Modeling of the free-surface shape in laser cutting of metals. 2. M odel of multiple reflection and absorption of radiation

A physical model of multiple reflection of focused laser radiation propagating in narrow channels and slots is proposed to be applied in laser treatment of metals. Based on the laws of geometric optics, an algorithm for calculating the shape of the surface formed by interaction of laser radiation and metal with the use of the trajectory technique is proposed. The method used allows one to describe energy transfer inward the channel in simulation of laser-treatment processes (drilling, cutting, and welding). It is shown that the efficiency of multiple reflection is most significant in cutting thick materials with a large ratio of the plate thickness to the Gaussian beam width.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 16–20, January–February, 2005     

On the Shape and Dimensions of Three-Dimensional Cavities in Supercavitating Flows

The shape of long, trailing cavities behind three-dimensional headforms is discussed. The case of a flat elliptic wing is specifically treated. Three distinct shape regimes are found: quasi-planar, long-flat, spheroidal. These appear in successively higher speed ranges (lower cavitation numbers, ). It is argued that the cavities may be replaced by surrogates in the form of slender ellipsoids. The pressures on these are almost constant and correspond to a cavitation number equal to twice their longitudinal added mass coefficient, k₁. A heuristic theory based on kinetic energy fields is given, relating k₁ to the product of headform drag and cavity length. This theory correlates with an exact theory in the same form given by Garabedian for axi-symmetric cones and also with its extension to planar flows. Results are given here for the shape of the cavity behind an elliptic wing of any aspect ratio, given drag, and cavitation number. Specific formulae are given in the form, = f (C_D/AR), for the transition between the quasi-planar and long-flat regime, and the long-flat and spheroidal regime.     

Numerical approach to pulsed laser heating of semi-infinite aluminum substance

Processing of the reflective materials, such as aluminum, with a pulsed CO₂ laser beam depends largely on laser output power and pulse form. To enhance the understanding of the effect of pulse parameters on laser machining a modeling of laser induced heating is essential. The present study develops the heat transfer model allowing temporal variation of CO₂ laser output pulse, phase change process and temperature dependent thermal properties. A numerical technique is introduced to solve the resulting heat transfer equation. Aluminum is selected as workpiece and its surface reflectivity is taken into account in the computation. Thermal integration due to repetitive pulsing is also discussed. It is found that time corresponding to maximum temperature can be predicted by proper selection of pulsed parameters and the ability of the material to follow the laser pulse profile depends upon the pulse shape.     

Effect of the recoil pressure induced by evaporation on motion of powder particles in the light field during laser cladding

A model is proposed, which takes into account acceleration of powder particles by a force induced by recoil of material vapors from the irradiated region of the particle surface. Results of a numerical analysis of heat and mass transfer in the case of motion of individual stainless steel powder particles in a gas flow and in a light field of laser radiation under conditions of laser cladding are presented. Acceleration of particles is found to depend on their diameter, carrier gas velocity, powder material properties, laser radiation power, and degree of attenuation of the power density in the laser beam in the direction of its action on the substrate. The calculated results are compared with experimental data on light-propulsion acceleration of individual particles (of aluminum, aluminum oxide, and graphite) under the action of pulsed laser radiation.     

激光与材料相互作用研究中的气体物理学

强激光辐照材料时,烧蚀蒸气吸收部分或全部激光辐射,成为部分离化等离子体.它的传播称为激光支持的吸收波(LSAW).LSAW屏蔽入射激光,同时发射易被材料表面吸收的短波长辐射.研究这些过程,可用辐射流体力学描述蒸气的运动。为了求解辐射流体力学方程,必须利用气体物理力学方法,算出蒸气的状态方程和不透明度.本文对涉及的一些气体物理力学问题,进行了概略介绍.      

Solutions to the Pólya–Szegö Conjecture and the Weak Eshelby Conjecture

Eshelby showed that if an inclusion is of elliptic or ellipsoidal shape then for any uniform elastic loading the field inside the inclusion is uniform. He then conjectured that the converse is true, that is, that if the field inside an inclusion is uniform for all uniform loadings, then the inclusion is of elliptic or ellipsoidal shape. We call this the weak Eshelby conjecture. In this paper we prove this conjecture in three dimensions. In two dimensions, a stronger conjecture, which we call the strong Eshelby conjecture, has been proved: if the field inside an inclusion is uniform for a single uniform loading, then the inclusion is of elliptic shape. We give an alternative proof of Eshelby’s conjecture in two dimensions using a hodographic transformation. As a consequence of the weak Eshelby’s conjecture, we prove in two and three dimensions a conjecture of Pólya and Szegö on the isoperimetric inequalities for the polarization tensors (PTs). The Pólya–Szegö conjecture asserts that the inclusion whose electrical PT has the minimal trace takes the shape of a disk or a ball.     

激光与材料相互作用研究中的气体物理学

强激光辐照材料时,烧蚀蒸气吸收部分或全部激光辐射,成为部分离化等离子体.它的传播称为激光支持的吸收波(LSAW).LSAW屏蔽入射激光,同时发射易被材料表面吸收的短波长辐射.研究这些过程,可用辐射流体力学描述蒸气的运动。为了求解辐射流体力学方程,必须利用气体物理力学方法,算出蒸气的状态方程和不透明度.本文对涉及的一些气体物理力学问题,进行了概略介绍.     

Water vapor cooling when radiation of wavelength λ=2.8 μm is absorbed

Investigations of the processes arising under the influence of electromagnetic radiation on resonantly absorbing gaseous media have now been widely developed. Particular interest is shown in the penetration of a pulse of laser radiation through the atmosphere. The main component absorbing the radiation of both CO₂ and HF lasers (wavelengths, respectively, 10.6 and 2.8 m) in the earth's atmosphere is water vapor [1]. Numerous experimental investigations show that the integrated coefficient of laser radiation absorption by water vapor is fairly large [1–3], while at the same time the energy absorption leads to the heating of the medium in a channel around the beam and, as a consequence, to its defocusing. However, all these investigations were carried out with continuous sources of laser radiation or with pulses of fairly great duration. It will be shown below that gas cooling in the channel around the beam is possible when a pulse of radiation with wavelength 2.8 m whose duration is less than the vibrational-translational (V-T) relaxation time of the energy absorbed by the H₂O molecules passes through a stationary medium containing water vapor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 141–151, May–June, 1986.     

Real-time determination and controlof the laser-drilled holes depth

We present an optodynamical method for the real-time determination of the depth of laser-drilled holes. The method consists of the detection of shock waves generated during the interaction of the laser beam with the irradiated material using a piezoelectric transducer (PZT), and measurement of the shock waves propagation time through the sample using the PZT signal. The experimental observations reveal that the propagation time has an almost exponential decay with the number of pulses and is strongly dependent on the laser radiation wavelength. The quantity of ablated substrate material per laser pulse is a nonlinear function of the number of consecutive laser pulses incident on the same spot at the irradiated sample surface.Received: 29 September 2003, Accepted: 30 September 2004, Published online: 27 January 2005[/PUBLISHED]Correspondence to: M. Stafe and C. Negutu     

Full-Field Surface 3D Shape and Displacement Measurements Using an Unfocused Plenoptic Camera

Full-field surface 3D shape and displacement measurements using a single commercial unfocused plenoptic camera (Lytro Illum) are reported in this work. Before measurements, the unfocused plenoptic camera is calibrated with two consecutive steps, including lateral calibration and depth calibration. Each raw image of a checkerboard pattern recorded by Lytro Illum is first extracted to an array of sub-aperture images (SAIs), and the center sub-aperture images (CSAIs) at diverse poses are used for lateral calibration to determine intrinsic and extrinsic parameters. The parallax maps between the CSAI and the remaining SAIs at each pose are then determined for depth parameters estimation using depth calibration. Furthermore, a newly developed physical-based depth distortion model is established to correct the serious distortion of the depth field. To realize shape and deformation measurements, the raw images of a test sample with speckle patterns premade on its surface are captured by Lytro Illum and extracted to arrays of SAIs. The parallax maps between the CSAI and the target SAIs are obtained using subset-based digital image correlation. Based on the pre-computed intrinsic and depth parameters and the disparity map, the full-field surface 3D shape and displacement of a test object are finally determined. The effectiveness and accuracy of the proposed approach are evaluated by a set of experiments involving the shape reconstruction of a cylinder, in-plane and out-of-plane displacement measurements of a flat plate and 3D full-field displacement measurements of a cantilever beam. The preliminary results indicate that the proposed method is expected to become a novel approach for full-field surface 3D shape and displacement measurements.     

Shape Recovery of Viscoelastic Beams After Stowage

The deployment of viscoelastic structures that have been held stowed for a given time duration can be formulated as a viscoelastic boundary value problem in which the prescribed condition switches from constant displacement to constant traction. This paper presents closed-form expressions for the load relaxation and shape recovery of a linear viscoelastic beam subject to such time-varying constraints. It is shown that a viscoelastic beam recovers to its original shape asymptotically over time. The analytical solutions are employed to investigate the effect of temperature and stowage time on the time required to achieve recovery with a specified precision. Based on the time-temperature equivalence principle, the relationship between recovery time and holding duration is concisely presented on a single plot. It is found that recovery time increases with holding duration but with a diminishing effect.     

压电曲梁单元及其形状控制

航空航天等领域对结构形状要求非常严格,利用压电材料的逆压电效应控制结构变形是现代空间结构形状控制中一个很好的选择。本文基于一般曲梁单元,推导了空间压电曲梁单元的方程表达式,主体壳结构与压电单元之间利用约束方程连接。在此基础上进一步采用最小二乘法得到了压电控制单元上的最优电压,实现了压电曲梁单元的变形控制。数值算例表明了...     

Shape Monitoring of a Beam Structure from Measured Strain or Curvature

This paper presents results of numerical simulations and an experimental investigation of a method to determine shape of a beam from curvature and/or strain measurements. The purpose of this work was to develop an efficient and accurate method that can be used in real time shape monitoring of beam type structures with possible extension to more complex systems. A method based upon solving a set of continuity equations is presented. Numerical simulations were implemented to minimize the number of sensors and to determine the most beneficial sensor locations and sensor/model configuration to capture the shape in a timely and effective manner. Simulations showed that dividing the beam into segments (elements) and placing sensors at the Gauss point locations of each segment gave only 0.14% systematic error while using three elements and two Gauss points per element. An experiment was designed using an aluminum beam combined with a data acquisition system and a shape reconstruction algorithm. The real-time reconstruction of shape from curvature data was accomplished using strain gages for the curvature estimates. The results were compared to a technique based on position only data and point cloud image data. Overall, consistent results were obtained. The percent difference between the experimental and photogrammetry results fluctuated from 1.4 to 3.5% when various magnitudes of concentrated loads were applied to the beam. This methodology may be useful in real-time shape control and shape modification systems with potential applications in structural health monitoring and damage detection.     

Heat Transfer Study of the Hencken Burner Flame

The Hencken burner flame is often used in combustion laser diagnostics as a calibration flame because of its near adiabatic condition. For a fast burning H₂ flame, it can tolerate high flow rate and the flame is indeed near adiabatic; however, for a slow burning CH₄ flame, the flow rate is not always high enough to maintain near adiabatic conditions. The heat transfer of the H₂ and CH₄ Hencken burner flames are studied numerically and experimentally. Three heat loss mechanisms are analyzed: the burner surface radiation, the hot gas radiation, and the convection heat transfer between the main flow and the co-flow. The surface radiation produces negligible temperature drop while the gas radiation and the convection heat loss contribute significant temperature drop. Reducing the co-flow rate can decrease the convection heat loss slightly. The temperature drop caused by the heat loss is inversely proportional to the main flow rate. Increasing the burner size and running the flame premixed mode can increase the flow rate and reduce the temperature deviation from the adiabatic equilibrium value. Based on the heat loss and temperature drop analysis, suggestions are given to maintain the flame at near adiabatic conditions.     

Simulation of an optically induced asymmetric deformation of a liquid–liquid interface

Deformations of liquid interfaces by the optical radiation pressure of a focused laser wave were generally expected to display similar behavior, whatever the direction of propagation of the incident beam. Recent experiments showed that the invariance of interface deformations with respect to the direction of propagation of the incident wave is broken at high laser intensities. In the case of a beam propagating from the liquid of smaller refractive index to that of larger one, the interface remains stable, forming a nipple-like shape, while for the opposite direction of propagation, an instability occurs, leading to a long needle-like deformation emitting micro-droplets. While an analytical model successfully predicts the equilibrium shape of weakly deformed interface, very few work has been accomplished in the regime of large interface deformations. In this work, we use the Boundary Integral Element Method (BIEM) to compute the evolution of the shape of a fluid–fluid interface under the effect of a continuous laser wave, and we compare our numerical simulations to experimental data in the regime of large deformations for both upward and downward beam propagation. We confirm the invariance breakdown observed experimentally and find good agreement between predicted and experimental interface hump heights below the instability threshold.     

DNS of Turbulent Flows in Ducts with Complex Shape

We carry out Direct Numerical Simulation (DNS) of flows in closed straight ducts with complex peripheral shape. To perform the simulations the Navier-Stokes equations in cylindrical coordinates are discretized by a second-order finite difference scheme, and the immersed-boundary technique is used to resolve the flow close to walls of complex shape. The basic geometry is a circular pipe of radius R, with imposed sinusoidal perturbations of the type \(\eta R \sin (N_{w}\theta )\). Simulations by varying N _w at fixed η were performed to investigate the effect of the perturbation wavenumber. Additional simulations by fixing N _w and varying η also allow to investigate the influence of the amplitude of the wall corrugations. The modifications of the near-wall structures due to change in the shape of the walls are well depicted through contour plots of the radial component of the vorticity. The presence of geometrical disturbances anchors the structures at the locations where curvature changes, and the shape of the structures is strongly linked to the amplitude of the wall corrugation. Our interest is also in understanding the influence of the shape of the surface on wall friction. We were expecting some changes in the profile of the total stress with respect to that of the circular pipe, which instead were not found. This is a first indication that changes in the near-wall region do not affect the outer region, and that Townsend’s similarity hypothesis holds.     

智能梁的静态形状控制

直接从位移函数出发，用Hamilton原理推导了压电智能梁结构的有限元方程，并采用灵敏度分析方法来确定结构的优化控制电压，在此基础上建立了结构自适应梁。最后采用数值分析来验证其有效性，从仿真结果可以看出文中的方法对梁结构的静态形状控制，有较好的控制精度。     

Shape optimization of beam due to lateral buckling problem

Based on a non-linear mathematical model of lateral buckling of a slender beam with a narrow rectangular cross section, the variational formulation of the two-parametric optimization problem is given in the dimensionless form. An optimal shape is obtained by solving the variational problem using the Rayleigh–Ritz method with the orthogonal system of trigonometric functions. By a partial solution of the Euler–Lagrange differential equation of the variational problem, a proof is given that in the case of the optimal shape, a maximal reference stress according to the total strain energy theory is constant along the beam. An example of extrapolation of the two-parametric optimization problem solution is represented.     

Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load

The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008.     

激光定向能量沉积的粉末尺度多物理场数值模拟

激光定向能量沉积技术作为一种同轴送粉式金属增材制造技术, 以其制造效率高、成形尺寸大等优势在航空、航天、交通等领域具有广阔的应用前景. 然而, 该技术在金属零件的尺寸精度和形状精度控制方面存在诸如尺寸偏差大、表面不平整等控形问题, 亟需发展高效高精度预测熔覆层成形尺寸形貌的数值模拟方法. 针对该问题, 本文建立了考虑激光-粉末-熔池交互过程的高保真多物理场数值模型. 其中, 采用高斯面热源等效激光光束, 利用拉格朗日质点法求解粉末输送及其与激光交互的过程, 进一步结合有限体积法和流体体积法求解粉末-熔池的交互及其流动凝固过程, 并通过TC17合金单道熔覆层实验结果进行了验证. 基于该模型, 首先预测了不同工艺参数下单道熔覆层形貌尺寸, 并对熔覆层形貌的变化趋势及其内在的物理机理进行了深入分析. 结果表明, 依赖于工艺参数的粉末温度分布和粉末基板能量分配比例对熔池流场和熔覆层尺寸有显著的影响. 本文所建立的数值模型可辅助激光定向能量沉积增材制造技术控形工艺参数优化, 所得结论可为成形件尺寸和形状精度控制提供理论指导.