Development of irradiation strategies for free curve laser forming

Although forming sheet metal by laser-induced thermal stresses (laser forming) has been extensively studied, the research has mainly focused on a single angle forming process. The task of free curve laser forming of sheet metal is to determine a set of process parameters such as laser scanning paths, laser power and scanning speed that will make a given shape. Two methods were used for generating the laser scanning paths and the bending angles of each path. Each method was analyzed by computer simulation and the two methods were compared. Experiments verified the applicability of the proposed methods.     

Deformation behavior of laser bending of circular sheet metal

The application of a thermal source in non-contact forming of sheet metal has long been used. However, the replacement of this thermal source with a laser beam promises much greater controllability of the process. This yields a process with strong potential for application in aerospace, shipbuilding, automobile, and manufacturing industries, as well as the rapid manufacturing of prototypes and adjustment of misaligned components. Forming is made possible through laser-induced non-uniform thermal stresses. In this letter, we use the geometrical transition from rectangular to circle-shaped specimen and ring-shaped specimen to observe the effect of geometry on deformation in laser forming. We conduct a series of experiments on a wide range of specimen geometries. The reasons for this behavior are also analyzed. Experimental results are compared with simulated values using the software ABAQUS. The utilization of line energy is found to be higher in the case of laser forming along linear irradiation than along curved ones. We also analyze the effect of strain hindrance. The findings of the study may be useful for the inverse problem, which involves acquiring the process parameters for a known target shape of a wide range of complex shape geometries.     

3D laser-forming strategies for sheet metal by geometrical information

Forming sheet metal by laser-induced thermal stress (laser forming) is considered to offer great potential for rapid prototyping and flexible manufacturing. Accordingly, many studies have been carried out in different areas of laser forming. However, in order to apply the laser-forming process to real 3D products, a method that encompasses the whole process planning is required, including the laser irradiation patterns, laser power, and travel speed, when the target shape is given. In this work, a new method for 3D laser forming of sheet metal is proposed. This method uses geometrical information rather than a complicated stress–strain analysis. Using this new method the total calculation time is reduced considerably while affording strong potential for enhanced accuracy. Two different target shapes were formed by laser irradiation with the proposed procedure to validate the algorithm.     

Finite element simulation of laser tube bending: Effect of scanning schemes on bending angle, distortions and stress distribution

Laser forming has received considerable attention in recent years. Within laser forming, tube bending is an important industrial activity, with applications in critical engineering systems like micro-machines, heat exchangers, hydraulic systems, boilers, etc. Laser tube bending utilizes the thermal stresses generated during laser scanning to achieve the desired bends. The parameters to control the process are usually laser power, beam diameter, scanning velocity and number of scans. Recently axial scanning has been used for tube bending instead of commonly used circumferential scans. However the comparison between the scanning schemes has involved dissimilar laser beam geometries with circular beam used for circumferential scanning and a rectangular beam for the axial scan. Thermal stresses generated during laser scanning are strongly dependent upon laser beam geometry and scanning direction and hence it is difficult to isolate the contribution made by these two variables. It has recently been established at the Corrosion and Protection Centre, University of Manchester, that corrosion properties of material during laser forming are affected by the number of laser passes. Depending on the material, the corrosion behaviour is either adversely or favourably affected by number of passes. Thus it is of great importance to know how different scanning schemes would affect laser tube bending. Moreover, any scanning scheme which results in greater bending angle would eliminate the need for higher number of passes, making the process faster. However, it is not only the bending angle which is critical, distortions in other planes are also extremely important. Depending on the use of the final product, unwanted distortions may be the final selection criteria. This paper investigates the effect of scanning direction on laser tube bending. Finite-element modelling has been used for the study of the process with some results also validated by experiments.     

A study of the effect of laser beam geometries on laser bending of sheet metal by buckling mechanism

Laser beam forming has emerged as a new and very promising technique to form sheet metal by thermal residual stresses. The objective of this work is to investigate numerically the effect of rectangular beam geometries, with different transverse width to length aspect ratio, on laser bending process of thin metal sheets, which is dominated by buckling mechanism. In this paper, a comprehensive thermal and structural finite element (FE) analysis is conducted to investigate the effect that these laser beam geometries have on the process and on the final product characteristics. To achieve this, temperature distributions, deformations, plastic strains, stresses, and residual stresses produced by different beam geometries are compared. The results suggest that beam geometries play an important role in the resulting temperature distributions on the workpiece. Longer beam dimensions in the scanning direction (in relation to its lateral dimension) produce higher temperatures due to longer beam–material interaction time. This affects the bending direction and the magnitude of the bending angles. Higher temperatures produce more plastic strains and hence higher deformation. This shows that the temperature-dependent yield stress plays a more dominant role in the deformation of the plate than the spread of the beam in the transverse direction. Also, longer beams have a tendency for the scanning line to curve away from its original position to form a concave shape. This is caused by buckling which develops tensile plastic strains along both ends of the scanning path. The buckling effect produces the opposite curve profile; convex along the tranverse direction and concave along the scanning path.     

A finite element model using multi-layered shell element in laser forming

Due to its enormously high flexibility laser forming has been gaining importance in recent years. This rapidness and flexibility demand very precise controlling strategies especially when simulating the process of large plates and challenging the limited computation power of the current workstation. A simple, robust and accurate modeling method of laser forming has been demonstrated to solve this problem. The simplified model is meshed by multi-layered shell element, simulated with a more real scanning method and fewer parameters. The intelligent meshing strategies have reduced the number of elements dramatically. Thus the simulation efficiency has been improved significantly. By comparing the simulation results under the simplified model with the results under the traditional model for laser forming, the applicability of proposed method has been proven. The method of these simplified models is also suitable to simulate complex finite element models, which take much time to simulate. It would throw some light on the thermal mechanically coupled-field simulation of large sheet.     

Classical phase space revealed by coherent light

We study the far-field characteristics of oval-resonator laser diodes made of an GaAs/Al(x)Ga(1-x)As quantum well. The resonator shapes are various oval geometries, thereby probing chaotic and mixed classical dynamics. The far-field pattern shows a pronounced fine structure that strongly depends on the cavity shape. Comparing the experimental data with ray-model simulations for a Fresnel billiard yields convincing agreement for all geometries and reveals the importance of the underlying classical phase space for the lasing characteristics.     

Detecting damage in vibrating structures with a scanning LDV

It has been demonstrated, through experiments on laboratory-scale structures, that structural defects such as cracks can be detected and located using a continuously scanning laser Doppler vibrometer (LDV) if vibration sufficient to flex the defect can be induced and if the defects are such as to produce localised mode shape discontinuities. This paper describes such a method of defect detection using a short linear scan at the crack location. Through-cracks are easily detected in thin metal plates whereas narrow slots in a solid cantilever beam have no easily identifiable effect unless they extend more than half-way through the thickness. Cracks in a reinforced-concrete beam introduced marked and identifiable discontinuities in mode shapes. Speckle noise affects the measurements, sometimes seriously. A simple low-pass filter may improve the signal quality.     

激光立体成形中熔池凝固微观组织的元胞自动机模拟

本文通过采用自适应网格技术, 将激光立体成形的宏观温度场模型和凝固微观组织的低网格各向异性元胞自动机模型(cellular automaton, CA)结合, 建立了适用于激光立体成形的集成数值模型. 模型包括基材的温度场分布, 熔池形貌和熔凝过程的凝固微观组织. 模拟了激光扫描速度为15 mm/s时, 激光作用在Fe-C单晶基材上形成熔池的形状以及熔池内凝固微观组织. 计算结果揭示了熔池内固液界面从平界面失稳到胞\枝晶的非稳态凝固过程, 并得到了平界面组织形成的白亮带. 白亮带上方形成了外延生长的枝晶列.     

面曝光选区激光熔化成形形状精度研究

主要研究面曝光选区激光熔化单层成形时,激光光斑搭接率和电流对形状精度的影响。实验通过控制变量法研究搭接率、曝光时间、电流等工艺参数对激光光斑、熔道、圆环、尖角等成形形状精度的影响。实验结果表明:一定范围内,电流越大,激光光斑更均匀,成形一致性更好;搭接率38.4%能够获得最低的形状误差的熔道;搭接率一定,圆环成形误差随电流的增加而增加;尖角成形误差随着电流增加,呈现先增后减的趋势;搭接率为46.1%、38.4%时,零级衍射带来的形状误差降低。     

SOI纳米光波导激光熔凝光整加工温度场的数值模拟及分析北大核心CSCD

激光表面熔凝技术可有效降低纳米光波导侧壁粗糙度进而减小光传输的散射损耗。为明确波导侧壁在KrF准分子激光表面熔凝过程的温度场演化规律,考虑材料参数随温度变化和相变潜热的影响,建立了纳米光波导侧壁激光熔凝的二维有限元数值模型,研究了熔池边界的推进行为与不同工艺参数的映射关系。结果表明:熔池形成于波导上表面与迎光侧壁夹角处;激光入射角度一定时,熔池熔深与平均能量密度正相关;熔池形貌受控于激光入射角度,随着入射角度的减小,熔池形貌由单边U形过渡为单边V形最终呈带钝角单边V形。分析表明,较大激光入射角对应的熔池形貌更有利于波导侧壁的光整加工;据此提出先确定激光入射角度以优化熔池形貌,再选取合适平均能量密度以获得足够熔化深度的工艺方法。     

Optimum Shapes of Elastic Bodies: Equistrong Wings of Aircrafts and Equistrong Underground Tunnels

Since the times of Plato (424?-347 BC) and Aristotle (384-322 BC), the form has been considered as a fundamental notion of not only the physical universe, but also the spiritual world. The forms and perfect shapes are like jewels in the rock—their search and discovery make up the highest delight to human beings. This is what constituted the motive and driving force of science and scientists beginning from Pythagoras (ca. 570-ca. 500 BC), Archimedes (ca. 287-ca. 212 BC), Euclid (ca. 330-ca. 260 BC) and all that came after. In the introduction to the present article, a brief account of Plato’s theory of forms and Aristotle’s addition to this theory are given; the theory of optimum shapes of elastic bodies can be considered as a footnote to the Plato’s theory. In the framework of the theory of elasticity, the optimal shape of a body is the shape that meets the principle of equal strength or equistrength advanced by this author in 1963. According to this principle, the safety criterion like ultimate or failure stress is simultaneously satisfied in the utmost part of the body—this body or structure is called equistrong in this case. The equistrong structure has a minimum weight for a given material and safety factor, or a maximum safety factor for a given material and weight. As distinct from traditional problems, there are no existence theorems for equistrong shapes—a success in their search depends on skills of a researcher. In the present paper, a summary of common equistrong shapes and structural elements is brought out, namely: equistrong cable of bathysphere, equistrong tower or skyscraper, equistrong beam by Galileo Galilei, equistrong rotating disk, equistrong heavy chain, equistrong pressure vessels, equistrong arcs, plates and shells, equistrong underground tunnels, equistrong perforated plates, and others. A variety of the swept wings of aircrafts is found out to be equistrong; the front and rear edges of such wings are rectilinear in the plan view, and their chord in the flight direction depends on the task of an aircraft; the equistrong design exists for any task, from transport aviation to hypersonic jet fighters. Some new equistrong shapes of elastic solids with any number of infinite branches being pulled out of a body are also discovered for plane strain and plane stress.     

Maximum likelihood identification of non-stationary operational data

In-operation modal analysis has become a valid alternative for structures where a classic input-output test would be difficult if not impossible to conduct. Due to practical considerations, measurements are sometimes performed in patches (roving sensor setups) instead of covering the entire structure at once. In practice, one is often confronted with non-stationary ambient excitation sources (e.g., wind, traffic, waves, etc.). Since the scaling of operational mode shape estimates depends on the unknown level of the ambient excitation, an extra effort is required in order to correctly merge the different parts of the mode shapes. In this contribution, two different approaches, for merging operational mode shapes from non-stationary data, are proposed. Both methods are based upon a single maximum likelihood estimation procedure. For comparison and validation, both techniques were applied to non-stationary data sets obtained by scanning laser vibrometry as well as the Z24 bridge bench mark data.     

Springback control in sheet metal bending by laser-assisted bending: Experimental analysis, empirical and neural network modelling

The present investigation deals with the control of springback phenomena in the bending process of aluminium sheets by hybrid forming process. Metal substrates were pre-bent to nominal shapes on a built-ad-hoc mould after being constrained on it. Then, they were post-treated by high power diode laser to prevent the deformation of the pre-bent sheets after the release of the constraints. The extent of springback phenomena were estimated by measuring the difference between the nominal bending angles and those achieved on the unconstrained substrates after laser post-treatments. Analytical models, aimed at predicting the springback by varying the setting of the operational parameters of the forming process, were developed. Neural network solutions were also proposed to improve the matching between experimental and numerical data, with the Multi-Layer Perceptrons trained by Back-Propagation algorithm being the fittest one. On this basis, a control modulus very useful to practitioners for automation and simulation purposes was built-on.     

Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method

The theory for designing distributed piezoelectric modal sensors is well established for beam structures. However, the current modal sensor theory is limited in scope in that it can only be applied in the case of classical boundary conditions (i.e., either clamped, free, simply supported or sliding). In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a beam with arbitrary boundary conditions is proposed, using the Adomian decomposition method (ADM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a function of the second spatial derivative of the structural mode shape function. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then the shapes of the designed modal sensors are obtained. Finally, some numerical examples are given to demonstrate the feasibility of the proposed modal sensors. It is shown that, for classical boundary conditions, the shapes of the modal sensors based on the ADM agree well with analytical and numerical results given in the literature. For general boundary conditions it is found that the shape of the modal sensors is influenced by the number of modes of interest because the second spatial derivatives of the mode shapes are not orthogonal to one another. The modal sensors for general boundary conditions can be considered as modal filters within a limited frequency band.     

Effect of different heating methods on deformation of metal plate under upsetting mechanism in laser forming

In a laser forming process, different forming mechanisms have different deformation behaviors. The aim of laser forming is to acquire plane strain under an upsetting mechanism, while a plate undergoes a small bending deformation. In some industrial applications, the bending strain should not occur. To achieve high-precision forming, the deformation behaviors of a metal plate when an upsetting mechanism plays a dominant role are studied in the paper. Several heating methods are proposed to reduce the plane strain difference along the thickness direction and little bending deformation resulting from a small temperature difference between the top and bottom surfaces of the plate. The results show that negligible bending deformation and a uniform plastic plane strain field can be obtained by simultaneously heating the top and bottom surfaces with the same process parameters. A conventional scanning method needs a larger spot diameter and slower scanning speed under the upsetting mechanism, but a smaller spot diameter and quicker scanning speed may be selected using the simultaneous heating method, which can greatly widen the potential scope of process parameters.     

Modelling of heat and mass transfer in the laser cladding during direct metal deposition

A physical and mathematical model has been proposed for computing the thermal state and shape of the individual deposited track at the laser powder cladding. A three-dimensional statement of the two-phase problem of Stefan type with curved moving boundaries is considered. One of the boundaries is the melting-crystallization boundary, and the other is the boundary of the deposited layer, where the conservation laws are written from the condition of the inflow of the additional mass and energy. To describe the track shape the equation of kinematic compatibility of the points of a surface is used, the motion of which occurs at the expense of the mass of powder particles supplied to the radiation spot. An explicit finite difference scheme on a rectangular nonuniform grid is used for numerical solution of equations. The computations are carried out by through computation without an explicit identification of curved boundaries by using a modification of the immersed boundary method. The computational results are presented for the thermal state and the shape of the surface of the forming individual track depending on physical parameters: the substrate initial temperature, laser radiation intensity, scanning speed, powder feeding rate, etc.     

A Prototype laser forming system

A non-contact laser forming (LF) demonstrator system was developed to demonstrate the process on a large primitive shape. The research that led to this development is described in this article. A fundamental study was carried out which examined the effects of laser-forming parameters on tokens of an aluminium and a titanium alloy. Energy, geometrical and metallurgical influences were investigated and are summarised here. Results of the study showed that LF of these aerospace materials is possible using a large operating envelope of laser-processing parameters. A range of metallurgical effects resulted on the titanium alloy and these are traced here. Depending on how the energy input was supplied to the plate surface, various geometrical effects resulted. These effects are discussed. Using the knowledge gathered from the fundamental study, a prototype LF system was built. The components of the system and the forming of a primitive shape on it are discussed. Conclusions from the study indicate that the future work lies in the development of the demonstrator for primitive 3-D shapes and the integration of a knowledge-based system.     

Design of shaped piezoelectric modal sensors for cantilever beams with intermediate support by using differential transformation method

In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a cantilever beam with intermediate support is proposed by using the differential transformation method (DTM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a linear function of the second spatial derivative of the structural mode shape function. By using boundary condition and continuity condition equations at intermediate support, the closed-form series solution of the second spatial derivative of the mode shapes can be determined based on DTM. Then the shapes of the designed modal sensors are obtained. Finally, numerical examples are given to demonstrate the feasibility of the proposed modal sensors for the cantilever beam with intermediate support.     

Free vibration of super elliptical plates with constant and variable thickness by Ritz method

In this study free vibration of simply supported and clamped super elliptical plates is investigated. This class of plates includes a wide range of external boundaries varying from an ellipse to a rectangle. Although studies on the upper and lower bounds of these plate geometries, namely circle and rectangle, are quite extensive, contributions on the mid-shapes, especially for simply supported boundary edges are very limited. The Kirchhoff plate model with isotropic and homogeneous material is studied. The super elliptical powers are chosen from 1 to 10. The Ritz method is employed for the solution of the energy equations of the plates. The effects of Poisson's ratio, which should not be neglected for simply supported plates with curved boundaries, and the aspect ratio of the plate are both examined in detail. The effect of thickness variation is also considered in this study. In order to avoid long computational run times, physically pertinent trial functions are utilized. The frequency parameters obtained are presented and compared with published results for plate shapes that match the current cases.