Shape Control Of Beams Research Articles

Dynamic ultraviolet harmonic beam pattern control by programmable spatial wavefront modulation of near-infrared fundamental beam

Abstract The ultraviolet (UV) wavelength regime is attracting increasing attention because of its growing demand in semiconductor lithography, spectroscopy, and imaging applications owing to its high spatial resolution and high photon energy. However, beam shape control, beam delivery, and wavefront manipulation of UV laser beams usually require highly dedicated optics because of the strong UV absorption of most optical materials and the high surface precision required for tailoring short wavelengths, thus limiting a broader application of UV wavelengths. Here, we demonstrate a novel dynamic UV harmonic beam pattern control by manipulating the near-infrared (NIR) wavefront of the fundamental wavelength of a femtosecond pulse laser. The temporal and spatial coherences in an optical harmonic generation are known to be well preserved. Therefore, the spatial beam distribution of UV harmonic beams (λ = 400 and 266 nm for second and third harmonics, respectively) could be readily controlled by tailoring the wavefront of the driving infrared (IR) beam, and this approach can be expanded to higher-order harmonics in the vacuum ultraviolet (VUV) or extreme ultraviolet (EUV) regimes. Moreover, this enables fast polarization-sensitive UV beam switching at a speed of 6.7 frames/s in a depth-resolving manner. To efficiently separate the UV beam from the strong fundamental IR background beam, a non-collinear harmonic generation configuration is introduced. This facile dynamic UV beam control technique enables arbitrary wavefront control of UV laser beams for high-precision laser patterning, polarization-sensitive encryption, and 3D holograms.

Beam shape control system by machine learning on the NISSIN BeyEX medium current ion implanter

Beam shape control system by machine learning on the NISSIN BeyEX medium current ion implanter

Cantilever beam shape control with light activated polymers using hierarchical particle swarm optimizer

A shape control with light activated polymers (LAPs) is designed in present article. Under ultraviolet light irradiation, the structures of crosslink networks in LAPs alter. Such alterations lead to macroscopical deformation. On this basis, LAPs possess the potential to be actuators. For shape control, so many parameters of actuators could be optimized. A three-layer hierarchical particle swarm optimizer (HPSO) algorithm is proposed to search the appropriate group of LAPs numbers, locations and lengths. Numerical simulations (monotonic function shape control and non-monotonic function shape control) illustrate that HPSO is effective.

Thickness validation of modeling tools for laser cutting applications

Laser cutting of metal sheets is a well-established industrial process, however, major process changes are constantly being introduced by newer technologies, e.g. new laser technologies, higher power sources, polarization and beam shaping control units, and gas flow optimizations. The multi-physical nature of the laser cutting process makes detailed simulations complex and demanding in terms of computational and implementation efforts. The gap between accurate modeling and industrial requirements makes an experimental approach often more economically realistic. Nevertheless, efficient assessment models that utilize a trade-off between model complexity and accuracy of the response to be assessed are attractive. Such models can be used for further technological development by efficiently supporting engineers in designing and selecting optical systems. This paper revisits model assumptions of an in-house developed laser cutting model as it is validated for larger thicknesses. This model assesses polarization and beam shaping effects on the cutting performance of thin sheets. In this work, dedicated cutting experiments to assess the maximum cutting speed of stainless steel 304L of 2, 6, and 10 mm thickness for a wide range of focal point positions are conducted and compared to the model prediction. The results show that R2 of this comparison decreases from 0.99 for 2 mm thickness, to 0.58 for 10 mm. It can be concluded that the trend prediction accuracy degrades for thicker plates. Analysis of the experiments and simulation data for 10 mm plates reveals two possible phenomena that become more important with thickness: multiple reflections and instability of the melt flow dynamics.

Theoretical prediction and experimental verification of shape control of beams with piezoelectric patches and resistive circuits

This paper presents one-dimensional analytical, three-dimensional numerical and experimental results for shape control of beam-type structures. The beam structures under consideration are assumed to be slender and the surface of the elastic substrate is covered by several piezoelectric patches whose electrodes are connected by a resistor network. In general, the structure will deform, if an external load acts on the system and no control action is present. Therefore, the question arises how to choose the network configuration, in order to completely suppress deflections or vibrations at several desired locations along the beam axis. This aim is also known as shape control. As a practical example, a cantilever beam subjected to a tip-force is considered. First we present shape control results for the one-dimensional extended Bernoulli–Euler theory and three-dimensional finite element calculations with ANSYS for static loads and time-harmonic excitations. Then the theory is verified by an experimental setup and it is shown by several frequency sweep excitations and by a monofrequent harmonic excitation close to the first eigenfrequency that shape control may be achieved approximately, proving the applicability of the proposed control method.

Surface profiling of X-ray mirrors for shaping focused beams.

Grazing incidence mirrors are a standard optic for focusing X-rays. Active mirrors, whose surface profile can be finely adjusted, allow control of beam shape and size at the sample. However, progress towards their routine use for beam shaping has been hampered by the strong striations in reflected beams away from the focal plane. Re-entrant (partly concave and partly convex) surface modifications are proposed for shaping X-ray beams to a top-hat in the focal plane while reducing the striations caused by unavoidable polishing errors. A method for constructing such surfaces with continuous height and slope (but only piecewise continuous curvature) will be provided. Ray tracing and wave propagation calculations confirm its effectiveness. A mirror system is proposed allowing vertical beam sizes in the range 0.5 to 10μm. A prototype will be fabricated and is expected to have applications on many synchrotron X-ray beamlines.

Shape control of a beam consisting of triangular meso-structure segments with multiple V-shaped flexure springs

This paper presents a direct displacement synthesis method for the design of shape control of meso-structure beams with multiple V-shaped flexure springs. The objective is to design a beam that will deform to a desired final shape when under a specific load. The method uses a ground structure geometry which can facilitate variable bending stiffness along the length of the beam using compliant spring members. The synthesis procedure involves the use of direct displacement to determine how the bending stiffness of the beam must vary to produce the desired shape change. The direct displacement synthesis method differs from other compliant mechanism synthesis methods found in literature, such as pseudo-rigid-body and continuum structure optimisation, in the approach taken to solve for the unknown variables in the system. By using direct displacement to determine how the structure must respond to a specific load to achieve the desired shape change, the unknown variables within the system can be extracted directly without the use of optimisation techniques. The method is detailed and sensitivities explored. With this method and no iterations, the spring configuration values can be determined such that the resulting shape is within 1% of the target shape.

Passive shape control of force-induced harmonic lateral vibrations for laminated piezoelastic Bernoulli-Euler beams-theory and practical relevance

The present paper is devoted to vibration canceling and shape control of piezoelastic slender beams. Taking into account the presence of electric networks, an extended electromechanically coupled Bernoulli-Euler beam theory for passive piezoelectric composite structures is shortly introduced in the first part of our contribution. The second part of the paper deals with the concept of passive shape control of beams using shaped piezoelectric layers and tuned inductive networks. It is shown that an impedance matching and a shaping condition must be fulfilled in order to perfectly cancel vibrations due to an arbitrary harmonic load for a specific frequency. As a main result of the present paper, the correctness of the theory of passive shape control is demonstrated for a harmonically excited piezoelelastic cantilever by a finite element calculation based on one-dimensional Bernoulli-Euler beam elements, as well as by the commercial finite element code of ANSYS using three-dimensional solid elements. Finally, an outlook for the practical importance of the passive shape control concept is given: It is shown that harmonic vibrations of a beam with properly shaped layers according to the presented passive shape control theory, which are attached to an resistor-inductive circuit (RL-circuit), can be significantly reduced over a large frequency range compared to a beam with uniformly distributed piezoelectric layers.

Modeling of wireless remote shape control for beams using nonlinear photostrictive actuators

Photostrictive materials produce mechanical strain when irradiated by ultraviolet light, thus may be used in wireless remote control of smart microstructures. This paper presents an investigation into modelling and static shape control of beams with nonlinear photostrictive actuators. Governing equations of beams bonded with photostrictive actuator patches are derived to study the interaction between the photostrictive actuators and the host beams. An analytical solution method is presented to solve the governing equations of the beams with discretely distributed photostrictive actuators. An iterative procedure is developed to find optimal light intensities in photostrictive actuators that best match the actuated shape to the desired one. An example is given to illustrate the model and shape control of a beam with PLZT actuators.

Shape control and damage identification of beams using piezoelectric actuation and genetic optimization

This paper deals with the shape control of beams under general loading conditions, using piezoelectric patch actuators that are surface bonded onto beams to provide the control forces. The mathematical formulation of the model is based on the shear deformation beam theory (Timoshenko theory) and the linear theory of piezoelectricity. The numerical solution of the model is based on the development of superconvergent (locking-free) finite elements using the form of the exact solution of the Timoshenko beam theory and Hamilton’s principle. The optimal values for the locations of the piezo-actuators are determined and optimal voltages for shape control are obtained for cantilever beams by using a genetic optimization procedure. Finally, a simplified related damage identification problem is formulated and solved using static data and genetic optimization.

A New High-intensity, Low-momentum Muon Beam for the Generation of Low-energy Muons at PSI

At the Paul Scherrer Institute (PSI, Villigen, Switzerland) a new high-intensity muon beam line with momentum p < 40 MeV/c is currently being commissioned. The beam line is especially designed to serve the needs of the low-energy, polarized positive muon source (LE-μ +) and LE-μ SR spectrometer at PSI. The beam line replaces the existing μE4 muon decay channel. A large acceptance is accomplished by installing two solenoidal magnetic lenses close to the muon production target E that is hit by the 590-MeV PSI proton beam. The muons are then transported by standard large aperture quadrupoles and bending magnets to the experiment. Several slit systems and an electrostatic separator allow the control of beam shape, momentum spread, and to reduce the background due to beam positrons or electrons. Particle intensities of up to 3.5 × 108 μ +/s and 107 μ −/s are expected at 28 MeV/c beam momentum and 1.8 mA proton beam current. This will translate into a LE-μ + rate of 7,000/s being available at the LE-μSR spectrometer, thus achieving μ + fluxes, that are comparable to standard μSR facilities.

Precise deflection analysis of beams with piezoelectric patches

Precise deflection models of beams with n pairs of piezoelectric patches are developed analytically. To formulate the models, the first-order and higher-order beam theories are used. The analytical solutions are obtained with the aid of the state-space approach and Jordan canonical form. A case study is presented to evaluate the performance of the authors’ previously reported models. Through a demonstrative example, a comparative study of the first-order and higher-order beams with two piezoelectric pairs is attained. It is shown that the first-order beam lacks that ability to accurately predict the beam behavior in the region of the patches when compared with the results of the higher-order beam. Further applications of the solutions are presented by investigating the effects of patch lengths and locations on the deflected shape of beams with two piezoelectric pairs. For clamped–hinged and clamped–clamped (C–C) beams, the deflected shape switches from negative to positive when the piezoelectric pairs are moved toward the supports. The results of C–C beams show that increasing the patch lengths does not necessarily increase the deflection. The presented solutions can be used in the design process to obtain detailed deformation information of beams with various boundary conditions. Moreover, the presented analysis can be readily used to perform precise shape control of beams with n pairs of piezoelectric patches.

Exact deflection solutions of beams with shear piezoelectric actuators

Exact deflection models of beams with n actuators of shear piezoelectric are developed analytically. To formulate the models, the first-order and higher-order beam theories are used. The exact solutions are obtained with the aid of the state-space approach and Jordan canonical form. A case study is presented to evaluate the performance of the authors’ previously reported models. Through a demonstrative example, a comparative study of the first-order and higher-order beams with two shear piezoelectric actuators is attained. It is shown that the first-order beam cannot predict the beam behavior when compared with the results of the higher-order beam. Further applications of the solutions are presented by investigating the effects of actuators lengths and locations on the deflected shapes of beams with two piezoelectric actuators. Some interesting deflection curves are presented. For example, the deflection curve of a H–H beam resembles saw teeth that rotate clockwise about the central location with the increase of actuators lengths. The presented exact solutions can be used in the design process to obtain detailed deformation information of beams with various boundary conditions. Moreover, the presented analysis can be readily used to perform precise shape control of beams with n actuators of shear piezoelectric.

Improved Calculation of Eigenvalue Variation in Dynamic System

100 s. At 215 s, Va is stepped back to the 200-V level, and the gun is turned on immediately thereafter. With the circuit reestablished, Va is then ramped slowly to 200 V to generate a strain of 8 π. Va and the gun current are then deactivated again to demonstrate the permanence of the shape changes. The current is then reestablished by returning to the original Va, and gun current levels and the piezoelectric strain is ramped back toward zero. Clearly evident in this simple test are the controllability, reversibility, and short-term stability of piezoelectric strains stimulated by electron gun charge and Va inputs. Conclusions Strain control of a piezoelectric plate using an electron gun to deposit charge on the bare face of the material and a single distributed electrode on the opposite side was demonstrated to be stable, controllable, and repeatable. The responses observed while using the 300- and400-eVelectron beamsare similarinlinearity andhysteresistopiezoelectricresponsesusingtheconventionalpairedelectrode method. It was also demonstrated in tests using a 400-eV beam that charge input can be applied to the material and that the resultant strains will remain for a signie cant period of time after the removal of the electron beam. Clearly nonlinear behavior due to unstable points in the secondary emission curve were evident in the 250-eV beam tests, indicating that higher beam energies are more desirable for stable operation. The electron beam shape control method appears to hold potential for applications requiring high-resolution shape control of a large structure with extremely high resolution. Given that electron guns require vacuum to operate effectively, space is obviously one place to look for potential applications. Two specie c possible uses involve the gathering of light. First, solar thermal propulsion units could utilize the shape correction possibilities of an electron gun controlled mirror to gather and focus the desired solar radiation. Second, orbital telescopes used in cosmology or Earth observations could take advantage of the ability to control very large surface areas to optical tolerances. The advantage of a large telescope is that the more light that is gathered then the better the telescope performs. The manufacture of extremely large primary and secondary ree ectors may become much easier and cheaper if a practical method of on-orbit shape correction can be developed and implemented. Based on the research performed to date, electron gun shape control of piezoelectric materials may provide one possible avenue for performing on-orbit shape tuning of extremely large optical components.

Shape Control of Beams by Piezoelectric Actuators

The shape control of beams by piezoelectric actuators is addressed analytically. Solutions are presented for a beamsubjectedto differentboundaryconditions.Thesolutionsshowhowandhowmuchthepiezoelectricactuators can ine uence the shape of a beam. Several case studies arealso presented to show the applications of the analytical solutions in the various analyses relevant to shape control of beams by piezoelectric actuators. The limitation of the actuation forces produced by piezoelectric actuators makes it dife cult to realize global and local precise shape control. In this application, the actuation forces produced by piezoelectric actuators are used to change the shapes of e exible structures. Some work has been reported on the shape control of beams, plates, and shells during the past few years. Some numerical methods, includ- ing the Ritz method, 3,4 e nite difference method, 5 and e nite element method 6i 10 have been used to model and analyze the problems rel- evant to shape control of e exible structures by piezoelectric actua- tors. However, due to the approximation of the numerical methods, the reported results can only give rough information of the global shape changes of the structures induced by piezoelectric actuators. Theycannot showthe detailed localshapechange information,such as information on the slope or curvature change of a structure at one point. The detailed local shape change information induced by piezoelectricactuators,whichshowshowthepiezoelectricactuators can change the shape of a structure or what types of shape change the piezoelectric actuators can make to a structure, is important for the design and analysis of such a piezoelectric smart structure. To obtain this information, one needs to analytically solve the problem of shape control. In general, it is very dife cult and complicated to solveanalyticallytheproblemforatwo-dimensionalplate;however, a one-dimensional beam is another case, and an analytical solution can be possibly obtained with acceptable complexity. The conclu- sions for a two-dimensional plate can be drawn from those for a one-dimensional beam. Thispaperwillpresenttheanalyticalsolutionsofthedee ectionof a beam induced by both piezoelectric actuators and external forces. In accordance with the solutions, the detailed local shape change information induced by piezoelectric actuators will be addressed. Using the solutions, one can analytically perform various analyses relevant to the shape control of beams by piezoelectric actuators. Case studies will also be carried out to show the applications of the solution.

Robust shape control of beams with load uncertainties by optimally placed piezo actuators

The shape of a laminated beam is controlled by an optimally placed piezo actuator so as to minimize its maximum deflection. The locations and magnitudes of the external loads are not known a priori and belong to a specified load uncertainty domain. The optimal actuator location is obtained for any load combinations and locations which are determined so as to produce the maximum deflection corresponding to the worst case of loading. In this sense, loading uncertainties lead to an anti-optimization problem which is coupled to the optimization problem via the design parameter and loading. The resulting coupled problems are solved simultaneously to compute the optimal actuator location and the least favourable loading condition. Multiple load cases are also considered. Numerical results are given to assess the effect of load uncertainty and actuator length on the actuator location and the design efficiency which is defined with respect to the corresponding uncontrolled beam.

Optimal piezo-actuator locations/lengths and applied voltage for shape control of beams

Shape control of beams under general loading conditions is implemented using piezoceramic actuators to provide the control forces. The objective of the shape-control is to minimize the maximum deflection of the beam to obtain a min-max deflection configuration with respect to loading and piezo-actuators. In practice, the loading on a beam is a variable quantity with respect to its magnitude, and this aspect can be handled easily by optimizing the magnitude of the applied voltage to achieve the min-max deflection. This property of the smart materials technology overcomes the problem of one-off conventional optimal designs which become suboptimal when the loading magnitude changes. In addition to the magnitude of the applied voltage, the optimal values for the locations and the lengths of the piezo-actuators are determined to achieve the min-max deflection. Due to the complexity of the governing equations involving finite length piezo patches, the numerical results are obtained by the finite-difference method. The analysis of the problem shows the effect of the actuator locations, lengths and the applied voltage on the maximum deflection. The optimal values for the actuator locations and the voltage are determined as functions of the load locations and load magnitudes, respectively. The effect of the actuator length on the min-max deflection is investigated and it is observed that the optimal length depends on the applied voltage. Finally, it is shown that using multiple actuators are more effective than a single actuator in the cases of complicated loading.

Shape control of beams by piezoelectric actuators

Shape control of beams by piezoelectric actuators

An analytical investigation of static models of piezoelectric patches attached to beams and plates

On the basis of the deformation compatibility of piezoelectric patches and a beam or plate, equations for determining their interaction force are given. Their solutions show that the interaction force arises from structural deformation and the electric field imposed on the piezoelectric patches as well, and demonstrate that deformation of the beam and the plate may be caused by imposing an electric field on the piezoelectric patches, while the deformation may also lead to the variation of the static capacitance of the piezoelectric patches. Therefore, it is possible to retrieve information about the deformation of the beam and plate from the change of the static capacitance of patches which simultaneously take the role of actuators. However, their sensitivity to deformation is dependent on the area of the interface of the patches and the beam or plates; meanwhile it is also affected by the piezoelectric anisotropy of the patches when the patches are bonded to a plate. As an application, the static models are then used to investigate the feasibility of using piezoelectric patches to actively adjust the shape of the beam and plate, and the imposed voltage required for the shape control of beams and plates is predicted.

Improvement of electron beam shape control in radiation processing

The development of radiation processing using electron accelerators requires good control of the treatment parameters to improve the dosimetry quality. Especially, the analysis of the shape of the scanned electron beam that interacts with the product, is of prime necessity. A Multiwire Beam Shape Analyser (MBSA) has been developed by the AERIAL Laboratory in order to insure good monitoring of the scanning length and uniformity. This device consists of an aluminum beam-stop covered with a mesh of individually insulated stainless steel wires, placed under the scanning cone. The current generated by the impact of the electron beam on each wire is converted into voltage. After pulse shaping and multiplexing of the different channels, the beam profile can be displayed on an oscilloscope or on a PC screen. A prototype is now operating on an experimental irradiation plant based on a 2.5 MeV /300 W Van de Graaff electron accelerator. It allows almost continuous visualization of the beam profile (between two conveyor passes) and its response was compared to classical film dosimeters (Gafchromic, FWT 60.00). Considering FWHM and homogeneous treatment regions of the profiles, MBSA and the dosimeters give similar responses and variations remain lower than ± 12%. The acquisition of an electrical signal corresponding to the beam profile in air constitutes the original aspect of the MBSA and is in keeping with the general pattern of continuous control and automation of the irradiation processes. Hereafter, much work has to be done to adapt this device to an industrial use (higher energy, high power electron beams, non-destructive measurements…).