曲面零件连续成形的理论与数值模拟研究及控制软件开发
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摘要
曲面零件具有质量轻、流线型好、承载能力强等特点，被广泛应用于工业生产的各个领域。随着经济的发展和社会的进步，对各种曲面件的需求开始从大批量单一产品向小批量或单件多样化的产品转变。模具成形是加工曲面零件的重要方法，但每一种零件都要开发相应的模具，并且模具的设计、调试周期长，尤其加工大型曲面件时，成形设备的体积大、制造成本高。因此，开展新的曲面件成形工艺研究具有重要的理论意义和实用价值。
卷板成形是一种传统的连续成形方式，曲面连续成形将传统卷板成形的直辊用可弯曲的柔性辊代替，形成一种快速、高效的板料加工技术，适用于不同形状大型双曲度曲面件的成形。目前，曲面连续成形工艺虽然已有一定的研究工作，但在板料连续成形理论、成形曲面件的精度、数值模拟的有限元模型及成形过程控制等方面还有许多亟待解决的问题，迫切需要进一步深入研究，提高工程应用价值，以融入到现代制造业的行列中。本文通过对连续成形过程中板料双向弯曲变形的理论分析，建立了成形过程横向与纵向形状控制模型，并开发了成形过程控制软件。
本文研究的主要内容和结论如下：
1.根据板料连续成形的变形历史，对连续成形过程提出了一种平板横向弯曲与柱面纵向弯曲组合的曲面形成机制。板料连续成形时，在局部变形区先形成横向曲率变为柱面，再由上辊下压使柱面发生纵向弯曲变为双曲度曲面，并通过柔性辊滚动实现板料连续进给完成曲面件的成形。由此可见，曲面连续成形的最终曲率要综合考虑单向弯曲回弹及横向与纵向弯曲的相互影响。基于三种不同的材料模型，给出单向弯曲变形中弯矩与回弹比的计算公式。分析了连续成形过程中横向与纵向弯曲的相互影响，结果表明：纵向成形的曲率越大，对横向弯曲形成的附加弯矩越大，上辊下压前后横向曲率的变化值也就越大；横向弯曲对纵向曲率的影响主要体现在截面形状方面，不同的横向曲率形成不同的横截面形状，纵向压下量不变时在横截面上产生的弯矩和惯性矩不同，使纵向弯曲的相对回弹比随横向曲率的减小呈指数递减。
2.描述了不同曲面件的连续成形原理。根据成形曲面的扫略特性，给出成形曲面的数学描述形式。基于横向回弹及纵向弯曲对横向曲率的影响，对横向目标截面线方程进行补偿，得到上、下柔性辊的轴线方程及每个控制点的调形量，建立了横向弯曲的形状控制模型。分析纵向滚弯成形过程中柔性辊与板料接触点和弯曲角的变化，考虑纵向回弹和横向曲率对纵向成形的影响，得到上辊下压量与成形目标曲率的关系式，建立了纵向弯曲的形状控制模型。采用本文建立的控制理论与方法进行数值模拟，成形的曲面件精度较高，验证了该方法的有效性。
3.提出了一种连续柔性辊的有限元建模方法。连续柔性辊模型中接触方式为光滑曲线接触，避免压痕产生，提高了成形件的表面质量；应力、应变分布更加均匀；成形曲面件的精度较高。对柔性辊调形过程进行有限元仿真，分析控制点数量对调形形状及成形精度的影响，结果表明：控制点数量越多，调形形状越接近于目标形状，成形曲面件的精度也越高。给出了柔性辊调形误差的补偿方法，补偿后成形曲面件的精度提高，验证了补偿方法的可行性。
4.分析了不同材料和板厚对柔性辊产生的作用力，结果表明：随着弹性模量和屈服强度的增加，板料对柔性辊的作用力提高，随着板厚的增加，对柔性辊的作用力也会增加，而且上辊受到的作用力要大于下辊。分析了材料性能、板厚、上辊下压量、柔性辊形状及下辊中心距对成形误差的影响规律，结果表明：横向与纵向成形误差随弹性模量的增加而减小；随板厚的增加而减小；随上辊压下量的增加而减小；随横向曲率半径的减小而减小；随下辊中心距的增加而增大。给出了横向与纵向弯曲的相互影响曲线，压下量不变时，横向曲率半径增加，纵向曲率半径有减小的趋势；柔性辊形状不变时，上辊压下量增大，横向曲率半径增加。
5.基于给出的连续成形过程横向与纵向的控制理论与方法，在VC++平台开发了曲面连续成形过程的控制软件。该软件主要包括曲面造型模块、工艺参数设置模块、程序计算模块及图形显示模块。曲面造型模块可以实现NURBS曲面重构；工艺参数设置模块的功能是输入设备参数、材料力学性能及板料尺寸；程序计算模块能够根据目标曲面横向与纵向曲率，计算出上辊压下量及柔性辊上每个控制点的调形量；图形显示模块结合OpenGL库函数，用来虚拟显示曲面连续成形过程。
6.开发了连续成形过程的计算机控制系统。应用该系统成形典型曲面件并与数值模拟件进行对比，实验结果与数值模拟结果吻合较好。采用数值模拟方法为部分正高斯曲率和负高斯曲率曲面件建立了控形数据库。通过连续成形过程控制系统实现了不同类型曲面件的成形，以鞍面件和凸面件为目标曲面件，分析成形件表面质量和成形精度，结果证明曲面连续成形工艺加工的曲面件质量和精度都符合要求。
The surface parts, which have the characteristics of light quality, good streamline, highbearing capacity, etc., are widely used in various industrial fields. With the development ofeconomy and the progress of society, the demand for surface parts shifts from mass productionfor single product to small batches or single-piece production for wide-variety of products. Dieforming is an important method for forming surface parts. However, each part needs a kind ofdie, and it has the disadvantages of long development and debugging cycle. When forminglarge scale surface parts, the volume of the die forming device is large and the manufacturingcosts are high. Therefore, it has great theoretical significance and utility value for studying thenovel surface parts forming technology.
Roll bending is a traditional continuous forming method. Continuous forming employsthree flexible rolls instead of straight rolls of roll bending, which is a rapid and efficientforming technology. It is suitable for forming large scale parts with doubly curved surface. Theresearch on continuous forming has made some progress, but there are many urgent problemsto be solved. For improving the engineering application value, the continuous forming theory,accuracy of forming surface part, finite element model of numerical simulation and formingprocess control need to be further studied. In this paper, the double bending theory of sheetmetal in continuous forming process was analyzed, and the transverse and longitudinal shapecontrol models were established. Then, the control software of continuous forming process wasdeveloped.
The main contents and conclusions in this paper are as follows:
1. According to the deformation history of sheet metal in continuous forming process, thesurface forming mechanism was provided, which is a combination of flat plate transverselybending and cylindrical surface longitudinally bending. In continuous forming process, first thesheet metal is bent in transverse direction in local deformation region, then the sheet metal isbent in longitudinal direction by top roll, finally the sheet metal is changed into doubly curvedsurface part by the rotation of the flexible rolls. Therefore, the formed part needs to consider the one-direction springback and the influence between transverse and longitudinal bending. Basedon the three different material models, the bending moment and springback ratio of singlebending was given. The influence between transverse and longitudinal bending was analyzed.The results show that the difference of transverse radius before and after springback decreaseswith the decrease of longitudinal curvature, and the longitudinal relative springback ratio is anexponential decline curve with the increase transverse radius.
2. The principle of continuous forming for different types of surface parts was described.According to the feature of swept surface, the mathematic equation of formed surface wasgiven. Based on the transverse springback and the influence of longitudinal bending ontransverse curvature, the axis equations of the top and bottom flexible rolls and the adjustingvalue of each control point can be obtained by compensating the equation of transverse sectionline of target surface, and then the transverse shape control model was established. Consideringthe unloading stage and the influence of transverse bending on longitudinal curvature, therelation between the downward displacement of top roll and the longitudinal target curvaturecan be acquired, and the longitudinal shape control model was established. The numericalsimulations were carried out by the control theory and method provided in this paper. It isfound that the quality and accuracy of the formed part is good.
3. The modeling method with continuous flexible roll was put forward. The contact linebetween flexible rolls and sheet metal is smooth, which can avoid impression and improve thesurface quality. The distribution of stress and strain in that model is uniform, and the accuracyof the formed part is high. The flexible roll adjusting process was simulated, and the influenceof the number of control point on adjusting shape and forming precision were studied. Theadjusting shape approaches the target shape with the increase of the number of control point.And the forming precision also increases with the increase of the number of control point. Dueto the adjusting errors of flexible roll, a compensation method was proposed and the adjustingerrors decreased after compensation, which was verified through numerical simulations.
4. The influence of different materials and thickness of sheet metal on reaction forces onflexible rolls was analyzed. The results show that the reaction forces on flexible roll increasewith the increase of the elastic modulus and yield strength of material and the plate thickness.The reaction forces on top flexible roll are larger than those on bottom flexible rolls. Theinfluence rules of material, plate thickness, downward displacement of top roll, shape offlexible roll and center distance between bottom rolls on forming accuracy of sheet metal werestudied. The results show that the forming errors decrease with the decrease of elastic module,decrease with increase of thickness of sheet metal, decrease with the decrease of the downwarddisplacement of top roll, decrease with the decrease of transverse radius of curvature andincrease with the increase of the center distance of the two bottom flexible rolls. The correlationship curve between transverse and longitudinal bending was obtained. When thedownward displacement of top roll remains the same, the longitudinal curvature increase withthe decrease of the transverse radius of curvature. When the shape of flexible roll remainsunchanged, the transverse radius of curvature increase with the increase of the downwarddisplacement of top roll.
5. Based on the control theory and method established above, the continuous formingcontrol software is developed on VC++platform. The control software was divided into foursections: surface constructing module, parameter setting module, computing module and graphdisplaying module. The first module can reconstruct the target surface by importing the digitaldata points. The second module can be used for inputting the device parameters, materialproperty and dimension of sheet metal. The third module can calculate the downwarddisplacement of top roll and the adjusting value of each control point. The fourth module candisplay the continuous forming process with the help of OpenGL.
6. The computer control system of continuous forming process was developed bycombining the control software with the experimental set. The numerical simulations andforming experiments of typical surface parts were carried out, and the results show that theexperimental results agree well with the simulated results. The shape control databases ofsurface parts with positive and negative Gaussian curvatures were established. The differenttypes of doubly curved surface parts were formed by continuous forming process controlsystem. The smoothness and dimensional accuracy of the saddle and torus surface parts wereanalyzed, and the results demonstrate that the surface quality and precision of surface partsformed by continuous forming technology meet the requirement.
卷板成形是一种传统的连续成形方式，曲面连续成形将传统卷板成形的直辊用可弯曲的柔性辊代替，形成一种快速、高效的板料加工技术，适用于不同形状大型双曲度曲面件的成形。目前，曲面连续成形工艺虽然已有一定的研究工作，但在板料连续成形理论、成形曲面件的精度、数值模拟的有限元模型及成形过程控制等方面还有许多亟待解决的问题，迫切需要进一步深入研究，提高工程应用价值，以融入到现代制造业的行列中。本文通过对连续成形过程中板料双向弯曲变形的理论分析，建立了成形过程横向与纵向形状控制模型，并开发了成形过程控制软件。
本文研究的主要内容和结论如下：
1.根据板料连续成形的变形历史，对连续成形过程提出了一种平板横向弯曲与柱面纵向弯曲组合的曲面形成机制。板料连续成形时，在局部变形区先形成横向曲率变为柱面，再由上辊下压使柱面发生纵向弯曲变为双曲度曲面，并通过柔性辊滚动实现板料连续进给完成曲面件的成形。由此可见，曲面连续成形的最终曲率要综合考虑单向弯曲回弹及横向与纵向弯曲的相互影响。基于三种不同的材料模型，给出单向弯曲变形中弯矩与回弹比的计算公式。分析了连续成形过程中横向与纵向弯曲的相互影响，结果表明：纵向成形的曲率越大，对横向弯曲形成的附加弯矩越大，上辊下压前后横向曲率的变化值也就越大；横向弯曲对纵向曲率的影响主要体现在截面形状方面，不同的横向曲率形成不同的横截面形状，纵向压下量不变时在横截面上产生的弯矩和惯性矩不同，使纵向弯曲的相对回弹比随横向曲率的减小呈指数递减。
2.描述了不同曲面件的连续成形原理。根据成形曲面的扫略特性，给出成形曲面的数学描述形式。基于横向回弹及纵向弯曲对横向曲率的影响，对横向目标截面线方程进行补偿，得到上、下柔性辊的轴线方程及每个控制点的调形量，建立了横向弯曲的形状控制模型。分析纵向滚弯成形过程中柔性辊与板料接触点和弯曲角的变化，考虑纵向回弹和横向曲率对纵向成形的影响，得到上辊下压量与成形目标曲率的关系式，建立了纵向弯曲的形状控制模型。采用本文建立的控制理论与方法进行数值模拟，成形的曲面件精度较高，验证了该方法的有效性。
3.提出了一种连续柔性辊的有限元建模方法。连续柔性辊模型中接触方式为光滑曲线接触，避免压痕产生，提高了成形件的表面质量；应力、应变分布更加均匀；成形曲面件的精度较高。对柔性辊调形过程进行有限元仿真，分析控制点数量对调形形状及成形精度的影响，结果表明：控制点数量越多，调形形状越接近于目标形状，成形曲面件的精度也越高。给出了柔性辊调形误差的补偿方法，补偿后成形曲面件的精度提高，验证了补偿方法的可行性。
4.分析了不同材料和板厚对柔性辊产生的作用力，结果表明：随着弹性模量和屈服强度的增加，板料对柔性辊的作用力提高，随着板厚的增加，对柔性辊的作用力也会增加，而且上辊受到的作用力要大于下辊。分析了材料性能、板厚、上辊下压量、柔性辊形状及下辊中心距对成形误差的影响规律，结果表明：横向与纵向成形误差随弹性模量的增加而减小；随板厚的增加而减小；随上辊压下量的增加而减小；随横向曲率半径的减小而减小；随下辊中心距的增加而增大。给出了横向与纵向弯曲的相互影响曲线，压下量不变时，横向曲率半径增加，纵向曲率半径有减小的趋势；柔性辊形状不变时，上辊压下量增大，横向曲率半径增加。
5.基于给出的连续成形过程横向与纵向的控制理论与方法，在VC++平台开发了曲面连续成形过程的控制软件。该软件主要包括曲面造型模块、工艺参数设置模块、程序计算模块及图形显示模块。曲面造型模块可以实现NURBS曲面重构；工艺参数设置模块的功能是输入设备参数、材料力学性能及板料尺寸；程序计算模块能够根据目标曲面横向与纵向曲率，计算出上辊压下量及柔性辊上每个控制点的调形量；图形显示模块结合OpenGL库函数，用来虚拟显示曲面连续成形过程。
6.开发了连续成形过程的计算机控制系统。应用该系统成形典型曲面件并与数值模拟件进行对比，实验结果与数值模拟结果吻合较好。采用数值模拟方法为部分正高斯曲率和负高斯曲率曲面件建立了控形数据库。通过连续成形过程控制系统实现了不同类型曲面件的成形，以鞍面件和凸面件为目标曲面件，分析成形件表面质量和成形精度，结果证明曲面连续成形工艺加工的曲面件质量和精度都符合要求。
The surface parts, which have the characteristics of light quality, good streamline, highbearing capacity, etc., are widely used in various industrial fields. With the development ofeconomy and the progress of society, the demand for surface parts shifts from mass productionfor single product to small batches or single-piece production for wide-variety of products. Dieforming is an important method for forming surface parts. However, each part needs a kind ofdie, and it has the disadvantages of long development and debugging cycle. When forminglarge scale surface parts, the volume of the die forming device is large and the manufacturingcosts are high. Therefore, it has great theoretical significance and utility value for studying thenovel surface parts forming technology.
Roll bending is a traditional continuous forming method. Continuous forming employsthree flexible rolls instead of straight rolls of roll bending, which is a rapid and efficientforming technology. It is suitable for forming large scale parts with doubly curved surface. Theresearch on continuous forming has made some progress, but there are many urgent problemsto be solved. For improving the engineering application value, the continuous forming theory,accuracy of forming surface part, finite element model of numerical simulation and formingprocess control need to be further studied. In this paper, the double bending theory of sheetmetal in continuous forming process was analyzed, and the transverse and longitudinal shapecontrol models were established. Then, the control software of continuous forming process wasdeveloped.
The main contents and conclusions in this paper are as follows:
1. According to the deformation history of sheet metal in continuous forming process, thesurface forming mechanism was provided, which is a combination of flat plate transverselybending and cylindrical surface longitudinally bending. In continuous forming process, first thesheet metal is bent in transverse direction in local deformation region, then the sheet metal isbent in longitudinal direction by top roll, finally the sheet metal is changed into doubly curvedsurface part by the rotation of the flexible rolls. Therefore, the formed part needs to consider the one-direction springback and the influence between transverse and longitudinal bending. Basedon the three different material models, the bending moment and springback ratio of singlebending was given. The influence between transverse and longitudinal bending was analyzed.The results show that the difference of transverse radius before and after springback decreaseswith the decrease of longitudinal curvature, and the longitudinal relative springback ratio is anexponential decline curve with the increase transverse radius.
2. The principle of continuous forming for different types of surface parts was described.According to the feature of swept surface, the mathematic equation of formed surface wasgiven. Based on the transverse springback and the influence of longitudinal bending ontransverse curvature, the axis equations of the top and bottom flexible rolls and the adjustingvalue of each control point can be obtained by compensating the equation of transverse sectionline of target surface, and then the transverse shape control model was established. Consideringthe unloading stage and the influence of transverse bending on longitudinal curvature, therelation between the downward displacement of top roll and the longitudinal target curvaturecan be acquired, and the longitudinal shape control model was established. The numericalsimulations were carried out by the control theory and method provided in this paper. It isfound that the quality and accuracy of the formed part is good.
3. The modeling method with continuous flexible roll was put forward. The contact linebetween flexible rolls and sheet metal is smooth, which can avoid impression and improve thesurface quality. The distribution of stress and strain in that model is uniform, and the accuracyof the formed part is high. The flexible roll adjusting process was simulated, and the influenceof the number of control point on adjusting shape and forming precision were studied. Theadjusting shape approaches the target shape with the increase of the number of control point.And the forming precision also increases with the increase of the number of control point. Dueto the adjusting errors of flexible roll, a compensation method was proposed and the adjustingerrors decreased after compensation, which was verified through numerical simulations.
4. The influence of different materials and thickness of sheet metal on reaction forces onflexible rolls was analyzed. The results show that the reaction forces on flexible roll increasewith the increase of the elastic modulus and yield strength of material and the plate thickness.The reaction forces on top flexible roll are larger than those on bottom flexible rolls. Theinfluence rules of material, plate thickness, downward displacement of top roll, shape offlexible roll and center distance between bottom rolls on forming accuracy of sheet metal werestudied. The results show that the forming errors decrease with the decrease of elastic module,decrease with increase of thickness of sheet metal, decrease with the decrease of the downwarddisplacement of top roll, decrease with the decrease of transverse radius of curvature andincrease with the increase of the center distance of the two bottom flexible rolls. The correlationship curve between transverse and longitudinal bending was obtained. When thedownward displacement of top roll remains the same, the longitudinal curvature increase withthe decrease of the transverse radius of curvature. When the shape of flexible roll remainsunchanged, the transverse radius of curvature increase with the increase of the downwarddisplacement of top roll.
5. Based on the control theory and method established above, the continuous formingcontrol software is developed on VC++platform. The control software was divided into foursections: surface constructing module, parameter setting module, computing module and graphdisplaying module. The first module can reconstruct the target surface by importing the digitaldata points. The second module can be used for inputting the device parameters, materialproperty and dimension of sheet metal. The third module can calculate the downwarddisplacement of top roll and the adjusting value of each control point. The fourth module candisplay the continuous forming process with the help of OpenGL.
6. The computer control system of continuous forming process was developed bycombining the control software with the experimental set. The numerical simulations andforming experiments of typical surface parts were carried out, and the results show that theexperimental results agree well with the simulated results. The shape control databases ofsurface parts with positive and negative Gaussian curvatures were established. The differenttypes of doubly curved surface parts were formed by continuous forming process controlsystem. The smoothness and dimensional accuracy of the saddle and torus surface parts wereanalyzed, and the results demonstrate that the surface quality and precision of surface partsformed by continuous forming technology meet the requirement.
引文
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