基于图像分析的超塑性自由胀形实验测量与力学解析
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摘要
本文是我的导师宋玉泉教授关于超塑性力学解析理论和成形规律研究的组成部分。由于超塑性自由胀形的真实轮廓为轴对称旋转曲面,随着对超塑胀形力学研究的不断深入,以往建立在球面假设条件下的力学解析已不能真实反映胀形过程。因此,要想得出精确的定量解析结果,就必须准确测量出旋转曲面胀形件轮廓的几何形状以及胀形过程中轮廓上各点的变形情况。基于此,本文通过对球面假设条件下、以及非球面真实情况下的力学解析基本理论的介绍,分析了轴对称旋转曲面的主曲率半径和弧长等基本特性。采用图像测量方法对实验过程中胀形件几何参量和变形进行测量,并对超塑胀形实验实验装置的加热、加载以及控制系统等进行改造设计。选择典型超塑性材料ZnAl22自由胀形进行测量实验,介绍了几何参量和胀形变形测算的基本方法。根据对非球面胀形几何形状数学模型的分析,建立胀形件几何参数测量公式和厚度分布模型,以及应用图像测量建立胀形基本力学方程的方法。本文的研究内容为进行超塑性非球面自由胀形理论和实验研究提供了方法和手段,对进一步深入研究超塑性胀形力学规律有着重要的意义。
Superplasticity is a brach of materials science frontiers, and superplastic forming has become an important method in the field of the modern forming technology.The development of metal superplastic experiences the stages, composed by the observation of some superplasticity phenomenon, further research on the mechanical properties and deformation mechanism, with its application. Today, more and more applications of the thoery on superplastic forming have put into reality in the fields of aerospace, construction, transportation and electronics, especially indispensable metal processing method in the aerospace. Put forword by the development of modern aerospace industrial, research and development with experiment validations after years, the technology of superplastic forming (SPF) and diffusion bonding (DB) has been an important advanced manufacturing technology. It promotes the developments of modern aerospace structural design concepts and breaks throught the tranditional sheet metal forming methods. The development and application level of this technology has been the sympol on measuring the capacity and potential on aerospace of a country in recent years.
With the research and development of a variety of new materials and technics, there comes out a series of questions in the industrial applications, which need common answers and the guidance of regularity based on mechanical thorey. That is the further process to superplastic technology. Researchers have paid close attention to analyze on Superplasticity Mechanics. Superplastic bulging is a typical one of superplastic forming technics, which plays an important role in the aspect of experiment measurements and mechanical analysis on superplastic. An experiment is the basis of theoretical analysis and the important method of science research.
Scholars drew a series of important conclusions about superplastic free bulging based on the sphere assumptions. Under the assumptions, any point on the surface is in the state of equivalentdouble tensile stress, which makes the analysis and solution simplified. Generally, it is the height of the pole of the bulging sample that a researcher only measured in the experiments and catched the ralationship about time and height. Then the basic analysis mechanical equations of superplastic bulging were established based on it.
It has been proved that the profile of the bulding sample is axisymmetric rotating surfaces, the points on the sample, except the pole, are not in the state of equal pairs of tensile stress, with the principal strain not equle along the radial and latitudinal. As further research on mechanics of superplastic bulging going on, the theory of spherical assumption can not reflect the process of bulging, and can not catch the precise quantitative analysis results. It ought to measure the geometrical shape and the deformation of the point on the profile of the sample precisely, that is a means to esteblish the geometric equation of the profile. My tutor brings forward the method, which is to watch the real-time process of bulging by a digital camera, measure and calculate the geometry parameters by image processing techniques. The thesis creates the mathematic model of non-spherical geometry shapes of the bulging sample, used the above method, builds the basic mechanical equations, and catches the model of thickness changing rules. The main are as follows:
Firstly, to analyze the basical mechanics in the circumstance of both sphere assumption and aspheric, and create the computing formula of the meridional curvature radius ,ρr, and the circumferential curvature radius ,ρθ, in the axisymmetric rotating surface, based on the defitination and feature analysis of the surface in the differential geometry about surface theory.
Secondly, to measure the realtime contour shape and deformation of the bulging sample by the non-contact monocular two-dimensional image measurement system. It introduces the hardware components of the image measurement system, with the basic method and process of the image measurement, deduces the error correction formula using monocular image system to measure the rotating surface, provides a means to camera calibration, including pose adjustment of the camera, experimental measurement and caculation of the camera intrinsic parameters, measurement of distance between the optical centre and measured surface, and etc. In order to keep real-time with bulging, there are two steps of image measurement.
The first is to foucs on the height of the pole on the profile and save the image data during bulging in scheduled way before experiment.
The second is to process the digital image data, such as to measure the profile and deformation, and to analyze. The measurement of the profile is to do edge detection of the sample image directly. The measurement of the space between the deformation is get in another way. The sample is signed with a group of the concentric circles which have the same centre, the pole, before bulging. After found the angular points, which are the intersections of the profile edge and the concentric circles in the images, the degree of the deformation is defined by the changes of distances between the neighbour angular points. The feather of the sample shape must be taken into account while image processing algorithms composing. The corner detection relies on the changes of grey scale along the symmetry axis combined with edge detection, which is depending on Canny operator. In order to improve the measurement precision, sub-pixel algorithm is used to locate the edge and corners precisely.
Thirdly, to renovate the experimental apparatus for superplastic bulging according to the exist questions.
First, the heating-up system renavation improves the temperature control accuracy, makes the thermal insulation properties better, expands the flat-temperature zone, and prolongs the life of heating-ware extent mainly on the aspects of loading and controlling system.
Second, the loading system improves the precision and sensitivity of loading controllment, achieves loading pressure jump, and redesign the control systems.
Third, the control system consists of the main control PC, as the host computer, and SCM system, as Lower machine. An operator implements system calibration and system test, sets parameters, and selects loading mode through the human-computer interaction interface on the main control PC. It controls not only the image measurement system to collect and process the image data, but also the SCM controlling system to gather the pressure signals. SCM controlling system selects the high-performance microcontroller,C8051F120, as the core, combining with the software programming, which controls the loading paths for bulging experiment. It improves the experimental apparatus on the aspects of both the measuring accuracy and performance.
Forthly, to select the typical superplastic materials, ZnAl22, for bulging experiment in constant pressure, do curve fitting about the profile coordinate from the experiment by Polynomial fitting and custom functions fitting respectively, and contrast the results of the two.
Fively, to measure and calculate some geometric parameters, such as meridional curvature radius ,ρr, circumferential curvature radius,ρθ,and flattening , N ,based on the curve fitting. It also measures and caculates circumferential strainεθ, meridional strainεs and thick strainεt, after measured the deformation.
The last, to create geometry model for non-spherical free bulging, estabilsh the two sets of principal curvature radius formula about any point on the curve and arc length formula for points along meridional line, analyze the rules of the thinkness while bulging, and create the basic mechanical equation based on the experiment.
It is significant to measure the geometry shape of bulging sample, and caculate the geometric parameters and mechanical parameters based on it. It is the need to do further more research on the analysis relationships between the material mechanical parameters which include strain rate sensitivity exponent,m, and Strain hardening exponent n, and geometric parameters, also the mechanical quantity fields. The method to measure the geometric parameters and deformation using the image measuring has the advantage of non-contact, high speed and rich information, and so on. It can measure the real-time deformation of the sample online., and catch geometric parameters in any height by only one sample. It not only saves experimental materials, but also improves the operability and precision.The calculation accuracy is also improved by the method of polynomial fitting. Though the experiment data, geometric parameters and mathematical model are related with the material, the typical superplastic material, ZnAl22, it bas the common sense on ideas and methods. The thesis provides a new experiment method for the research on Superplastic non-spherical free bulge forming, which is important to the research on the rules of superplastic bulging mechanics.
Superplasticity is a brach of materials science frontiers, and superplastic forming has become an important method in the field of the modern forming technology.The development of metal superplastic experiences the stages, composed by the observation of some superplasticity phenomenon, further research on the mechanical properties and deformation mechanism, with its application. Today, more and more applications of the thoery on superplastic forming have put into reality in the fields of aerospace, construction, transportation and electronics, especially indispensable metal processing method in the aerospace. Put forword by the development of modern aerospace industrial, research and development with experiment validations after years, the technology of superplastic forming (SPF) and diffusion bonding (DB) has been an important advanced manufacturing technology. It promotes the developments of modern aerospace structural design concepts and breaks throught the tranditional sheet metal forming methods. The development and application level of this technology has been the sympol on measuring the capacity and potential on aerospace of a country in recent years.
With the research and development of a variety of new materials and technics, there comes out a series of questions in the industrial applications, which need common answers and the guidance of regularity based on mechanical thorey. That is the further process to superplastic technology. Researchers have paid close attention to analyze on Superplasticity Mechanics. Superplastic bulging is a typical one of superplastic forming technics, which plays an important role in the aspect of experiment measurements and mechanical analysis on superplastic. An experiment is the basis of theoretical analysis and the important method of science research.
Scholars drew a series of important conclusions about superplastic free bulging based on the sphere assumptions. Under the assumptions, any point on the surface is in the state of equivalentdouble tensile stress, which makes the analysis and solution simplified. Generally, it is the height of the pole of the bulging sample that a researcher only measured in the experiments and catched the ralationship about time and height. Then the basic analysis mechanical equations of superplastic bulging were established based on it.
It has been proved that the profile of the bulding sample is axisymmetric rotating surfaces, the points on the sample, except the pole, are not in the state of equal pairs of tensile stress, with the principal strain not equle along the radial and latitudinal. As further research on mechanics of superplastic bulging going on, the theory of spherical assumption can not reflect the process of bulging, and can not catch the precise quantitative analysis results. It ought to measure the geometrical shape and the deformation of the point on the profile of the sample precisely, that is a means to esteblish the geometric equation of the profile. My tutor brings forward the method, which is to watch the real-time process of bulging by a digital camera, measure and calculate the geometry parameters by image processing techniques. The thesis creates the mathematic model of non-spherical geometry shapes of the bulging sample, used the above method, builds the basic mechanical equations, and catches the model of thickness changing rules. The main are as follows:
Firstly, to analyze the basical mechanics in the circumstance of both sphere assumption and aspheric, and create the computing formula of the meridional curvature radius ,ρr, and the circumferential curvature radius ,ρθ, in the axisymmetric rotating surface, based on the defitination and feature analysis of the surface in the differential geometry about surface theory.
Secondly, to measure the realtime contour shape and deformation of the bulging sample by the non-contact monocular two-dimensional image measurement system. It introduces the hardware components of the image measurement system, with the basic method and process of the image measurement, deduces the error correction formula using monocular image system to measure the rotating surface, provides a means to camera calibration, including pose adjustment of the camera, experimental measurement and caculation of the camera intrinsic parameters, measurement of distance between the optical centre and measured surface, and etc. In order to keep real-time with bulging, there are two steps of image measurement.
The first is to foucs on the height of the pole on the profile and save the image data during bulging in scheduled way before experiment.
The second is to process the digital image data, such as to measure the profile and deformation, and to analyze. The measurement of the profile is to do edge detection of the sample image directly. The measurement of the space between the deformation is get in another way. The sample is signed with a group of the concentric circles which have the same centre, the pole, before bulging. After found the angular points, which are the intersections of the profile edge and the concentric circles in the images, the degree of the deformation is defined by the changes of distances between the neighbour angular points. The feather of the sample shape must be taken into account while image processing algorithms composing. The corner detection relies on the changes of grey scale along the symmetry axis combined with edge detection, which is depending on Canny operator. In order to improve the measurement precision, sub-pixel algorithm is used to locate the edge and corners precisely.
Thirdly, to renovate the experimental apparatus for superplastic bulging according to the exist questions.
First, the heating-up system renavation improves the temperature control accuracy, makes the thermal insulation properties better, expands the flat-temperature zone, and prolongs the life of heating-ware extent mainly on the aspects of loading and controlling system.
Second, the loading system improves the precision and sensitivity of loading controllment, achieves loading pressure jump, and redesign the control systems.
Third, the control system consists of the main control PC, as the host computer, and SCM system, as Lower machine. An operator implements system calibration and system test, sets parameters, and selects loading mode through the human-computer interaction interface on the main control PC. It controls not only the image measurement system to collect and process the image data, but also the SCM controlling system to gather the pressure signals. SCM controlling system selects the high-performance microcontroller,C8051F120, as the core, combining with the software programming, which controls the loading paths for bulging experiment. It improves the experimental apparatus on the aspects of both the measuring accuracy and performance.
Forthly, to select the typical superplastic materials, ZnAl22, for bulging experiment in constant pressure, do curve fitting about the profile coordinate from the experiment by Polynomial fitting and custom functions fitting respectively, and contrast the results of the two.
Fively, to measure and calculate some geometric parameters, such as meridional curvature radius ,ρr, circumferential curvature radius,ρθ,and flattening , N ,based on the curve fitting. It also measures and caculates circumferential strainεθ, meridional strainεs and thick strainεt, after measured the deformation.
The last, to create geometry model for non-spherical free bulging, estabilsh the two sets of principal curvature radius formula about any point on the curve and arc length formula for points along meridional line, analyze the rules of the thinkness while bulging, and create the basic mechanical equation based on the experiment.
It is significant to measure the geometry shape of bulging sample, and caculate the geometric parameters and mechanical parameters based on it. It is the need to do further more research on the analysis relationships between the material mechanical parameters which include strain rate sensitivity exponent,m, and Strain hardening exponent n, and geometric parameters, also the mechanical quantity fields. The method to measure the geometric parameters and deformation using the image measuring has the advantage of non-contact, high speed and rich information, and so on. It can measure the real-time deformation of the sample online., and catch geometric parameters in any height by only one sample. It not only saves experimental materials, but also improves the operability and precision.The calculation accuracy is also improved by the method of polynomial fitting. Though the experiment data, geometric parameters and mathematical model are related with the material, the typical superplastic material, ZnAl22, it bas the common sense on ideas and methods. The thesis provides a new experiment method for the research on Superplastic non-spherical free bulge forming, which is important to the research on the rules of superplastic bulging mechanics.
引文
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