furnace to the quenching tank was less than 5 seconds.In the quenching operation,the blanks were immersed in water in a direction perpendicular to the water surface.The immersing speed can be controlled by a pneumatic lifting system.The immersing process was recorded by a high-resolution camera to calculate the immersing speed.The records showed that the immersing time of the blank from touching the water to submerging into the water completely was approximately 0.3 seconds.Thus,the immersing speed was considered a constant of 1 m/s.
Fig.1 True stress versus true strain curves of 2219 aluminum alloy sheet with different heat treatment states.
Fig.2 Schematic diagram of quenching process.
2.3.Spinning of complex thin-walled components
The one-pass cold shear spinning experiments were conducted on a CZ900/2CNC spinning machine, as shown in Fig.3.The diameters of the mandrel and the spinning roller are shown in Fig.4.In Fig.4,the mandrel and corresponding target component consist of the spherical and conical part.The conical part is tangential to the spherical part with a half cone of 50°.The key process parameters in the experiments are listed in Table 2.The blank surface was coated with MoS2as a lubricant.
2.4.Analysis of forming precision
The distribution of wall thickness, component-mandrel gap and roundness of spun components were measured to obtain the forming precision of spun components.The componentmandrel gap reflects the contour difference between the component and the mandrel, i.e., the distance from the inner surface of the component to the outer surface of the mandrel.As shown in Fig.5, two mutually perpendicular paths (path 1 and path 2) along the generatrix direction were chosen to measure the component-mandrel gap, and one of the two paths passes the starting point S of spinning.The wall thickness of the spun components at different positions on path 1 and path 2 was measured using an in-hand ultrasonic thickness-measuring instrument(PX-7DL).For the determination of the component-mandrel gap, a three-coordinate measuring machine (GLOBAL STATUS121510) was used to measure the contour points of the inner surface of the components along path 1 and path 2.Then, based on the measured contour points, the component-mandrel gap was obtained by using Computer Aided Design(CAD)software.Thus,the wall thickness and component-mandrel gap along the generatrix direction can be obtained by calculating the average wall thickness and component-mandrel gap on path 1 and path 2.
It can be shown from Fig.5 that circle 1,circle 2 and circle 3 are the three cross-section paths near the small end,the middle and the big end of the spun components, respectively.The shapes of cross-section paths are considered ellipses.The ratio of the minimum and maximum diameter on each cross-section is roundness.The diameters were calculated based on the coordinate points measured by the three-coordinate measuring machines along the three cross-section paths.Similarly, for the simulation results, the distribution of wall thickness,component-mandrel gap and roundness of the spun components can also be calculated according to the node coordinates.
In this work, FE analysis was carried out for both quenching and subsequent shear spinning processes.The blank quenching process and the component spinning process were simulated in a three-dimensional(3D)elastic–plastic FE model using ABAQUS/Standard and ABAQUS/Explicit, respectively.In the simulation of the spinning process, the distortion and residual stress produced in the quenching process were considered into the blank.
Fig.3 Machine used in shear forming process.
Fig.4 Dimension of dies (unit: mm).
Table 2 Fundamental parameters of 3D FE analysis for spinning.
3.1.Blank quenching analysis
The details of the FE modeling of the quenching process of thin sheets have been shown in previous works.8In this study,only some key modeling parameters and controlling processes were given.The FE model for the quenching process was established using ABAQUS/Standard (version 6.14) platform.Tables 3 and 48describe the material properties and the thermal parameters used in this study.The measured water cooling curve and the temperature dependent water-blank HTC (heat transfer coefficient) curves of 2219 aluminum alloy blank are shown in Fig.6 (a) and (b), respectively.8The air-blank HTC between air and blank was regarded as a constant of 20 W/(m2∙℃).
Fig.5 Paths and circles used to measure wall thickness,component-mandrel gap and roundness.
In the quenching process, the blank with an initial temperature of 530 ℃was first immersed in water at 25 ℃at a speed of 1 m/s after 5 seconds of air cooling and cooled below 30 ℃thereafter.Fig.7(a)and 7(b)exhibit the FE model and meshed geometry used for quenching, respectively.In the quenching FE model, the free meshing technique was used.The free meshing technique is conducive to dividing the area of the blank uniformly, thereby ensuring that the blank is immersed in water at a uniform speed8The type of the meshes was 8-node linear heat transfer brick element (DC3D8) and 8-node linear reduced integration brick element(C3D8R)in the simulations for heat transfer analysis and stress/distortion analysis,respectively.The total number of the element was 108645,and the number through the thickness was 3.The maximum size of the element was 2 mm.
Table 4 Elastic modulus and yield strength at different temperatures.
3.2.Spinning forming analysis
The developed FE model is established using ABAQUS/Explicit,as shown in Fig.8(a).In this model,the blank is defined as the deformable body.The isotropic material hardening model is used to describe the mechanical behavior of blank.The material properties of the as-annealed and as-quenched 2219 aluminum alloy blank are shown in Fig.1.
The mandrel and roller are set as rigid bodies.In order to ensure that the blank can rotate with the mandrel,the tie constraint is set between the top of the mandrel and the bottom of the blank.Coulomb’s friction model is applied to describe the friction behavior between tools and blank.The roller path is set as the typical shear forming path according to the law of sines.The main processing parameters are listed in Table 2.
Some researches indicated that more accurate simulation results with higher computing efficiency can be achieved by using the sweep mesh than the free mesh in spinning simulation.19–21Besides, the free meshing technique may result in local stress peaks due to inhomogeneous mass distribution in the rotating blank.Thus, the blank was meshed using the sweep meshing technique,and the type of mesh was 8-node linear reduction integration continuum elements (C3D8R).The total number of the element was 55,056 with 3 elements through the thickness (Fig.8 (b)).
3.3.Transfer of quenching distortion and residual stress
After quenching, the blanks exhibit obvious distortion and residual stress.Thus, in the spinning model, the effect of the quenching distortion and residual stress on the spinning process should be considered.However, on account of the different types and sizes of the meshes for the blanks used in the quenching and spinning model,the information about the distortion and stress of the blank obtained from the quenching simulation cannot be directly transferred into the spinning model.In this section, a new method to obtain the sweep meshes with initial distortion and stress based on the free meshes in quenching blank was given.
3.3.1.Transfer of quenching distortion
Fig.6 Water cooling curve and inversely determined HTC curve8.
Fig.7 FE model and meshed geometry used for quenching.
Fig.8 FE model used for shear spinning.
Based on the free mesh with quenching distortion characteristics,the sweep mesh with the same distortion characteristics is obtained.Fig.9(a)shows the free mesh with quenching distortion.In the xyz coordinate system, the coordinates of the nodes Niare indicated by (xi, yi, zi).The nodes of the upper or bottom surface of the free mesh with distortion characteristics are projected onto the x´o´z´ plane which is parallel to xoz plane (Fig.9 (b)).The projected nodes Ni´ are indicated by(xi´,0,zi´)in the x´y´z´coordinate system.On the x´o´z´plane,based on these projected nodes around the inner and outer edges(indicated by blue points in Fig.9 (b)), the spline curves fi(x´,z´) and fo(x´, z´) in the inner and outer edge, respectively, are obtained.
Then, according to the distribution density of the nodes of the sweep mesh used in spinning model along the circumference, some lines l´(x´, z´) (such as l1´, l2´, l3´ and l4´ showing in Fig.9(c))crossing the point o´are created.The angles between the adjacent lines are equal.These lines have intersection points(xj´,0,zj´)with the spline curves fi(x´,z´)and fo(x´,z´).These intersection points are seen as the projected points of the edge node of the sweep mesh on the x´o´z´plane.Similarly,according to the distribution density of the nodes of the sweep mesh along the radial direction, the coordinates of other nodes between the inner and outer edge nodes on the same line are calculated by linear interpolation.In this way, all the nodes of the sweep mesh projected on the x´o´z´plane can be obtained,and numbered as Nj´(xj´,0,zj´).Thus,if Nj´(xj´,0,zj´)are projected back to the upper or bottom surface of the free mesh and the projected points are numbered as Nj(xj, yj,zj), the coordinates of Nj(xj,yj,zj)are the node coordinates of the sweep mesh with distortion characteristics.
Now, the coordinates of Nj(xj, yj, zj) should be determined based on Nj´(xj´,0,zj´).First,when Nj´is projected on the surface of the sweep mesh with distortion characteristics, we need to know which element of the sweep mesh the Nj´ could project on and which nodes make up this element.For example, as shown in Fig.9 (c), the point N0´ is the node of sweep mesh on the projection plane, and N1´, N2´, N3´ and N4´ are the four nodes belonging to the element E´.The element E belonging to the sweep mesh with distortion characteristics is the element projected from the element E´.If the sum of the area of the triangles N0´N1´N2´, N0´N2´N3´, N0´N3´N4´ and N0´N1´N4´ is equal to the area of the quadrilateral N1´N2´N3´N4´,we can determine that N0´is in the element E´.Otherwise, N0´ is outside the element E´.Then, according to the node numbers of the four nodes (N1´,N2´, N3´ and N4´), the corresponding nodes (N1, N2, N3and N4) in the free mesh with distortion characteristics can be found.Finally, N0´ is projected on the plane composed of the nodes (N1, N2, N3and N4) in the free mesh with distortion characteristics, and it is easy to obtain the coordinates of the projection point (N0) in the xoz system.The coordinates of the projection points are the coordinates of the desired Nj.Repeating the above steps, all the node coordinates of the upper or bottom surface of the sweep mesh with distortion characteristics are obtained, and the obtained sweep mesh is smoothed by the Laplace method.
Fig.9 Schematic diagram of method to obtain sweep mesh based on free mesh with quenching distortion characteristics.
The nodes are considered to be equidistant along the thickness.Based on the obtained node coordinates of the upper or bottom surfaces of the sweep mesh with distortion characteristics,the node coordinates in other layers of the sweep mesh can be calculated by linear interpolation(Fig.9(d)).Finally,all of the nodes and elements in the obtained sweep mesh are numbered.In this way, the distortion produced in quenching is introduced into the spinning process.Based on the above analysis, the interpolation program is written in Python language to obtain the sweep mesh with quenching distortion, and the solution procedure of the distortion transfer analysis is given in Fig.10.
3.3.2.Transfer of quenching residual stress
In this section,the stress distribution of the free mesh obtained from the quenching simulation results was introduced into the sweep mesh with quenching distortion characteristics, as shown in Fig.11.In Fig.11, the black curves, as shown in Fig.11 (a), and red curves, as shown in Fig.11 (b), represent the free mesh and sweep mesh, respectively.The black and red points are used to mark the integration points of the elements in free and sweep mesh, respectively.
Based on the sweep mesh obtained in Section 3.2.1, as shown in Fig.11(c),the interpolation cylinder with a thickness of 0.2 mm is constructed, and the center of the cylinder is the integration point of the element in the sweep mesh.The six stress components of the free mesh elements contained in the cylinder(such as 1,2,and 3 in Fig.11(c))are used to calculate the stress state at the integration point of the sweep mesh element in sweep mesh.Since there are three layers of elements through the thickness of the blank,the thickness of each layer of elements is about 0.7 mm and only one layer is contained in the interpolated cylinder.In this way, the distribution characteristics of the residual stress in the thickness direction can be retained.Moreover, the radius R of the interpolation cylinder is set as 2 mm which is the largest element size of the free mesh.Thus,it is ensured that at least two element stresses in the free mesh are used to calculate the stress of the element in sweep mesh, and the calculated stress also has the same characteristics as the local stress gradient of the sweep element.Based on the above analysis, the interpolation program is written in Python language to calculate the stress distribution of sweep mesh,and the solution procedure of the stress transfer analysis is given in Fig.12.
Fig.10 Solution procedure of distortion transfer analysis.
Fig.11 Schematic diagram of method to obtain stress distribution of sweep meshes based on free meshes with quenching stress.
To verify the combined FE model proposed in this study, the distortion characteristics and the residual stress distribution of quenched blank were compared with those of spinning blank first.Then, the shear spinning experiments were conducted to confirm the reliability of the combined FE model.
4.1.Analysis of quenching distortion characteristic and residual stress distribution
Using the method proposed in Section 3.3.1 and 3.3.2, the quenching distortion and residual stress were transferred into the spinning blank.The distortion degree was characterized by the bending height of path1(immersing direction)and path 2 (horizontal direction), as shown in Fig.13 (a), i.e., the distance from the path to the connecting line through two endpoints of the path.In Fig.13, the bending height of quenched blank (the solid curves in Fig.13(b)) and the spinning blank (the dashed curves in Fig.13(b)) were compared.The results show that the bending height of the two blanks along path 1 and path 2 is close.Moreover, since the bending height along path 1 is much larger than that along path 2, the concave and convex surface of the blank is defined according to the bending direction of path 1.
After quenching,the residual stress of the blank in the×direction (horizontal direction), y direction (thickness direction)and z direction(immersing direction)can be obtained from the quenching simulation results.For the quenched blank, the ycomponent is not analyzed in this study, because the residual stress in the thickness direction is very small.Fig.14 (a) and 14(b) illustrate the x-component (σxin Fig.14) and zcomponent (σz) residual stress distributions of the quenched blank obtained from the quenching simulation.The spinning blank with initial stress transferred from quenching simulation result by using the method proposed in Section 3.3.2 is presented in Fig.14(c)and 14(d).It can be seen from Fig.14 that both x-component and z-component residual stress distributions of the spinning blank are close to the quenched blank.
For the x-component residual stress, the tensile stress (the value is positive) and the compressive stress (the value is negative) are distributed in the central region of the concave surface and the upper edge of the convex surface, respectively.The differences in the maximum tensile stress and the compressive stress in the x-component between the two blanks are 8.0%and 20.0 %,respectively.For the z-component residual stress, the tensile stress is distributed in the central region of the concave and convex surfaces and the compressive stress is distributed near the side edges.The differences in the maximum tensile stress and the compressive stress in the zcomponent between the two blanks are 13.0 % and 10.3 %,respectively.
Fig.12 Solution procedure of stress transfer analysis.
4.2.Comparison of experiment and simulation results for spun components
Subsequently,the quenched blanks are spun.The interval time between quenching and spinning was less than 1 hour.In the shear spinning experiment, the quenched blank is installed on the mandrel in the way that the concave surface is in contact with the mandrel, as shown in Fig.15 (a).The blank dimensions and other spinning process parameters used in the experiments and simulations are given in Table 2.When the quenching distortion and stress of blank are considered for spinning, the spun components obtained from the experiment and simulation are shown in Fig.15(b)and 15(c),respectively.The simulation results without considering the quenching distortion and stress of the blank are shown in Fig.15(d).Comparing Fig.15(c)and 15(d),it can be seen that whether the quenching distortion and stress of the blank are considered for spinning has a significant effect on the shape and stress distribution of the formed component.
Fig.16 shows the distribution of wall thickness,component-mandrel gap and roundness of the spun components obtained from experiments and simulations.In Fig.16,‘‘Annealing”and ‘‘Quenching”mean spinning using the asannealed and as-quenched blanks, respectively.The ‘‘Error”indicates an absolute error.‘‘Simulation-Y”and‘‘Simulation-N”represent the simulation results when the quenching distortion and residual stress are considered and not considered into the blank in spinning, respectively.The‘‘Error-Y”and‘‘Error-N”represent the corresponding prediction errors.
It can be seen from Fig.16(a)that the wall thickness distribution of the components obtained from the simulation and experiment has a similar variation trend along the radial direction.When the as-annealed blank is used for spinning, the maximum prediction error is 0.03 mm.For the as-quenched blank, the maximum prediction error for the wall thickness is reduced from 0.09 mm to 0.05 mm when the quenching distortion and residual stress are considered.
From Fig.16 (b), it can be observed that the componentmandrel gap of the component increases exponentially along the radial direction.When the as-annealed blank is used for spinning, the maximum prediction error of the componentmandrel gap is 0.57 mm.For the as-quenched blank,the maximum prediction error for the component-mandrel gap is reduced from 0.63 mm to 0.25 mm when the quenching characteristics of the blank are considered.
Fig.16 (c) shows the roundness distribution.For the asannealed blank, the maximum prediction error is 0.006 and the roundness tends to decrease from the big end to the small end of the component.For the as-quenched blank, when the quenching distortion and residual stress of the blank are not considered, the variation characteristics of the roundness are the same as those when the as-annealed blank is used for spinning.However, the roundness of the components becomes smaller and the roundness of the big end is slightly larger than that of the small end when considering the quenching distortion and residual stress of the blank, and this variation trend is consistent with the experimental results.Additionally, after considering the quenching distortion and residual stress for the as-quenched blank, the maximum prediction error for the roundness is reduced from 0.008 to 0.003.Based on the above analysis, it can be seen that the combined FE model established in this work is reliable.
Fig.13 Comparison of bending height between blank after quenching and blank used in spinning along path 1 and path 2.
Fig.14 Comparison of residual stresses on quenched blanks.
It can be known from Section 4 that the 2219 aluminum alloy blanks exhibit obvious distortion and residual stress after quenching.The pre-existing distortion and stress can affect the spinning process of the complex thin-walled components.In this section, the effects of the quenching distortion and residual stress on spinning forming precision are analyzed using the established FE model.
5.1.Univariate design
Fig.15 Comparison of spinning experiment and simulation results.
The quenching mainly leads to the change in the material property, the shape and the stress of the blank used in spinning.These changes can significantly affect the forming process and the final forming precision of the component.The influence of these changes on the spinning process was analyzed with the help of the proposed FE model.The analysis scheme is shown in Table 5.The material properties of asannealed and as-quenched blanks are shown in Fig.1.In the analysis scheme, 8 cases were designed.For the as-annealed blanks,their initial shape is plane and has no initial stress,that is,case 1 in the table.For the as-quenched blanks,their initial shape becomes concave or convex because of the existence of quenching distortion.If the distortion degree is very small and can be ignored,the initial shape of the blank is considered plane, that is, cases 2, 5 and 6 in the table.The blanks with concave and convex initial shape can only exhibit the concave and convex initial stress distributions, namely cases 7 and 8 in the table.If the stress is very small and can be ignored,the initial stress of the blank is considered‘‘No”,that is,cases 3 and 4 in the table.Based on the combined FE model, the effect of quenching on the shear spinning process is investigated.
5.2.Analysis of forming precision
In this study, the forming precision of the component is evaluated by the wall thickness, the component-mandrel gap and the roundness along the radial direction.Fig.17 (a) shows the wall thickness distribution of the component.It can be seen from Fig.17(a)that the difference in the wall thickness of the components formed by different blanks is not noticeable when the radius is less than 60 mm, as marked with a red circle in Fig.17 (a).However, in the part where the radius is greater than 60 mm, the wall thickness of the component formed by the as-annealed blank is significantly smaller than that formed by the as-quenched blank.Additionally, for the components formed by as-quenched blank,when the quenching distortions are considered,i.e.,when the initial shapes are concave or convex,the wall thickness becomes larger,as marked with a black square in Fig.17 (a).Therefore, the quenching leads to the increase of wall thickness of the spun component, and the increase of material strength and the existence of the distortion of the blank after quenching play a major role.
Fig.17 (b) shows the component-mandrel gap of the spun component along the radial direction.For all the cases with different blanks, the component-mandrel gap of the component increases with the radius of the component.Additionally,the component-mandrel gap of the component formed by the as-quenched blank is significantly larger than that formed by the as-annealed blank.Moreover, the existence of the initial distortion for the as-quenched blank also increases the component-mandrel gap of the spun component, as marked with a black square in Fig.17(b).For the blank without initial distortion, when the quenching residual stress is considered into the blank for spinning, the component-mandrel gap of the component becomes smaller, as marked with a red circle in Fig.17 (b), that is, the existence of initial stress can significantly reduce the component-mandrel gap.Moreover, when the effects of quenching distortion and residual stress are considered together, it is conducive to reducing the componentmandrel gap when the quenched blank with a concave initial shape is used for spinning.
Fig.16 Comparison of forming precision of components obtained by simulation and experiment.
Fig.17 (c) shows the roundness of the components along the radial direction.It can be seen from the figure that the roundness of the components formed by the blank with distortion is lower than that without considering the blank distortion.The roundness of the top of the component formed by the plane and concave blank is slightly higher than that of the bottom, while the roundness of the top is obviously lower for the component formed by the convex blank, as pointed by the red arrows in Fig.17 (c).Additionally, when both the effects of quenching distortion and residual stress are considered, the roundness of the component is better for the case using the concave blank than that for the case using the convex blank.
To quantify the influence of blank quenching on the forming precision of the components, the average deviations of the wall thickness, component-mandrel gap and roundness of the components were calculated.
Table 5 Analysis scheme.
where n indicates the total number of the measuring points along the radial direction.
where n indicates the total number of the measuring points along the radial direction.
where n indicates the total number of the measuring points along the radial direction.
Table 6 shows the average deviation of wall thickness,component-mandrel gap and roundness of the components spun by blanks with different initial states.It can be seen that when the initial shape of the quenched blank is concave and the residual stress is not considered (No.5), the deviation of the wall thickness and component-mandrel gap of the formed components are the largest.However,when the effect of initial stress is considered, the deviation of the wall thickness and component-mandrel gap of the components formed by the concave blanks are significantly smaller than that formed by convex blank (No.6).Therefore, there is an obvious interaction between the initial shape and stress of the blanks on forming precision of the components.
Fig.17 Effect of blank quenching on spinning precision of components.
Based on the analysis of Table 6, the sums of squares and the effect estimate are estimated, as shown in Table 7.The sum of squares is the sum of the squares of the differences between each index and its mean value.In Table 7,the percent contribution is used to measure the percentage contribution of each factor term to the total sum of squares,which is an effective guide to the relative importance of each factor term.It can be noted that the most significant factor affecting the wall thickness is the property of the blank, followed by the shape,the stress,and the shape-stress interaction.The property is also the dominant factor affecting the component-mandrel gap,followed by the shape,the shape-stress interaction,and the stress.However, the shape of the blank has a major effect on the roundness, and the effect of other factors is very small.
Table 6 Forming precision of components spun by blanks with different initial states.
Table 7 Effect estimate summary for factorial design.
Based on the analyses in Section 5, it is known that the quenching blanks with different initial states lead to the different forming precision of components.In this section,the effect mechanism of the blank quenching on forming precision of the components was discussed with the help of the simulation.
6.1.Evolution of stress distribution during spinning
The distributions of the circumferential stress of the workpieces spinning with different blanks are shown in Fig.18.Comparing Fig.18 (a) and Fig.18 (b), we can see that the degree of non-uniform distribution of the circumferential stress in the spinning area is larger when the as-quenching blank is used to spin than that when the as-annealing is used to spin because of the increase of the material strength of the blank after quenching.As shown in Fig.18(b),the circumferential compressive stress in the spinning area is concentrated away from the deformation area of the workpiece.This nonuniform stress distribution indicates an increase in the degree of inhomogeneous deformation of the workpiece during spinning.Fig.18 (c) and 18(d) show the circumferential stress distributions when the as-quenched blanks with the concave and convex initial shape are used for spinning, respectively.Compared with Fig.18 (b), it can be known that the nonuniformity of stress distribution and the maximum of circumferential compression stress increase when the quenching distortion of the blank is considered for spinning.Fig.18(b), 18(e) and 18(f) show that the effect of the initial stress of the blank on the stress distribution of the workpieces during the spinning process is not noticeable, while initial stress can significantly influence the magnitude of spinning stress.It has relatively larger circumferential compressive stress for the case using convex stress blank.The increase of the circumferential stress and its non-uniform degree of the workpiece in spinning is the cause of the increase of inhomogeneous deformation degree and springback of the workpiece.As a result,the component-mandrel gap of the components increases.
Fig.19 (a) and 19(b) show the variations of maximum circumferential stress of the workpiece spun with the concave and convex blanks, respectively.In Fig.19, the black and red points represent the maximum circumferential compressive stress of the workpiece at different spinning stages.The black and red curves obtained by fitting the data points represent the corresponding variation trend of the maximum circumferential compressive stress.In the figure, the black dotted line is the dividing line between the spherical part and the conical part of the workpiece, i.e., it indicates that the spinning of the spherical part and the conical part is being performed when the spinning stage is on the left and right of the black dotted line, respectively.
It can be seen from Fig.19 that the maximum circumferential compressive stress increases rapidly first and then decreases slightly during the spinning process of the spherical part, and the curve presents a stress peak.When spinning to the conical part, the maximum circumferential stress increases first, and then tends to be stable.In Fig.19, the black curves show the variation trends of the maximum circumferential compressive stress during the spinning process of the spherical part using the blanks with different shapes and without initial stress.By comparison, it is worth noting that the drop in the maximum circumferential compressive stress after reaching the peak is larger when the convex blank is used for spinning than that when using the concave blank in Fig.19 (a) and 19(b).This is the main reason why the forming precision of the component is better when the convex blank without initial stress is used for spinning, especially for the smaller component-mandrel gap.
Fig.18 σθdistribution of workpieces spun with different initial state blanks.
Fig.19 Variations of maximum circumferential stress of workpiece in spinning for blanks with different initial states.
However, in the case of spinning with the concave blank,there is an obvious stress drop after reaching the peak stress of 361.7 MPa when considering the effect of residual stress(Fig.19 (a)).This stress drop can reduce the componentmandrel gap of the component.Additionally,for spinning with the blanks of different shapes, the maximum circumferential compressive stress of the workpiece is smaller when the residual stress is considered than that when the residual stress is not considered in spinning, so the forming precision of the spun component is better (Fig.17 (b)).
6.2.Evolution of flange swing height during spinning
As well known,the flange swing height(FSH)during spinning reflects the stability of the forming process and is related to the forming precision.22The FSH is evaluated by the height difference in the axial direction between the edge of the flange and the reference line (Fig.20 (a)).The reference line marked in Fig.20(a)is the line that has the same height in the axial direction during spinning as the reference point,as shown in Fig.20(b).The reference point is the point farthest from the spinning area during spinning.Thus,the position where the FSH is zero indicates that the height of the flange edge is the same as the reference point.The FSH is defined as a positive value when the flange edge is higher than the reference line in the axial direction, as shown in Fig.20 (a).Conversely, it is defined as a negative value.The fluctuation amplitude of the FSH, i.e.,the difference between the maximum and minimum FSH, is usually used to characterize the severity of flange wrinkling.
Fig.20 Illustration of flange swing height.
Fig.21 illustrates the influence of material properties(Fig.21(a)),quenching distortion(Fig.21(b))and quenching stress (Fig.21 (c)) on the FSH in different spinning stages(40 %, 60 % and 80 %).The FSHs of workpieces during the spinning with the blanks of ‘‘A-Shape (Plane)-Stress (No)”and ‘‘Q-Shape (Plane)-Stress (No)”states are compared to analyze the effects of material property.It can be seen from Fig.21(a)that the fluctuation amplitude increases as the spinning process progresses.At the early stage of the spinning process(40%),there is little difference between the two variation curves of FSH for the workpieces spinning with the asannealed and as-quenched blanks.At the middle stage of the spinning process(60%),the FSH increases for both the workpieces spinning with as-quenched and as-annealed blanks,and their fluctuation amplitudes are close.However, at the middle stage, the variation curve is steeper for the workpiece spun with the as-quenched blank than that spun with the asannealed blank, which indicates that the degree of the uneven flow of the material increases in spinning.At the later stage(80 %), the fluctuation amplitude of the workpiece spinning with the as-quenched blank increases rapidly and becomes much larger than that spinning with the as-annealed blank.Larger FSH fluctuation amplitude and higher circumferential compressive stress (Fig.18) will result in increased material flow in the circumferential direction of the workpiece during the spinning process.As a result, when the radius of the component is larger than 60 mm, the wall thickness and the component-mandrel gap increase rapidly, as shown in Fig.17 (a) and 17(b).
Fig.21 Effects of initial states of blank on FSH of workpiece in different spinning stages.
The FSHs of workpieces in spinning with the blanks of‘‘QShape (Concave)-Stress (No)”, ‘‘Q-Shape (Convex)-Stress(No)”and‘‘Q-Shape(Plane)-Stress(No)”states are compared to analyze the effects of initial shape, as shown in Fig.21 (b).When the plane blank is used for spinning, the fluctuation amplitude of the FSH during the entire spinning process is smaller than that when the concave and convex blanks are used for spinning.It is worth noting that the peak of the FSH variation curves (peak A in Fig.21 (b)) with the largest distance from the reference line is positive at the early stage of the spinning process (40 %) when the convex blank is used to spin, that is, the flange shows a state inclined to the spun area of the workpiece.However,peak A changes from positive to negative at the middle stage of the spinning process(60%),and the flange is inclined to the mandrel.This change causes the flange of the workpiece to overturn, and deteriorates the roundness of the top of the component.
The FSHs of workpieces in spinning with the blanks of‘‘QShape (Plane)-Stress (No)”, ‘‘Q-Shape (Plane)-Stress (Concave)”and‘‘Q-Shape(Plane)-Stress(Convex)”states are compared to analyze the effect of initial stress,as shown in Fig.21(c).It can be seen that the effect of the quenching residual stress on the fluctuation amplitude of FSH is not noticeable.However, it can be known from Section 5.2 that there is an obvious interaction effect between the initial shape and stress of the blanks on forming precision of the component.Therefore, in the following content, the effect of this interaction on FSH is also discussed.
The fluctuation amplitude of FSH for the workpieces spun with the distorted blanks with and without quenching residual stress is compared in Fig.22.Taking the 40 % spinning stage as an example,we can see that when both quenching distortion and residual stress are considered (the dashed line in Fig.22),the fluctuation amplitudes of FSH during spinning are significantly smaller than those when only quenching distortion is considered (the solid line in Fig.22).This is because the existence of residual stress results in the decrease of the maximum circumferential compressive stress of the workpiece during the spinning process (Fig.19).Therefore, it can be seen from Fig.17(b)that the component-mandrel gap of the component is smaller when the quenching residual stress is considered into the blank for spinning.
Fig.22 FSH of workpiece in 40%spinning stage when distorted blanks with and without residual stress are used to spin.
The effect of blank quenching on spinning forming precision of 2219 aluminum alloy complex thin-walled components is investigated using the combined FE simulation and experiments.The main conclusions can be drawn as follows:
(1) A combined FE model including blank quenching and subsequent spinning process of the components is established to investigate the effect of quenching on spinning forming precision.In this model,through the projection of the node coordinates and the interpolation of element stress between meshes with different types and sizes, the quenching distortion and residual stress of the blank obtained in quenching simulation results are transferred to the blank in the spinning model.
(2) The material property and shape of the blanks play a major role in affecting the wall thickness and component-mandrel gap of the components.The increase of material strength and the existence of distortion for the blank after quenching lead to the increase of non-uniformity of circumferential compressive stress in the spinning area and the increase of the flange swing height during spinning.These changes lead to a significant increase in the wall thickness and componentmandrel gap of the spun components.
(3) The existence of quenching residual stress is beneficial to decrease the maximum circumferential compressive stress and flange swing height of workpieces during spinning,which results in the component-mandrel gap of the component after spinning becoming smaller.Quenching distortion is the main factor affecting the roundness,and the roundness becomes lower when the convex blank is used to spin due to the overturning of the workpiece flange in spinning.
(4) When the quenched blank considering both quenching distortion and residual stress is installed on the mandrel in such a way that the concave surface is in contact with the mandrel for spinning,it is conducive to reducing the component-mandrel gap and increasing the roundness.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This study was co-supported by the Young Scientists Fund of the National Natural Science Foundation of China (No.52105417),the Foundation of Civil Aviation Flight University of China(Nos.J2022-067,ZJ2022-003 and JG2022-27)and the National Science Fund for Excellent Young Scholars of China(No.52122509).
